Difference between revisions of "Propulsion"

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(Created page with " Category:Propulsion Theory Propulsion equation. This is the equation that links the electrical power, the propulsive force and the ISP. Pe = F x ISP *9,81 / 2n or Pe =...")
 
 
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[[Category:Propulsion]]
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The propulsive force is the force an engine produces to push a vehicle. This is factor of the available energy, the engine efficiency and the propulsive system ISP and ejection velocity.  The energy may come from a chemical reaction, a nuclear reaction or external sources (solar or kinetic).
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From Newton's third law of motion, the force exerted on a body by a second body is equal and inverse to the force exerted by the second body on the first body.  F<sub>1</sub>=-F<sub>2</sub>
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For a rocket, the first body is the exhaust, a "body" of gas,  and the second body is the rocket nozzle and by extension the entire rocket.  Since the force is directly proportional to the energy in the exhaust, then the energy added to the system must be equal to exactly twice the energy in the rocket exhaust, minus the system losses.  Half of the energy added to the engine will go the the exhaust as kinetic energy, and the other half will go to the vehicle as kinetic energy.
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==Equations==
  
[[Category:Propulsion]]
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===Propulsion equation===
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This is the equation that links the power, the propulsive force and the ISP.
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P = F x Isp x 9,81 / 2ɳ  or P= F x V<sub>e</sub> /2ɳ
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where:
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P = Power (Watts)
  
Theory
 
Propulsion equation. This is the equation that links the electrical power, the propulsive force and the ISP.
 
Pe = F x ISP *9,81 / 2n  or Pe = F x Ev /2n
 
Pe = electric power (Watts)
 
 
F = Engine force (Newtons)
 
F = Engine force (Newtons)
ISP = Specific impulse (Seconds)
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n = efficiency of electric engine
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Isp = Specific impulse (Seconds)
9,81 conversion factor
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Ev = Exhaust velocity (m/s)
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ɳ = efficiency of engine, for an [[ion thruster]] this is between 0,2 and 0,8, for a [[Propellant|chemical rocket]], or [[Nuclear thermal propulsion|nuclear thermal rocket]], essentially 1.
Specific impulse.
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ISP = Ev / 9,81
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9,81 conversion factor, Earth gravity (m/s<sup>2</sup>)
ISP = Specific impulse (Seconds)
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Ev = Exhaust velocity (m/s)
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V<sub>e</sub> = Exhaust Velocity (m/s)
Fuel consumption
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m = F/Ev
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===Specific impulse===
m = Fuel consumption (kg/s)
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Isp = V<sub>e</sub> / 9,81
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Isp = Specific impulse (Seconds)
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V<sub>e</sub> = Exhaust velocity (m/s)
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===Fuel consumption===
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= F/V<sub>e</sub>
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= Fuel consumption (kg/s)
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F = Force (Newtons)
 
F = Force (Newtons)
Ev = Exhaust velocity (m/s)
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Velocity
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V<sub>e</sub> = Exhaust velocity (m/s)
V = Ev x ln(Mo/Mf)
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Ev = Exhaust velocity (m/s)
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===Velocity (Rocket equation)===
V = ship final velocity (m/s)
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V<sub>f</sub> = V<sub>o</sub> + V<sub>e</sub> x ln(M<sub>o</sub>/M<sub>f</sub>)
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V<sub>e</sub> = Exhaust velocity (m/s)
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V<sub>f</sub> = ship final velocity (m/s)
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V<sub>o</sub> = Initial velocity (m/s)
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ln = natural logarithm
 
ln = natural logarithm
Mo = Initial mass of the ship (kg)
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Mf = Final mass of the ship (kg)
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M<sub>o</sub> = Initial mass of the ship (kg)
Key performance parameters
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Propulsive force (Thrust)
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M<sub>f</sub> = Final mass of the ship (kg)
The propulsive force is the force the engines produce to push the ship. This is factor of the available electrical energy, the engine efficiency and the propulsive system ISP and ejection velocity.
 
For the Enterprise: Available electrical energy = 2,5 GWe
 
ISP = 5000
 
Efficiency (n) = 80%
 
Thrust = 2 500 000 000 W x 2 x 0,8 / (5000*9,81) = 84 000 N = 8 300 kg = 8,3 Tons
 

Latest revision as of 05:32, 27 August 2021

The propulsive force is the force an engine produces to push a vehicle. This is factor of the available energy, the engine efficiency and the propulsive system ISP and ejection velocity. The energy may come from a chemical reaction, a nuclear reaction or external sources (solar or kinetic).

From Newton's third law of motion, the force exerted on a body by a second body is equal and inverse to the force exerted by the second body on the first body. F1=-F2

For a rocket, the first body is the exhaust, a "body" of gas, and the second body is the rocket nozzle and by extension the entire rocket. Since the force is directly proportional to the energy in the exhaust, then the energy added to the system must be equal to exactly twice the energy in the rocket exhaust, minus the system losses. Half of the energy added to the engine will go the the exhaust as kinetic energy, and the other half will go to the vehicle as kinetic energy.

Equations

Propulsion equation

This is the equation that links the power, the propulsive force and the ISP.

P = F x Isp x 9,81 / 2ɳ or P= F x Ve /2ɳ

where:

P = Power (Watts)

F = Engine force (Newtons)

Isp = Specific impulse (Seconds)

ɳ = efficiency of engine, for an ion thruster this is between 0,2 and 0,8, for a chemical rocket, or nuclear thermal rocket, essentially 1.

9,81 conversion factor, Earth gravity (m/s2)

Ve = Exhaust Velocity (m/s)

Specific impulse

Isp = Ve / 9,81

Isp = Specific impulse (Seconds)

Ve = Exhaust velocity (m/s)

Fuel consumption

ṁ = F/Ve

ṁ = Fuel consumption (kg/s)

F = Force (Newtons)

Ve = Exhaust velocity (m/s)

Velocity (Rocket equation)

Vf = Vo + Ve x ln(Mo/Mf)

Ve = Exhaust velocity (m/s)

Vf = ship final velocity (m/s)

Vo = Initial velocity (m/s)

ln = natural logarithm

Mo = Initial mass of the ship (kg)

Mf = Final mass of the ship (kg)