# Did H. Oberth use scientific experimentation or the scientific theory to prove the validity of the Oberth effect?

I recently started reading an interesting piece of history called the Space Handbook and I found something that surprised me a bit. I learned that the Oberth Effect is named after one of the early pioneers of rocketry.

In his 1927 book "Ways to Spaceflight" Oberth reportedly described the effect in detail. According to the Space Handbook:

The principal early work in the technological field of space flight was done in Russia, Germany, and the United States. The chief United States effort was that of Goddard. The early German work was done by H. Oberth, beginning in the 1920's. Russian efforts commenced at a substantially earlier date, giving them a clear and valid claim to a "first." Russian activity began with the work of Mescherskii and Tsiolkovskii near the end of the 19th century. Tsiolkovskii is generally recognized as the father of astronautics. Considerable work, both theoretical and experimental, was accomplished in the U. S. S. R. in the 1920's and 1930's.

Serious and substantial Government-sponsored rocket-research programs were established in Germany in about 1930, in the Soviet Union sometime in or before 1934, and in the United States in 1942. The astronautical activities of the United States and the U. S. S. R. will be discussed in greater detail below.

In flipping through Herr Oberth's book I found the following:

The rocketry theorist must always be aware of the entirely different conditions under which the rocket works and cannot adopt any models that have proved theuselves in the calculation of other propulsion devices without first testing them. It took me, for exauple, over 10 yesrs to work out the theory of rocketry. Not every one is suited for such a method of work, which is one reason wliy, until 15 years ago, no theory of rocketrj* existed.

Did Oberth himself use scientific experimentation or the scientific theory to validate his assertion? If not Oberth himself, has anyone used scientific theory to prove the Oberth Effect is real?

• I am trying to read through H. Oberth's book but the translation is making it difficult. – Lumberjack Jun 10 '16 at 21:19
• Seems like a really bad OCR of the book, messing up the text. – SF. Jun 10 '16 at 22:55
• Not sure about the history of the vis viva equation but I'm guessing it was well known shortly after Newton. Also well known, kinetic energy = 1/2 mv^2. I'm guessing mathematical models gave Oberth a fair amount confidence. – HopDavid Jun 11 '16 at 15:54

I can't source this, but if with a couple years of messing around I can understand and explain the basis, mr. Oberth, with 10 years of thorough study would have no problems developing the maths that prove it.

Experimental confirmation is costly and difficult here, but the theory is sound and fairly simple (if a little counter-intuitive).

Change of speed as propellant is ejected, in the rocket-propellant frame of reference (say, bound to center of mass of rocket and ejected propellant) is directly derived from conservation of momentum.

$$\Delta v_{ship} \cdot m_{ship} = \Delta v_{propellant} \cdot m_{propellant}$$

Note how this completely disregards initial/external conditions like speed of the rocket, its altitude, direction and so on - it's an inertial frame of reference, where initially the speed of both is zero (relative to the frame of reference) and no external conditions influence it.

Burning a fixed amount of fuel, as result ejecting a fixed amount of propellant, at a fixed speed relative to the rocket, we obtain a fixed change of velocity, completely regardless of external conditions.

Now, Energy of the rocket can't be taken in such a willy-nilly frame of reference. We must take it relative to a planet. Potential energy - altitude, and kinetic - speed relative to the planet.

How does the kinetic energy change if we perform a burn - as before, eject a fixed amount of mass, at fixed speed relative to the rocket?

$$\Delta E_k = {1\over 2} m (v + \Delta v)^2 - {1\over 2} m v^2$$

The square here is the key. We're turning a fixed amount of chemical energy of the fuel into kinetic energy that scales with square of speed. If initial speed is 0 and we accelerate a mass of 2kg by 1m/s, we have

$\Delta E_k = 1^2 - 0^2 = 1-0 = 1J$.

If we apply exactly the same acceleration to the same mass but with initial speed of 100m/s,

$\Delta E_k = 101^2 - 100^2 = 10201 - 10000 = 201 J$.

We've just gained 200 Joules by the mere fact our mass was moving fast when the acceleration occurred; we used the same amount of fuel/propellant though, and all the rest of the parameters remained unchanged.

This is an immense gain of kinetic energy. And that, in order converts to potential energy - our ability to escape gravity wells. And in our favor, this one scales with inversely to distance from the planet. So, linear "burn size" causes geometric growth of kinetic energy, and so, geometric growth of our "range" - ability to reach higher orbits, or depart the system. Burn the same fuel at twice the speed, extend your apoapsis altitude four times as much.

That is all pretty basic physics, and it really doesn't take much guessing. So, even without experimental confirmation, mr. Oberth would have no problems just deriving this mathematically. It feels counter-intuitive because the energy gain seems free, and we all know TANSTAAFL. But it only seems so. We first need to spend energy to accelerate the rocket and the propellant to these speeds, and that costs.

This is an extreme simplification. It proves this works, it's enough to get a funding for further research if you're in mr. Oberth's position, and it promises immense savings. But the reality is this is based all on a point burn. Which would be equivalent to blowing up an explosive charge to separate some reaction mass. This is not how it works in reality. The additions and substractions need to be replaced with integrals over mass, velocity, energy which change over time themselves. (as the ship accelerates, so does the fuel on it, contributing more to the efect...). This also gives the rough idea how much the orbit extends, but none where to. We don't just want to fling the spaceship out into a random direction in space, we want it to head towards a specific destination - so the burn must be performed in precise conditions that give the craft the proper trajectory. We're treating this as a two-body problem, the craft and the planet. We must take into account the rest of the solar system too.

That's how this simple page of explanation turns into ten years of research, and this is the source of mr. Oberth's doubts. The fact the effect works was beyond doubt. It was the calculations to make it practically useful, that required extensive testing.

It seems to me Oberth is referring to design work on rocket engines. The behavior of an engine couldn't be modeled comprehensively at the time, so you need experiments to verify your design works.

The Oberth Effect, on the other hand is basic physics. There's no complex modeling involved, so he could be confident it'd work without experimentation.