FIRST STEPS TOWARD SPACE - Smithsonian Institution Libraries

130 SMITHSONIAN ANNALS OF FLIGHT
certain speed, it will maintain its direction and
speed as long as nothing else happens. But, when
a space pilot, sitting on the pole, cuts little pieces
off the end of the pole, and throws them backwards,
then not only will these small pieces change their
speed, but also the remaining part of the pole will
get an impulse in the opposite direction. The forward
speed of the pole will be increased less if
the cut-off pieces are small and move slowly, and
more if the pieces are large and move at high speed.
In the same way, the increase in speed would be
equally high if, instead of one big piece, many small
pieces were to be exhausted or thrown off. It does
not matter whether these pieces push against something,
or whether they sail through the vacuum
of space. There would also be an increase in speed
if the thrown-off parts were gas molecules. The increase
can be considerable when large quantities of
gas are exhausted at high speed.
In general, it is not as important how much
knowledge a person has, but, rather, what he does
with his knowledge. In this sense, there were many
stumbling blocks in the field of rocketry. Knowledgeable
engineers and even university professors
had postulated that repulsion would not work in
a vacuum. I nevertheless continued in my belief
that it would prove out in actual fact. There was
even a colonel, head of the German Missile Post
in East Prussia, who in 1927 tried to prove the
impossibility of space travel. Among other things,
he said that although the law of the conservation
of the center of gravity was valid, the gas would
expand so much in outer space that it would
lose its entire mass and therefore would not have
any moment of inertia. To the contrary, I maintained
that a pound of propellant would always
remain a pound of propellant, no matter how
much space into which it might expand.
From 1910 to 1912, I learned infinitesimal calculus
in the Bischof-Teutsch-Gymnasium in Schassburg.
This school, more humanistic than scientific
in nature, resembled a car which has only small
headlights in front, but which illuminates very
brightly the way it has already traveled, thus helping
light the way for others. I also had bought the
book, Mathematik fur Jedermann [Mathematics
for Everybody], by August Shuster, which covered
differential calculus and helped me overcome a
certain lack of training.
As a student I had little occasion to do experi­
ments. In order to accomplish something with
my time, I pondered the theoretical problems of
rocket technology and space travel, and attempted
to solve some of them. No one of whom I had
knowledge had done so thoroughly. Dr. Goddard
in 1919, for instance, wrote that it would be impossible
to express for a rocket trajectory the
interactions of propellant consumption, exhaust
velocity, air drag, influence of gravity, etc., in closed
numerical equations. 1 In 1910 I had begun to
investigate these mathematical relationships and
to derive the equations; these investigations were
completed by 1929.
One of my first discoveries was the optimum
speed at which losses in performance, caused by
air drag and gravity, were reduced to a minimum.
I found this by a sort of differentiation process
and called the term v. When a rocket rises perpendicularly
to the earth's surface with the velocity
v, the air drag is equal to the weight of the rocket.
If the rocket rises faster, it has to fight against its
weight for a shorter time; but since the air drag
increases with the square of the velocity, the total
losses are greater; and if it rises too slowly, it has
to fight against its own weight for a longer time.
All rockets built before 1920 had flown too fast.
Early rockets also were not large enough, for there
is a kind of competition between the weight of the
rocket and the air density. If, or example, vc — 2gH,
then the optimum speed does not change at all
when the rocket rises. Consequently the rocket
can only escape from the atmosphere if the ratio
between takeoff mass and burnout mass is infinite;
that is, if the propellant weighed infinitely as
much as the rest of the rocket. In this equation c
denotes the exhaust velocity, H the height at which
the air pressure will have decreased to \/e, which
is 1 divided by the base of natural logarithms
(1/2.71828 = 0.36788 of the initial value), and g
denotes the acceleration of gravity.
If the rocket were small, then even U would
decrease with time: the air does not become thinner
at the same rate at which the rocket loses weight.
The rocket will, so to speak, remain stuck in the
air. If the rocket, however, is big and heavy, the
forces caused by the drag will be less in comparison
to the other forces. In this case, v is higher, and
the rocket reaches thinner layers of air sooner.
For example, a cannon ball will not be retarded