Revision as of 00:49, 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)

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 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)

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

Delta V (dV)

1. For atmospheric dV value, use atmospheric thrust values.
2. For vacuum dV value, use vacuum thrust values.
3. 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

1. 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 =