User:Milton Beychok/Sandbox: Difference between revisions

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==Rocket thrust and specific impulse==


Thrust is the [[force]] ('''''F''''')  which moves a rocket through the air. Thrust is generated by the rocket engine through the reaction  of [[acceleration|accelerating]] a mass of gas. The gas is accelerated to the the rear and the rocket is accelerated in the opposite direction. Force may be mathematically expressed as:<ref name=NASAThrust>[http://exploration.grc.nasa.gov/education/rocket/rktthsum.html Rocket Thrust Summary] from a website page of the [[National Aeronautics and Space Administration]] (NASA)</ref><ref name=NASAIsp>[http://exploration.grc.nasa.gov/education/rocket/specimp.html Specific Impulse] from a website page of the National Aeronautics and Space Administration (NASA)</ref>
:<math>F = \dot {m} V_e + (p_e - P_o)A_e</math>
and also this form, by defining a new term '''''v<sub>eq</sub>'''''&thinsp;:
:<math>F = \dot {m} V_{eq} = \dot {m} \left [V_e + \frac {(p_e - P_o)A_e}{\dot {m}} \right ]</math>
The total impulse of a rocket (&thinsp;'''''I'''''&thinsp;) is defined as the average thrust multiplied by the total time (&thinsp;'''''t'''''&thinsp;) of propellant burning:<ref name=NASAIsp/>
:<math>I = F \Delta t = \int {F dt} = \int {\dot {m} V_{eq}\, dt} = \dot {m} V_{eq}</math>
The specific impulse (&thinsp;'''''I<sub>sp</sub>'''''&thinsp;) is the total impulse divided by the [[weight]] of the exhaust gas:<ref name=NASAIsp/>
:<math>I_{sp} = \frac {I}{\text {weight}} = \frac {I}{\dot {m} g_o} = \frac{V_{eq}}{g_o} = \frac {F}{\dot {m} g_o} </math>
:where:
:&nbsp; &nbsp;&thinsp;'''''F''''' = [[force]] in [[newton]]s, N
:&nbsp;&nbsp;'''''&#7745;'''''&thinsp; = [[mass]] flow rate of exhaust gas, kg/s
:'''''V<sub>eq</sub>''''' = equivalent exhaust velocity at nozzle exit, m/s
:&nbsp;'''''V<sub>e</sub>''''' = exhaust velocity at nozzle exit, m/s
:&nbsp;'''''p<sub>e</sub>''''' = absolute pressure of exhaust gas at nozzle exit, Pa
:&nbsp;'''''p<sub>o</sub>''''' = external ambient pressure, Pa
:&thinsp;'''''A<sub>e</sub>''''' = cross-sectional area of nozzle exhaust exit, m²
:&nbsp; &nbsp;'''''t'''''&thinsp; = time, s
:&nbsp; &nbsp;'''''I'''''&thinsp; = total impulse, N
:&thinsp;'''''g<sub>o</sub>''''' = [[gravitational acceleration]] on Earth at sea level = 9.807 m/s²
:&thinsp;'''''I<sub>sp</sub>''''' = specific impulse, s
Different rocket engines have different values of specific impulse. The higher is the specific impulse, the more  efficient is the engine because it produces more thrust for the same amount of propellant.
{{reflist}}

Revision as of 22:42, 24 March 2010

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