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.

Mathematics

Delta-v (Δv)

Basic calculation

Use the atmospheric and vacuum thrust values for atmospheric and vacuum Δv, respectively. $\Delta {v}=ln\left({\frac {M_{start}}{M_{end}}}\right)\cdot I_{sp}\cdot g_{0}$

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:

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

• 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, the craft will not lift off the ground.

• Equation:

${\text{TWR}}={\frac {F}{m\cdot g}}$

• Explained:

${\text{TWR}}={\frac {\text{Thrust force}}{{\text{Total mass}}\cdot {\text{Local gravitational acceleration}}}}$

• Example:

200 kN rocket engine under a 15 t rocket launching from Kerbin.

${\text{TWR}}={\frac {200kN}{15t\cdot 9.81{\frac {m}{s^{2}}}}}=1.36$

The TWR is higher than 1, so the craft will lift off!

Combined specific impulse (I_sp)

1. If the I_sp is the same for all engines in a stage, then the I_sp is equal to a single engine. So six engines with 200 s of I_sp still yield only an I_sp of 200 s.
2. If the I_sp is different for engines in a single stage, then use the following equation:

• Equation:

$I_{sp}={\frac {(F_{1}+F_{2}+\dots )}{{\frac {F_{1}}{I_{sp1}}}+{\frac {F_{2}}{I_{sp2}}}+\dots }}$

• Explained:

$I_{sp}={\frac {{\text{Thrust of engine 1}}+{\text{Thrust of engine 2}}+\dots }{{\frac {\text{Thrust of engine 1}}{\text{Specific impulse of engine 1}}}+{\frac {\text{Thrust of engine 2}}{\text{Specific impulse of engine 2}}}+\dots }}$

• Example:

Two engines, the first one with 200 N of thrust and 120 s of I_sp; the second one with 50 N of thrust and 200 s of I_sp.

$I_{sp}={\frac {200N+50N}{{\frac {200N}{120s}}+{\frac {50N}{200s}}}}=130.89s$

See also

Links to collections of reference materials.

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