Mission Fuel Mass Calculator Formula

Understand the math behind the mission fuel mass calculator. Each variable explained with a worked example.

Use the Mission Fuel Mass Calculator

Formulas Used

Required Fuel Mass

fuel_mass = dry_mass * (exp(delta_v / exhaust_velocity) - 1)

Total Launch Mass

total_mass = dry_mass * exp(delta_v / exhaust_velocity)

Fuel Fraction

fuel_fraction = 1 - 1 / exp(delta_v / exhaust_velocity)

Variables

VariableDescriptionDefault
dry_massDry Mass (payload + structure)(kg)5000
delta_vRequired Delta-V(m/s)3000
exhaust_velocityExhaust Velocity(m/s)3000

How It Works

Mission Fuel Mass

From the Tsiolkovsky equation, the fuel needed for a given delta-v depends exponentially on the ratio dv/ve.

Formula

m_fuel = m_dry * (exp(dv / ve) - 1)

  • *m_dry* = payload plus structural mass
  • *dv* = required velocity change
  • *ve* = exhaust velocity

    • This shows why high delta-v missions are so demanding on fuel.

    Worked Example

    5000 kg dry mass, 3000 m/s delta-v, 3000 m/s exhaust velocity.

    dry_mass = 5000delta_v = 3000exhaust_velocity = 3000
    1. 01m_fuel = m_dry * (exp(dv/ve) - 1)
    2. 02dv/ve = 3000/3000 = 1
    3. 03exp(1) = 2.7183
    4. 04m_fuel = 5000 * (2.7183 - 1) = 5000 * 1.7183
    5. 05m_fuel = 8591 kg

    Ready to run the numbers?

    Open Mission Fuel Mass Calculator