Rocket Equations:did I get this right?
The ship being modeled is a freighter for hauling ore from the asteroid belt to Earth (it’s for a SF universe). It can carry 2000 tons of cargo,and has another 200 tons of spaceframe,engine etc. It has a mass ratio of 4,giving it 6,600 tons of propellant (8,800 tons total “wet”mass). It uses a DT fusion drive,which has an exhaust velocity of 22,000 m/s.
The Tsiolovski equation for Delta V is Delta V = Exhaust Velocity ln (Initial Mass in kg/Final Mass in kg). So:
Dv = 22,000 ln (8,800,000 / 2,200,000)
Dv = 30.5 km/s
The energy production necessary to get a certain delta V is determined by the equation 1/2m(v^2) where m is the mass of propellant and v is the exhaust velocity.
So in this case that’s 1/2(6,600,000)(22,000^2) = 1.6 X 10^15 joules.
If it accelerates at 1 m/s^2 that’s 52.5 GW assuming perfect energy efficiency (unrealistic,obviously).
Actually Tsiolkovsky’s equation is
Dv= Ve ln(m0/mf) [1]
where:
m0 –the initial total mass
mf –the final total mass
Ve –the effective exhaust velocity
Dv is the delta-v in m/s (or ft/s)
m0= 2,000,000 + 200,000 + 6,600,000 = 8,800,000 kg(check)
mf = 2,000,000 + 200,000 = 2,200,000 kg (check)
Dv= 22,000 ln (8,800,000/2,200,000 )=
Dv=30,500 m/s (check)
With energy/power calculations I have a problem.
P= 0.5 mf Ve Dv
P= 0.5 x 2,200,000 x 22,000 x 30,500
P= 0.5 x 2.2 E+6 x 22 E+3 x 30.5E +3
P=738 E+12 W
P=738 TerraWats
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