Cheat sheet

Kerbal Space Program rocket scientist's cheat sheet: Delta-v maps, equations and more for your reference so you can get from here to there and back again.

Delta-v (Δv)

Basic calculation

1. For atmospheric ΔV value, use atmospheric thrust values.
2. For vacuum 6Delta;v value, use vacuum thrust values.
3. Use this equation to figure out the Δv per stage:

• Equation:

$\Delta {v}=ln({\frac {M_{start}}{M_{end}}})\cdot I_{sp}\cdot g$

• Explained:

$\Delta {v}=ln({\frac {StartingMass}{EndingMass}})\cdot SpecificImpulse\cdot 9.81{\frac {m}{s^{2}}}$

• Example:

Single stage rocket that weighs 23 t when full, 15 t when fuel is emptied, and has an engine with a specific impulse of 120 s.

$\Delta {v}=ln({\frac {23t}{15t}})\cdot 120s\cdot 9.81{\frac {m}{s^{2}}}=1803.2{\frac {m}{s^{2}}}$

Transitional Δv (true Δv when launching from Kerbin)

1. How to calculate the Δv of a rocket stage that transitions from Kerbin atmosphere to vacuum.
2. Assumption: It takes approximately 1000 m/s² of Δv to escape Kerbin's atmosphere before vacuum Δv values take over for the stage powering the transition.
3. Note: This equation is an approximation and not completely accurate, so the results will vary a bit depending on the TWR and such. The result is accurate enough for normal purposes though.

• Equation:

$\Delta {v}_{T}={\frac {\Delta {v}_{atm}-1000{\frac {m}{s^{2}}}}{\Delta {v}_{atm}}}\cdot \Delta {v}_{vac}+1000{\frac {m}{s^{2}}}$

• Explained:

$Transitional\Delta {v}={\frac {Atmospheric\Delta {v}-1000{\frac {m}{s^{2}}}}{Atmospheric\Delta {v}}}\cdot Vacuum\Delta {v}+1000{\frac {m}{s^{2}}}$

• Example:

Single stage with total atmospheric Δv of 5000 m/s² and with a Δv of 6000 m/s² in vacuum.

$\Delta {v}_{T}={\frac {5000{\frac {m}{s^{2}}}-1000{\frac {m}{s^{2}}}}{5000{\frac {m}{s^{2}}}}}\cdot 6000{\frac {m}{s^{2}}}+1000{\frac {m}{s^{2}}}=5800{\frac {m}{s^{2}}}$

Δv maps

Various maps developed by KSP fans.

• Δv Total Values

1. http://wiki.kerbalspaceprogram.com/w/images/7/73/KerbinDeltaVMap.png
2. http://www.skyrender.net/lp/ksp/system_map.png

• Δv Change Values

1. http://i.imgur.com/duY2S.png

• Δv KSP Nomogram

1. http://ubuntuone.com/1kD39BCoV38WP1QeG6MtO6

Thrust to weight ratio (TWR)

1. This is Newton's Second Law.
2. If ratio is less than 1, you will not lift off the ground.

• Equation:

TWR = F / (m * g) > 1

• Explained:

TWR = Force of Thrust / ( Total Mass X 9.81 ) > 1

• Example:

200 kiloNewton rocket engine on a 15 ton rocket launching from Kerbin Space Center.

TWR = 200 kN / ( 15 Tons total Mass X 9.81 m/s2 ) = 1.36 which is > 1 which means liftoff!

Combined specific impulse (Isp)

1. When Isp is the same for all engines in a stage, then the Isp is equal to a single engine. So six 200 Isp engines still yields only 200 Isp.
2. When Isp is different for engines in a single stage, then use the following equation:

• Equation:

Isp = ( F1 + F2 + ... ) / ( ( F1 / Isp1 ) + ( F2 / Isp2 ) + ... )

• Explained:

Isp = ( Force of Thrust of 1st Engine + Force of Thrust of 2nd Engine...and so on... ) / ( ( Force of Thrust of 1st Engine / Isp of 1st Engine ) + ( Force of Thrust of 2nd Engine / Isp of 2nd Engine ) + ...and so on... )

• Example:

Two engines, one rated 200 Newtons and 120 Specific Impulse; another engine rated 50 Newtons and 200 Specific Impulse.

Isp = (200 Netwons + 50 Newtons) / ( ( 200 Newtons / 120 ) + ( 50 Newtons / 200 ) = 130.89 Specific Impulse

See also

Links to collections of reference materials.

• Tutorials
• The Drawing Board: A library of tutorials and other useful information