Rocket Delta-V Calculator Formula

Understand the math behind the rocket delta-v calculator. Each variable explained with a worked example.

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Formulas Used

Delta-V

delta_v = exhaust_velocity * log(mass_initial / mass_final)

Delta-V (km/s)

delta_v_kms = exhaust_velocity * log(mass_initial / mass_final) / 1000

Mass Ratio

mass_ratio = mass_initial / mass_final

Variables

VariableDescriptionDefault
exhaust_velocityExhaust Velocity (ve)(m/s)3000
mass_initialInitial Mass (m0)(kg)100000
mass_finalFinal Mass (mf)(kg)10000

How It Works

Rocket Delta-V (Tsiolkovsky Equation)

Delta-v is the total change in velocity a rocket can achieve by expelling all its propellant.

Formula

dv = ve * ln(m0 / mf)

  • *ve* = effective exhaust velocity
  • *m0* = initial (wet) mass
  • *mf* = final (dry) mass
  • *ln* = natural logarithm

    • The logarithmic dependence means that most of a rocket's mass must be propellant to achieve high delta-v.

    Worked Example

    ve = 3000 m/s, m0 = 100 000 kg, mf = 10 000 kg.

    exhaust_velocity = 3000mass_initial = 100000mass_final = 10000
    1. 01dv = ve * ln(m0 / mf)
    2. 02mass ratio = 100000 / 10000 = 10
    3. 03dv = 3000 * ln(10)
    4. 04dv = 3000 * 2.3026 = 6907.8 m/s

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