Difference between revisions of "Cheat sheet"

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*If ratio is less than 1, you will not lift off the ground.
 
*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 gravity of planet you're on ) > 1
 
TWR = Force of Thrust / ( Total Mass X gravity of planet you're on ) > 1
 
'''TWR = F / (m * g) > 1'''
 
  
 
Example:
 
Example:
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*When Isp is different for engines in a single stage, then use the following equation:
 
*When Isp is different for engines in a single stage, then use the following equation:
  
 +
Equation:
 
'''Isp = ( F1 + F2 + ... ) / ( ( F1 / Isp1 ) + ( F2 / Isp2 ) + ... )'''
 
'''Isp = ( F1 + F2 + ... ) / ( ( F1 / Isp1 ) + ( F2 / Isp2 ) + ... )'''
  
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*Use this equation to figure out the dV per stage:
 
*Use this equation to figure out the dV per stage:
  
 +
Equation:
 +
'''dV = ln ( Mstart / Mend ) * Isp * g'''
 +
 +
Explained:
 
dV = ln ( Starting Mass / Ending Mass ) X Isp X gravity of planet you're on
 
dV = ln ( Starting Mass / Ending Mass ) X Isp X gravity of planet you're on
 
'''dV = ln ( Mstart / Mend ) * Isp * g'''
 
  
 
Example:
 
Example:
Line 49: Line 54:
 
How to calculate the dV of a rocket stage that transitions from Kerbin atmosphere to vacuum.
 
How to calculate the dV of a rocket stage that transitions from Kerbin atmosphere to vacuum.
  
 +
Equation:
 +
'''TdV = ( ( dVatm - 1000 ) / dVatm ) * dVvac + 1000'''
 +
 +
Explained:
 
Transitional dV = ( ( Total dV in atmosphere - 1000 m/s2) / Total dV in atmosphere ) X Total dV in vacuum + 1000  
 
Transitional dV = ( ( Total dV in atmosphere - 1000 m/s2) / Total dV in atmosphere ) X Total dV in vacuum + 1000  
 
'''TdV = ( ( dVatm - 1000 ) / dVatm ) * dVvac + 1000'''
 
  
 
Example:
 
Example:
 
*Single Stage with total atmospheric dV of 5000 m/s2, and rated 6000 dV in vacuum.
 
*Single Stage with total atmospheric dV of 5000 m/s2, and rated 6000 dV in vacuum.
 
:Transitional dV = ( ( 5000 dVatm - 1000 dV Required to escape Kerbin atmosphere ) / 5000 dVatm ) X 6000 dVvac + 1000 dV Required to escape Kerbin atmosphere =
 
:Transitional dV = ( ( 5000 dVatm - 1000 dV Required to escape Kerbin atmosphere ) / 5000 dVatm ) X 6000 dVvac + 1000 dV Required to escape Kerbin atmosphere =

Revision as of 00:46, 25 June 2013

Introduction

Kerbal Space Program's Rocket Scientist Cheat Sheet Delta V Maps and Equations for Your Reference So You Can Get From Here to There and Back Again.

Delta V Maps

Various maps developed by KSP fans.

  1. dV Total Values
  2. dV Change Values

Thrust to Weight Ratio (TWR)

  • This is Newton's Second Law.
  • 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 gravity of planet you're on ) > 1

Example:

  • 200 Newton rocket engine on a 15 ton rocket launching from Kerbin Space Center.
TWR = 200 Newtons / ( 15 Tons total Mass X 9.86 m/s2 ) = 1.36 which is > 1 which means liftoff!

Combined Specific Impulse (Isp)

  • 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.
  • 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

Delta V (dV)

  • For atmospheric dV value, use atmospheric thrust values.
  • For vacuum dV value, use vacuum thrust values.
  • Use this equation to figure out the dV per stage:

Equation: dV = ln ( Mstart / Mend ) * Isp * g

Explained: dV = ln ( Starting Mass / Ending Mass ) X Isp X gravity of planet you're on

Example:

  • Single Stage Rocket that weighs 23 tons when full, 15 tons when fuel is emptied, and engine that outputs 120 Isp.
dV = ln ( 23 Tons / 15 Tons ) X 120 Specific Impulse X 9.86m/s = Total dV of 1803.2 m/s2

Transitional Delta V (dV) aka True dV when launching from Kerbin

How to calculate the dV of a rocket stage that transitions from Kerbin atmosphere to vacuum.

Equation: TdV = ( ( dVatm - 1000 ) / dVatm ) * dVvac + 1000

Explained: Transitional dV = ( ( Total dV in atmosphere - 1000 m/s2) / Total dV in atmosphere ) X Total dV in vacuum + 1000

Example:

  • Single Stage with total atmospheric dV of 5000 m/s2, and rated 6000 dV in vacuum.
Transitional dV = ( ( 5000 dVatm - 1000 dV Required to escape Kerbin atmosphere ) / 5000 dVatm ) X 6000 dVvac + 1000 dV Required to escape Kerbin atmosphere =