rocket fuel problem: solve for the % of mass that is....

[walt111]

rocket problem: solve for percentage of mass that is final mass (engines,tank and payload) and initial mass that is propellant.

1-e to delta v / ve power where ve=4.5km/sec and delta v=9.7km/s

eulers constant I believe is approx. 2.71

I don't understand how they get the answer of .884% of total mass to be propellant and remainder of .116 to be engines tank and payload (is an subtraction from 100 )

Thanks
Walt

 

[TchrWill]

Re: rocket fuel problem

rocket problem: solve for percentage of mass that is final mass (engines,tank and payload) and initial mass that is propellant.

1-e to delta v / ve power where ve=4.5km/sec and delta v=9.7km/s

eulers constant I believe is approx. 2.71

I don't understand how they get the answer of .884% of total mass to be propellant and remainder of .116 to be engines tank and payload (is an subtraction from 100 )

Wo = ignition weight
Wf = final burnoutr weight
Wp = weight of propellant
Wo/Wf = e^(deltaV/Ve)

Sorry for the earlier misdirection.

Delta V = 9700m/s
Ve (exhaust velocity) = 4500 m/s

Therefore, Wo/Wf = e^(9700/4500 = e^2.15555... = 8.632.

Wo = 8.632Wf
Wf + Wp = Wo = 8.632Wf
Wp = 7.632Wf
Propellant fraction Therefore = 7.632/8.632 = .884
Inert weight fraction = 1 - .884 = .116

If I misinterpreted, or misused, some number, please let me know.