Rocket equation

The Tsiolkovsky rocket equation, classical rocket equation, or ideal rocket equation is a mathematical equation that describes the motion of vehicles that follow the basic principle of a rocket: a device that can apply acceleration to itself using thrust by expelling part of its mass with high velocity can thereby move due to the conservation of momentum.




Δ
v
=

v

e


ln
⁡



m

0



m

f




=

I

sp



g

0


ln
⁡



m

0



m

f






{\displaystyle \Delta v=v_{\text{e}}\ln {\frac {m_{0}}{m_{f}}}=I_{\text{sp}}g_{0}\ln {\frac {m_{0}}{m_{f}}}}
where:




Δ
v



{\displaystyle \Delta v\ }
is delta-v – the maximum change of velocity of the vehicle (with no external forces acting).





m

0




{\displaystyle m_{0}}
is the initial total mass, including propellant, a.k.a. wet mass.





m

f




{\displaystyle m_{f}}
is the final total mass without propellant, a.k.a. dry mass.





v

e


=

I

sp



g

0




{\displaystyle v_{\text{e}}=I_{\text{sp}}g_{0}}
is the effective exhaust velocity, where:





I

sp




{\displaystyle I_{\text{sp}}}
is the specific impulse in dimension of time.





g

0




{\displaystyle g_{0}}
is standard gravity.




ln


{\displaystyle \ln }
is the natural logarithm function.

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