%0 Journal Article
%T Derivation of a Revised Tsiolkovsky Rocket Equation That Predicts Combustion Oscillations
%A Zaki Harari
%J Advances in Aerospace Science and Technology
%P 10-27
%D 2024
%I
%R 10.4236/aast.2024.91002
%X Our
study identifies a subtle deviation from Newton¡¯s third law in the derivation of the ideal rocket
equation, also known as the Tsiolkovsky Rocket Equation (TRE). TRE can be
derived using a 1D elastic collision model of the momentum exchange between the
differential propellant mass element (dm)
and the rocket final mass (m1), in
which dm initially travels forward to
collide with m1 and rebounds to exit
through the exhaust nozzle with a velocity that is known as the effective exhaust
velocity ve. We observe that such a
model does not explain how dm was
able to acquire its initial forward velocity without the support of a reactive
mass traveling in the opposite direction. We show instead that the initial
kinetic energy of dm is generated
from dm itself by a process of
self-combustion and expansion. In our ideal rocket with a single particle dm confined inside a hollow tube with
one closed end, we show that the process of self-combustion and expansion of dm will result in a pair of differential
particles each with a mass dm/2, and
each traveling away from one another along the tube axis, from the center of
combustion. These two identical particles represent the active and reactive
sub-components of dm, co-generated in
compliance with Newton¡¯