More on Thrust


 

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). The law of Conservation of Mass tells us mass is neither created nor destroyed. This means for every pound of fuel being being consumed, one pound of gas will be created. This is regardless of the pressure, density or volume of the gas.

Combining these facts it is easy to find the thrust a rocket will produce.

 

 
    "Liquid Fueled Rocket" http://science.howstuffworks.com/rocket4.htm  
           
   

Increase Thrust In A Nutshell


Increase Ve by adjusting An, increase Tf (hotter burning fuels, burn more fuel)

Increase the rate the mass is ejected. (burn more fuel, or heavier fuel)


 

 
       
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