Engineering
Tsiolkovsky Ideal Rocket Equation formula: Delta-v = Isp * g0 * LN(m0 / mf)
Calculate ideal delta-v from initial and final mass at constant specific impulse, and invert the model for a propellant fraction.
Define the masses and the ideal model
The model assumes constant effective exhaust velocity and neglects external forces, including gravity and aerodynamic losses. Delta-v here is an ideal velocity-change budget, not a prediction of attained launch speed or orbital success.
Initial mass includes all mass before the burn; final mass includes structure, payload and any remaining propellant. Final mass equals dry mass only if all usable propellant is consumed. Propellant is not just fuel: for a chemical rocket it includes the oxidizer.
Isp in seconds is converted with standard g0=9.80665 m/s^2, not local planetary gravity. Keep B3 at that value for the stated Isp convention. Positive Isp and masses are required, initial mass must be at least final mass, and target delta-v cannot be negative.
The inverse fraction is relative to mass at the start of the modeled burn, not necessarily launch liftoff mass. It does not include reserve margins or stage separation. At large targets the rounded fraction may display 1 even though the mathematical fraction is below 1 for finite input.
| Spacecraft Stage Input | Cell / Formula | Orbital Stage Spec | Astrodynamics Output |
|---|---|---|---|
| Engine Isp & Standard g0 | B2 = 320 s, B3 = 9.80665 m/s^2 | Exhaust velocity v_e = B2 * B3 | 3,138.13 m/s |
| Initial m0 & Final Mass mf | B4 = 100,000 kg, B5 = 20,000 kg | Mass ratio 5 (80% expelled propellant) | LN(5) = 1.6094 |
| Stage Delta-v Capability | B2 * B3 * LN(B4 / B5) | 3,138.128 * 1.609438 | 5,050.62 m/s |
| Propellant Fraction for 3 km/s | 1 - EXP(-B6 / (B2 * B3)) | Target B6 = 3,000 m/s | 61.56% initial-mass propellant fraction |
Tsiolkovsky stage Delta-v in meters per second (m/s)
The mass ratio must be at least 1. Equal masses imply no expelled propellant and zero ideal delta-v.
=IF(COUNT(B2:B6)<>5,"Invalid inputs",IF(OR(B2<=0,B3<>9.80665,B4<=0,B5<=0,B4<B5,B6<0),"Invalid inputs",ROUND(B2 * B3 * LN(B4 / B5), 2)))Required Propellant Mass Fraction for a target Delta-v maneuver
This fraction is the ideal proportion of initial burn mass that must be expelled for the chosen target under the same constant-Isp assumptions.
=IF(COUNT(B2:B6)<>5,"Invalid inputs",IF(OR(B2<=0,B3<>9.80665,B4<=0,B5<=0,B4<B5,B6<0),"Invalid inputs",ROUND(1 - EXP(-B6 / (B2 * B3)), 4)))Try the example
Use the original values or change them to test your understanding.