How to Reach Mass Depletion After Finite Thrust Maneuver Execution

Hi everyone!

I am trying to model a spacecraft and its propulsion system. Assuming that the spacecraft have four thrusters, and every thruster has its unique fuel tank. So, what I need to achieve is determine the fuel mass inside the fuel tanks after a maneuver. I have tried to achieve it by defining four finite thrust maneuvers at the same time in the same direction. The only difference between these maneuvers are their ISP. The problem is, I do not know how to reach the total mass consumption for every individual maneuver. In conclusion, how can I get the mass depletion for after every maneuver which have the same start time, burn duration and direction, but the isp.

Thank in advance,
Uzay

Hi @uzayt

You’ll have to compute it by yourself using the Isp definition: F = q g₀ Isp where F is the thrust in Newtons, q is the flow rate (q = -dm/dt if you consider m to be the spacecraft mass, q = +dm/dt if you consider m to be the consumed mass), g₀ is the standard gravity (g₀ = 9.80665 m/s² exactly as it is a standardized constant) and Isp is the specific impulse in seconds. From this, you can extract q = F / (g₀ Isp) and then can integrate it over maneuver duration time: Δm = F Δt / (g₀ Isp) where Δt is the maneuver duration.

This equation holds for each thruster independantly, and would also work if the thrusters had both different thrust and different Isp.

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