Difference between revisions of "Cheat sheet"

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m (→‎See also: * forum link to interwiki.)
(* use <math> tags for some formulas. ! other stuff.)
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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.
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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.
  
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== Delta-V (dV) ==
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== Delta-v (&Delta;v) ==
 
=== Basic calculation ===
 
=== Basic calculation ===
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#For atmospheric dV value, use atmospheric thrust values.
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#For atmospheric &Delta;V value, use atmospheric thrust values.
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#For vacuum dV value, use vacuum thrust values.
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#For vacuum 6Delta;v value, use vacuum thrust values.
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#Use this equation to figure out the dV per stage:
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#Use this equation to figure out the &Delta;v per stage:
  
 
*Equation:
 
*Equation:
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::'''dV = ln ( Mstart / Mend ) * Isp * g'''
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:<math>\Delta{v} = ln(\frac{M_{start}}{M_{end}}) \cdot I_{sp} \cdot g</math>
  
 
*Explained:
 
*Explained:
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::dV = ln ( Starting Mass / Ending Mass ) X Isp X 9.81
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:<math>\Delta{v} = ln(\frac{Starting Mass}{Ending Mass}) \cdot Specific Impulse \cdot 9.81 \frac{m}{s^2}</math>
  
 
*Example:
 
*Example:
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:Single Stage Rocket that weighs 23 tons when full, 15 tons when fuel is emptied, and engine that outputs 120 Isp.
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:Single stage rocket that weighs 23&nbsp;t when full, 15&nbsp;t when fuel is emptied, and has an engine with a specific impulse of 120&nbsp;s.
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:dV = ln ( 23 Tons / 15 Tons ) X 120 Specific Impulse X 9.81m/s = Total dV of 1803.2 m/s2
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:<math>\Delta{v} = ln(\frac{23t}{15t}) \cdot 120 s \cdot 9.81 \frac{m}{s^2} = 1803.2 \frac{m}{s^2}</math>
  
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=== Transitional dV (a.k.a. true dV when launching from Kerbin) ===
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=== Transitional &Delta;v (true &Delta;v when launching from Kerbin) ===
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#How to calculate the dV of a rocket stage that transitions from Kerbin atmosphere to vacuum.
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#How to calculate the &Delta;v of a rocket stage that transitions from Kerbin atmosphere to vacuum.
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#Assumption: It takes approximately 1000 m/s2 of dV to escape Kerbin's atmosphere before vacuum dV values take over for the stage powering the transition.
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#Assumption: It takes approximately 1000&nbsp;m/s<sup>2</sup> of &Delta;v to escape Kerbin's atmosphere before vacuum &Delta;v values take over for the stage powering the transition.
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#Note: This equation is an guess, approximation, and is not 100% accurate. Per Chris: "The results will vary a bit depending on your TWR and such, but it should usually be pretty darn accurate."
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#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:
 
*Equation:
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::'''TdV = ( ( dVatm - 1000 ) / dVatm ) * dVvac + 1000'''
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:<math>\Delta{v}_T = \frac{\Delta{v}_{atm} - 1000 \frac{m}{s^2}}{\Delta{v}_{atm}} \cdot \Delta{v}_{vac} + 1000 \frac{m}{s^2}</math>
  
 
*Explained:
 
*Explained:
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::Transitional dV = ( ( Total dV in atmosphere - 1000 m/s2) / Total dV in atmosphere ) X Total dV in vacuum + 1000  
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:<math>Transitional \Delta{v} = \frac{Atmospheric \Delta{v} - 1000 \frac{m}{s^2}}{Atmospheric \Delta{v}} \cdot Vacuum \Delta{v} + 1000 \frac{m}{s^2}</math>
  
 
*Example:
 
*Example:
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:Single Stage with total atmospheric dV of 5000 m/s2, and rated 6000 dV in vacuum.
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:Single stage with total atmospheric &Delta;v of 5000&nbsp;m/s<sup>2</sup> and with a &Delta;v of 6000 m/s<sup>2</sup> in vacuum.
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:Transitional dV = ( ( 5000 dVatm - 1000 dV Required to escape Kerbin atmosphere ) / 5000 dVatm ) X 6000 dVvac + 1000 dV Required to escape Kerbin atmosphere = Total dV of 5800 m/s2
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:<math>\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}</math>
  
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=== &Delta;v maps ===
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=== dV maps ===
 
 
Various maps developed by KSP fans.
 
Various maps developed by KSP fans.
  
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*dV Total Values
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*&Delta;v Total Values
 
#http://wiki.kerbalspaceprogram.com/w/images/7/73/KerbinDeltaVMap.png
 
#http://wiki.kerbalspaceprogram.com/w/images/7/73/KerbinDeltaVMap.png
 
#http://www.skyrender.net/lp/ksp/system_map.png
 
#http://www.skyrender.net/lp/ksp/system_map.png
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*dV Change Values
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*&Delta;v Change Values
 
#http://i.imgur.com/duY2S.png
 
#http://i.imgur.com/duY2S.png
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*dV KSP Nomogram
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*&Delta;v KSP Nomogram
 
#http://ubuntuone.com/1kD39BCoV38WP1QeG6MtO6
 
#http://ubuntuone.com/1kD39BCoV38WP1QeG6MtO6
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== Thrust to weight ratio (TWR) ==
 
== Thrust to weight ratio (TWR) ==

Revision as of 17:02, 25 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.

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:
  • Explained:
  • 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.

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

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.

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