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| − | {{Outdated|
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| − | * 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.
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| − | * Due to [[Kerbal_Space_Program_Wiki:Migration_problems|migration problems]], The Δv map cannot be updated.
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| − | }}
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| − | 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.
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| − |
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| − | == Mathematics ==
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| − | === Thrust-to-weight ratio (TWR) ===
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| − | {{See also|Thrust-to-weight ratio}}
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| − | 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.
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| − |
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| − | {{Formula|math=\text{TWR} = \frac{F_T}{m \cdot g} > 1|where=* <math>F_T</math> is the thrust of the engines
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| − | * <math>m</math> the total mass of the craft
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| − | * <math>g</math> the local gravitational acceleration (usually surface gravity)}}
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| − |
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| − | === Combined specific impulse (I<sub>sp</sub>) ===
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| − | {{See also|Specific impulse#Multiple engines|Specific impulse}}
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| − | 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:
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| − |
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| − | <math>I_{sp} = \frac{(F_1 + F_2 + \dots)}{\frac{F_1}{I_{sp1}} + \frac{F_2}{I_{sp2}} + \dots}</math>
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| − |
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| − | === Delta-v (Δv) ===
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| − | ==== Basic calculation ====
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| − | {{See also|Tutorial:Advanced Rocket Design}}
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| − | Basic calculation of a rocket's Δv. Use the atmospheric and vacuum thrust values for atmospheric and vacuum Δv, respectively.
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| − | {{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
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| − | * <math>M_{start}</math> is the starting mass in the same unit as <math>M_{end}</math>
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| − | * <math>M_{end}</math> is the end mass in the same unit as <math>M_{start}</math>
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| − | * <math>I_{sp}</math> is the specific impulse of the engine in seconds}}
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| − |
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| − | ==== True Δv of a stage that crosses from atmosphere to vacuum ====
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| − | {| class="wikitable" style="float:left;margin:0.5em;"
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| − | ! Body !! Δv<sub>out</sub>
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| − | |-
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| − | | [[Kerbin]] || 1000 m/s
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| − | |-
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| − | | colspan="2" | other bodies' data missing
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| − | |}
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| − | Calculation of a rocket stage's Δv, taking into account transitioning from atmosphere to vacuum. Δv<sub>out</sub> is the amount of Δv required to leave a body's atmosphere, ''not'' reach orbit. This equation is useful to figure out the actual Δv of a stage that ''transitions'' from atmosphere to vacuum.
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| − |
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| − | <math>\Delta{v}_T = \frac{\Delta{v}_{atm} - \Delta{v}_{out}}{\Delta{v}_{atm}} \cdot \Delta{v}_{vac} + \Delta{v}_{out}</math>
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| − | {{clear|left}}
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| − |
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| − | ==== Maps ====
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| − | Various fan-made maps showing the Δv required to travel to a certain body.
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| − |
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| − | '''Subway style Δv map ''(KSP 1.2.1)'':'''
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| − | [[File:KerbinDeltaVMap.png|center|600px|Δv to all bodies in the [[Kerbol System]]]]
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| − | '''Total Δv values'''
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| − | * http://www.skyrender.net/lp/ksp/system_map.png
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| − | '''Δv change values'''
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| − | * http://i.imgur.com/duY2S.png
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| − | '''Δv with Phase Angles'''
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| − | * http://i.imgur.com/dXT6r7s.png
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| − | '''Precise Total Δv values'''
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| − | * http://i.imgur.com/UUU8yCk.png
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| − | '''WAC's Δv Map for KSP 1.0.4'''
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| − | * http://i.imgur.com/q0gC9H7.png
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| − |
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| − | ==== Maximum Δv chart ====
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| − | :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 ΔV without staging to shed mass or using the slingshot maneuver.
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| − | :{| class="wikitable"
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| − | |-
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| − | ! ISP(Vac) (s) !! Max Δv (m/s) !! Engines
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| − | |-
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| − | | 250 || 5394 || O-10 "Puff"
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| − | |-
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| − | | 290 || 6257 || LV-1R "Spider" <br /> 24-77 "Twitch"
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| − | |-
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| − | | 300 || 6473 || KR-1x2 "Twin-Boar"
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| − | |-
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| − | | 305 || 6581 || CR-7 R.A.P.I.E.R. <br /> Mk-55 "Thud"
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| − | |-
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| − | | 310 || 6689 || LV-T30 "Reliant" <br /> RE-M3 "Mainsail"
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| − | |-
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| − | | 315 || 6797|| LV-1 "Ant" <br /> KS-25 "Vector" <br /> KS-25x4 "Mammoth"
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| − | |-
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| − | | 320 || 6905 || 48-7S "Spark" <br /> LV-T45 "Swivel" <br /> RE-I5 "Skipper"
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| − | |-
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| − | | 340 || 7336 || KR-2L+ "Rhino" <br /> T-1 "Dart"
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| − | |-
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| − | | 345 || 7444 || LV-909 "Terrier"
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| − | |-
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| − | | 350 || 7552 || RE-L10 "Poodle"
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| − | |-
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| − | | 800 || 21837 || LV-N "Nerv"
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| − | |-
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| − | | 4200 || 33751 || IX-6315 "Dawn"
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| − | |}
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| − | (Version: 1.2.2)
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| − |
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| − | == Math examples ==
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| − | === TWR ===
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| − | *Copy template:
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| − | ::'''TWR = F / (m * g) > 1'''
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| − |
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| − | === I<sub>sp</sub> ===
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| − | #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>.
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| − | #When I<sub>sp</sub> is different for engines in a single stage, then use the following equation:
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| − |
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| − | *Equation:
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| − | <math>I_{sp} = \frac{(F_1 + F_2 + \dots)}{\frac{F_1}{I_{sp1}} + \frac{F_2}{I_{sp2}} + \dots}</math>
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| − |
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| − | *Simplified:
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| − | ::'''I<sub>sp</sub> = ( F1 + F2 + ... ) / ( ( F1 / I<sub>sp</sub>1 ) + ( F2 / I<sub>sp</sub>2 ) + ... )'''
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| − |
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| − | *Explained:
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| − | ::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... )
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| − |
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| − | *Example:
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| − | :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>.
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| − | :Isp = (200 newtons + 50 newtons) / ( ( 200 newtons / 120 ) + ( 50 newtons / 200 ) = 130.4347826 seconds I<sub>sp</sub>
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| − |
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| − | === Δv ===
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| − | #For atmospheric Δv value, use atmospheric <math>I_{sp}</math> values.
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| − | #For vacuum Δv value, use vacuum <math>I_{sp}</math> values.
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| − | #Use this equation to figure out the Δv per stage:
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| − |
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| − | *Equation:
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| − | <math>\Delta{v} = ln\left(\frac{M_{start}}{M_{dry}}\right) \cdot I_{sp} \cdot 9.81 \frac{m}{s^2}</math>
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| − |
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| − | *Simplified:
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| − | ::'''Δv = ln ( Mstart / Mdry ) * I<sub>sp</sub> * g'''
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| − |
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| − | *Explained:
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| − | ::Δv = ln ( starting mass / dry mass ) X Isp X 9.81
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| − |
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| − | *Example:
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| − | :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>.
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| − | :Δv = ln ( 23 Tons / 15 Tons ) × 120 seconds I<sub>sp</sub> × 9.81m/s² = Total Δv of 503.0152618 m/s
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| − |
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| − | === Maximum Δv ===
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| − | :Simplified version of the Δv calculation to find the maximum Δv 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.
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| − | *Equation:
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| − | ::<math>\Delta{v} = 21.576745349086 \cdot I_{sp}</math>
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| − |
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| − | *Simplified:
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| − | ::'''Δv =21.576745349086 * I<sub>sp</sub>'''
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| − |
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| − | *Explained / Examples:
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| − | :This calculation only uses the mass of the fuel tanks and so the ln ( Mstart / Mdry ) part of the Δv 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.
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| − | :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>.
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| − | :Δv = ln ( 18 Tons / 2 Tons ) × 380 seconds I<sub>sp</sub> × 9.81m/s² = Maximum Δv of 8199.1632327878 m/s
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| − | :Δv = 2.1972245773 × 380 seconds I<sub>sp</sub> × 9.82m/s² = Maximum Δv 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)
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| − | :Δv = 21.576745349086 × 380 seconds I<sub>sp</sub> = Maximum Δv of 8199.1632327878 m/s (Reduced to its most simple form by combining all the constants)
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| − | === True Δv ===
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| − | #How to calculate the Δv of a rocket stage that transitions from Kerbin atmosphere to vacuum.
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| − | #Assumption: It takes approximately 1000 m/s of Δv to escape Kerbin's atmosphere before vacuum Δv values take over for the stage powering the transition.
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| − | #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."
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| − |
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| − | *Equation for Kerbin atmospheric escape:
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| − | <math>\Delta{v}_T = \frac{\Delta{v}_{atm} - \Delta{v}_{out}}{\Delta{v}_{atm}} \cdot \Delta{v}_{vac} + \Delta{v}_{out}</math>
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| − | {{clear|left}}
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| − |
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| − | *Simplified:
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| − | ::'''True Δv = ( ( Δv atm - 1000 ) / Δv atm ) * Δv vac + 1000'''
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| − |
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| − | *Explained:
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| − | ::True Δv = ( ( Total Δv in atmosphere - 1000 m/s) / Total Δv in atmosphere ) X Total Δv in vacuum + 1000
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| − |
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| − | *Example:
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| − | :Single stage with total atmospheric Δv of 5000 m/s, and rated 6000 Δv in vacuum.
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| − | :Transitional Δv = ( ( 5000 Δv atm - 1000 Δv required to escape Kerbin atmosphere ) / 5000 Δv atm ) X 6000 Δv vac + 1000 Δv required to escape Kerbin atmosphere = Total Δv of 5800 m/s
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| − | == See also ==
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| − |
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| − | * [[Tutorials]]
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| − | * [[Terminology]]
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| − | * [[thread:28352|The Drawing Board: A library of tutorials and other useful information]]
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