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
against the force of gravity. It must be able to lift itself and
its payload up many thousands, even hundreds of thousands of
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
of the curve of the force of gravity from the horizontal axis.
Key: 1. Amount of the Earth's force of gravity at various
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
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).
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.
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
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
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.
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
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
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
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
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
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. 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
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,
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
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
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
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
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.
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
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
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
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
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
Ratio of the travel Efficiency of the
velocity v to the Reaction hr
velocity of expulsion c
v/c hr in percentages
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
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
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
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
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
1 2 3
Travel Efficiency of the Reaction Total
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
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
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
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).
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;
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
The following formula provides an explanation on this point:
Table 4 was prepared using this formula.
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
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
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
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
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
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.
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.
Key: 1. Velocity of motion; 2. Final mass; 3. Exhaust velocity; 4.
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
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
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
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
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
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,
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
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
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
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
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
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
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
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
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
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.
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
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
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
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
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;
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.
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. 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.
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.
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
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
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
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
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
Two Other Important
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
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
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
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
Key: 1. Departure velocity; 2. Earth's surface; 3. Descent velocity; 4.
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
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. 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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
This page compliments of Marisa
Created: Friday, March 28, 2003;
Wednesday, January 02, 2013
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