Rocket Equation (Delta-v)
Rocket Equation (Delta-v)
Tsiolkovsky’s rocket equation links the achievable velocity change to how much of the rocket is propellant — the master equation of spaceflight.
The delta-v is Δv = v_e·ln(m_0/m_f). where v_e is the effective exhaust velocity and m_0, m_f the initial and final masses.
Inputs
v_e := 3000 m/s=3000 m/s
m_0 := 50000 kg=50000 kg
m_f := 15000 kg=15000 kg
Apply the Tsiolkovsky rocket equation.
dv := v_e·ln(m_0/m_f)=3611.92 m/s
Results
Because the relationship is logarithmic, reaching high delta-v demands a very large propellant fraction — the tyranny of the rocket equation, and why staging helps.
Assumptions & limitations
- Constant exhaust velocity.
- No external forces (gravity/drag) in this ideal form.
- Single burn.