Fundamentals of Rocket Science

Liftoff

Rocket engines are different from car or jet engines in two fudamental ways.

1. Unlike cars, rockets don't need to "push off" of anything to propel themselves forward.

2. Rockets are self-contained. In other words they don't need oxygen from the atmosphere to provide fuel for energy.

Rockets operate using the law of conservation of linear momentum. This law states that whenever two or more particles interact, the total momentum of the system remains constant. In this case the shuttle and it's fuel can be considered separate particles.

A rocket moves by ejecting its fuel out the nose at extremely high velocities (approx. 6000 mph). The fuel is given momentum as it is being ejected. To insure conservation of linear momentum, the shuttle must be given a compensating momentum in the opposite direction.

Rockets move exactly like Dr. Newman would if he were on a sheet of ice with 3 million pounds of baseballs throwing them at a rate of 22,000 lbs/sec. Actually Dr. Newman would move quite a bit faster, because he has MUCH less mass than the space shuttle.

To quickly summarize, thrust is equal to the exhaust velocity multiplied by the amount fuel leaving with respect to time. This is illustrated by the equation:

Thrust = ve(dM/dt)

This tells us the only way to increase the amount of thrust acting on the rocket, is by increasing the velocity of the exhaust, or the amount of fuel, M, leaving per second.

* This is why space shuttles don't hurl baseballs out the back of the rockets. It's takes a lot of energy to accelerate a baseball to 6000 mph!

Rocket Scientist (they don't call them that for nothing) prefer to use the ideal gas law: An ideal gas is one for which PV/nT is constant at all pressures.

* Fuel and an Oxidizing agent, usually liquid oxygen and hydrogen respectively, are forced into the combustion chamber where they are ignited. The temperature increases which forces the pressure in the chamber to increase to insure PV/T remains constant.

Volume inside the chamber is constant so:

Pi/Ti = Pf/Tf, => Pf = PiTf/Ti

Using Bernoulli's equation we can determine the velocity of the gas exiting the Nozzle:

Ve = Ac[2(Pc - Pn)/(p(Ac^2-An^2))]^(1/2)

where V = velocity, A = cross sectional area, P = pressure, p = density of the fluid, and n,c = defines Nozzle and Combustion Chamber respectively.

The final step is to find the rate the mass is being ejected (dM/dt).