How to use it
- Choose what to find: the delta-v, the propellant needed or the specific impulse.
- Give the engine as a specific impulse in seconds or an exhaust velocity in m/s.
- Enter the start (wet) and final (dry) mass, or the target delta-v, and pick the mass unit.
- Read the delta-v, the mass ratio, the propellant mass and its share of the start mass.
Formulas
- Rocket equation: Δv = vₑ × ln(m₀ ÷ m_f), vₑ = Isp × g₀, g₀ = 9.80665 m/s²
- Start mass for a delta-v: m₀ = m_f × e^(Δv ÷ vₑ)
- Exhaust velocity for a delta-v: vₑ = Δv ÷ ln(m₀ ÷ m_f), Isp = vₑ ÷ g₀
- Propellant: m₀ − m_f, as a share (m₀ − m_f) ÷ m₀
Worked example
A stage of 100 t with 60 t of propellant (40 t dry) and an engine with Isp = 300 s:
- vₑ = 300 × 9.80665 = 2,942 m/s
- m₀ ÷ m_f = 100 ÷ 40 = 2.5, ln 2.5 = 0.91629
- Δv = 2,942 × 0.91629 = 2,695.7 m/s
For Δv = 3,000 m/s with vₑ = 3,000 m/s and 40 t dry, m₀ = 40 × e¹ = 108.731 t, so 68.731 t of propellant.
To get 9,000 m/s from 100 t down to 10 t the engine needs vₑ = 9,000 ÷ ln 10 = 3,908.7 m/s, an Isp of 398.6 s.
Tips
- Use the dry mass of everything that stays, including payload and the empty stage.
- Stage the rocket. Dropping empty tanks resets the mass ratio, which is why big rockets have stages; add the delta-v of each stage.
- Isp in vacuum and at sea level differ for the same engine; use the one that matches where it burns.