The Power of Gravity

The most critical obstacle standing in the way of traveling in space is the gravitation of the Earth. Because a vehicle that is supposed to travel in outer space must be able not only to move; it must primarily and first of all move away from the Earth--i.e., against the force of gravity. It must be able to lift itself and its payload up many thousands, even hundreds of thousands of kilometers!

Because the force of gravity is an inertial force, we must first of all understand the other inertial forces existing in nature and, moreover, briefly examine what causes these forces, namely the two mechanical fundamental properties of mass; because the entire problem of space travel is based on these issues.

The first of these properties lies in the fact that all masses mutually attract (Law of Gravitation). The consequence of this phenomenon is that every mass exerts a so-called "force of mutual attraction" on every other mass. The attractive force that the celestial bodies exert on other masses by virtue of their total mass is called the force of gravity. The "force of gravity" exerted by the Earth is the reason that all objects on the Earth are "heavy", that is, they have more or less "weight" depending on whether they themselves have a larger or smaller mass. The force of mutual attraction (force of gravity) is then that much more significant, the greater the mass of the objects between which it acts. On the other hand, its strength decreases with increasing distance (more specifically, with the square of the latter), nevertheless without its effective range having a distinct boundary (Figure 1). Theoretically, the force becomes zero only at an infinite distance. Similar to the Earth, the sun, Moon and, for that matter, every celestial body exerts a force of gravity corresponding to its size.

Figure 1. The curve of the Earth's force of mutual attraction (force of gravity). The strength of the attraction, which decreases with the square of increasing distance is represented by the distance of the curve of the force of gravity from the horizontal axis.

Key: 1. Amount of the Earth's force of gravity at various distances; 2. Curve of the force of gravity; 3. Magnitude of the force of gravity on the Earth's surface; 4. Earth; 5. Radius of the Earth=6,380 km.

The second fundamental property of mass lies in the fact that every mass is always striving to continue to remain in its current state of motion (Law of Inertia). Consequently, any mass whose motion is accelerated, decelerated or has its direction changed will resist this tendency by developing counteracting, so-called "forces of inertial mass" (Figure 2).

Figure 2.

Key: 1. Object; 2. Driving force; 3. Center of mass; 4. Inertia

In general, these are designated as inertia, or in a special case also as centrifugal force. The latter is the case when those forces occur due to the fact that mass is forced to move along a curved path. As is well known, the centrifugal force is always directed vertically outward from the curve of motion (Figure 3). All of these forces: force of gravity, inertia and the centrifugal force are inertial forces.

Figure 3.

Key: 1. Path of motion of the object; 2. Centrifugal force; 3. Object; 4. Center of gravity.

As mentioned previously, the effect of the Earth's force of gravity extends for an infinite distance, becoming weaker and weaker. We can consequently never completely escape the attractive range (the gravitational field) of the Earth, never reaching the actual gravitational boundary of the Earth. It can, nevertheless, be calculated what amount of work would theoretically be required in order to overcome the Earth's total gravitational field. To this end, an energy not less than 6,380 meter-tons would have to be used for every kilogram of load. Furthermore, it can be determined at what velocity an object would have to be launched from the Earth, so that it no longer returns to Earth. The velocity is 11,180 meters per second. This is the same velocity at which an object would strike the Earth's surface if it fell freely from an infinite distance onto the Earth. In order to impart this velocity to a kilogram of mass, the same amount of work of 6,380 meter-tons is required that would have to be expended to overcome the total Earth's gravitational field per kilogram of load.

If the Earth's attractive range could never actually be escaped, possibilities would nevertheless exist for an object to escape from the gravitational effect of the Earth, and more specifically, by the fact that it is also subjected to the effect of other inertial forces counterbalancing the Earth's force of gravity. According to our previous consideration about the fundamental properties of mass, only the following forces are possible: either the forces of mutual attraction of neighboring heavenly bodies or forces of inertial mass self-activated in the body in question.


The Practical Gravitational Boundary of the Earth

First of all, we want to examine the previously cited possibility. Because like the Earth every other celestial body also has a gravitational field that extends out indefinitely, losing more and more strength the further out it goes, we aretheoretically, at leastalways under the simultaneous gravitational effect of all heavenly bodies. Of this effect, only the gravitational effect of the Earth and, to some degree, that of our Moon is noticeable to us, however. In the region close to the Earth's surface, in which mankind lives, the force of the Earth's attraction is so predominately overwhelming that the gravitational effect exerted by other celestial bodies for all practical purposes disappears compared to the Earth's attraction.

Something else happens, however, as soon as we distance ourselves from the Earth. Its attractive force continually decreases in its effect, while, on the other hand, the

Figure 4. The curve of the gravitational fields of two neighboring heavenly body G1 and G2 is represented as in Figure 1, with the exception that the gravitational curve of the smaller celestial body G2 was drawn below the line connecting the centers because its attractive force counteracts that of the larger entity G1. The point free of gravitational effects is located where both gravitational fields are opposite and equal to one another and, therefore, offset their effects.

Key: 1. Point free of gravitational effects

effect of the neighboring heavenly bodies increases continually. Since the effect counterbalances the Earth's force of gravity, a point must existseen from the Earth in every directionat which these attractive forces maintain equilibrium concerning their strengths. On this side of that location, the gravitational effect of the Earth starts to dominate, while on the other side, that of the neighboring planet becomes greater. This can be designated as a practical boundary of the gravitational field of the Earth, a concept, however, that may not be interpreted in the strict sense, taking into consideration the large difference and continual changing of the position of the neighboring planets in relation to the Earth.

At individual points on the practical gravitational boundary (in general, on those that are on the straight line connecting the Earth and a neighboring planet), the attractive forces cancel one another according to the direction, such that at those points a completely weightless state exists. A point of this nature in outer space is designated as a socalled "point free of gravitational effects" (Figure 4). However, we would find ourselves at that point in an only insecure, unstable state of weightlessness, because at the slightest movement towards one side or the other, we are threatened with a plunge either onto the Earth or onto the neighboring planet.


Free Orbit

In order to attain a secure, stable state of weightlessness, we would have to escape the effect of gravity in the second way: with the aid of inertial forces.

Figure 5. Circular free orbiting of an object around the Earth. The object's weight is offset by the centrifugal force generated during the orbiting. The object is, therefore, in a stable state of free suspension in relation to the Earth.

Key: 1. Centrifugal force; 2. Orbiting object; 3. Weight; 4. Are opposite and equal to one another; 5. Earth; 6. Circular free orbit

This is attained when the attracting celestial body, for example, the Earth, is orbiting in a free orbit at a corresponding velocity (gravitational motion). The centrifugal force occurring during the orbit and always directed outward maintains equilibrium with the attractive forceindeed, it is the only force when the motion is circular (Figure 5)or simultaneously with other inertial forces occurring when the orbit has another form (ellipse, hyperbola, parabola, Figure 6).

Figure 6. Various free orbits around a celestial body. In accordance with the laws of gravitational movement, a focal point of the orbit (the center in the case of a circle) must always coincide with the center of mass (center of gravitaty) of the orbiting celestial body.

Key: 1. Parabolic orbit; 2. Hyperbolic orbit; 3. Celestial body; 4. Elliptical orbit; 5. Circular orbit

All Moon and planet movements occur in a similar fashion. Because, by way of example, our Moon continuously orbits the Earth at an average velocity of approximately 1,000 meters per second, it does not fall onto the Earth even though it is in the Earth's range of attraction, but instead is suspended freely above it. And likewise the Earth does not plunge into the sun's molten sea for the simple reason that it continuously orbits the sun at an average velocity of approximately 30,000 meters per second. As a result of the centrifugal force generated during the orbit, the effect of the sun's gravity on the Earth is offset and, therefore, we perceive nothing of its existence. Compared to the sun, we are "weightless" in a "stable state of suspension;" from a practical point of view, we have been "removed from its gravitational effect."

The shorter the distance from the attracting celestial body in which this orbiting occurs, the stronger the effect of the attractive force at that point. Because of this, the counteracting centrifugal force and consequently the orbiting velocity must be correspondingly greater (because the centrifugal force increases with the square of the orbiting velocity). While, by way of example, an orbiting velocity of only about 1,000 meters per second suffices at a distance of the Moon from the Earth, this velocity would have to attain the value of approximately 8,000 meters per second for an object that is supposed to orbit near the Earth's surface in a suspended state (Figure 7).

Figure 7. The orbiting velocity is that much greater the closer the free orbit movement occurs to the center of attraction.

Key: 1. Moon; 2. Approximately 1,000 meters per second; 3. Approximately 8,000 meters per second; 4. Earth

In order to impart this velocity to an object, that is, to bring it into a stable state of suspension in relation to the Earth in such a manner, and as a result to free it from the Earth's gravity, an amount of work of about 3,200 metertons per kilogram of weight is required.


Maneuvering in the Gravitational Fields of Outer Space

Two basic possibilities exist in order to escape the gravitational effect of the Earth or of another heavenly body: reaching the practical gravitational boundary or transitioning into a free orbit. Which possibility will be employed depends on the intended goals.

Thus, for example, in the case of longdistance travel through outer space, it would generally depend on maneuvering in such a fashion that those celestial bodies, in whose range of attraction (gravitational field) the trip

takes place, will be circled in a free orbit suspended in space (that is, only in suspension without power by a manmade force) if there is no intention to land on them. A longer trip would consist, however, of parts of orbits of this nature (suspension distances), with the transition from the gravitational field of one heavenly body into that of a neighboring one being caused generally by power from a manmade force.

If we want to remain at any desired altitude above a celestial body (e.g., the Earth) for a longer period, then we will continuously orbit that body at an appropriate velocity in a free circular orbit, if possible, and, therefore, remain over it in a stable state of suspension.

When ascending from the Earth or from another planet, we must finally strive either to attain the practical gravitational boundary and, as a result, the "total separation" (when foregoing a stable state of suspension) or transitioning into a free orbit and as a result into the "stable state of suspension" (when foregoing a total separation). Or, finally, we do not intend for the vehicle continually to escape the gravitational effect when ascending at all, but are satisfied to raise it to a certain altitude and to allow it to return immediately to Earth again after reaching this altitude (ballistic trajectory).

In reality, these differing cases will naturally not always be rigorously separated from one another, but frequently supplement one another. The ascent, however, will always have to take place by power from a manmade force and require a significant expenditure of energy, whichin the case when an ascending object is also to escape from the gravitational effectfor the Earth represents the enormous value of around 3,200 up to 6,400 metertons per kilogram of the load to be raised. Orwhich amounts to the same thingit requires imparting the huge, indeed cosmic velocity of approximately 8,000 to 11,200 meters per second, that is about 12 times the velocity of an artillery projectile!


The Armor Barrier of the Earth's Atmosphere

Besides the force of gravity, the atmosphere, which many celestial bodies havenaturally that of the Earth, in particularalso plays an extremely important role for space travel. While the atmosphere is very valuable for the landing, it, on the other hand, forms a particularly significant obstacle for the ascent.

According to observations of falling meteors and the northern lights phenomena, the height of the entire atmosphere of the Earth is estimated at several hundred (perhaps 400) kilometers (Figure 8). Nevertheless, only in its deepest layers several kilometers above the Earth, only on the "bottom of the sea of air" so to speak, does the air density exist that is necessary for the existence of life on Earth. For the air density decreases very quickly with increasing altitude and is, by way of example, onehalf as great at an altitude of 5 km and only onesixth as great at an altitude of 15 km as it is at sea level (Figure 9).

Figure 8. Assuming that the atmosphere is approximately 400 km high, the diagram shows its correct ratio to the Earth.

This condition is of critical importance for the question of space travel and is beneficial to it because, as is well known, air resists every moving object. During an increasing velocity of motion, the resistance increases, however, very rapidly, and more specifically, in a quadratic relationship. Within the dense air layers near the Earth, it reaches such high values at the extreme velocities considered for space travel that as a result the amount of work necessary for overcoming the gravitational field during ascent, as mentioned previously, is increased considerably and must also be taken into consideration to a substantial degree when building the vehicle. However, since the density of the air fortunately decreases rapidly with increasing altitude, its resistance also becomes smaller very quickly and can as a result be maintained within acceptable limits. Nevertheless, the atmosphere is a powerful obstacle during ascent for space travel. It virtually forms an armored shield surrounding the Earth on all sides. Later, we will get to know its importance for returning to Earth.


The Highest Altitudes Reached to Date

There has been no lack of attempts to reach the highest altitudes. Up to the present, mankind has been able to reach an altitude of 11,800 meters in an airplane, 12,000 meters in a free balloon, and 8,600 meters on Mount Everest (Figure 9).

Figure 9. With increasing altitude, the density of air decreases extremely rapidly, as can be seen from the curve drawn on the right and from the intensity of the shading.

Key: 1. Altitude in km; 2. Balloon probe 35 km; 3. Projectile of the German longrange cannon; 4. Airplane 8 km; 5. Free balloon 12 km; 6. Scale for the density of air at various altitudes; 7. Normal density of air above sea level

Socalled balloon probes have attained even higher altitudes. They are unmanned rubber balloons that are supposed to carry very lightweight recording devices as high as possible. Since the air pressure decreases continually with increasing altitude, the balloon expands more and more during the ascent until it finally bursts. The recording devices attached to a parachute gradually fall, recording automatically pressure, temperature and the humidity of the air. Balloon probes of this type have been able to reach an altitude up to approximately 35 kilometers. Moreover, the projectiles of the famous German longrange cannon, which fired on Paris, reached an altitude of approximately 40 kilometers. Nevertheless, what is all of this in comparison to the tremendous altitudes to which we would have to ascend in order to reach into empty outer space or even to distant celestial bodies!


The Cannon Shot into Outer Space

It appears obvious when searching for the means to escape the shackles of the Earth to think of firing from a correspondingly powerful giant cannon. This method would have to impart to the projectile the enormous energy that it requires for overcoming gravity and for going beyond the atmosphere as a kinetic force, that is, in the form of velocity. This requires, however, that the projectile must have already attained a velocity of not less than around 12,000 meters per second when leaving the ground if, besides the lifting energy, the energy for overcoming air drag is also taken into account.

Even if the means of present day technology would allow a giant cannon of this type to be built and to dare firing its projectile into space (as Professor H. Lorenz in Danzig has verified, we in reality do not currently have a propellant that would be sufficiently powerful for this purpose)the result of this effort would not compensate for the enormous amounts of money required to this end. At best, such an "ultra artillerist" would be able to boast about being the first one to accelerate an object from the Earth successfully or perhaps to have also fired at the

Moon. Hardly anything more is gained by this because everything, payload, recording devices, or even passengers taken in this "projectile vehicle" during the trip, would be transformed into mush in the first second, because no doubt only solid steel would be able to withstand the enormous inertial pressure acting upon all parts of the projectile during the time of the firing, during which the projectile must be accelerated out of a state of rest to a velocity of 12,000 meters per second within a period of only a few seconds (Figure 10), completely ignoring the great heat occurring as a result of friction in the barrel of the cannon and especially in the atmosphere to be penetrated.

where is figure 10?


The Reactive Force

This method is, for all practical purposes, not useable. The energy that the space vehicle requires for overcoming gravity and air drag, as well as for moving in empty space, must be supplied to it in another manner, that is, by way of example, bound in the propellants carried on board the vehicle during the trip. Furthermore, a propulsion motor must also be available that allows the propulsion force during the flight to change or even shut off, to alter the direction of flight, and to work its way up gradually to those high, almost cosmic velocities necessary for space flight without endangering passengers or the payload.

But how do we achieve all of this? How is movement supposed to be possible in the first place since in empty space neither air nor other objects are available on which the vehicle can support itself (or push off from, in a manner of speaking) in order to continue its movement in accordance with one of the methods used to date? (Movement by foot for animals and human beings, flapping of wings by birds, driving wheels for rolling trucks, screws of ships, propellers, etc.)

Figure 11. The "reactive force" or recoil when firing a rifle

Key: 1. Powder gases; 2. Recoil; 3. Pressure of the powder gases.

A generally known physical phenomenon offers the means for this. Whoever has fired a powerful rifle (and in the present generation, these people ought not to be in short supply) has, no doubt, clearly felt the socalled "recoil" (maybe the experience was not altogether a pleasant one). This is a powerful action that the rifle transfers to the shooter against the direction of discharge when firing. As a result, the powder gases also press back onto the rifle with the same force at which they drive the projectile forward and, therefore, attempt to move the rifle backwards (Figure 11).

Figure 12. Even when a person quickly shoves an easily movable, bulkier object (e.g., a freely suspended iron ball) away from himself, he receives a noticeable "reactive force" automatically.

1. Action; 2. Reaction.

However, even in daily life, the reaction phenomenon can be observed again and again, although generally not in such a total sense: thus, for example, when a movable object is pushed away with the hand (Figure 12), exactly the same thrust then imparted to the object is, as is well known, also received by us at the same time in an opposite direction as a matter of course. Stated more precisely: this "reaction" is that much stronger, and we will as a result be pushed back that much further, the harder we pushed. However, the "velocity of repulsion," which the affected object being pushed away attains as a result, is also that much greater. On the other hand, we will be able to impart a velocity that much greater to the object being pushed away with one and the same force, the less weight the object has (i.e., the smaller the mass). And likewise we will also fall back that much further, the lighter we are (and the less we will fall back, the heavier we are).

The physical law that applies to this phenomenon is called the "law maintaining the center of gravity." It states that the common center of gravity of a system of objects always remains at rest if they are set in motion only by internal forces, i.e., only by forces acting among these objects.

In our first example, the pressure of powder gases is the internal force acting between the two objects: projectile and rifle. While under its influence the very small projectile receives a velocity of many hundreds of meters per second, the velocity, on the other hand, that the much heavier rifle attains in an opposite direction is so small that the resulting recoil can be absorbed by the

Figure 13. If the "reaction" of the rifle is not absorbed, it continually moves backwards (after firing), and more specifically, in such a manner that the common center of gravity of rifle and projectile remains at rest.

Key: 1. Prior to firing; 2. Common center of gravity of the rifle and projectile; 3. After firing

shooter with his shoulder. If the person firing the rifle did not absorb the recoil and permitted the rifle to move backwards unrestrictedly (Figure 13), then the common center of gravity of the projectile and rifle would actually remain at rest (at the point where it was before firing), and the rifle would now be moving backwards.


The Reaction Vehicle

If the rifle was now attached to a lightweight cart (Figure 14) and fired, it would be set in motion by the force of the recoil. If the rifle was fired continually and rapidly, approximately similar to a machine gun, then the cart would be accelerated, and could also climb, etc. This would be a vehicle with reaction propulsion, not the most perfect, however. The continual movement of a vehicle of this type takes place as a result of the fact that it continually accelerates parts of its own mass (the projectiles in the previous example) opposite to the direction of motion and is repelled by these accelerated parts of mass.

Figure 14. A primitive vehicle with reaction propulsion: The cart is moved by continuous firing of a rifle, as a result of the "reaction" generated thereby.

Key: 1. The masses flung away (the projectiles in this case); 2. Recoil; 3. Direction of travel

It is clear as a result that this type of propulsion will then be useful when the vehicle is in empty space and its environment has neither air nor something else available by which a repulsion would be possible. Indeed, the propulsion by recoil will only then be able to develop its greatest efficiency because all external resistances disappear.

For the engineering design of a vehicle of this type, we must now strive to ensure that for generating a specific propulsive force, on the one hand, as little mass as possible must be expelled and, on the other hand, that its expulsion proceeds in as simple and operationally safe way, as possible.

To satisfy the first requirement, it is basically necessary that the velocity of expulsion be as large as possible. In accordance with what has already been stated, this can be easily understood even without mathematical substantiation, solely through intuition: for the greater the velocity with which I push an object away from me, the greater the force I have to apply against it; in accordance with what has already been stated, then the greater the opposite force will be that reacts on me as a result; this is the reaction produced by the expulsion of precisely this mass.

Furthermore, it is not necessary that larger parts of mass are expelled over longer time intervals, but rather that masses as small as possible are expelled in an uninterrupted sequence. Why this also contributes to keeping the masses to be expelled as low as possible, follows from mathematical studies that will not be used here, however. As can be easily understood, the latter must be required in the interest of operational safety, because the propulsive thrust would otherwise occur in jolts, something that would be damaging to the vehicle and its contents. Only a propulsive force acting as smoothly as possible is useful from a practical standpoint.


The Rocket

These conditions can best be met when the expulsion of the masses is obtained by burning suitable substances carried on the vehicle and by permitting the resulting gases of combustion to escape towards the rear"to exhaust." In this manner, the masses are expelled in the smallest particles (molecules of the combustion gases), and the energy being freed during the combustion and being converted into gas pressure provides the necessary "internal power" for this process.

The well known fireworks rocket represents a vehicle of this type in a simple implementation (Figure 15). Its purpose is to lift a socalled "bursting charge": there are all sorts of fireworks that explode after reaching a certain altitude either to please the eye in a spectacular shower of sparks or (in warfare, by way of example) to provide for lighting and signaling.

The continual movement (lifting) of a fireworks rocket of this type takes place as a result of a powder charge carried in the rocket, designated as the "propellant." It is ignited when the rocket takes off and then gradually burns out during the climb, with the resulting combustion gases escaping towards the rear (downward) and as a result by virtue of its reaction effectproducing a continuous propulsion force directed forward (up) in the same way as was previously discussed.

However, a rocket that is supposed to serve as a vehicle for outer space would, to be sure, have to look considerably different from a simple fireworks rocket.

Figure 15. Fireworks rocket in a longitudinal section. The attached guide stick serves to inhibit tumbling of the rocket.

Key: 1. Bursting charge; 2. Propellant; 3. Combustion of the propellant; 4. Reaction of the escaping combustion gases; 5. Guide stick; 6. Escaping combustion gases.


Previous Researchers Addressing the Problem of Space Flight

The idea that the reaction principle is suitable for the propulsion of space vehicles is not new. Around 1660,

the Frenchman Cyrano de Bergerac in his novels described, to be sure in a very fantastic way, space travels in vehicles lifted by rockets. Not much later, the famous English scholar Isaac Newton pointed out in a scientific form the possibilities of being able to move forward even in a vacuum using the reaction process. In 1841, the Englishman Charles Golightly registered a patent for a rocket flight machine. Around 1890, the German Hermann Ganswindt and a few years later the Russian Tsiolkovsky made similar suggestions public for the first time. Similarly, the famous French author Jules Verne discussed in one of his writings the application of rockets for purposes of propulsion, although only in passing. The idea of a space ship powered by the effects of rockets emerged, however, very definitely in a novel by the German physicist Kurt Lauwitz.

Yet only in the most recent times, have serious scientific advances been undertaken in this discipline, and indeed apparently from many sides at the same time: a relevant work by Professor Dr. Robert H. Goddard appeared in 1919. The work of Professor Hermann Oberth, a Transylvanian Saxon, followed in 1923. A popular representation by Max Valier, an author from Munich, was produced in 1924, and a study by Dr. Walter Hohmann, an engineer from Essen, in 1925. Publications by Dr. Franz Edler von Hoefft, a chemist from Vienna, followed in 1926. New relevant writings by Tsiolkovsky, a Russian professor, were published in 1925 and 1927.*

Also, several novels, which treated the space flight problem by building on the results of the most recent scientific research specified above, have appeared in the last few years, in particular, those from Otto Willi Gail standing out.

Before we turn our attention now to the discussion of the various recommendations known to date, something first must be said regarding the fundamentals of the technology of motion and of the structure of rocket space vehicles.


The Travel Velocity and the Efficiency of Rocket Vehicles

It is very important and characteristic of the reaction vehicle that the travel velocity may not be selected arbitrarily, but is already specified in general due to the special type of its propulsion. Since continual motion of a vehicle of this nature occurs as a result of the fact that it expels parts of its own mass, this phenomenon must be regulated in such a manner that all masses have, if possible, released their total energy to the vehicle following a successful expulsion, because the portion of energy the masses retain is irrevocably lost. As is well known, energy of this type constitutes the kinetic force inherent in every object in motion. If now no more energy is supposed to be available in the expelling masses, then they must be at rest visavis the environment (better stated: visavis their state of motion before starting) following expulsion. In order, however, to achieve this, the travel velocity must be of the same magnitude as the velocity of expulsion, because the velocity, which the masses have before their expulsion (that is, still as parts of the vehicle), is just offset by the velocity that was imparted to them in an opposite direction during the expulsion (Figure 16). As a result of the expulsion, the masses subsequently arrive in a relative state of rest and drop vertically to the ground as free falling objects.

Figure 16. The travel velocity is equal to the velocity of expulsion. Consequently, the velocity of the expelled masses equals zero after the expulsion, as can be seen from the figure by the fact that they drop vertically.

Key: 1. Expelled masses; 2. Velocity of expulsion; 3. Travel velocity; 4. Cart with reactive propulsion

Under this assumption in the reaction process, no energy is lost; reaction itself works with a (mechanical) efficiency of 100 percent (Figure 16). If the travel velocity was, on the other hand, smaller or larger than the velocity of expulsion, then this "efficiency of reactive propulsion" would also be correspondingly low (Figure 17). It is completely zero as soon as the vehicle comes to rest during an operating propulsion.

This can be mathematically verified in a simple manner, something we want to do here by taking into consideration the critical importance of the question of efficiency for the rocket vehicle. If the general expression for efficiency is employed in the present case: "Ratio of the

Figure 17. The travel velocity is smaller (top diagram) or larger (lower diagram) than the velocity of expulsion. The expelled masses still have, therefore, a portion of their velocity of expulsion (top diagram) or their travel velocity (lower diagram) following expulsion, with the masses sloping as they fall to the ground, as can be seen in the figure.

Key: 1. Expelled masses; 2. Velocity of expulsion; 3. Travel velocity; 4. Cart with reactive propulsion energy gained to the energy expended", then the following formula is arrived at as an expression for the efficiency of the reaction hr as a function of the instantaneous ratio between travel velocity v and the velocity of repulsion c.

In Table 1, the efficiency of the reaction hr is computed for various values of this v/c ratio using the above formula. If, for example, the v/c ratio was equal to 0.1 (i.e., v=0.1 c, thus the travel velocity is only onetenth as large as the velocity of expulsion), then the

efficiency of the reaction would only be 19 percent. For v/c=0.5 (when the travel velocity is onehalf as large as the velocity of repulsion), the efficiency would be 75

Table 1

Ratio of the travel Efficiency of the velocity v to the Reaction hr velocity of expulsion c v/c hr in percentages (roundedup)

0 0 0

0.01 0.0199 2

0.05 0.0975 10

0.1 0.19 19

0.2 0.36 36

0.5 0.75 75

0.8 0.96 96

1 1 100

1.2 0.96 96

1.5 0.75 75

1.8 0.36 36

2 0 0

2.5 1.25 125

3 3 300

4 8 800

5 15 1500

percent, and for v/c=1 (the travel velocity equals the velocity of expulsion)in agreement with our previous considerationthe efficiency would even be 100 percent. If the v/c ratio becomes greater than 1 (the travel velocity exceeds the velocity of expulsion), the efficiency of the reaction is diminished again and, finally, for v/c=2 it again goes through zero and even becomes negative (at travel velocities more than twice as large as the velocity of expulsion).

The latter appears paradoxical at first glance because the vehicle gains a travel velocity as a result of expulsion and apparently gains a kinetic force as a result! Since the loss of energy, resulting through the separation of the expulsion mass loaded very heavily with a kinetic force due to the large travel velocity, now exceeds the energy gain realized by the expulsion, an energy loss nevertheless results for the vehicle from the entire processdespite the velocity increase of the vehicle caused as a result. The energy loss is expressed mathematically by the negative sign of the efficiency. Nonetheless, these efficiencies resulting for large values of the v/c ratio have, in reality, only a more or less theoretical value.

It can, however, clearly and distinctly be seen from the table how advantageous and, therefore, important it is that the travel velocity approaches as much as possible that of the expulsion in order to achieve a good efficiency of reaction, but slight differences (even up to v=0.5 c and/or v=1.5 c) are, nevertheless, not too important because fluctuations of the efficiency near its maximum are fairly slight. Accordingly, it can be stated that the optimum travel velocity of a rocket vehicle is approximately between onehalf and one and onehalf times its velocity of expulsion.

When, as is the case here, the reaction vehicle is a rocket vehicle and consequently the expulsion of masses takes place through appropriate combustion and exhausting of propellants carried on the vehicle, then, in the sense of the requirement just identified, the travel velocity must be as much as possible of the same magnitude as the exhaust velocity (Figure 18). To a certain extent, this again requires, however, that the travel velocity conforms to the

Figure 18. For a rocket vehicle, the travel velocity must as much as possible be equal to the exhaust velocity.

Key: 1. Exhausted gases of combustion; 2. Exhaust velocity; 3. Travel velocity; 4. Cart with rocket propulsion

type of propellants used in each case, because each has its own maximum achievable exhaust velocity.

This fundamental requirement of rocket technology is above all now critical for the application of rocket vehicles. According to what has already been stated, the velocity of repulsion should then be as large as possible.

Actually, the possible exhaust velocities are thousands of meters per second and, therefore, the travel velocity must likewise attain a correspondingly enormous high value that is not possible for all vehicles known to date, if the efficiency is supposed to have a level still useable in a practical application.

This can be clearly seen from Table 2, in which the efficiencies corresponding to the travel velocities at various velocities of expulsion are determined for single important travel velocities (listed in Column 1). It can be seen from Column 2 of the table, which lists the efficiency of reaction, how uneconomical the rocket propulsion is at velocities (of at most several hundred kilometers per hour) attainable by our present vehicles.

This stands out much more drastically if, as expressed in Column 3, the total efficiency is considered. This is arrived at by taking into account the losses that are related to the generation of the velocity of expulsion (as a result of combustion and exhausting of the propellants). These losses have the effect that only an exhaust velocity smaller than the velocity that would be theoretically attainable in the best case for those propellants can ever be realized in practice. As will subsequently be discussed in detail, the practical utilization of the propellants could probably be brought up to approximately 60 percent. For benzene by way of example, an exhaust velocity of 3,500 meters per second at 62 percent and one of 2,000 meters per second at 20 percent would result. Column 3 of Table 2 shows the total efficiency for both cases (the efficiency is now only 62 percent and/or 20 percent of the

Table 2

1 2 3

Travel Efficiency of the Reaction Total

velocity Efficiency

of the

v vehicle



for benzene

and liquid

in oxygen as


Expressed in percentages for the following

velocities of repulsion c in m/sec:

km/h m/s 1000 2000 2500 3000 3500 4000 5000 2000 3500

40 11 2.2 1.2 0.9 0.7 0.6 0.5 0.4 0.2 0.4

100 28 4.6 2.8 2.2 1.8 1.6 1.4 1.2 0.6 1

200 56 11 5.5 4.5 3.8 3.2 2.8 2.2 1.1 2

300 83 16 8 6.5 5.5 4.7 4 3.4 1.6 3

500 140 26 13 11 9 8 7 5.5 2.7 5

700 200 36 19 15 13 11 10 8 4 7

1000 300 51 28 23 19 16 14 12 6 10

1800 500 75 44 36 31 27 23 19 9 17

3000 1000 100 75 64 56 50 44 36 15 31

5400 1500 75 94 84 75 67 60 51 19 42

7200 2000 0 100 96 89 81 75 64 20 50

9000 2500 125 94 100 97 92 86 75 19 57

10800 3000 300 75 96 100 98 94 84 15 61

12600 3500 525 44 84 97 100 99 91 9 62

14400 4000 800 0 64 89 98 100 96 0 61

18000 5000 1500 125 0 56 81 94 100 25 50

21600 6000 300 96 0 50 75 96 61 31

25200 7000 520 220 77 0 44 70 111 0

28800 8000 800 380 175 64 0 64 160 40

36000 10000 1500 800 440 250 125 0 300 160

45000 12500 1500 900 560 350 125 350

corresponding values in Column 2, in the sense of the statements made).

As can be seen from these values, the total efficiencyeven for travel velocities of many hundreds of kilometers per houris still so low that, ignoring certain special purposes for which the question of economy is not important, a farreaching practical application of rocket propulsion can hardly be considered for any of our customary means of ground transportation.

On the other hand, the situation becomes entirely different if very high travel velocities are taken into consideration. Even at supersonic speeds that are not excessively large, the efficiency is considerably better and attains even extremely favorable values at still higher, almost cosmic travel velocities in the range of thousands of meters per second (up to tens of thousands of kilometers per hour), as can be seen in Table 2.

It can, therefore, be interpreted as a particularly advantageous encounter of conditions that these high travel velocities are not only possible (no resistance to motion in empty space!) for space vehicles for which the reaction represents the only practical type of propulsion, but even represent an absolute necessity. How otherwise could those enormous distances of outer space be covered in acceptable human travel times? A danger, however, that excessively high velocities could perhaps cause harm does not exist, because we are not directly aware whatsoever of velocity per se, regardless of how high it may be. After all as "passengers of our Earth," we are continually racing through space in unswerving paths around the sun at a velocity of 30,000 meters per second, without experiencing the slightest effect. However, the "accelerations" resulting from forced velocity changes are a different matter altogether, as we will see later.

Table 3 permits a comparison to be made more easily

Table 3

Kilometers Meters Kilometers

per hour per second per second

km/hour m/sec km/sec

5 1.39 0.00139

10 2.78 0.00278

30 8.34 0.00834

50 13.9 0.0139

70 19.5 0.0195

90 25.0 0.0250

100 27.8 0.0278

150 41.7 0.0417

200 55.6 0.0556

300 83.4 0.0834

360 100 0.1

500 139 0.139

700 195 0.195

720 200 0.2

1000 278 0.278

1080 300 0.3

1190 330 0.33

1800 500 0.5

2000 556 0.556

2520 700 0.7

3000 834 0.834

3600 1000 1

5400 1500 1.5

7200 2000 2

9000 2500 2.5

10800 3000 3

12600 3500 3.5

14400 4000 4

18000 5000 5

21600 6000 6

25200 7000 7

28800 8000 8

36000 10000 10

40300 11180 11.18

45000 12500 12.5

54000 15000 15

72000 20000 20

among the various travel velocities under consideration here something that is otherwise fairly difficult due to the difference of the customary systems of notation (kilometers per hour for present day vehicles, meters or kilometers per second for space travel).


The Ascent

Of the important components of space fightthe ascent, the longdistance travel through outer space, and the return to Earth (the landing)we want to address only the most critical component at this point: the ascent. The ascent represents by far the greatest demands placed on the performance of the propulsion system and is also, therefore, of critical importance for the structure of the entire vehicle.

Figure 19. Vertical ascent"steep ascent"of a space rocket.

Key: 1. Climbing velocity=0; 2. Climbing altitude that is supposed to be reached; 3. Free ascent (without power as a "hurl upwards"): the climbing velocity decreases gradually as a result of the decelerating effect of the Earth's gravity; 4. Measure for the climbing velocity at various altitudes; 5. Climbing velocity="highest velocity of climbing"; 6. Power ascent: the climbing velocity increases continuously thanks to the accelerating effect of the propulsion system; 7. Launch.

For implementing the ascent, two fundamental possibilities, the "steep ascent" and "flat ascent," present themselves as the ones mentioned at the beginning in the section about movement in the gravity fields of outer space. In the case of the steep ascent, the vehicle is lifted in at least an approximately vertical direction. During the ascent, the climbing velocity, starting at zero, initially increases continuously thanks to the thrusting force of the reaction propulsion system (Figure 19); more specifically, it increases until a high climbing velocity is attainedwe will designate it as the "maximum velocity of climbing"such that now the power can be shut off and the continued ascent, as a "hurl upward," can continually proceed up to the desired altitude only under the effect of the kinetic energy that has been stored in the vehicle.

In the case of the flat ascent, on the other hand, the vehicle is not lifted vertically, but in an inclined (sloped) direction, and it is a matter not so much of attaining an altitude but rather, more importantly, of gaining horizontal velocity and increasing it until the orbiting velocity necessary for free orbital motion and consequently the "stable state of suspension" are attained (Figures 5 and 20). We will examine this type of ascent in more detail later.

Figure 20. "Flat ascent" of a space rocket. The expenditure of energy for the ascent is the lowest in this case.

Key: 1. Free circular orbit; 2. Earth; 3. Earth rotation; 4. Vertical direction; 5. Inclined direction of launch; 6. This altitude should be as low as possible!; 7. Ascent curve (an ellipse or parabola)

First, however, we want to examine some other points, including the question: How is efficiency varying during the ascent? For regardless how the ascent takes place, the required final velocity can only gradually be attained in any case, leading to the consequence that the travel (climbing) velocity of the space rocket will be lower in the beginning and greater later on (depending on the altitude of the final velocity) than the velocity of expulsion. Accordingly, the efficiency of the propulsion system must also be constantly changing during the power ascent, because the efficiency, in accordance with our previous definitions, is a function of the ratio of the values of the velocities of travel and expulsion (see Table 1, page 29). Accordingly in the beginning, it will only be low, increasing gradually with an increasing climbing velocity, and will finally exceed its maximum (if the final velocity to be attained is correspondingly large) and will then drop again.

In order to be able to visualize the magnitude of the efficiency under these conditions, the "average efficiency of the propulsion system" hrm resulting during the duration of the propulsion must be taken into consideration. As can be easily seen, this efficiency is a function, on the one hand, of the velocity of expulsion c, which we want to assume as constant for the entire propulsion phase, and, on the other hand, of the final velocity v' attained at the end of the propulsion period.

The following formula provides an explanation on this point:

Table 4 was prepared using this formula.

Table 4

Ratio of the final Average efficiency of

velocity v' to the the propulsion system

velocity of expulsion hrm during the

c: acceleration phase


hrm hrm in percentages

0 0 0

0.2 0.18 18

0.6 0.44 44

1 0.58 58

1.2 0.62 62

1.4 0.64 64

1.591.8 0.65 65

2 0.64 64

2.2 0.63 63

2.6 0.61 61

3 0.54 54

4 0.47 47

5 0.30 30

6 0.17 17

7 0.09 9

0.04 4

The table shows the average efficiency of the propulsion system as a function of the ratio of the final velocity v' attained at the end of the propulsion phase to the velocity of expulsion c existing during the propulsion phase, that is, a function of v'/c. Accordingly by way of example at a velocity of expulsion of c=3,000 meters per second and for a propulsion phase at the end of which the final velocity of v=3,000 meters per second is attained (that is, for v'/c=1), the average efficiency of the propulsion system would be 58 percent. It would be 30 percent for the final velocity of v=12,000 meters per second (that is, v'/c=4), and so on. In the best case (that is, for v'/c=1.59) in our example, the efficiency would even attain 65 percent for a propulsion phase at a final velocity of v'=4,770 meters per second.

In any case it can be seen that even during the ascent, the efficiency is generally still not unfavorable despite the fluctuations in the ratio of the velocities of travel and expulsion.

Figure 21. As long as the vehicle has to be supported (carried) by the propulsion system during the ascent, the forward thrust of the vehicle is decreased by its weight.

Key: 1. Direction of flight (ascent); 2. Total reactive force; 3. Remaining propulsive force available for acceleration; 4. Weight of the vehicle; 5. Direction of expulsion (exhaust).

Besides the efficiency problem being of interest in all cases, a second issue of extreme importance exists especially for the ascent. As soon as the launch has taken place and, thus, the vehicle has lifted off its support (solid base or suspension, watersurface, launch balloon, etc.), it is carried only by the propulsion system (Figure 21), somethingaccording to the nature of the reactive forcethat depends on to a continual expenditure of energy (fuel consumption). As a result, that amount of propellants required for the liftoff is increased by a further, not insignificant value. This condition lasts only untildepending on the type of ascent, steep or flateither the necessary highest climbing velocity or the required horizontal orbiting velocity is attained. The sooner this happens, the shorter the time during which the vehicle must be supported by the propulsion system and the lower the related propellant consumption will be. We see then that a high velocity must be attained as rapidly as possible during the ascent.

Figure 22. During the duration of propulsion, forces of inertia are activated in the vehicle due to the acceleration of the vehicle (increase in velocity) caused by propulsion; the forces manifest themselves for the vehicle like an increase in gravity.

Key: 1. Actual acceleration of climb; 2. Reaction; 3. Normal weight; 4. Force of inertia; 5. Total increased effect of gravity (equals the total reactive force of the propulsion system).

However, a limit is soon set in this regard for space ships that are supposed to be suitable for transporting people. Because the related acceleration always results in the release of inertial forces during a forced velocity increase (as in this case for the propulsion system) and not caused solely by the free interaction of the inertial forces. These forces are manifested for the vehicle during the ascent like an increase in gravity (Figure 22) and may not exceed a certain level, thus ensuring that the passengers do not suffer any injuries. Comparison studies carried out by Oberth as well as by Hohmann and previous experiences in aviation (e.g., during spiral flights) indicate that an actual acceleration of climb up to 30 m/sec2 may be acceptable during a vertical ascent. In this case during the duration of propulsion, the vehicle and its contents would be subjected to the effect of the force of gravity of four times the strength of the Earth's normal gravity. Do not underestimate what this means! It means nothing less than that the feet would have to support almost four times the customary body weight. Therefore, this ascent phase, lasting only a few minutes, can be spent by the passengers only in a prone position, for which purpose Oberth anticipated hammocks.

Taking into account the limitations in the magnitude of the acceleration, the highest climbing velocity that would be required for the total separation from the Earth can be attained only at an altitude of approximately 1,600 km with space ships occupied by humans during a vertical ascent. The rate of climb is then around 10,000 meters per second and is attained after somewhat more than 5 minutes. The propulsion system must be active that long. In accordance with what was stated previously, the vehicle is supported (carried) by the propulsion system during this time, and furthermore the resistance of the Earth's atmosphere still has to be overcome. Both conditions cause, however, an increase of the energy consumption such that the entire energy expenditure necessary for the ascent up to the total separation from the Earth finally becomes just as large as if an ideal highest velocity of around 13,000 meters per second would have to be imparted in total to the vehicle. Now this velocity (not the actual maximum climbing velocity of 10,000 meters per second) is critical for the amount of the propellants required.

Somewhat more favorable is the case when the ascent does not take place vertically, but on an inclined trajectory; in particular, when during the ascent the vehicle in addition strives to attain free orbital motion around the Earth as close to its surface as practical, taking the air drag into account (perhaps at an altitude of 60 to 100 km above sea level). And only thenthrough a further increase of the orbiting velocitythe vehicle works its way up to the highest velocity necessary for attaining the desired altitude or for the total separation from the Earth ("flat ascent," Figure 20).

The inclined direction of ascent has the advantage that the Earth's gravity does not work at full strength against the propulsion system (Figure 23), resulting, therefore, in a greater actual acceleration in the case of a uniform ideal acceleration (uniform propulsion)which, according to what has been previously stated, is restricted when taking the wellbeing of the passengers into account. The greater acceleration results in the highest velocity necessary for the ascent being attained earlier.

However, the transition into the free orbital motion as soon as possible causes the vehicle to escape the Earth's gravity more rapidly than otherwise (because of the larger effect of the centrifugal force). Both conditions now cause the duration to be shortened during which the vehicle must be carried by the propulsion system, saving on the expenditure of energy as a result. Consequently, the ideal highest velocity to be imparted to the vehicle for totally separating from the Earth is only around 12,000 meters per second when employing this ascent maneuver, according to Oberth. In my opinion, however, we should come closest to the actually attainable velocity in practice when assuming an ideal highest velocity of approximately 12,500 meters per second.

Figure 23. Acceleration polygon for: 1.) vertical ascent, 2.) inclined ascent, 3.) flat ascent. It can clearly be seen that the actual acceleration from 1.) to 3.) becomes greater and greater, despite a constant ideal acceleration (force of the propulsion system). (The acceleration polygon for 2.) is emphasized by hatched lines.)

Key: 1. Direction of the effect of the propulsion system; 2. Direction of the actual ascent; 3. Acceleration of gravity; 4. Ideal acceleration; 5. Actual acceleration.

Regardless of how the ascent proceeds, it requires in every case very significant accelerations, such that the vehicle attains a velocity of a projectile at an altitude of several kilometers. This conditionbecause of the thick density of the deepest layers of air closest to the surface of the Earthresults in the air drag reaching undesirably high values in the very initial phases of the ascent, something that is particularly true for space rockets without people on board. Considerably greater accelerations of climb can be employed in unmanned vehicles than in manned ones because health is not a consideration for the former.

To come to grips with this disadvantage, the launch will take place from a point on the Earth's surface as high as possible, e.g., from a launch balloon or another air vehicle or from a correspondingly high mountain. For very large space ships, however, only the latter option is possible due to their weight, even though in this case the launch would preferably be carried out at a normal altitude.


General Comments about the Structure of the Space Rocket

Corresponding to the variety of purposes and goals possible for space ship flights, the demands placed on the vehicle will also be very different from mission to mission. For space ships, it will, therefore, be necessary to make the structure of the vehicle compatible with the uniqueness of the respective trip to a far greater extent than for the vehicles used for transportation to date. Nevertheless, the important equipment as well as the factors critical for the structure will be common for all space ships.

The external form of a space vehicle will have to be similar to that of a projectile. The form of a projectile is best suited for overcoming air drag at the high velocities attained by the vehicle within the Earth's atmosphere (projectile velocity, in accordance with previous statements!).

Fundamental for the internal structure of a rocket vehicle is the type of the propellants used. They must meet with the following requirements:

That they achieve an exhaust velocity as high as possible because the necessity was recognized previously for an expulsion velocity of the exhaust masses as high as possible.

That they have a density as high as possible (high specific weight), so that a small tank would suffice for storing the necessary amount of weight. Then, on the one hand, the weight of the tank is decreased and, on the other hand, the losses due to air drag also become smaller.

That their combustion be carried out in a safe way compatible with generating a constant forward thrust.

That handling them cause as few difficulties as possible.

Any type of gunpowder or a similar material (a solid propellant), such as used in fireworks rockets, would be the most obvious to use. The structure of the vehicle could then be relatively simple, similar to that of the familiar fireworks rocket. In this manner it would, no doubt, be possible to build equipment for various special tasks, and this would in particular pave the way for military technology, a point to be discussed below.

However for purposes of traveling in outer space, especially when the transportation of people is also to be made possible, using liquid propellants should offer far more prospects for development options, despite the fact that considerable engineering problems are associated with these types of propellants; this point will be discussed later.

The most important components of a space ship for liquid propellants are as follows: the propulsion system, the tanks for the propellants, the cabin and the means of landing. The propulsion system is the engine of the space ship. The reactive force is produced in it by converting the onboard energy stored in the propellant into forward thrust. To achieve this, it is necessary to pipe the propellants into an enclosed space in order to burn them there and then to let them discharge (exhaust) towards the rear. Two basic possibilities exist for this:

The same combustion pressure continuously exists in the combustion chamber. For the propellants to be injected, they must, therefore, be forced into the combustion chamber by overcoming this pressure. We will designate engines of this type as "constant pressure rocket engines."

The combustion proceeds in such a fashion that the combustion chamber is continuously reloaded in a rapid sequence with propellants, repeatedly ignited (detonated) and allowed to exhaust completely every time. In this case, injecting the propellants can also take place without an overpressure. Engines of this type we will designate as "detonation (or explosion) rocket engines."

The main components of the constant pressure rocket engines are the following: the combustion chamber, also called the firing chamber, and the nozzle located downstream from the combustion chamber (Figure 24). These components can exist in varying quantities, depending on the requirements.

The operating characteristics are as follows: the propellants (fuel and oxidizer) are forced into the combustion chamber in a proper state by means of a sufficient overpressure and are burned there. During the combustion, their chemically bonded energy is converted into heat andin accordance with the related temperature increasealso into a pressure of the combustion gases generated in this manner and enclosed in the combustion chamber. Under the effect of this pressure, the gases of combustion escape out through the nozzle and attain as a result that velocity previously designated as "exhaust velocity." The acceleration of the gas molecules associated with this gain of velocity results, however, in the occurrence of counteracting forces of inertia (counter pressure, similar to pushing away an object!), whose sum now produces the force of "reaction" (Figure 24) that will push the vehicle forward in the same fashion as has already been discussed earlier. The forward thrust is obtained via heat, pressure, acceleration and reaction from the energy chemically bonded in the fuel.

Figure 24. The combustion or firing chamber and the nozzle, the main components of the constant pressure rocket motor.

Key: 1. Escaping gases of combustion; 2. Reactive force; 3. Propellants flowing in, e.g., fuel and oxygen; 4. Combustion chamber.

So that this process is constantly maintained, it must be ensured that continually fresh propellants are injected into the combustion chamber. To this end, it is, however, necessary, as has been stated previously, that the propellant be under a certain overpressure compared to the combustion chamber. If an overpressure is supposed to be available in the tanks, then they would also have to have an appropriate wall thickness, a property, however, that for larger tanks could present problems. Otherwise, pumps will have to be carried on board in order to put the propellants under the required pressure.

Furthermore, related equipment, such as injectors, evaporators and similar units are required so that the on board liquid propellants can also be converted into the state suitable for combustion. Finally, the vehicle designers must also make provisions for sufficient cooling of the combustion chamber and nozzle, for control, etc.

The entire system has many similarities to a constant pressure gas turbine. And similar to that case, the not so simple question also exists in this case of a compatible material capable of withstanding high temperatures and of corresponding cooling options for the combustion chamber and nozzle. On the other hand, the very critical issue of a compressor for a gas turbine is not applicable for the rocket motor.

Similarly, the detonation rocket engine exhibits many similarities to the related type of turbine, the detonation (explosion) gas turbine. As with the latter, the advantage of a simpler propellant injection option must also be paid for in this case by a lower thermal efficiency and a more complicated structure.

Which type of construction should be preferred can only be demonstrated in the future development of the rocket motor. Perhaps, this will also be, in part, a function of the particular special applications of the motor. It would not suffice to have only a motor functioning in completely empty space. We must still have the option of carrying on board into outer space the necessary amounts of energy in the form of propellant. Consequently, we are faced with a critically important question: the construction of the tanks for the fuel and oxidizer.

Figure 25.

Key: 1. Following a completed propulsion phase: The rocket is brought to the desired velocity of motion; 2. Remaining "final mass" of the rocket.; 3. Consumed for the propulsion; 4. During the propulsion phase: The rocket is accelerated; 5. Rocket mass (namely, the propellants) is continually expelled.; 6. In the launchready state: The rocket is at rest.; 7. "Initial mass" of the rocket.

How large, in reality, is the amount of propellants carried on board? We know that the propulsion of the rocket vehicle occurs as a result of the fact that it continually expels towards the rear parts of its own mass (in our case, the propellants in a gasified state). After the propulsion system has functioned for a certain time, the initial mass of the vehicle (that is, its total mass in the launchready state) will have been decreased to a certain final mass by the amount of propellants consumed (and exhausted) during this time (Figure 25). This final mass represents, therefore, the total load that was transported by means of the amount of propellants consumed, consisting of the payload, the vehicle itself and the remaining amounts of propellants.

The question is now as follows (Figure 26): How large must the initial mass M0 be when a fixed final mass M is supposed to be accelerated to a velocity of motion v at a constant exhaust velocity c? The rocket equation provides an answer to this question: M0=2.72v/cM.

Figure 26.

Key: 1. Velocity of motion; 2. Final mass; 3. Exhaust velocity; 4. Initial mass.

According to the above, the initial mass M0 of a space rocket is calculated as shown below. This mass should be capable of imparting the previously discussed ideal highest climbing velocity of 12,500 meters per second, approximately necessary for attaining complete separation from the Earth.

M0=520 M, for c=2,000 meters per second

M0=64 M, for c=3,000 meters per second

M0=23 M, for c=4,000 meters per second

M0=12 M, for c=5,000 meters per second.

This implies the following: for the case that the exhaust velocity c is, by way of example, 3,000 meters per second, the vehicle, at the beginning of the propulsion phase, must be 64 times as heavy with the propellants necessary for the ascent as after the propellants are consumed. Consequently, the tanks must have a capacity to such an extent that they can hold an amount of propellants weighing 63 times as much as the empty space rocket, including the load to be transported, or expressed differently: an amount of propellants that is 98.5 percent of the total weight of the launchready vehicle.

An amount of propellants of 22 times the weight would also suffice if the exhaust velocity is 4,000 meters per second and only 11 times if the exhaust velocity increases up to 5,000 meters per second. Ninetysix and 92 percent of the total weight of the launchready vehicle is allocated to the propellants in these two cases.

As has been frequently emphasized, the extreme importance of an expulsion (exhaust) velocity as high as possible can clearly be recognized from these values. (The velocity is the expression of the practical energy value of the propellant used!) However, only those rockets that are supposed to be capable of imparting the maximum climbing velocity necessary for the total separation from the Earth must have a propellant capacity as large as that computed above. On the other hand, the "ratio of masses" (ratio of the initial to the final mass of the rocket: M0/M) is considerably more favorable for various types of applications (explained later) in which lower highest velocities also suffice.

In the latter cases from a structural engineering point of view, fundamental difficulties would not be caused by the demands for the propellant capacity of the vehicle and/or of the tanks. By way of example, a space rocket that is supposed to attain the final velocity of v=4,200 meters per second at an exhaust velocity of c=3,000 meters per second would have to have a ratio of masses of M0/M=4, according to the rocket equation. That is, the rocket would have to be capable of storing an amount of propellant that is 75 percent of its total launch weight, a capability that can certainly be achieved from a structural engineering point of view.

To be sure, space rockets of that can carry on board the amounts of propellants necessary for the complete separation from the Earth (according to what has already been stated, the amounts of propellants are 98.5 percent of the launch weight at an exhaust velocity of c=3,000 meters per second), could, for all practical purposes, not be easily realized. Fortunately, there is a trick making it possible to circumvent this structural difficulty in a very simple manner: the socalled staging principle that both Goddard and Oberth recognized independently of one another as a fundamental principle of rocket technology.

In accordance with this principle, the desired final velocity need not be attained with a single rocket; but rather, the space rocket is divided into multiple units (stages), each one always forming the load for the next largest unit. If, for example, a threestage space rocket is used, then it consists of exactly three subrockets: the subrocket 3 is the smallest and carries the actual payload. It forms (including this payload) the load of subrocket 2 and the latter again (including subrocket 3 and its payload) the load of subrocket 1. During ascent, subrocket 1 functions first. As soon as this stage is used up, its empty shell is decoupled and subrocket 2 starts to function. When it is spent, it also remains behind and now subrocket 3 functions until the desired final velocity is attained. Only the latter arrives at the destination with the payload.

Because the final velocities of three subrockets are additive in this process, each individual one must be able to generate only 1/3 of the total required final velocity.

In the case of a 3stage space rocket, which is supposed to attain the highest climbing velocity of 12,500 meters per second necessary for the total separation from the Earth, only a final velocity to be attained of around 4,200 meters per second would consequently be allocated to each subrocket. For that, however, the propellant capacity, certainly implementable from an engineering point of view, of 75 percent (ratio of masses M0/M=4) suffices, as we determined previously, at an exhaust velocity of c=3,000 meters per second, for example. If the individual subrockets can, however, be manufactured, then no doubt exists about the possibility of erecting the complete rocket assembled from all subrockets.

As a precautionary measure, let's examine the absolute values of the rocket masses or rocket weights resulting from the above example. Assume a payload of 10 tons is to be separated from the Earth; the individual subrockets may be built in such a fashion that their empty weight is as large as the load to be transported by them. The weights of the subrockets in tons result then as follows:

Subrocket Load Empty Final weight M Initial weight M0 weight

3 10 10 10 + 10=201) 4 x 20=802)

2 + 3 80 80 80 + 80=160 4 x 160=640

1 + 2 + 3 640 640 640 + 640=1280 4 x 1280=5120

1) The final weight M is equal to the empty weight plus the load when the rocketas in this casefunctions until its propellants are completely consumed.

2) The initial weight M0 is, in this case, equal to 4 times the final weight M because, as has been stated previously in our example, each subrocket approaches the ratio of masses (weights) M0/M=4.

The initial weight of the total space rocket consisting of 3 stages would be 5,120 tons, a number that is not particularly impressive, considering the fact that technology is capable of building, for example, an ocean liner weighing 50,000 tons.

In this fashionby means of the staging principleit would actually be possible to attain any arbitrary final velocity, in theory at least. For all practical purposes in this regard, fixed limitations will, of course, result, in particular when taking the absolute values of the initial weights into consideration. Nevertheless an irrefutable proof is inherent in the staging principle to the effect that it would be fundamentally possible to build space rockets capable of separating from the Earth even with the means available today.

That does not mean the staging principle represents the ideal solution for constructing space rockets in the described form, because it leads to an increase of the dead weight and as a result of the propellants necessary for transportation. This, however, is not now a critical point. Initially, we are only concerned with showing "that it is possible in the first place." Without a doubt every type of space rocket construction, regardless of which one, will have to employ the fundamental concept expressed in the staging principle: during the duration of propulsionfor the purpose of saving propellantsevery part of the vehicle that has become unnecessary must be immediately released (jettisoned) in order not to carry dead weight uselessly and, at the same time, to have to accelerate further with the remaining weight. It is assumed, of course, that we are dealing with space rockets that are supposed to attain greater final velocities.

From a structural engineering point of view, we do not want to conceal the fact that certainly quite a few difficulties will arise as a result of the still significant demands imposed on the capacity of the propellant tanksdespite the staging principle. In this regard, it will be necessary in part to use construction methods deviating fundamentally from the customary ones, because all parts of the vehicle, in particular the tanks, must be made as lightweight as possible. Nevertheless, the tanks must have sufficient strength and stiffness to be able to withstand both the pressure of mass and the atmospheric stagnation pressure during the ascent, taking into account that many of the usual metals become brittle and, therefore, lose strength at the extreme lower temperatures to which the tanks may be exposed.

Moreover in a space ship, a compartment (cell) must exist for housing the pilot and passengers and for storing supplies of the life support necessities and other equipment, as well as for storing freight, scientific devices for observations, etc. The compartment must be airsealed and must have corresponding precautionary measures for artificially supplying air for breathing and for maintaining a bearable temperature. All equipment necessary for controlling the vehicle are also stored in the compartment, such as manual controls for regulating the propulsion system; recorders for time, acceleration, velocity, and path (altitude); and for determining the location, maintaining the desired direction of flight, and similar functions. Even space suits (see the following), hammocks, etc. must be available. Finally, the very important aids for landing, such as parachutes, wings, etc. also belong to the equipment of a space ship.


Proposals To Date

The following are the various recommendations made to date for the practical solution of the space flight problem:

Professor Goddard uses a smokeless powder, a solid substance, as a propellant for his space rockets. He has not described any particular device, but recommends only in general packing the powder into cartridges and injecting it automatically into the combustion chamber, in a fashion similar to that of a machine gun. The entire rocket should be composed of individual subrockets that are jettisoned one after the other during the ascent, as soon as they are spent, with the exception of that subrocket containing the payload, and it alone reaches the destination. First of all, he intends to make unmanned devices climb to an altitude of several hundred kilometers. Subsequently, he also wants to try to send up an unmanned rocket to the Moon carrying only several kilograms of luminous powder. When landing on the Moon, the light flare is supposed to flash, so that it could then be detected with our large telescopes, thus verifying the success of the experiment. Reportedly, the American Navy is greatly interested in Goddard's devices.

The results of practical preliminary experiments conducted and published by Goddard to date are very valuable; the means for carrying out these experiments were provided to him in a very generous manner by the famous Smithsonian Institution in Washington. He was able to attain exhaust velocities up to 2,434 meters per second with certain types of smokeless powder when appropriately shaping and designing the nozzles. During these experiments, he was successful in using 64.5 percent of the energy chemically bonded in the powder, that is, to convert it into kinetic energy of the escaping gases of combustion. The result agrees approximately with the experiences of ballistics, according to which about 2/3 of the energy content of the powder can be used, while the remainder is carried as heat by the exhaust gases and, as a result, is lost. Perhaps, the efficiency of the combustion chamber and nozzle can be increased somewhat during further engineering improvements, to approximately 70 percent.

Therefore, an "internal efficiency" of approximately 60 percent could be expected for the entire propulsion systemthe rocket motorafter taking into consideration the additional losses caused by the various auxiliary equipment (such as pumps and similar devices) as well as by other conditions. This is a very favorable result considering that the efficiency is hardly more than 38 percent even for the best thermal engines known to date.

It is a good idea to distinguish the internal efficiency just considered from that addressed previously: the efficiency of the reactive force, which could also be designated as the "external efficiency" of the rocket motor to distinguish it from the internal efficiency. Both are completely independent from one another and must be considered at the same time in order to obtain the total efficiency of the vehicle (which is just the product of the internal and external efficiency). As an example, the values of the efficiency for benzene as the fuel are listed in Column 3 of Table 2, page 32.

Differing from Goddard, Professor Oberth suggests using liquid propellants, primarily liquid hydrogen and also alcohol, both with the amounts of liquid oxygen necessary for their combustion. The hydrogenoxygen mixturecalled "detonating gas"has the highest energy content (3,780 calories per kilogram compared to approximately 1,240 for the best smokeless powder) per unit of weight of all known substances. Accordingly, it yields by far the highest exhaust velocity. Oberth figured being able to attain approximately 3,8004,200 meters per second. If we were successful in using the energy chemically bonded in detonating gas up to the theoretically highest possible limit, then its exhaust velocity could even exceed 5,000 meters per second. The gas resulting from the combustion is water vapor.

Unfortunately, the difficulty of carrying and using the gas in a practical sense is a big disadvantage compared to the advantage of its significant energy content and therefore relatively high exhaust velocity, due to which the detonating gas would in theory appear to be by far the most suitable propellant for space rockets. Storing hydrogen as well as oxygen in the rocket is possible only in the liquefied state for reasons of volume.

However, the temperature of liquid oxygen is 183, and that of the liquid hydrogen only 253 Celsius. It is obvious that this condition must considerably complicate the handling, even disregarding the unusual requirements being imposed on the material of the tanks. Additionally, the average density (specific weight) of detonating gas is very low even in a liquefied state so that relatively large tanks are necessary for storing a given amount of the weight of the gas.

In the case of alcohol, the other fuel recommended by Oberth, these adverse conditions are partially eliminated but cannot be completely avoided. In this case, the oxygen necessary for combustion must also be carried on board in the liquid state. According to Oberth, the exhaust velocity is approximately 1,5301,700 meters per second for alcohol, considerably lower than for hydrogen. It does have a greater density, however.

Due to these properties, Oberth uses alcohol together with liquid oxygen as propellants for the initial phase of the ascent, because the resistance of the dense layers of air near the Earth's surface must be overcome during the ascent. Oberth viewed a large crosssectional loading (i.e., the ratio of the total mass of a projectile to the air drag cross section of the projectile) as advantageous even for rockets and recommended, besides other points: "to increase the mass ratio at the expense of the exhaust velocity". This is, however, attained when alcohol and oxygen are used as propellants.

Oberth's space rocket has, in general, the external shape of a German Sprojectile and is composed of individual subrockets that are powered either with hydrogen and oxygen (hydrogen rocket) or with alcohol and oxygen (alcohol rocket). Oberth also described in more detail two examples of his space vehicle. Of the two, one is a smaller, unmanned model, but equipped with the appropriate recording instruments and is supposed to ascend and perform research on the higher and highest layers of air. The other one is a large space ship designed for transporting people.

Figure 27. A longitudinal cross section through the main rocket of Oberth's small rocket model is shown schematically. The hydrogen rocket is inserted in the forward part of the alcohol rocket.

Key: 1. Parachute; 2. Tank; 3. Space for the recording instruments; 4. Propulsion system; 5. Control fins.

The smaller model (Figure 27) consists of a hydrogen rocket that is inserted into the forward part of a considerably larger alcohol rocket. Space for storing the recording instruments is located below the tank of the hydrogen rocket. At the end of the alcohol rocket, movable fins are arranged that are supposed to stabilize and to control the vehicle. The entire apparatus is 5 meters long, measures 56 cm in diameter and weighs 544 kg in the launchready state.

Furthermore, a socalled "booster rocket" (Figure 28)

is provided that is 2 meters high, 1 meter in diameter and weights 220 kg in the launchready state. Launching takes place from dirigibles at an altitude of 5,500 meters or more (Figure 29). Initially the booster rocket, which later will be jettisoned, lifts the main rocket to an altitude of 7,700 meters and accelerates it to a velocity of 500 meters per

Figure 28. The booster rocket of Oberth's small rocket model.

Figure 29. Launching the rocket from dirigibles, according to Oberth.

second (Figure 30). Now, the rocket is activated automatically: first the alcohol rocket and, after it is spent and decoupled, the hydrogen rocket. Fiftysix seconds after the launch, a highest climbing velocity of 5,140 meters per second is attained, which suffices for the remaining hydrogen rocket, now without propulsion, to reach a final altitude of approximately 2,000 km in a free ascent. The return to Earth takes place by means of a selfdeploying parachute stored in the tip of the hydrogen rocket.

Figure 30. The ascent of Oberth's small (unmanned) rocket model.

Key: 1. Free ascent up to an altitude of 2,000 km; 2. Powered ascent lasting 56 seconds; 3. The highest climbing velocity of 5,140 m/sec is attained; 4. Hydrogen rocket; 5. Alcohol rocket; 6. Complete rocket; 7. Altitude of 7,700 m, climbing velocity of 500 m/sec; 8. Booster rocket; 9. Altitude of 5,500 m, climbing velocity of 0; 10. Powered ascent by the hydrogen rocket; 11. The empty alcohol rocket is jettisoned. The hydrogen rocket starts to operate;

12. Power ascent by the alcohol rocket; 13. The empty booster rocket is jettisoned; the main rocket, beginning with its alcohol rocket, starts to operate; 14. Powered ascent by the booster rocket; 15. The launchready vehicle, suspended from dirigibles, as shown in Figure 29.

In the case of the second model, the large rocket space ship designed for transporting people (Figure 31), the total forward part of the vehicle consists of a hydrogen rocket set atop an alcohol rocket in the rear. The cabin designed for passengers, freight, etc. and equipped with all control devices, is located in the forward part of the hydrogen rocket. The parachute is stored above it. Towards the front, the vehicle has a metal cap shaped like a projectile, which later is jettisoned as unnecessary ballast along with the alcohol rocket (Figure 32), because the Earth's atmosphere is left behind at this point, i.e., no further air drag must be overcome. From here on, stabilization and controlling is no longer achieved by means of fins, but by control nozzles.

For this model, launching is performed over the ocean. In this case, the alcohol rocket operates first. It accelerates the vehicle to a climbing velocity of 3,0004,000 meters per second, whereupon it is decoupled and left behind (Figure 32); the hydrogen rocket then begins to work in order to impart to the vehicle the necessary maximum climbing velocity or, if necessary, also a horizontal orbital velocity. A space ship of this nature, designed for transporting an observer, would, according to Oberth's data, weigh 300 metric tons in the launchready state.

Figure 31. A longitudinal cross section of Oberth's large rocket for transporting people is shown schematically. The hydrogen rocket is set atop the alcohol rocket.

Key: 1. Parachute; 2. Cabin; 3. Hydrogen tank; 4. Oxygen tank; 5. Propulsion system; 6. Alcohol tank.

Figure 32. The ascent of Oberth's larger (manned) rocket model.

Key: 1. Horizontal velocity; 2. Parachute; 3. Hydrogen rocket; 4. Alcohol rocket; 5. Ocean; 6. Climbing velocity; 7. Cap; 8. Powered ascent by the hydrogen rocket. Depending on the purpose (vertical ascent or free orbiting), this rocket imparts either a climbing velocity or a horizontal velocity; 9. The empty alcohol rocket and the cap are jettisoned; the hydrogen rocket starts to operate. The climbing velocity attained up to this point is 3,000 to 4,000 meters per second; 10. Powered ascent by the alcohol rocket; 11. The launchready vehicle floating in the ocean.

In both models, the subrockets are independent; each has, therefore, its own propulsion system as well as its own tanks. To save weight, the latter are very thinwalled and obtain the necessary stiffness through inflation, that is, by the existence of an internal overpressure, similar to nonrigid dirigibles. When the contents are being drained, this overpressure is maintained by evaporating the remaining liquid. The oxygen tank is made of copper and the hydrogen tank of lead, both soft metals, in order to prevent the danger of embrittlement caused by the extreme low temperatures discussed previously.

Figure 33. The propulsion system of Oberth's rocket:

Right: the small model. The combustion chamber discharges into only one nozzle.

Left: the large model. A common combustion chamber discharges into many nozzles arranged in a honeycombed fashion.

Key: 1. Sectional view; 2. Pumps; 3. Injectors; 4. Combustion chamber; 5. Nozzles; 6. View from the rear; 7. Nozzle.

The propulsion equipment is located in the rear part of each rocket (Figure 33). For the most part, that equipment consists of the combustion chamber and one or more thin sheet metal exhaust nozzles connected to it, as well as various pieces of auxiliary equipment necessary for propulsion, such as injectors and other devices. Oberth uses unique pumps of his own design to produce the propellant overpressure necessary for injection into the combustion chamber. Shortly before combustion, the oxygen is gasified, heated to 700 and then blown into the chamber, while the fuel is sprayed into the hot oxygen stream in a finely dispersed state. Arrangements are made for appropriately cooling the chamber, nozzles, etc.

It should be noted how small the compartment for the payload is in comparison to the entire vehicle, which consists principally of the tanks. This becomes understandable, however, considering the fact that the amounts of propellants previously calculated with the rocket equation and necessary for the ascent constitute as much as 20 to 80 percent of the total weight of the vehicle, propellant residuals, and payload!

However, the cause for this enormous propellant requirement lies not in an insufficient use of the propellants, caused perhaps by the deficiency of the reaction principle used for the ascent, as is frequently and incorrectly thought to be the case. Naturally, energy is lost during the ascent, as has previously been established, due to the circumstance that the travel velocity during the propulsion phase increases only gradually and, therefore, is not of an equal magnitude (namely, in the beginning smaller, later larger) with the exhaust (repulsion) velocity (Figure 17). Nevertheless, the average efficiency of the reaction would be 27 percent at a constant exhaust velocity of 3,000 meters per second and 45 percent at a constant exhaust velocity of 4,000 meters per second, if, for example, the vehicle is supposed to be accelerated to the velocity of 12,500 meters per second, ideally necessary for complete separation from the Earth. According to our previous considerations, the efficiency would even attain a value of 65 percent in the best case, i.e., for a propulsion phase in which the final velocity imparted to the vehicle is 1.59 times the exhaust velocity.

Since the internal efficiency of the propulsion equipment can be estimated at approximately 60 percent on the basis of the previously discussed Goddard experiments and on the experiences of ballistics, it follows that an average total efficiency of the vehicle of approximately 16 to 27 percent (even to 39 percent in the best case) may be expected during the ascent, a value that, in fact, is no worse than for our present day automobiles! Only the enormous work necessary for overcoming such vast altitudes requires such huge amounts of propellants.

If, by way of example, a road would lead from the Earth into outer space up to the practical gravitational boundary, and if an automobile were supposed to drive up that road, then an approximately equal supply of propellants, including the oxygen necessary for combustion, would have to be carried on the automobile, as would be necessary for the propellants of a space ship with the same payload and altitude.

It is also of interest to see how Oberth evaluated the question of costs. According to his data, the previously described smaller model including the preliminary experiments would cost 10,000 to 20,000 marks. The construction costs of a space ship, suitable for transporting one observer, would be over 1 million marks. Under favorable conditions, the space ship would be capable of carrying out approximately 100 flights. In the case of a larger space ship, which transports, besides the pilot together with the equipment, 2 tons of payload, an ascent to the stable state of suspension (transition into a free orbit) would require approximately 50,000 to 60,000 marks.

The study published by Hohmann about the problem of space flight does not address the construction of space rockets in more detail, but rather thoroughly addresses all fundamental questions of space flight and provides very valuable recommendations related to this subject. As far as questions relating to the landing process and distant travel through outer space are concerned, they will be addressed later.

What is interesting at this point is designing a space vehicle for transporting two people including all necessary equipment and supplies. Hohmann conceives a vehicle structured in broad outlines as follows: the actual vehicle should consist only of the cabin. In the latter, everything is storedwith the exception of the propellant. A solid, explosivelike substance serving as the propellant would be arranged below the cabin in the shape of a spire tapering upward in such a way that the cabin forms its peak (Figure 34). As a result of a gradual burning of this propellant spire, thrust will be generated similar to that of a fireworks rocket. A prerequisite for this is that explosive experts find a substance that, on the one hand, has sufficient strength to keep itself in the desired shape and that, on the other hand, also has that energy of combustion necessary for generating a relatively large exhaust velocity.

Figure 34. The space rocket according to Hohmann.

Key: 1. Cabin cell; 2. Propellant tower; 3. Exhaust gases of combustion.

Assuming that this velocity is 2,000 meters per second, a space vehicle of this nature would weigh, according to Hohmann, a total of 2,800 tons in the launchready state, if it is to be capable of attaining an altitude of 800,000 km (i.e., twice the distance to the Moon). This corresponds approximately to the weight of a small ocean liner. A round trip of this nature would last 30.5 days.

Recent publications by von Hoefft are especially noteworthy. His original thought was to activate the propulsion system of space ships using the space ether. For this purpose, a unidirectional ether flow is supposed to be forced through the vehicle by means of an electrical field. Under Hoefft's assumption, the reaction effect of the ether would then supply the propulsive force of the vehicle, a concept that assumes ether has mass. Hoefft, however, maintained that was assured if the opinion held by Nernst and other researchers proved to be correct. According to this view, the space ether should possess a very significant internal energy (zero point energy of the ether); this was believed to be substantiated by the fact that energy is also associated with mass in accordance with Einstein's Law.

He intends initially to launch an unmanned recording rocket to an altitude of approximately 100 km for the purpose of exploring the upper layers of the atmosphere. This rocket has one stage, is powered by alcohol and liquid oxygen, and is controlled by means of a gyroscope like a torpedo. The height of the rocket is 1.2 meters, its diameter is 20 cm, its initial (launch) weight is 30 kg and its final weight is 8 kg, of which 7 kg are allocated to empty weight and 1 kg to the payload. The latter is composed of a meteorograph stored in the top of the rocket and separated automatically from the rocket as soon as the final altitude is attained, similar to what happens in recording balloons. The meteorograph then falls alone slowly to Earth on a selfopening parachute, recording the pressure, temperature and humidity of the air. The ascent is supposed to take place at an altitude of 10,000 meters from an unmanned rubber balloon (pilot balloon) to keep the rocket from having to penetrate the lower, dense layers of air.

As the next step, von Hoefft plans to build a larger rocket with an initial weight of 3,000 kg and a final weight of 450 kg, of which approximately 370 kg are allocated to empty weight and 80 kg to the payload. Similar to a projectile, the rocket is supposed to cover vast distances of the Earth's surface (starting at approximately 1,500 km) in the shortest time on a ballistic trajectory (Keplerian ellipses) and either transport mail or similar articles or photograph the regions flown over (for example, the unexplored territories) with automatic camera equipment. Landing is envisaged in such a manner that the payload is separated automatically from the top before the descent, similar to the previously described recording rocket, descending by itself on a parachute.

This singlestage rocket could also be built as a twostage rocket and as a result be made appropriate for a Moon mission. For this purpose, it is equipped, in place of the previous payload of approximately 80 kg, with a second rocket of the same weight; this rocket will now carry the actual, considerably smaller payload of approximately 5 to 10 kg. Because the final velocities of both subrockets in a twostage rocket of this type are additive in accordance with the previously explained staging principle, a maximum climbing velocity would be attained that is sufficiently large to take the payload, consisting of a load of flash powder, to the Moon. When landing on the Moon, this load is supposed to ignite, thus demonstrating the success of the experiment by a light signal, as also proposed by Goddard. Both this and the aforementioned mail rocket are launched at an altitude of 6,000 meters from a pilot balloon, a booster rocket, or a mountain top.

In contrast to these unmanned rockets, the large space vehicles designed for transporting people, which Hoefft then plans to build in a followon effort, are supposed to be launched principally from a suitable body of water, like a seaplane, and at the descent, land on water, similar to a plane of that type. The rockets will be given a special external shape (somewhat similar to a kite) in order to make them suitable for their maneuvers.

The first model of a space vehicle of this type would have a launch weight of 30 tons and a final weight of 3 tons. Its purpose is the following: on the one hand, to be employed similarly to the mail rocket yet occupied by people who are to be transported and to cover great distances of the Earth's surface on ballistic trajectories (Keplerian ellipses) in the shortest time; and, on the other hand, it would later have to serve as an upper stage of larger, multistage space ships designed for reaching distant celestial bodies. Their launch weights would be fairly significant: several hundred metric tons, and even up to 12,000 tons for the largest designs. 


Comments Regarding Previous Design Proposals

Regarding these various proposals, the following is added as supplementary information: as far as can be seen from today's perspective, the near future belongs in all probability to the space rocket with liquid propellants. Fully developed designs of such rockets will be achieved when the necessary technical conditions have been created through practical solutions (obtained in experiments) of the questions fundamental to their design: 1. methods of carrying the propellants on board, 2. methods of injecting propellants into the combustion chamber, and 3. protection of the chamber and nozzle from the heat of combustion.

For this reason, we intentionally avoided outlining our own design recommendations here. Without a doubt, we consider it advisable and necessary, even timely, at least as far as it is possible using currently available experiences, to clarify the fundamentals of the vehicle's structure; the question of propellant is predominantly in this context. As stated earlier, hydrogen and oxygen, on the one hand, and alcohol and oxygen, on the other, are suggested as propellants.

In the opinion of the author, the pure hydrocarbon compounds (together with the oxygen necessary for combustion) should be better suited than the ones mentioned in the previous paragraph as propellants for space rockets. This becomes understandable when the energy content is expressed as related to the volume instead of to the weight, the author maintaining this as being the most advantageous method in order to be able to evaluate the value of a rocket fuel in a simple fashion. Not only does it matter what amount of fuel by weight is necessary for a specific performance; still more important for storing the fuel, and as a result for designing the vehicle, is what amount of fuel by volume must be carried on board. Therefore, the energy content (thermal units per liter) of the fuel related to the volume provides the clearest information.

This energy content is the more significant the greater the specific weight as well as the net calorific value of the fuel under consideration are, and the less oxygen it requires for its combustion. In general, the carbon rich compounds are shown to be superior to the hydrogen rich ones, even though the calorific value per kilogram of the latter is higher. Consequently, benzene would appear very suitable, for example. Pure carbon would be the best. Because the latter, however, is not found in the fluid state, attempts should be made to ascertain whether by mechanical mixing of a liquid hydrocarbon (perhaps benzene, heptane, among others) with an energy content per liter as high as possible with finely dispersed carbon as pure as possible (for instance carbon black, the finest coal dust or similar products), the energy content per liter could be increased still further and as a result particularly high quality rocket fuel could be obtained, which may perhaps be overall the best possible in accordance with our current knowledge of substances.

Of course, an obvious condition for the validity of the above considerations is that all fuels work with the same efficiency. Under this assumption by way of example, a space rocket that is supposed to attain the final velocity of 4,000 meters per second would turn out to be smaller by about one half and have a tank surface area smaller by one third when it is powered with benzene and liquid oxygen than when powered by liquid hydrogen and oxygen (Figure 35).

Figure 35. Size relationship between a hydrogen rocket and a benzene rocket of the same performance, when each one is supposed to be capable of attaining a velocity of 4,000 meters per second.

Key: 1. Hydrogen rocket; 2. Benzene rocket.

Therefore, the benzene rocket would not only be realized sooner from an engineering point of view, but also constructed more cheaply than the hydrogen rocket of the same efficiency, even though the weight of the necessary amount of fuel is somewhat higher in the former case and, therefore, a larger propulsion force and, consequently, stronger, heavier propulsion equipment would be required. Instead, the fuel tanks are smaller for benzene rockets and, furthermore, as far as they serve the purposes of benzene at least, can be manufactured from any lightweight metal because benzene is normally liquid. When considering its abnormally low temperature (253 Celsius) according to Oberth, a point made previously, rockets for liquid hydrogen would have to be made of lead (!). This discussion ignores completely the many other difficulties caused by this low temperature in handling liquid hydrogen and the method of using this fuel; all of these difficulties disappear when using benzene.

Figure 36. Size relationship between a hydrogen rocket and a benzene rocket of the same performance, when each one is supposed to be capable of attaining a velocity of 12,500 meters per second (complete separation from the Earth!).

Key: 1. Hydrogen rocket; 2. Benzene rocket

However, this superiority of liquid hydrocarbons compared to pure hydrogen diminishes more and more at higher final velocities. Nevertheless, a benzene rocket would still turn out to be smaller by one third than a hydrogen rocket, even for attaining a velocity of 12,500 meters per second as is ideally necessary for complete separation from the Earth (Figure 36). Only for the final velocity of 22,000 meters per second would the volumes of propellants for the benzene rocket be as large as for the hydrogen rockets. Besides these energy efficient advantages and other ones, liquid hydrocarbons are also considerably cheaper than pure liquid hydrogen. 


The Return to Earth

The previous explanations indicate that obstacles stand in the way of the ascent into outer space which, although significant, are nonetheless not insurmountable. Based solely on this conclusion and before we address any further considerations, the following question is of interest: Whether and how it would be possible to return to Earth after a successful ascent and to land there without experiencing any injuries. It would arouse a terrible horror even in the most daring astronaut if he imagined, seeing the Earth as a distant sphere ahead of him, that he will land on it with a velocity of no less than approximately 12 times the velocity of an artillery projectile as soon as he, under the action of gravity, travels towards it or more correctly stated, crashes onto it.

The rocket designer must provide for proper braking. What difficult problem is intrinsic in this requirement is realized when we visualize that a kinetic energy, which about equals that of an entire express train moving at a velocity of 70 km/hour, is carried by each single kilogram of the space ship arriving on Earth! For, as described in the beginning, an object always falls onto the Earth with the velocity of approximately 11,000 meters per second when it is pulled from outer space towards the Earth by the Earth's gravitational force. The object has then a kinetic energy of around 6,000 metric ton meters per kilogram of its weight. This enormous amount of energy must be removed in its entirety from the vehicle during braking.

Only two possibilities are considered in this regard: either counteracting the force by means of reaction propulsion (similar to the "reverse force" of the machine when stopping a ship), or braking by using the Earth's atmosphere. When landing according to the first method, the propulsion system would have to be used again, but in an opposite direction to that of flight (Figure 37). In this regard, the vehicle's descent energy would be removed from it by virtue of the fact that this energy is offset by the application of an equally large, opposite energy. This requires, however, that the same energy for braking and, therefore, the same amount of fuel necessary for the ascent would have to be consumed. Then, since the initial velocity for the ascent (highest climbing velocity) and the final velocity during the return (descent velocity) are of similar magnitudes, the kinetic energies, which must be imparted to the vehicle in the former case and removed in the latter case, differ only slightly from one another.

Figure 37. Landing with reaction braking. The descending vehicle is supposed to be "cushioned" by the propulsion system, with the latter functioning "away from the Earth" opposite to the direction of flight, exactly similar to the ascent.

Key: 1. The space ship descending to the Earth; 2. Direction of effect of the propulsion system; 3. Earth

For the time being, this entire amount of fuel necessary for braking must still and this is critical be lifted to the final altitude, something that means an enormous increase of the climbing load. As a result, however, the amount of fuel required in total for the ascent becomes now so large that this type of braking appears in any case extremely inefficient, even nonfeasible with the performance levels of currently available fuels. However, even only a partial usage of the reaction for braking must be avoided if at all possible for the same reasons.

Another point concerning reaction braking in the region of the atmosphere must additionally be considered at least for as long as the travel velocity is still of a cosmic magnitude. The exhaust gases, which the vehicle drives ahead of it, would be decelerated more by air drag than the heavier vehicle itself and, therefore, the vehicle would have to travel in the heat of its own gases of combustion.

Figure 38. Landing during a vertical descent of the vehicle using air drag braking.

Key: 1. Descent velocity of 11,000 m/sec; 2. Parachute; 3. The space ship descending to Earth; 4. Braking distance, i.e., the altitude of the layers of the atmosphere (approx. 100 km) probably suitable for braking; 5. Earth.

The second type of landing, the one using air drag, is brought about by braking the vehicle during its travel through the Earth's atmosphere by means of a parachute or other device (Figure 38). It is critical in this regard that the kinetic energy, which must be removed from the vehicle during this process, is only converted partially into air movement (eddying) and partially into heat. If now the braking distance is not sufficiently long and consequently the braking period is too short, then the resulting braking heat cannot transition to the environment through conduction and radiation to a sufficient degree, causing the temperature of the braking means (parachute, etc.) to increase continuously.

Now in our case, the vehicle at its entry into the atmosphere has a velocity of around 11,000 meters per second, while that part of the atmosphere having sufficient density for possible braking purposes can hardly be more than 100 km in altitude. According to what was stated earlier, it is fairly clear that an attempt to brake the vehicle by air drag at such high velocities would simply lead to combustion in a relatively very short distance. It would appear, therefore, that the problem of space flight would come to nought if not on the question of the ascent then for sure on the impossibility of a successful return to Earth.


Hohmann's Landing Maneuver

The German engineer Dr. Hohmann deserves the credit for indicating a way out of this dilemma. According to his suggestion, the vehicle will be equipped with wings for landing, similar to an airplane. Furthermore, a tangential (horizontal) velocity component is imparted to the vehicle at the start of the return by means of reaction so that the vehicle does not even impact on the Earth during its descent, but travels around the Earth in such a manner that it approaches within 75 km of the Earth's surface (Figure 39).

Figure 39. During Hohmann's landing process, the return trajectory is artificially influenced to such an extent that the space ship does not even impact the Earth, but travels around it at an altitude of 75 km.

Key: 1. Tangential (horizontal) velocity of approx. 100 m/sec; 2. Return trajectory (descent to Earth); 3. At an altitude 75 km above the Earth's surface; 4. Descent velocity of approximately 11,000 m/sec; 5. Earth

This process can be explained in a simple fashion as follows: if a stone is thrown horizontally instead of allowing it to simply drop, then it hits the ground a certain distance away, and, more specifically, at a greater distance, the greater the horizontal velocity at which it was thrown. If this horizontal velocity could now be arbitrarily increased such that the stone falls not a distance of 10 or 100 meters, not even at distances of 100 or 1,000 km, but only reaches the Earth at a distance of 40,000 km away, then in reality the stone would no longer descend at all because the entire circumference of the Earth measures only 40,000 km. It would then circle the Earth in a free obit like a tiny moon. However, in order to achieve this from a point on the Earth's surface, the very high horizontal velocity of approximately 8,000 meters per second would have to be imparted to the stone. This velocity, however, becomes that much smaller the further the position from which the object starts is distant from the Earth. At a distance of several hundred thousand km, the velocity is only around 100 meters per second (Figure 39). This can be understood if we visualize that the vehicle gains velocity more and more solely due to its descent to Earth. According to what was stated previously, if the descent velocity finally attains the value of 11,000 meters per second, it is then greater by more than 3,000 meters per second than the velocity of exactly 7,850 meters per second that the vehicle would have to have so that it would travel around the Earth (similar to the stone) in a free circular orbit at an altitude of 75 km.

Figure 40. If the centrifugal force becomes extremely large due to excessively rapid travel, it hurls the automobile off the road.

Key: 1. Friction of the wheels on the ground; 2. Direction of motion of the automobile being hurled out (tangential); 3. Centrifugal force; 4. Road.

Due to the excessive velocity, the space ship is now more forcefully pushed outward by the centrifugal force than the force of gravity is capable of pulling it inward towards the Earth. This is a process similar, for instance, to that of an automobile driving (too "sharply") through a curve at too high a speed (Figure 40). Exactly as this automobile is hurled outward because the centrifugal force trying to force it off the road is greater than the friction of the wheels trying to keep it on the road, our space ship will in an analogous way also strive to exit the free circular orbit in an outward direction and, as a result, to move again away from the Earth (Figure 41).

Figure 41. Due to the travel velocity (11,000 instead of 7,850 m/sec!) which is excessive by around 3,000 m/sec, the centrifugal force is greater than the force of gravity, consequently forcing the space ship outward out of the free circular orbit.

Key: 1. Descent trajectory; 2. Free circular orbit; 3. Velocity in the free circular orbit of 7,850 m/sec; 4. Earth; 5. Force of gravity; 6. Descent velocity of around 11,000 m/sec; 7. Centrifugal force.


Landing in a Forced Circular Motion

The situation described above can, however, be prevented through the appropriate use of wings. In the case of a standard airplane, the wings are pitched upward so that, as a result of the motion of flight, the lift occurs that is supposed to carry the airplane (Figure 42). In our case, the wings are now adjusted in the opposite direction, that is, pitched downward (Figure 43). As a result, a pressure directed downward towards the Earth occurs, exactly offsetting the centrifugal force excess by properly selecting the angle of incidence and in this fashion forcing the vehicle to remain in the circular flight path (Figure 44).

Figure 42. The fundamental operating characteristics of wings during standard heavier-than-air flight: The "lift" caused by air drag is directed upward and, therefore, carries the airplane.

Key: 1. Lift; 2. Air drag; 3. Direction of flight; 4. Weight of the vehicle; 5. Wings; 6. Surface of the Earth.

For performing this maneuver, the altitude was intentionally selected 75 km above the Earth's surface, because at that altitude the density of air is so thin that the space ship despite its high velocity experiences almost the same air drag as a normal airplane in its customary altitude.

Figure 43. The operating characteristics of wings during the "forced circular motion" of a landing space ship. Here, air drag produces a "negative lift" directed towards the Earth (downward), offsetting the excessive centrifugal force.

Key: 1. Centrifugal force excess; 2. Air drag; 3. Direction of flight; 4. Negative lift; 5. Wings; 6. Surface of the Earth.

During this "forced circular motion," the travel velocity is continually being decreased due to air drag and, therefore, the centrifugal force excess is being removed more and more. Accordingly, the necessity of assistance from the wings is also lessened until they finally become completely unnecessary as soon as the travel velocity drops to 7,850 meters per second and, therefore, even the centrifugal force excess has ceased to exist. The space ship then circles suspended in a circular orbit around the Earth ("free circular motion," Figure 44).

Since the travel velocity continues to decrease as a result of air drag, the centrifugal force also decreases gradually and accordingly the force of gravity asserts itself more and more. Therefore, the wings must soon become active again and, in particular, acting exactly like the typical airplane (Figure 42): opposing the force of gravity, that is, carrying the weight of the space craft ("gliding flight," Figure 44).

Figure 44. Landing in a "forced circular motion." (The atmosphere and the landing spiral are drawn in the figure for the purpose of a better overview higher compared to the Earth than in reality. If it was true to scale, it would have to appear according to the ratios of Figure 8.)

Key: 1. Return (descent) trajectory; 2. Travel velocity of 11,000 m/sec; 3. Free circular motion; 4. The part of the atmosphere 100 km high useable for landing; 5. Free Orbit, in which the space ship would again move away from the Earth if the wings fail to function; 6. Forced circular motion; 7. Landing; 8. An altitude of 75 km above the Earth's surface; 9. Start of braking; 10. Boundary of the atmosphere; 11. Gliding flight; 12. Earth; 13. Rotation of the Earth.

Finally, the centrifugal force for all practical purposes becomes zero with further decreasing velocity and with an increasing approach to the Earth: from now on, the vehicle is only carried by the wings until it finally descends in gliding flight. In this manner, it would be possible to extend the distance through the atmosphere to such an extent that even the entire Earth would be orbited several times. During orbiting, however, the velocity of the vehicle could definitely be braked from 11,000 meters per second down to zero partially through the effect of the vehicle's own air drag and its wings and by using trailing parachutes, without having to worry about "overheating." The duration of this landing maneuver would extend over several hours. 


Landing in Braking Ellipses

In the method just described, transitioning from the descent orbit into the free circular orbit and the required velocity reduction from 11,000 to 7,850 meters per second occurred during the course of the "forced circular motion." According to another Hohmann recommendation, this can also be achieved by performing so-called "braking ellipses" (Figure 45). In this landing procedure, the wings are not used initially, but braking is performed as vigorously as the previously explained danger of excessive heating will permit by means of a trailing parachute as soon as the vehicle enters into sufficiently dense layers of air.

Figure 45. Landing in "braking ellipses." (The atmosphere and landing orbit are drawn here higher than in reality, exactly similar to Figure 44. Reference Figure 8.)

Key: 1. First braking ellipse; 2. Second braking ellipse; 3. Third braking ellipse; 4. Fourth braking ellipse; 5. Glided flight; 6. Earth; 7. Rotation of the Earth; 8. Braking distance of the ellipses; 9. Landing; 10. Return (descent) orbit.

However, the travel velocity, as a result, cannot be decreased to such an extent as would be necessary in order to transition the space ship into free circular motion. An excess of velocity, therefore, still remains and consequently also a centrifugal force that pushes the vehicle outward so that it again exits the atmosphere and moves away from the Earth in a free orbit of an elliptical form (first braking ellipse). The vehicle, however, will not move away to that distance from which it originally started the return flight because its kinetic energy has already decreased during the braking (Figure 45). Due to the effect of gravity, the vehicle will re-return to Earth after some time, again travel through the atmosphere with a part of its velocity again being absorbed by parachute braking; it will move away from the Earth once again, this time, however, in a smaller elliptical orbit (second braking ellipse), then return again, and so on.

Therefore, narrower and narrower so-called "braking ellipses" will be passed through one after the other corresponding to the progressive velocity decrease, until finally the velocity has dropped to 7,850 meters per second and as a result the free circular motion has been reached. The further course of the landing then occurs with the help of wings in gliding flight, just as in the previously described method. The entire duration of the landing from the initial entry into the atmosphere to the arrival on the Earth's surface is now around 23 hours; it is several times longer than with the method previously described. Therefore, the wings provided anyway for the Hohmann landing will be used to their full extent even at the start and consequently the landing will be performed better in a forced circular motion. 


Oberth's Landing Maneuver

The situation is different, however, when wings are not to be used at all, as recommended by Oberth, who also addresses the landing problem in more detail in the second edition of his book. As described above, the first part of the landing is carried out as previously described using braking ellipses (Figure 45), without a need for wings. The subsequent landing process, however, cannot take place in gliding flight because there are no wings. Although the parachute will be inclined with respect to the direction of flight by shortening one side of the shroud, resulting in some lift (an effect similar to that of wings). The use of the propulsion system to a very extensive degree could prove necessary in order to prevent an excessively rapid descent of the vehicle. Therefore, a landing maneuver without the wings could only be achieved at the expense of a fairly significant load of propellants. This assumes that applying reaction braking within the atmosphere would be feasible at all in view of a previously stated danger (a threat due to the vehicle's own gases of combustion). All things considered, the landing according to Hohmann in a "forced circular motion" by means of wings appears, therefore, to represent the most favorable solution.


The Result To Date

We have seen that not only the ascent into outer space but also the assurance of a controlled return to Earth is within the range of technical possibility, so that it does not appear at all justified to dismiss out of hand the problem of space flight as utopia, as people are traditionally inclined to do when they judge superficially. No fundamental obstacles whatsoever exist for space flight, and even those scientific and engineering prerequisites that are available today allow the expectation that this boldest of all human dreams will eventually be fulfilled. Of course, years and decades may pass until this happens, because the technical difficulties yet to be overcome are very significant, and no serious thinking person should fool himself on this point. In many respects, it will probably prove necessary in the practical implementation to alter extensively the recommendations that were proposed to date without a sufficient experimental basis. It will cost money and effort and perhaps even human life. After all, we have experienced all this when conquering the skies! However, as far as technology is concerned, once we had recognized something as correct and possible, then the implementation inevitably followed, even when extensive obstacles had to be overcome provided, however, that the matter at hand appeared to provide some benefits.


Two Other Important Questions

Therefore, we now want to attempt to show which prospects the result indicated above opens up for the future and to clarify two other existing important questions, because up to this point we have addressed only the technical side of the problem, not its economical and physiological sides. What are the practical and other advantages that we could expect from implementing space travel, and would they be sufficiently meaningful to make all the necessary, and certainly very substantial expenditures appear, in fact, to be beneficial? And, on the other hand, could human life be made possible at all under the completely different physical conditions existing in empty space, and what special precautions would be necessary in this regard?

The answer to these questions will become obvious when we examine in more detail in the following sections the prospective applications of space travel. Usually, one thinks in this context primarily of traveling to distant celestial bodies and walking on them, as has been described in romantic terms by various authors. However, regardless of how attractive this may appear, it would, in any case, only represent the final phase of a successful development of space travel. Initially, however, there would be many applications for space travel that would be easier to implement because they would not require a complete departure from the vicinity of Earth and travel toward alien, unknown worlds.


The Space Rocket in an Inclined Trajectory

For the rocket, the simplest type of a practical application as a means of transportation results when it climbs in an inclined (instead of vertical) direction from the Earth, because it then follows a parabolic trajectory (Figure 46). It is well known that in this case the range is greatest when the ballistic angle (angle of departure)in our case, the angle of inclination of the direction of ascent is 45 (Figure 47).

Figure 46. Inclined trajectory.

Key: 1. Parabolic trajectory; 2. Ballistic (departure) velocity; 3. Angle of departure; 4. Range; 5. Impact velocity.

Figure 47. The greatest distance is attained for a given departure velocity when the angle of departure is 45.

Key: 1. Direction of departure; 2. Greatest distance.

In this type of application, the rocket operates similarly to a projectile, with the following differences, however: a cannon is not necessary to launch it; its weight can be much larger than that of a typical, even very large projectile; the departure acceleration can be selected as small as desired; however, such high departure velocities would be attainable that there would theoretically be no terrestrial limit whatsoever for the ballistic (firing) range of the space rocket.

Therefore, a load could be carried in an extremely short time over very great distances, a fact that could result in the opinion that this method could be used for transporting, for example, urgent freight, perhaps for the post office, telecommunication agency, or similar service organization.

The latter application would, however, only be possible if the descent velocity of the incoming rocket were successfully slowed down to such a degree that the vehicle impacts softly because otherwise it and/or its freight would be destroyed. According to our previous considerations, two braking methods are available in this regard as follows: either by means of reaction or by air drag. Because the former must absolutely be avoided, if at all possible, due to the enormous propellant consumption, only the application of air drag should be considered.

Braking could obviously not be achieved with a simple parachute landing, because, considering the magnitudes of possible ranges, the rocket descends to its destination with many times the velocity of a projectile. For this reason, however, the braking distance, which would be available in the atmosphere even in the most favorable case, would be much too short due to the very considerable steepness of the descent. As an additional disadvantage, that the main part of the descent velocity would have to be absorbed in the lower, dense layers of air.

This is equally valid even when, as suggested by others, the payload is separated from the rocket before the descent so that it can descend by itself on a parachute, while the empty rocket is abandoned. Neither the magnitude of the descent velocity nor the very dangerous steepness of the descent would be favorably influenced by this procedure.

In order to deliver the freight undamaged to its destination, braking, if it is to be achieved by air drag, could only happen during a sufficiently long, almost horizontal flight in the higher, thin layers of air selected according to the travel velocity that is, according to Hohmann's landing method (glided landing). Baking would consequently be extended over braking distances not that much shorter than the entire path to be traveled. Therefore, proper ballistic motion would not be realized whatsoever for the case that braking should occur before the impact but rather a type of trajectory would result that will be discussed in the next section entitled "The Space Rocket as an Airplane."

With an inclined ballistic trajectory, the rocket could only be used when a "safe landing" is not required, for example, like a projectile used in warfare. In the latter case, solid fuels, such as smokeless powder and similar substances, could easily be used for propelling the rockets in the sense of Goddard's suggestion, as has been previously pointed out.

To provide the necessary target accuracy for rocket projectiles of this type is only a question of improving them from a technical standpoint. Moreover, the large targets coming mainly under consideration (such as large enemy cities, industrial areas, etc.) tolerate relatively significant dispersions. If we now consider that when firing rockets in this manner even heavy loads of several tons could safely be carried over vast distances to destinations very far into the enemy's heartland, then we understand what a terrible weapon we would be dealing with. It should also be noted that after all almost no area of the hinterland would be safe from attacks of this nature and there would be no defense against them at all.

Figure 48. The greater the range, the greater the descent velocity will be (corresponding to the greater departure velocity and altitude necessary for this).

Key: 1. Departure velocity; 2. Earth's surface; 3. Descent velocity; 4. Atmosphere.

Nevertheless, its operational characteristics are probably not as entirely unlimited as might be expected when taking the performance of the rocket propulsion system into consideration, because with a lengthening of the range the velocity also increases at which the accelerated object, in this case the rocket, descends to the target, penetrating the densest layers of air near the Earth's surface (Figure 48). If the range and the related descent velocity are too large, the rocket will be heated due to air drag to such an extent that it is destroyed (melted, detonated) before it reaches the target at all. In a similar way, meteorites falling onto the Earth only rarely reach the ground because they burn up in the atmosphere due to their considerably greater descent velocity, although at a much higher altitudes. In this respect, the Earth's atmosphere would probably provide us at least some partial protection, as it does in several other respects.

No doubt, the simplest application of the rocket just described probably doesn't exactly appear to many as an endorsement for it! Nevertheless, it is the fate of almost all significant accomplishments of technology that they can also be used for destructive purposes. Should, for example, chemistry be viewed as dangerous and its further development as undesirable because it creates the weapons for insidious gas warfare? And the results, which we could expect from a successful development of space rockets, would surpass by far everything that technology was capable of offering to date, as we will recognize in the following discussion.


The Space Rocket as an Airplane

As previously described, Hohmann recommends equipping the space ship with wings for landing. At a certain stage of his landing manoeuver, the space ship travels suspended around the Earth in a circular, free orbit ("carried" only by centrifugal force) at an altitude of 75 km and at a corresponding velocity of 7,850 meters per second ("free circular motion," Figure 44). However, because the travel velocity and also the related centrifugal force continually decrease in subsequent orbits, the vehicle becomes heavier and heavier, an effect that the wings must compensate so that the free orbital motion transitions gradually into a gliding flight. Accordingly, deeper and deeper, denser layers of air will be reached where, in spite of higher drag, the necessary lift at the diminished travel velocity and for the increased weight can be achieved ("gliding motion," Figure 44).

Since even the entire Earth can be orbited in only a few hours in this process, it becomes obvious that in a similar fashion terrestrial express flight transportation can be established at the highest possible, almost cosmic velocities: If an appropriately built space ship equipped with wings climbs only up to an altitude of approximately 75 km and at the same time a horizontal velocity of 7,850 meters per second is imparted to it in the direction of a terrestrial destination (Figure 49), then it could cover the distance to that destination without any further expenditure of energy in the beginning in an approximately circular free orbit, later more and more in gliding flight and finally just gliding, carried only by atmospheric lift. Some time before the landing, the velocity would finally have to be appropriately decreased through artificial air drag braking, for example, by means of a trailing parachute.

Figure 49. Schematic representation of an "express flight at a cosmic velocity" during which the horizontal velocity is so large (in this case, assumed equal to the velocity of free orbital motion) that the entire long-distance trip can be covered in gliding flight and must still be artificially braked before the landing.

Key: 1. Artificial braking; 2. Highest horizontal velocity of 7,850 m/sec; 3. Altitude of 75 km; 4. Long-distance trip in gliding flight (without power); 5. Ascent (with power).

Even though this type of landing may face several difficulties at such high velocities, it could easily be made successful by selecting a smaller horizontal velocity, because less artificial braking would then be necessary. From a certain initial horizontal velocity, even natural braking by the unavoidable air resistance would suffice for this purpose (Figure 50).

Figure 50. Schematic representation of an "express flight at a cosmic velocity" during which the highest horizontal velocity is just sufficient to be able to cover the entire long- distance trip in gliding flight when any artificial braking is avoided during the flight.

Key: 1. Highest horizontal velocity; 2. Altitude; 3. Long-distance travel in gliding flight without power and without artificial braking; 4. Ascent (with power)

In all of these cases, the vehicle requires no power whatsoever during the long-distance trip. If the vehicle is then powered only by a booster rocket that is, "launched" so to speak by the booster during the ascent (until it reaches the required flight altitude and/or the horizontal orbital velocity), then the vehicle could cover the longer path to the destination solely by virtue of its "momentum" (the kinetic energy received) and, therefore, does not need to be equipped with any propulsion equipment whatsoever, possibly with the exception of a small ancillary propulsion system to compensate for possible estimation errors during landing. Of course, instead of a booster rocket, the power could also be supplied in part or entirely by the vehicle itself until the horizontal orbital velocity is attained during the ascent. In the former case, it may be advantageous to let the booster rocket generate mainly the climbing velocity and the vehicle, on the other hand, the horizontal velocity.

Figure 51. Schematic representation of an "express flight at a cosmic velocity" during which the highest horizontal velocity is not sufficient for covering the entire long-distance trip in gliding flight so that a part of the trip must be traveled under power.

Key: 1. Highest horizontal velocity of 2,500 m/sec in the example; 2. Climb and flight altitude of 60 km in the example; 3. Gliding flight; 4. With or without artificial braking; 5. Power flight; 6. Velocity of travel of 2,500 m/sec in the example; 7. Long- distance trip; 8. Ascent (with power).

In the case of a still smaller horizontal velocity, a certain part of the long-distance trip would also have to be traveled under power (Figure 51). Regardless of how the ascent may take place, it would be necessary in any case that the vehicle also be equipped with a propulsion system and carry as much propellant as is necessary for the duration of the powered flight.

Assuming that benzene and liquid oxygen are used as propellants and thereby an exhaust velocity of 2,500 meters per second is attained, then in accordance with the previously described basic laws of rocket flight technology and for the purpose of attaining maximum efficiency, even the travel velocity (and accordingly the highest horizontal velocity) would have to be just as great during the period when power is being applied, that is, 2,500 meters per second. The optimal flight altitude for this flight would presumably be around 60 km, taking Hohmann's landing procedure into account. At this velocity, especially when the trip occurs opposite to the Earth's rotation (from east to west), the effect of centrifugal force would be so slight that the wings would have to bear almost the entire weight of the vehicle; in that case, the trip would almost be a pure heavier-than-air flight movement rather than celestial body motion.

In view of the lack of sufficient technical data, we will at this time refrain from discussing in more detail the design of an aerospace plane powered by reaction (rockets). This will actually be possible as was indicated previously in connection with the space rocket in general only when the basic problem of rocket motors is solved in a satisfactory manner for all practical purposes.

On the other hand, the operating characteristics that would have to be used here can already be recognized in substance today. The following supplements the points already discussed about these characteristics: Since lifting the vehicle during the ascent to very substantial flight altitudes (3575 km) would require a not insignificant expenditure of propellants, it appears advisable to avoid intermediate landings in any case. Moreover, this point is reinforced by the fact that breaking up the entire travel distance would make the application of artificial braking necessary to an increasing extent due to the shortening caused as a result of those air distances that can be covered in one flight; these intermediate landings, however, mean a waste of valuable energy, ignoring entirely the losses in time, inconveniences and increasing danger always associated with them. It is inherent in the nature of express flight transportation that it must be demonstrated as being that much more advantageous, the greater (within terrestrial limits, of course) the distances to be covered in one flight, so that these distances will still not be shortened intentionally through intermediate landings.

Consequently, opening up intermediate filling stations, for example, as has already been recommended for the rocket airplane, among others, by analogy with many projects of transoceanic flight traffic, would be completely counter to the characteristic of the rocket airplane. However, it is surely a false technique to discuss these types of motion by simply taking only as a model the travel technology of our current airplanes, because rocket and propeller vehicles are extremely different in operation, after all.

On the other hand, we consider it equally incorrect that rocket airplane travel should proceed not as an actual "flight" at all, but primarily more as a shot (similar to what was discussed in the earlier section), as many authors recommend. Because in this case, a vertical travel velocity component, including the horizontal one, can be slowed down during the descent of the vehicle. Due to the excessively short length of vertical braking distance possible at best in the Earth's atmosphere, this velocity component, however, cannot be nullified by means of air drag, but only through reaction braking. Taking the related large propellant consumption into account, the latter, however, must be avoided if at all possible.

The emergence of a prominent vertical travel velocity component must, for this reason, be inhibited in the first place, and this is accomplished when, as recommended by the author, the trip is covered without exception as a heavier-than-air flight in an approximately horizontal flight path where possible, chiefly in gliding flight (without power) that is, proceeding similarly to the last stage of Hohmann's gliding flight landing that, in our case, is started earlier, and in fact, at the highest horizontal velocity.

The largest average velocity during the trip, at which a given distance could be traveled in the first place during an express flight of this type, is a function of this distance. The travel velocity is limited by the requirement that braking of the vehicle must still be successful for landing when it is initiated as soon as possible, that is, immediately after attaining the highest horizontal velocity (Figure 52).

Figure 52. The highest average velocity during the trip is attained when the highest horizontal velocity is selected so large than it can just be slowed if artificial braking is started immediately after attaining that velocity. (In the schematic representations of Figures 49 through 52, the Earth's surface would appear curved in a true representation, exactly as in Figure 53.)

Key: 1. Highest horizontal velocity; 2. Long-distant trip in gliding flight completely with artificial braking; 3. Ascent (with power).

The "optimum highest horizontal velocity" for a given distance would be one that just suffices for covering the entire trip in gliding flight to the destination without significant artificial braking (Figures 50 and 53). In the opinion of the author, this represents without a doubt the most advantageous operating characteristics for a rocket airplane. In addition, it is useable for all terrestrial distances, even the farthest, if only the highest horizontal velocity is appropriately selected, primarily since a decreased travel resistance is also achieved at the same time accompanied by an increase of this velocity, because the greater the horizontal velocity becomes, the closer the flight approaches free orbital trajectory around the Earth, and consequently the vehicle loses weight due to a stronger centrifugal force. Also, less lift is necessary by the atmosphere, such that the flight path can now be repositioned to correspondingly higher, thinner layers of air with less drag also with a lower natural braking effect.

The magnitude of the optimum horizontal velocity is solely a function of the length of the distance to be traveled; however, this length can only be specified exactly when the ratios of lift to drag in the higher layers of air are studied at supersonic and cosmic velocities.

Figure 53. The most advantageous way of implementing an "express flight at a cosmic velocity" is as follows: The highest horizontal velocity is corresponding to the distance selected so large ("optimum horizontal velocity") that the entire long-distance trip can be made in gliding flight without power and without artificial braking (see Figure 50 for a diagram).

Key: 1. Gliding flight without power and without artificial braking; 2. Earth's surface; 3. Ascent (with power); 4. "Best case highest horizontal velocity".

However, even smaller highest horizontal velocities, at which a part of the trip would have to be traveled (investigated previously for benzene propulsion), could be considered on occasion. Considerably greater velocities, on the other hand, could hardly be considered because they would make operations very uneconomical due to the necessity of having to destroy artificially, through parachute braking, a significant portion of the energy.

It turns out that these greater velocities are not even necessary! Because when employing the "best case" highest horizontal velocities and even when employing the lower ones, every possible terrestrial distance, even those on the other side of the Earth, could be covered in only a few hours.

In addition to the advantage of a travel velocity of this magnitude, which appears enormous even for today's pampered notions, there is the advantage of the minimal danger with such an express flight, because during the long-distance trip, unanticipated "external dangers" cannot occur at all: that obstacles in the flight path occur is, of course, not possible for all practical purposes, as is the case for every other air vehicle flying at an appropriately high altitude. However, even dangers due to weather, which can occasionally be disastrous for a vehicle of this type, especially during very long-distance trips (e.g., ocean crossings), are completely eliminated during the entire trip for the express airplane, because weather formation is limited only to the lower part of the atmosphere stretching up to about 10 km the so-called "troposphere." The part of the atmosphere above this altitude the "stratosphere"is completely free of weather; express flight transportation would be carried out within this layer. Besides the always constant air streams, there are no longer any atmospheric changes whatsoever in the stratosphere.

Furthermore, if the "optimum velocity" is employed such that neither power nor artificial braking is necessary during the long-distance trip, then the "internal dangers" (ones inherent in the functioning of the vehicle) are reduced to a minimum. Just like external dangers, internal ones can only occur primarily during ascent and landing. As soon as the latter two are mastered at least to that level of safety characteristic for other means of transportation, then express airplanes powered by reaction will not only represent the fastest possible vehicles for our Earth, but also the safest.

Achieving a transportation engineering success of this magnitude would be something so marvelous that this alone would justify all efforts the implementation of space flight may yet demand. Our notions about terrestrial distances, however, would have to be altered radically if we are to be able to travel, for example, from Berlin to Tokyo or around the entire globe in just under one morning! Only then will we be able to feel like conquerors of our Earth, but at the same time justifiably realizing how small our home planet is in reality, and the longing would increase for those distant worlds familiar to us today only as stars. 


The Space Station in Empty Space

Up to this point, we have not even pursued the actual purpose of space ship travel. The goal with this purpose initially in mind would now be as follows: to ascend above the Earth's atmosphere into completely empty space, without having to separate completely from the Earth, however. Solely as a result of this effort, tremendous, entirely new vistas would open up.

Nevertheless, it is not sufficient in this regard to be able only to ascend and to land again. No doubt, it should be possible to perform many scientific observations during the course of the trip, during which the altitude is selected so high that the trip lasts days or weeks. A large-scale use of space flight could not be achieved in this fashion, however. Primarily because the necessary equipment for this purpose cannot be hauled aloft in one trip due to its bulk, but only carried one after the other, component- by-component and then assembled at the high altitude.

The latter, however, assumes the capability of spending time, even arbitrarily long periods, at the attained altitude. This is similar, for instance, to a captive balloon held aloft suspended for long periods without any expenditure of energy, being supported only by the buoyancy of the atmosphere. However, how would this be possible in our case at altitudes extending up into empty space where nothing exists? Even the air for support is missing. And still! Even when no material substance is available, there is nevertheless something available to keep us up there, and in particular something very reliable. It is an entirely natural phenomenon: the frequently discussed centrifugal force.

Introductory paragraphs indicated that humans could escape a heavenly body's gravitational effect not only by reaching the practical limit of gravity, but also by transitioning into a free orbit, because in the latter case the effect of gravity is offset by the emerging forces of inertia (in a circular orbit, solely by the centrifugal force, Figure 5), such that a stable state of suspension exists that would allow us to remain arbitrarily long above the heavenly body in question. Now in the present case, we also would have to make use of this possibility.

Accordingly, it is a matter not only of reaching the desired altitude during the ascent, but also of attaining a given orbital velocity exactly corresponding to the altitude in question (and/or to the distance from the Earth's center). The magnitude of this velocity can be computed exactly from the laws of gravitational motion. Imparting this orbital velocity, which in no case would have to be more than around 8,000 meters per second for the Earth, would present no difficulties, as soon as we have progressed to the point where the completed space vehicle is capable of ascending at that rate.

Among the infinitely large number of possible free orbits around the Earth, the only ones having significance for our present purpose are approximately circular and of these the only ones of particular interest are those whose radius (distance from the center of the Earth) is 42,300 km (Figure 54). At an assigned orbiting velocity of 3,080 meters per second, this radius corresponds to an orbital angular velocity just as great as the velocity of the Earth's rotation. That simply means that an object circles the Earth just as fast in one of these orbits as the Earth itself rotates: once per day ("stationary orbit").

Figure 54. Each object orbiting the Earth in the plane of the equator, 42,300 km from the center of the Earth in a circular orbit, constantly remains freely suspended over the same point on the Earth's surface.

Key: 1. Earth's axis; 2. Earth's rotation; 3. Free orbit; 4. Equator; 5. Earth; 6. Orbital velocity of 3,080 m/sec; 7. Orbiting object; 8. Common angular velocity of the Earth's rotation and of the orbital motion.

Furthermore, if we adjust the orbit in such a fashion that it is now exactly in the plane of the equator, then the object would continually remain over one and the same point on the equator, precisely 35,900 km above the Earth's surface, when taking into account the radius of the Earth of around 6,400 km (Figure 54). The object would then so to speak form the pinnacle of a enormously high tower that would not even exist but whose bearing capacity would be replaced by the effect of centrifugal force (Figure 55).

Figure 55. An object orbiting the Earth as in Figure 54 behaves as if it would form the pinnacle of a enormously giant tower (naturally, only imaginary) 35,900,000 meters high.

Key: 1. Earth's axis; 2. Earth's rotation; 3. Free orbit; 4. Equator; 5. Imaginary giant tower 35,900,000 meters high; 6. Freely orbiting object, like a pinnacle of a tower, remaining fixed over the Earth's surface.

This suspended "pinnacle of the tower" could now be built to any size and equipped appropriately. An edifice of this type would belong firmly to the Earth and even continually remain in a constant position relative to the Earth, and located far above the atmosphere in empty space: a space station at an "altitude of 35,900,000 meters above see level." If this "space station" had been established in the meridian of Berlin, for example, it could continually be seen from Berlin at that position in the sky where the sun is located at noon in the middle of October.

If, instead of over the equator, the space station were to be positioned over another point on the Earth, we could not maintain it in a constant position in relation to the Earth's surface, because it would be necessary in this case to impart to the plane of its orbit an appropriate angle of inclination with respect to the plane of the equator, and, depending on the magnitude of this angle of inclination, this would cause the space station to oscillate more or less deeply during the course of the day from the zenith toward the horizon. This disadvantage could, however, be compensated for in part when not only one but many space stations were built for a given location; with an appropriate selection of the orbital inclination, it would then be possible to ensure that always one of the space stations is located near the zenith of the location in question. Finally, the special case would be possible in which the orbit is adjusted in such a manner that its plane remains either vertical to the plane of the Earth's orbit, as suggested by Oberth, or to that of the equator.

In the same manner, the size (diameter) of the orbit could naturally be selected differently from the present case of a stationary orbit: for example, if the orbit for reasons of energy efficiency is to be established at a greater distance from the Earth (transportation station, see the following) or closer to it, and/or if continually changing the orientation of the space station in relation to the Earth's surface would be especially desired (if necessary, for a space mirror, mapping, etc, see the following).

What would life be like in a space station, what objectives could the station serve and consequently how would it have to be furnished and equipped? The special physical conditions existing in outer space, weightlessness and vacuum, are critical for these questions.

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