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
- For atmospheric ΔV value, use atmospheric thrust values.
- For vacuum Δv value, use vacuum thrust values.
- Use this equation to figure out the Δv per stage:
![{\displaystyle \Delta {v}=ln\left({\frac {M_{start}}{M_{end}}}\right)\cdot I_{sp}\cdot g_{0}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/9df0f23fd075cafe372f9aa67490344dc2f5420d)
![{\displaystyle \Delta {v}=ln\left({\frac {\text{Starting Mass}}{\text{Ending Mass}}}\right)\cdot {\text{Specific Impulse}}\cdot 9.81{\frac {m}{s^{2}}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/af6d74be7981349242faa901c1ae96cc252a2eb3)
- 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}}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/7120bd064eb2646b9c837f8f946b4ce814a1ec4d)
Transitional Δv (true Δv when launching from Kerbin)
- How to calculate the Δv of a rocket stage that transitions from Kerbin atmosphere to vacuum.
- 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.
- 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.
![{\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}}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/9025095c05e978ec6899e957e88a5cbeb19c3604)
![{\displaystyle Transitional\Delta {v}={\frac {Atmospheric\Delta {v}-1000{\frac {m}{s^{2}}}}{Atmospheric\Delta {v}}}\cdot Vacuum\Delta {v}+1000{\frac {m}{s^{2}}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/451f2ca57d4dd6a3472473f584b4fd6b7ffd348a)
- 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}}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/442d7c91da03902849e2a64d8685844881a430f4)
Δv maps
Various maps developed by KSP fans.
- http://wiki.kerbalspaceprogram.com/w/images/7/73/KerbinDeltaVMap.png
- http://www.skyrender.net/lp/ksp/system_map.png
- http://i.imgur.com/duY2S.png
- http://ubuntuone.com/1kD39BCoV38WP1QeG6MtO6
Thrust to weight ratio (TWR)
- This is Newton's Second Law.
- If ratio is less than 1, the craft will not lift off the ground.
![{\displaystyle TWR={\frac {F}{m\cdot g}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/6654eb540787a411c5f54d7114c165e9a6654889)
![{\displaystyle TWR={\frac {\text{Thrust Force}}{{\text{Total Mass}}\cdot {\text{Local gravitational acceleration}}}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/f2c03bee2b8bbcf9c392388ef7306845886299a5)
- 200 kN rocket engine under a 15 t rocket launching from Kerbin.
![{\displaystyle TWR={\frac {200kN}{15t\cdot 9.81{\frac {m}{s^{2}}}}}=1.36}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/a3da6b1bfc4d6bae7f6e5246438c4b9e2febf734)
- The TWR is higher than 1, so the craft will lift off!
Combined specific impulse (Isp)
- If the Isp is the same for all engines in a stage, then the Isp is equal to a single engine. So six engines with 200 s of Isp still yield only an Isp of 200 s.
- If the Isp is different for engines in a single stage, then use the following equation:
![I_{{sp}}={\frac {(F_{1}+F_{2}+\dots )}{{\frac {F_{1}}{I_{{sp1}}}}+{\frac {F_{2}}{I_{{sp2}}}}+\dots }}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/46bcf4093084840daf66659ffc0e439d50af6943)
![{\displaystyle I_{sp}={\frac {ThrustOfEngine1+ThrustofEngine2+...}{{\frac {ThrustOfEngine1}{I_{sp}OfEngine1}}+{\frac {ThrustOfEngine2}{I_{sp}OfEngine2}}+\dots }}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/244425706c4a08359a9bb993727bff309f42c72c)
- Two engines, the first one with 200 N of thrust and 120 s of Isp; the second one with 50 N of thrust and 200 s of Isp.
![{\displaystyle I_{sp}={\frac {200N+50N}{{\frac {200N}{120s}}+{\frac {50N}{200s}}}}=130.89s}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/da2bd9a590c3ec4e0e36d49a01ce96629fedc058)
See also
Links to collections of reference materials.