V = Vj ln(Mo/ Me)
where V is the maximum velocity of the rocket in gravity-free, drag-free flight, Vj is the rocket exhaust jet velocity, in is the natural logarithm, Mo is the initial or full rocket mass, and Me is the empty rocket mass.
The Tsiolkovsky equation states a key relationship for understanding the advantages and disadvantages of liquid hydrogen as a fuel. The equation shows that rocket vehicle velocity is directly proportional to the rocket exhaust jet velocity. Tsiolkovskiy understood this well, deriving the equation of flight based on the conservation of momentum, integrating, and using the initial and final conditions of the rocket to obtain his equation.
Tsiolkovsky drafted the first design of the liquid-fuel rockets that he outlined in his paper. He said in his own words
“Imagine the following configuration: a metal elongated .It would be powered by liquid oxygen and hydrogen, creating an explosive mixture in the narrow end of a tube. This would then be combusted, creating heated condensed gases, which would quickly cool and rarefy, escaping through a nozzle and creating a great force (thrust) that propels the rocket.
Law of Conservation of Momentum can be used to analyse rocket motion. Rocket engines generate thrust by burning fuel and expelling the resulting gases. Conservation of momentum means that as the gases move one way, the rocket moves the other. (Momentum before the burning is zero; hence the momentum after is also zero. The gases carry momentum in one direction down, and so the rocket carries an equal momentum in the opposite direction up, as described in newtons 3rd law..evry action has an equal and oppositr reaction.)
Forces experienced by astronauts
Note that two forces act upon an astronaut during launch: the upward thrust (T) as well as the downward weight (W or mg). Newton’s second law(F=Ma) can be used to derive a simple expression for acceleration of a rocket that is launched directly up (using the diagram above):
This equation is: a = (T – mg)/m Where a = acceleration
T = upwards thrust of the rocket
m = mass
g = gravity
This formula shows that the acceleration of a rocket is not uniform, it increases logarithmically as the launch proceeds. (See Fig. 1) This is because a lot of the rocket’s mass is fuel, and as fuel is burnt off, mass decreases.
This is proved by Newton’s Second Law, stating that Force is equal to mass times acceleration (F = ma). Force in the equation can be thought of as the thrust of the rocket engine. Mass in the equation is the amount of rocket fuel being burned and converted into gas that expands and then escapes from the rocket. Acceleration is the rate at which the gas escapes. Inside the rocket, the gas does not really move, but as it leaves the engine it picks up speed. So therefore, as
thrust (force) increases, and mass decreases due to the fuel being burnt, acceleration must increase, and as thrust is continuous until shut off, the rate of mass reduction will also be continuous and therefore the rate of acceleration will increase logarithmically., hence more force will be acting upon the astronauts/
Konstantin Eduardovitch Tsiolkovsky
V = Vj ln(Mo/ Me)
(A) liquid oxygen tank; (B) liquid hydrogen (or hydrocarbon) tank; (C) crew and equipment; (D) burning chamber; (E) exhaust nozzle; (F) control surfaces (in the stream of exhaust gases).
EVERY ACTION HAS AN EQUAL AND OPPOSITE REACTION
FORCES EXPERIENCED BY ASTRONAUTS
: a = (T – mg)/m
F = ma
