# NASASpaceFlight.com Forum

## General Discussion => Q&A Section => Topic started by: dinos55 on 01/20/2018 06:36 pm

Title: Multi-stage rocket Q&A
Post by: dinos55 on 01/20/2018 06:36 pm
Hello all,

If a rocket has 3 stages + upper stage, and the details I know are the total mass of the rocket, the inclination and the Propellant Mass, the Thrust, The Isp(specific impulse) and the combustion time, for each stage. Can I find the mass of the payload and the altitude of the orbit using these details? and if yes, how?

Title: Re: Q&A Multi-stage rocket
Post by: e of pi on 01/20/2018 07:14 pm
Short answer: not without a few more assumptions. Long answer: you can do it, but with some assumptions, research, and a bit of guess-and-check iteration.

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By definitition, T=Ve * m-dot, where T is thrust, Ve is the exhaust velocity velocity of the engine, and m-dot is the mass flow (kg/s) of propellant passing through the engine. Ve is also equal to ISp*9.81m/s^2. Thus, you can re-arrange to let you solve for m-dot of each stage given Thrust and ISp:

m-dot = T/ (ISp * (9.81m/s^2) )

With the m-dot of each stage, you can multiply by burn time to get the propellant load of each stage. As a check, that should sum to the same thing as the combined vehicle propellant load.

To find the delta-v of the combined rocket, you need to solve for the delta-v of each stage, with the payload being any stages above it. The problem is it sounds like you don't have the dry mass of each stage, so you'd need to make some assumptions. If you know the total mass of the stages empty, then you can get the combined stage dry masses, and then you need to figure out how much mass to assign to each stage. As a first approximation, you might be able to start by assuming that the stages will divide up the total dry mass roughly in proportion to how they divide the total propellant mass (i.e. if stage 1 is half the propellant, it might be something like half the dry mass) but this won't take into account that large stages tend to be more mass efficient (less dry mass per prop mass) and some fuel combinations end up with heavier tanks due to lower densities (hydrogen/lox being particularly "fluffy"). Some research on comparable vehicle stages may be in order to ground your assumptions.

Once you've made those assumptions, you can calculate each stage's delta-v by calculating the mass ratio given the stage dry mass (M_d), stage propellant mass (M_p) and payload mass (P):

MR = (P + M_d + M_p)/(P+M-d)
dV = Isp * (9.81m/s^2) * ln(MR)

Include any upper stages in the payload of the stage below. That is, the final stage's payload is the payload of the rocket. The payload of the second-from-last stage is the payload plus the entire fueled mass of the final stage, and so on. The vehicle's total delta-v is the sum of each stage delta-v: dV_total=dV1+dv2+....dVi. Assume a payload, and guess and check until you get a total delta-v that's in line with the orbit and inclination given the launch site (compare to other similar LVs to find).