Difference between revisions of "Cheat sheet"
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==Thrust to Weight Ratio (TWR)== | ==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: | + | *Equation: |
| − | '''TWR = F / (m * g) > 1''' | + | ::'''TWR = F / (m * g) > 1''' |
| − | Explained: | + | *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 |
| − | Example: | + | *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! | :TWR = 200 Newtons / ( 15 Tons total Mass X 9.86 m/s2 ) = 1.36 which is > 1 which means liftoff! | ||
==Combined Specific Impulse (Isp)== | ==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: | + | *Equation: |
| − | '''Isp = ( F1 + F2 + ... ) / ( ( F1 / Isp1 ) + ( F2 / Isp2 ) + ... )''' | + | ::'''Isp = ( F1 + F2 + ... ) / ( ( F1 / Isp1 ) + ( F2 / Isp2 ) + ... )''' |
| − | Explained: | + | *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... ) | + | ::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: | + | *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 | :Isp = (200 Netwons + 50 Newtons) / ( ( 200 Newtons / 120 ) + ( 50 Newtons / 200 ) = 130.89 Specific Impulse | ||
==Delta V (dV)== | ==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: | + | *Equation: |
| − | '''dV = ln ( Mstart / Mend ) * Isp * g''' | + | ::'''dV = ln ( Mstart / Mend ) * Isp * g''' |
| − | Explained: | + | *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 |
| − | Example: | + | *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 | :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== | ==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. | + | #How to calculate the dV of a rocket stage that transitions from Kerbin atmosphere to vacuum. |
| − | Equation: | + | *Equation: |
| − | '''TdV = ( ( dVatm - 1000 ) / dVatm ) * dVvac + 1000''' | + | ::'''TdV = ( ( dVatm - 1000 ) / dVatm ) * dVvac + 1000''' |
| − | Explained: | + | *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 |
| − | Example: | + | #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 = | :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 00:49, 25 June 2013
Contents
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.
- dV Total Values
- 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 =
