Difference between revisions of "Cheat sheet"

From Kerbal Space Program Wiki
Jump to: navigation, search
(* formulas to <math>. ! other stuff.)
m (Mathematics)
Line 9: Line 9:
  
 
*Equation:
 
*Equation:
:<math>\Delta{v} = ln(\frac{M_{start}}{M_{end}}) \cdot I_{sp} \cdot g</math>
+
:<math>\Delta{v} = ln\left(\frac{M_{start}}{M_{end}}\right) \cdot I_{sp} \cdot g_0</math>
  
 
*Explained:
 
*Explained:
:<math>\Delta{v} = ln(\frac{Starting Mass}{Ending Mass}) \cdot Specific Impulse \cdot 9.81 \frac{m}{s^2}</math>
+
:<math>\Delta{v} = ln\left(\frac{\text{Starting Mass}}{\text{Ending Mass}}\right) \cdot \text{Specific Impulse} \cdot 9.81 \frac{m}{s^2}</math>
  
 
*Example:
 
*Example:
 
:Single stage rocket that weighs 23&nbsp;t when full, 15&nbsp;t when fuel is emptied, and has an engine with a specific impulse of 120&nbsp;s.
 
:Single stage rocket that weighs 23&nbsp;t when full, 15&nbsp;t when fuel is emptied, and has an engine with a specific impulse of 120&nbsp;s.
:<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\left(\frac{23t}{15t}\right) \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) ====
Line 52: Line 52:
  
 
*Explained:
 
*Explained:
:<math>TWR = \frac{Thrust Force}{Total Mass \cdot 9.81}</math>
+
:<math>TWR = \frac{\text{Thrust Force}}{\text{Total Mass} \cdot \text{Local gravitational acceleration}}</math>
  
 
*Example:
 
*Example:
Line 64: Line 64:
  
 
*Equation:
 
*Equation:
:<math>I_{sp} = \frac{(F_1 + F_2 + ...)}{\frac{F_1}{I_{sp1}} + \frac{F_2}{I_{sp2}} + ...}</math>
+
:<math>I_{sp} = \frac{(F_1 + F_2 + \dots)}{\frac{F_1}{I_{sp1}} + \frac{F_2}{I_{sp2}} + \dots}</math>
  
 
*Explained:
 
*Explained:
:<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>
+
:<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} + \dots}</math>
  
 
*Example:
 
*Example:

Revision as of 18:45, 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.