Rocket Propulsion Contents: Review Types of Rockets Examples Whiteboards © Microsoft Encarta

So far we have: Impulse = F  t = m  v F = Force (N)  t = Elapsed time (s) m = Mass (kg)  v = Change in velocity (m/s) Rocket Propulsion

FtFt = mvmv So: F = engine thrust  t = time to burn fuel m = mass of fuel burned  v = exhaust gas velocity

Which Rocket Accelerates faster? A B Demo – F14

If we re-arrange this formula: m  v = F  t  t  t Rocket Propulsion

You get F = m  v  t Where: Rocket Propulsion F = Engine thrust (N) m = Fuel burn rate (kg/s)  t  v = Exhaust velocity (m/s)

Rocket Propulsion © Microsoft Encarta Solid Fuel Engine:

Rocket Propulsion © Microsoft Encarta Solid Fuel Engine: Thrust of the Engine: F = m  v  t Big  v means big F Big  v also means lots of pressure Danger Will Robinson!

© Estes

Lookout! m =.5 kg, F  t = 20 Ns F  t = m  v 20 Ns =.5kg  v  v = ? (x for mph) © Estes

Impulse is area under = (40 N)(6.0s) = 240 Ns t F 100 N 5.0 s Impulse – Area under F vs t graph

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Average F = 70 N, t = 8.0 s, Impulse = (70 N)(8.0 s) = 560 Ns What is the impulse? W 560 Ns t F 100 N 5.0 s

Impulse = (40 N)(3.0 s) + (70 N)(5.0 s)= 470 Ns What is the impulse? W 470 Ns t F 100 N 5.0 s

Impulse = (10. N)(1.73 s-0.11 s) + (28 N-10 N)( ) = Ns (about 20 Ns) What is the impulse of the D12 engine? W 20 Ns

Rocket Propulsion © Microsoft Encarta Liquid Fuel Engine: How do you keep it from tipping? Why the “steam” coming off?

Saturn V Animation (Flash in IE) Saturn V Rocket - Apollo missions First stageSecond stageThird stageL.E.MCommand Module Escape Tower

Rocket Propulsion Example 1: A rocket burns fuel at a rate of 1.2 kg/s, with an exhaust velocity of 1250 m/s. What thrust does it develop? F  t = m  v  v = 1250 m/s m = 1.2 kg  t = 1 s (F)(1 s) = (1.2 kg)(1250 m/s), F = 1500 N

Rocket Propulsion Example 2: A model rocket engine develops 12 N of thrust with an exhaust velocity of 718 m/s. What is its fuel burn rate? F  t = m  v F = 12 N  v = 718 m/s m = ? kg  t = 1 s (12 N)(1 s) = m(718 m/s), m =.0167 kg Burn rate =.0167 kg/s

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A certain rocket engine burns.0352 kg of fuel per second with an exhaust velocity of 725 m/s. What thrust does it generate? 25.5 N F  t = m  v F(1 s) = (.0352 kg)(725 m/s), F = 25.5 N W

The Saturn V’s first stage engines generated MN of thrust ( x 10 6 N ) with an exhaust velocity of m/s. What was its fuel burn rate? 15,000 kg/s F  t = m  v (33.82 x 10 6 N)(1 s) = m( m/s), m = 15,000 kg Burn Rate = 15,000 kg/s W

A D12 engine generates N of thrust burning fuel at a rate of.0143 kg/s. What is the exhaust velocity? m/s F  t = m  v (11.80 N)(1 s) = (.0143 kg)  v,  v = = m/s W

A model rocket has a total mass of 235 grams, 145 grams of which is fuel. The engine burns the fuel in 2.74 s, with an exhaust velocity of 890 m/s. What thrust does the engine generate? 47.1 N F  t = m  v F(2.74 s) = (.145 kg)(890 m/s), F = 47.1 N W

A model rocket has a total mass of 235 grams, 145 grams of which is fuel. The engine burns the fuel in 2.74 s, with an exhaust velocity of 890 m/s. What are the initial and final rocket masses? F = 47.1 N.235 kg and.090 kg Uh, initial =.235 kg Final =.235 kg kg =.090 kg W

A model rocket has a total mass of 235 grams, 145 grams of which is fuel. The engine burns the fuel in 2.74 s, with an exhaust velocity of 890 m/s. What is the initial rocket acceleration? F = 47.1 N m o =.235 kg, m =.090 kg, =ma (hint) initial = 191 m/s/s = (.235 kg)(a), a=44.8 N/.235 kg=191 m/s 2 W

A model rocket has a total mass of 235 grams, 145 grams of which is fuel. The engine burns the fuel in 2.74 s, with an exhaust velocity of 890 m/s. What is the final rocket acceleration? F = 47.1 N m o =.235 kg, m =.090 kg, =ma (hint) final = 514 m/s/s = (.090 kg)(a), a=44.8 N/.090 kg=514 m/s 2 W