Revision as of 00:45, 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.

TWR = Force of Thrust / ( Total Mass X gravity of planet you're on ) > 1

TWR = F / (m * g) > 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:

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:

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

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

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.

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:

• 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 =