Difference between revisions of "Cheat sheet"

Revision as of 15:07, 28 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

Basic calculation of a rocket's Δv. Use the atmospheric and vacuum thrust values for atmospheric and vacuum Δv, respectively.

$\Delta {v}=ln\left({\frac {M_{start}}{M_{end}}}\right)\cdot I_{sp}\cdot 9.81{\frac {m}{s^{2}}}$

Transitional (true) Δv

Body	Δv_out
Kerbin	1000 m/s²
other bodies'	data missing

Calculation of a rocket's Δv, taking an atmosphere into account. Δv_out is the amount of Δv required to leave a body's atmosphere.

$\Delta {v}_{T}={\frac {\Delta {v}_{atm}-\Delta {v}_{out}{\frac {m}{s^{2}}}}{\Delta {v}_{atm}}}\cdot \Delta {v}_{vac}+\Delta {v}_{out}{\frac {m}{s^{2}}}$

Maps

Various fan-made maps showing the Δv required to travel to a certain body.

Total Δv values

Δv change values

http://i.imgur.com/duY2S.png

Δv nomogram

http://ubuntuone.com/1kD39BCoV38WP1QeG6MtO6

Thrust to weight ratio (TWR)

This is Newton's Second Law. If the ratio is less than 1 the craft will not lift off the ground.

${\text{TWR}}={\frac {F}{m\cdot g}}$

Combined specific impulse (I_sp)

If the I_sp is the same for all engines in a stage, then the I_sp is equal to a single engine. If the I_sp is different for engines in a single stage, then use the following equation:

$I_{sp}={\frac {(F_{1}+F_{2}+\dots )}{{\frac {F_{1}}{I_{sp1}}}+{\frac {F_{2}}{I_{sp2}}}+\dots }}$

@@ Line 4: / Line 4: @@
 === Delta-v (&Delta;v) ===
 ==== Basic calculation ====
-#For atmospheric &Delta;V value, use atmospheric thrust values.
+Basic calculation of a rocket's &Delta;v. Use the atmospheric and vacuum thrust values for atmospheric and vacuum &Delta;v, respectively.
-#For vacuum &Delta;v value, use vacuum thrust values.
-#Use this equation to figure out the &Delta;v per stage:
-*Equation:
+<math>\Delta{v} = ln\left(\frac{M_{start}}{M_{end}}\right) \cdot I_{sp} \cdot 9.81 \frac{m}{s^2}</math>
-:<math>\Delta{v} = ln\left(\frac{M_{start}}{M_{end}}\right) \cdot I_{sp} \cdot g_0</math>
-*Explained:
+==== Transitional (true) &Delta;v ====
-:<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>
+{| class="wikitable" align="left"
+! Body !! &Delta;v<sub>out</sub>
+|-
+| [[Kerbin]] || 1000 m/s<sup>2</sup>
+|-
+| other bodies' || data missing
+|}
+Calculation of a rocket's &Delta;v, taking an atmosphere into account. &Delta;v<sub>out</sub> is the amount of &Delta;v required to leave a body's atmosphere.
-*Example:
+<math>\Delta{v}_T = \frac{\Delta{v}_{atm} - \Delta{v}_{out} \frac{m}{s^2}}{\Delta{v}_{atm}} \cdot \Delta{v}_{vac} + \Delta{v}_{out} \frac{m}{s^2}</math>
-: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.
+{{clear|left}}
-:<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>
+==== Maps ====
+Various fan-made maps showing the &Delta;v required to travel to a certain body.
-==== Transitional &Delta;v (true &Delta;v when launching from Kerbin) ====
+'''Total &Delta;v values'''
-#How to calculate the &Delta;v of a rocket stage that transitions from Kerbin atmosphere to vacuum.
+* http://wiki.kerbalspaceprogram.com/w/images/7/73/KerbinDeltaVMap.png
-#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.
+* http://www.skyrender.net/lp/ksp/system_map.png
-#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.
+'''&Delta;v change values'''
+* http://i.imgur.com/duY2S.png
-*Equation:
+'''&Delta;v nomogram'''
-:<math>\Delta{v}_T = \frac{\Delta{v}_{atm} - 1000 \frac{m}{s^2}}{\Delta{v}_{atm}} \cdot \Delta{v}_{vac} + 1000 \frac{m}{s^2}</math>
+* http://ubuntuone.com/1kD39BCoV38WP1QeG6MtO6
-*Explained:
-:<math>\text{Transitional Delta-v} = \frac{\text{Atmospheric Delta-v} - 1000 \frac{m}{s^2}}{\text{Atmospheric Delta-v}} \cdot \text{Vacuum Delta-v} + 1000 \frac{m}{s^2}</math>
-*Example:
-: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>
-==== &Delta;v maps ====
-Various maps developed by KSP fans.
-*&Delta;v Total Values
-#http://wiki.kerbalspaceprogram.com/w/images/7/73/KerbinDeltaVMap.png
-#http://www.skyrender.net/lp/ksp/system_map.png
-*&Delta;v Change Values
-#http://i.imgur.com/duY2S.png
-*&Delta;v KSP Nomogram
-#http://ubuntuone.com/1kD39BCoV38WP1QeG6MtO6
 === Thrust to weight ratio (TWR) ===
-#This is Newton's Second Law.
+This is Newton's Second Law. If the ratio is less than 1 the craft will not lift off the ground.
-#If ratio is less than 1, the craft will not lift off the ground.
-*Equation:
+<math>\text{TWR} = \frac{F}{m \cdot g}</math>
-:<math>\text{TWR} = \frac{F}{m \cdot g}</math>
-*Explained:
-:<math>\text{TWR} = \frac{\text{Thrust force}}{\text{Total mass} \cdot \text{Local gravitational acceleration}}</math>
-*Example:
-:200&nbsp;kN rocket engine under a 15&nbsp;t rocket launching from Kerbin.
-:<math>\text{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 (I<sub>sp</sub>) ===
-#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.
+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. If the I<sub>sp</sub> 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:
-:<math>I_{sp} = \frac{(F_1 + F_2 + \dots)}{\frac{F_1}{I_{sp1}} + \frac{F_2}{I_{sp2}} + \dots}</math>
-*Explained:
-:<math>I_{sp} = \frac{\text{Thrust of engine 1} + \text{Thrust of engine 2} + \dots}{\frac{\text{Thrust of engine 1}}{\text{Specific impulse of engine 1}} + \frac{\text{Thrust of engine 2}}{\text{Specific impulse of engine 2}} + \dots}</math>
-*Example:
+<math>I_{sp} = \frac{(F_1 + F_2 + \dots)}{\frac{F_1}{I_{sp1}} + \frac{F_2}{I_{sp2}} + \dots}</math>
-: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>.
-:<math>I_{sp} = \frac{200 N + 50 N}{\frac{200 N}{120 s} + \frac{50 N}{200 s}} = 130.89 s</math>
 == See also ==
-Links to collections of reference materials.
+Links to collections of reference material.
-*[[Tutorials]]
+* [[Tutorials]]
-*[[thread:28352|The Drawing Board: A library of tutorials and other useful information]]
+* [[Terminology]]
+* [[thread:28352|The Drawing Board: A library of tutorials and other useful information]]

Difference between revisions of "Cheat sheet"

Revision as of 15:07, 28 June 2013

Contents

Mathematics

Delta-v (Δv)

Basic calculation

Transitional (true) Δv

Maps

Thrust to weight ratio (TWR)

Combined specific impulse (I_sp)

See also

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Difference between revisions of "Cheat sheet"

Revision as of 15:07, 28 June 2013

Contents

Mathematics

Delta-v (Δv)

Basic calculation

Transitional (true) Δv

Maps

Thrust to weight ratio (TWR)

Combined specific impulse (Isp)

See also

Navigation menu

Search

Combined specific impulse (I_sp)