Difference between revisions of "Cheat sheet"

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{{Outdated|
 
* This page provides false information about the Δv required in planets with atmospheres. A lot of the information on this page has to be either removed or updated.
 
* Due to [[Kerbal_Space_Program_Wiki:Migration_problems|migration problems]], The Δv map cannot be updated.
 
}}
 
  
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 ==
 
=== Thrust-to-weight ratio (TWR) ===
 
{{See also|Thrust-to-weight ratio}}
 
This is Newton's Second Law. If the ratio is less than 1 the craft will not lift off the ground. Note that the local gravitational acceleration, which is usually the surface gravity of the body the rocket is starting from, is required.
 
 
{{Formula|math=\text{TWR} = \frac{F_T}{m \cdot g} > 1|where=* <math>F_T</math> is the thrust of the engines
 
* <math>m</math> the total mass of the craft
 
* <math>g</math> the local gravitational acceleration (usually surface gravity)}}
 
 
=== Combined specific impulse (I<sub>sp</sub>) ===
 
{{See also|Specific impulse#Multiple engines|Specific impulse}}
 
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:
 
 
<math>I_{sp} = \frac{(F_1 + F_2 + \dots)}{\frac{F_1}{I_{sp1}} + \frac{F_2}{I_{sp2}} + \dots}</math>
 
 
=== Delta-v (&Delta;v) ===
 
==== Basic calculation ====
 
{{See also|Tutorial:Advanced Rocket Design}}
 
Basic calculation of a rocket's &Delta;v. Use the atmospheric and vacuum thrust values for atmospheric and vacuum &Delta;v, respectively.
 
{{Formula|math=\Delta{v} = ln\left(\frac{M_{start} }{M_{end} }\right) \cdot I_{sp} \cdot 9.81 \frac{m}{s^2}|where=* <math>\Delta{v}</math> is the velocity change possible in m/s
 
* <math>M_{start}</math> is the starting mass in the same unit as <math>M_{end}</math>
 
* <math>M_{end}</math> is the end mass in the same unit as <math>M_{start}</math>
 
* <math>I_{sp}</math> is the specific impulse of the engine in seconds}}
 
 
==== True &Delta;v of a stage that crosses from atmosphere to vacuum ====
 
{| class="wikitable" style="float:left;margin:0.5em;"
 
! Body !! &Delta;v<sub>out</sub>
 
|-
 
| [[Kerbin]] || 1000&nbsp;m/s
 
|-
 
| colspan="2" | other bodies' data missing
 
|}
 
Calculation of a rocket stage's &Delta;v, taking into account transitioning from atmosphere to vacuum. &Delta;v<sub>out</sub> is the amount of &Delta;v required to leave a body's atmosphere, ''not'' reach orbit. This equation is useful to figure out the actual &Delta;v of a stage that ''transitions'' from atmosphere to vacuum.
 
 
<math>\Delta{v}_T = \frac{\Delta{v}_{atm} - \Delta{v}_{out}}{\Delta{v}_{atm}} \cdot \Delta{v}_{vac} + \Delta{v}_{out}</math>
 
{{clear|left}}
 
 
==== Maps ====
 
Various fan-made maps showing the &Delta;v required to travel to a certain body.
 
 
'''Subway style &Delta;v map ''(KSP 1.2.1)'':'''
 
[[File:KerbinDeltaVMap.png|center|600px|&Delta;v to all bodies in the [[Kerbol System]]]]
 
 
 
'''Total &Delta;v values'''
 
* http://www.skyrender.net/lp/ksp/system_map.png
 
'''&Delta;v change values'''
 
* http://i.imgur.com/duY2S.png
 
'''&Delta;v with Phase Angles'''
 
* http://i.imgur.com/dXT6r7s.png
 
'''Precise Total &Delta;v values'''
 
* http://i.imgur.com/UUU8yCk.png
 
'''WAC's &Delta;v Map for KSP 1.0.4'''
 
* http://i.imgur.com/q0gC9H7.png
 
 
==== Maximum &Delta;v chart ====
 
:This chart is a quick guide to what engine to use for a single stage interplanetary ship. No matter how much fuel you add you will never reach these &Delta;V without staging to shed mass or using the slingshot maneuver.
 
:{| class="wikitable"
 
|-
 
! ISP(Vac) (s) !! Max &Delta;v (m/s) !! Engines
 
|-
 
| 250 || 5394 || O-10 "Puff"
 
|-
 
| 290 || 6257 || LV-1R "Spider" <br /> 24-77 "Twitch"
 
|-
 
| 300 || 6473 || KR-1x2 "Twin-Boar"
 
|-
 
| 305 || 6581 || CR-7 R.A.P.I.E.R. <br /> Mk-55 "Thud"
 
|-
 
| 310 || 6689 || LV-T30 "Reliant" <br /> RE-M3 "Mainsail"
 
|-
 
| 315 || 6797|| LV-1 "Ant" <br /> KS-25 "Vector" <br /> KS-25x4 "Mammoth"
 
|-
 
| 320 || 6905 || 48-7S "Spark" <br /> LV-T45 "Swivel" <br /> RE-I5 "Skipper"
 
|-
 
| 340 || 7336 || KR-2L+ "Rhino" <br /> T-1 "Dart"
 
|-
 
| 345 || 7444 || LV-909 "Terrier"
 
|-
 
| 350 || 7552 || RE-L10 "Poodle"
 
|-
 
| 800 || 21837 || LV-N "Nerv"
 
|-
 
| 4200 || 33751 || IX-6315 "Dawn"
 
|}
 
(Version: 1.2.2)
 
 
== Math examples ==
 
=== TWR ===
 
*Copy template:
 
::'''TWR = F / (m * g) > 1'''
 
 
=== I<sub>sp</sub> ===
 
#When 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 200 I<sub>sp</sub> engines still yields only 200 I<sub>sp</sub>.
 
#When 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>
 
 
*Simplified:
 
::'''I<sub>sp</sub> = ( F1 + F2 + ... ) / ( ( F1 / I<sub>sp</sub>1 ) + ( F2 / I<sub>sp</sub>2 ) + ... )'''
 
 
*Explained:
 
::I<sub>sp</sub> = ( Force of thrust of 1st engine + Force of thrust of 2nd engine...and so on... ) / ( ( Force of thrust of 1st engine / I<sub>sp</sub> of 1st engine ) + ( Force of thrust of 2nd engine / I<sub>sp</sub> of 2nd engine ) + ...and so on... )
 
 
*Example:
 
:Two engines, one rated 200 newtons and 120 seconds I<sub>sp</sub> ; another engine rated 50 newtons and 200 seconds I<sub>sp</sub>.
 
:Isp = (200 newtons + 50 newtons) / ( ( 200 newtons / 120 ) + ( 50 newtons / 200 ) = 130.4347826 seconds I<sub>sp</sub>
 
 
=== &Delta;v ===
 
#For atmospheric &Delta;v value, use atmospheric <math>I_{sp}</math> values.
 
#For vacuum &Delta;v value, use vacuum <math>I_{sp}</math> values.
 
#Use this equation to figure out the &Delta;v per stage:
 
 
*Equation:
 
<math>\Delta{v} = ln\left(\frac{M_{start}}{M_{dry}}\right) \cdot I_{sp} \cdot 9.81 \frac{m}{s^2}</math>
 
 
*Simplified:
 
::'''&Delta;v = ln ( Mstart / Mdry ) * I<sub>sp</sub> * g'''
 
 
*Explained:
 
::&Delta;v = ln ( starting mass / dry mass ) X Isp X 9.81
 
 
*Example:
 
:Single stage rocket that weighs 23 tons when full, 15 tons when fuel is emptied, and engine that outputs 120 seconds I<sub>sp</sub>.
 
:&Delta;v = ln ( 23 Tons / 15 Tons ) × 120 seconds I<sub>sp</sub> × 9.81m/s² = Total &Delta;v of 503.0152618 m/s
 
 
=== Maximum &Delta;v ===
 
:Simplified version of the &Delta;v calculation to find the maximum &Delta;v a craft with the given ISP could hope to achieve. This is done by using a magic 0 mass engine and not having a payload.
 
*Equation:
 
::<math>\Delta{v} = 21.576745349086 \cdot I_{sp}</math>
 
 
*Simplified:
 
::'''&Delta;v =21.576745349086 * I<sub>sp</sub>'''
 
 
*Explained / Examples:
 
:This calculation only uses the mass of the fuel tanks and so the ln ( Mstart / Mdry ) part of the &Delta;v equation has been replaced by a constant as Mstart / Mdry is always 9 (or worse with some fuel tanks) regardless of how many fuel tanks you use.
 
:The following example will use a single stage and fuel tanks in the T-100 to Jumbo 64 range with an engine that outputs 380 seconds I<sub>sp</sub>.
 
:&Delta;v = ln ( 18 Tons / 2 Tons ) × 380 seconds I<sub>sp</sub> × 9.81m/s² = Maximum &Delta;v of 8199.1632327878 m/s
 
:&Delta;v = 2.1972245773 × 380 seconds I<sub>sp</sub> × 9.82m/s² = Maximum &Delta;v of 8199.1632327878 m/s (Replaced the log of mass with a constant as the ratio of total mass to dry mass is constant regardless of the number of tanks used as there is no other mass involved)
 
:&Delta;v = 21.576745349086 × 380 seconds I<sub>sp</sub> = Maximum &Delta;v of 8199.1632327878 m/s (Reduced to its most simple form by combining all the constants)
 
=== True &Delta;v ===
 
#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 of &Delta;v to escape Kerbin's atmosphere before vacuum &Delta;v values take over for the stage powering the transition.
 
#Note: This equation is an guess, approximation, and is not 100% accurate. Per forum user stupid_chris who came up with the equation: "The results will vary a bit depending on your TWR and such, but it should usually be pretty darn accurate."
 
 
*Equation for Kerbin atmospheric escape:
 
<math>\Delta{v}_T = \frac{\Delta{v}_{atm} - \Delta{v}_{out}}{\Delta{v}_{atm}} \cdot \Delta{v}_{vac} + \Delta{v}_{out}</math>
 
{{clear|left}}
 
 
*Simplified:
 
::'''True &Delta;v = ( ( &Delta;v atm - 1000 ) / &Delta;v atm ) * &Delta;v vac + 1000'''
 
 
*Explained:
 
::True &Delta;v = ( ( Total &Delta;v in atmosphere - 1000 m/s) / Total &Delta;v in atmosphere ) X Total &Delta;v in vacuum + 1000
 
 
*Example:
 
:Single stage with total atmospheric &Delta;v of 5000 m/s, and rated 6000 &Delta;v in vacuum.
 
:Transitional &Delta;v = ( ( 5000 &Delta;v atm - 1000 &Delta;v required to escape Kerbin atmosphere ) / 5000 &Delta;v atm ) X 6000 &Delta;v vac + 1000 &Delta;v required to escape Kerbin atmosphere = Total &Delta;v of 5800 m/s
 
 
== See also ==
 
 
* [[Tutorials]]
 
* [[Terminology]]
 
* [[thread:28352|The Drawing Board: A library of tutorials and other useful information]]
 

Revision as of 17:52, 17 March 2017