The Travel Velocity and the Efficiency of Rocket Vehicles

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

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

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

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

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

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

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

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

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

Table 1

Ratio of the travel Efficiency of the

velocity v to the Reaction hr