User:Milton Beychok/Sandbox: Difference between revisions
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==Rocket thrust and specific impulse== | ==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>[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>[http://exploration.grc.nasa.gov/education/rocket/specimp.html Specific Impulse] from a website page of the National Aeronautics and Space Administration (NASA)</ref> | 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> | :<math>F = \dot {m} V_e + (p_e - P_o)A_e</math> | ||
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:<math>F = \dot {m} V_{eq} = \dot {m} \left [V_e + \frac {(p_e - P_o)A_e}{\dot {m}} \right ]</math> | :<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 ( '''''I''''' ) is defined as the average thrust multiplied by the total time ( '''''t''''' ) of propellant burning: | The total impulse of a rocket ( '''''I''''' ) is defined as the average thrust multiplied by the total time ( '''''t''''' ) 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> | :<math>I = F \Delta t = \int {F dt} = \int {\dot {m} V_{eq}\, dt} = \dot {m} V_{eq}</math> | ||
The specific impulse ( '''''I<sub>sp</sub>''''' ) is the total impulse divided by the [[weight]] of the exhaust gas: | The specific impulse ( '''''I<sub>sp</sub>''''' ) is the total impulse divided by the [[weight]] of the exhaust gas:<ref name=NASAIsp/> | ||
:<math>I_{sp} = I | :<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: | :where: | ||
:'''''F''''' = force in | :  '''''F''''' = [[force]] in [[newton]]s, N | ||
:'''''ṁ'''''  = mass flow rate of exhaust gas, kg/s | : '''''ṁ'''''  = [[mass]] flow rate of exhaust gas, kg/s | ||
:'''''V<sub>eq</sub>''''' = equivalent exhaust velocity at nozzle exit, m/s | |||
:'''''V<sub>e</sub>''''' = exhaust velocity at nozzle exit, m/s | :'''''V<sub>e</sub>''''' = exhaust velocity at nozzle exit, m/s | ||
:'''''p<sub>e</sub>''''' = absolute pressure of exhaust gas at nozzle exit, Pa | :'''''p<sub>e</sub>''''' = absolute pressure of exhaust gas at nozzle exit, Pa | ||
:'''''p<sub>o</sub>''''' = external ambient pressure, Pa | :'''''p<sub>o</sub>''''' = external ambient pressure, Pa | ||
:'''''A<sub>e</sub>''''' = cross-sectional area of nozzle exhaust exit, m² | :'''''A<sub>e</sub>''''' = cross-sectional area of nozzle exhaust exit, m² | ||
:'''''t''''' = time, s | |||
:'''''I''''' = total impulse, N | |||
:'''''g<sub>o</sub>''''' = [[gravitational acceleration]] on Earth at sea level = 9.807 m/s² | |||
:'''''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}} | {{reflist}} | ||
Revision as of 21:15, 24 March 2010
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 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:[1][2]
and also this form, by defining a new term veq :
![{\displaystyle F={\dot {m}}V_{eq}={\dot {m}}\left[V_{e}+{\frac {(p_{e}-P_{o})A_{e}}{\dot {m}}}\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/00fdcb55fad6c2092aa5d59cb0ffb96e9998667f)
The total impulse of a rocket ( I ) is defined as the average thrust multiplied by the total time ( t ) of propellant burning:[2]
The specific impulse ( Isp ) is the total impulse divided by the weight of the exhaust gas:[2]
- where:
- F = force in newtons, N
- ṁ = mass flow rate of exhaust gas, kg/s
- Veq = equivalent exhaust velocity at nozzle exit, m/s
- Ve = exhaust velocity at nozzle exit, m/s
- pe = absolute pressure of exhaust gas at nozzle exit, Pa
- po = external ambient pressure, Pa
- Ae = cross-sectional area of nozzle exhaust exit, m²
- t = time, s
- I = total impulse, N
- go = gravitational acceleration on Earth at sea level = 9.807 m/s²
- Isp = 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.
- ↑ Rocket Thrust Summary from a website page of the National Aeronautics and Space Administration (NASA)
- ↑ 2.0 2.1 2.2 Specific Impulse from a website page of the National Aeronautics and Space Administration (NASA)