Difference between revisions of "Cheat sheet"

From Kerbal Space Program Wiki
Jump to: navigation, search
(* use <math> tags for some formulas. ! other stuff.)
(* formulas to <math>. ! other stuff.)
Line 1: Line 1:
 
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.
 
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 (&Delta;v) ==
+
== Mathematics ==
=== Basic calculation ===
+
=== Delta-v (&Delta;v) ===
 +
==== Basic calculation ====
 
#For atmospheric &Delta;V value, use atmospheric thrust values.
 
#For atmospheric &Delta;V value, use atmospheric thrust values.
#For vacuum 6Delta;v value, use vacuum thrust values.
+
#For vacuum &Delta;v value, use vacuum thrust values.
 
#Use this equation to figure out the &Delta;v per stage:
 
#Use this equation to figure out the &Delta;v per stage:
  
Line 17: Line 18:
 
:<math>\Delta{v} = ln(\frac{23t}{15t}) \cdot 120 s \cdot 9.81 \frac{m}{s^2} =  1803.2 \frac{m}{s^2}</math>
 
:<math>\Delta{v} = ln(\frac{23t}{15t}) \cdot 120 s \cdot 9.81 \frac{m}{s^2} =  1803.2 \frac{m}{s^2}</math>
  
=== Transitional &Delta;v (true &Delta;v when launching from Kerbin) ===
+
==== Transitional &Delta;v (true &Delta;v when launching from Kerbin) ====
 
#How to calculate the &Delta;v of a rocket stage that transitions from Kerbin atmosphere to vacuum.
 
#How to calculate the &Delta;v of a rocket stage that transitions from Kerbin atmosphere to vacuum.
 
#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.
 
#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.
Line 29: Line 30:
  
 
*Example:
 
*Example:
: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.
+
:Single stage with total atmospheric &Delta;v of 5000&nbsp;m/s<sup>2</sup> and with a &Delta;v of 6000&nbsp;m/s<sup>2</sup> in vacuum.
 
:<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>
 
:<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>
  
=== &Delta;v maps ===
+
==== &Delta;v maps ====
 
Various maps developed by KSP fans.
 
Various maps developed by KSP fans.
  
Line 43: Line 44:
 
#http://ubuntuone.com/1kD39BCoV38WP1QeG6MtO6
 
#http://ubuntuone.com/1kD39BCoV38WP1QeG6MtO6
  
== Thrust to weight ratio (TWR) ==
+
=== Thrust to weight ratio (TWR) ===
 
#This is Newton's Second Law.
 
#This is Newton's Second Law.
#If ratio is less than 1, you will not lift off the ground.
+
#If ratio is less than 1, the craft will not lift off the ground.
 
 
  
 
*Equation:
 
*Equation:
::'''TWR = F / (m * g) > 1'''
+
:<math>TWR = \frac{F}{m \cdot g}</math>
  
 
*Explained:
 
*Explained:
::TWR = Force of Thrust / ( Total Mass X 9.81 ) > 1
+
:<math>TWR = \frac{Thrust Force}{Total Mass \cdot 9.81}</math>
  
 
*Example:
 
*Example:
:200 kiloNewton rocket engine on a 15 ton rocket launching from Kerbin Space Center.
+
:200&nbsp;kN rocket engine under a 15&nbsp;t rocket launching from Kerbin.
:TWR = 200 kN / ( 15 Tons total Mass X 9.81 m/s2 ) = 1.36 which is > 1 which means liftoff!
+
:<math>TWR = \frac{200 kN}{15 t \cdot 9.81 \frac{m}{s^2}} = 1.36</math>
 
+
:The TWR is higher than 1, so the craft will lift off!
  
== Combined specific impulse (Isp) ==
+
=== Combined specific impulse (I<sub>sp</sub>) ===
#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.
+
#If the I<sub>sp</sub> is the same for all engines in a stage, then the I<sub>sp</sub> is equal to a single engine. So six engines with 200&nbsp;s of I<sub>sp</sub> still yield only an I<sub>sp</sub> of 200&nbsp;s.
#When Isp is different for engines in a single stage, then use the following equation:
+
#If the I<sub>sp</sub> is different for engines in a single stage, then use the following equation:
  
 
*Equation:
 
*Equation:
::'''Isp = ( F1 + F2 + ... ) / ( ( F1 / Isp1 ) + ( F2 / Isp2 ) + ... )'''
+
:<math>I_{sp} = \frac{(F_1 + F_2 + ...)}{\frac{F_1}{I_{sp1}} + \frac{F_2}{I_{sp2}} + ...}</math>
  
 
*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... )
+
:<math>I_{sp} = \frac{Thrust Of Engine 1 + Thrust of Engine 2 + ...}{\frac{Thrust Of Engine 1}{I_{sp} Of Engine 1} + \frac{Thrust Of Engine 2}{I_{sp} Of Engine 2} + ...}</math>
  
 
*Example:
 
*Example:
:Two engines, one rated 200 Newtons and 120 Specific Impulse; another engine rated 50 Newtons and 200 Specific Impulse.
+
:Two engines, the first one with 200&nbsp;N of thrust and 120&nbsp;s of I<sub>sp</sub>; the second one with 50&nbsp;N of thrust and 200&nbsp;s of I<sub>sp</sub>.
:Isp = (200 Netwons + 50 Newtons) / ( ( 200 Newtons / 120 ) + ( 50 Newtons / 200 ) = 130.89 Specific Impulse
+
:<math>I_{sp} = \frac{200 N + 50 N}{\frac{200 N}{120 s} + \frac{50 N}{200 s}} = 130.89 s</math>
  
 
== See also ==
 
== See also ==

Revision as of 18:23, 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.

Mathematics

Delta-v (Δv)

Basic calculation

  1. For atmospheric ΔV value, use atmospheric thrust values.
  2. For vacuum Δv 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, the craft will not lift off the ground.
  • Equation:
  • Explained:
  • Example:
200 kN rocket engine under a 15 t rocket launching from Kerbin.
The TWR is higher than 1, so the craft will lift off!

Combined specific impulse (Isp)

  1. If the Isp is the same for all engines in a stage, then the Isp is equal to a single engine. So six engines with 200 s of Isp still yield only an Isp of 200 s.
  2. If the Isp is different for engines in a single stage, then use the following equation:
  • Equation:
  • Explained:
  • Example:
Two engines, the first one with 200 N of thrust and 120 s of Isp; the second one with 50 N of thrust and 200 s of Isp.

See also

Links to collections of reference materials.