Difference between revisions of "Cheat sheet"

Revision as of 14:42, 28 June 2013

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

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

• Equation:

${\displaystyle \Delta {v}=ln\left({\frac {M_{start}}{M_{end}}}\right)\cdot I_{sp}\cdot g_{0}}$

• Explained:

${\displaystyle \Delta {v}=ln\left({\frac {\text{Starting mass}}{\text{Ending mass}}}\right)\cdot {\text{Specific impulse}}\cdot 9.81{\frac {m}{s^{2}}}}$

• 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.

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

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:

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

• Explained:

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

• Example:

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

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

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:

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

• Explained:

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

• Example:

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

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

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:

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

• Explained:

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

• 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.

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

See also

Links to collections of reference materials.

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