The Rocket into Planetary Space

Hermann Oberth

• Publisher: De Gruyter Oldenbourg
• Year: 2014
• ISBN:
  9783486990676
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

For all being interested in astronautics, this translation of Hermann Oberth's classic work is a truly historic event. Readers will be impressed with this extraordinary pioneer and his incredible achievement. In a relatively short work of 1923, Hermann Oberth laid down the mathematical laws governing rocketry and spaceflight, and he offered practical design considerations based on those laws.

§ 1. Introduction

1. At today’s state of science and technology, it is possible to build machines able to ascend beyond the limits of Earth’s atmosphere.

2. With additional refinement these machines will be able to attain such velocities that—left to themselves in the ether⁴—they will not fall back to Earth’s surface, and will even be able to leave the gravitational field of Earth.

3. These kinds of machines can be built in such a way that people can ascend within them (probably without health disadvantage).

4. Under certain economic conditions, the construction of such machines may even become profitable. Such conditions might arise within a few decades.

In the present document I intend to prove these four statements. First, I will derive some formulas, which will give us the necessary theoretical insights into the functioning and performance of these machines. In a second part I will show that their construction is technically feasible, and finally in a third part I will discuss the potential of this invention.

I endeavored to be concise. I could frequently simplify the mathematical derivations and formulas by using approximate values for certain parameters that simplified the calculations. I used this approach especially if it made the nature of a subject clearer when discussing a mathematical formula. (In addition, I have often supplied the accurate result or at least shown how it could be derived indirectly from the approximated value, and sometimes I simply estimated the error margin). I have only briefly discussed technical problems whose solvability no one doubts. In the third part, I have limited myself to suggestions, because the subjects dealt with lie still rather far in the future.

I did not want to provide more here than deemed necessary for understanding the invention and evaluating its feasibility, because:

First of all, by no means did I intend to describe in all details the design of a particular machine, but only to show that such machines are possible. [e.g., I do not have to calculate the maximum performance a specific rocket might actually achieve, if I can just show that it is able anyway to meet the defined requirements. Thus I assumed, for example, a constant exhaust velocity c (cf. p. 9), even though this value can vary by as much as 9% in some cases, and I discussed the case of a rocket traveling at a velocity

(cf. p. 11), although in this case the fuel is not at all optimized, among other examples. If I estimate the performance of a rocket based on

and the most unfavorable value for c, and find the rocket capable of reaching a required final velocity and altitude under these assumptions, then I have also proved that it surely can attain them in reality]. I am even convinced that the whole thing becomes much clearer if I do not go into too much detail.

Second, there are some things that I want to keep to myself (in particular, apparently quite favorable technical solutions) as they are unprotected intellectual property. Should my ideas be realized one day, I certainly would be happy to furnish exact plans, calculations, and methods of computation.

Finally, I will not hide the fact that I consider some of the devices in their present form by no means as definitive solutions. As I worked on my plans and computations I naturally had to consider every detail; and in doing so I could at least see that there were no insurmountable technical difficulties. At the same time, however, it was also clear to me that some specific questions could only be solved after most thorough research and perhaps years-long experimentation in order to find optimum solutions.

Part I

Principle of Operation and Performance

The flight of these machines is based on the reaction principle; i.e., the machine is lifted and moved by gases that are expelled under corresponding pressure like a rocket. Therefore, allow me a few words first on the theory of rockets.

A completely sealed vessel, in which the internal pressure is greater than the external pressure, stays at rest because the total pressure (which is the result of all pressure forces on any part of the vessel wall) is canceled by an equal and opposite pressure on the rest of the wall. But if part of a wall is missing (cf. Fig. 1), then 1. the content of the vessel is expelled through the opening and, 2. the vessel seeks to move in the opposite direction, because the total pressure on the side of the wall with the opening is now less than the pressure on the intact opposite side. Therefore, the force that would propel the vessel rearwards (we shall call it the reaction force and denote it with P) is equal and opposite to the force that propels the contents in the forward direction. If I denote the element of mass flowing out during the time period dt as dm and the exhaust velocity as c, then:

Fig. 1.

Henceforth, I will call every flight machine that moves in reaction to expelling gases a rocket.

Here we need only to investigate the case of a rocket ascending vertically. Let its velocity be v and its mass m. The vectors are pointing vertically either up or down; those pointing upward (e.g., P, v) we will define as positive, and those pointing downward (e.g., c), as negative.

Part of the reaction force P is used to overcome drag (-L) and gravity (-G); we will call this part Q (of course, we must consider Q, just as P, to be positive). The remaining force R provides the rocket with a certain acceleration

We therefore have:

(1)

We can also write dm

. Here c is an absolute number; P and dt are c positive, so it follows that dm < 0, i.e., that the mass decreases with time. It also follows that, if c is constant, then for a given c, ...