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Kerbal Space Program rocket scientist's cheat sheet: Deltav maps, equations and more for your reference so you can get from here to there and back again.
Contents
 1 Mathematics
 1.1 Thrusttoweight ratio (TWR)
 1.2 Specific Impulse (Isp)
 1.3 Deltav (Δv)
 1.3.1 Basic calculation
 1.3.2 True Δv of a stage that crosses from atmosphere to vacuum
 1.3.3 Maps
 1.3.4 Maximum Δv chart
 2 Math examples
 2.1 TWR
 2.2 Isp
 2.3 Δv
 2.4 Maximum Δv
 2.5 True Δv
 3 See also
Mathematics
Thrusttoweight ratio (TWR)
 → See also: Thrusttoweight ratio
How hard do your engines push UP? That's "thrust".
How hard does gravity pull DOWN? That's "weight".
The ratio of those two is, surprisingly, the "thrusttoweight" ratio.
If thrust is pushing harder than weight, your rocket goes up! Hooray!
If weight is pulling harder than thrust, your rocket does not go up. Sad!
That's the "thrusttoweight" ratio, or TWR, in a nutshell.
Where:
 is the thrust of the engines
 the total mass of the craft
 the local gravitational acceleration (usually surface gravity)
If TWR is less than one, then your rocket will not be going into space. You will need more engines, or perhaps MOAR BOOSTERZ!
If TWR is significantly above, say, 2.0, your rocket will ZOOM! But it might ZOOM too hard for your poor Kerbalnauts. Most rockets, straight off the launch pad, will utilize a TWR between 1.5 and 2.0.
Specific Impulse (I_{sp})
 → See also: Specific impulse
Specific impulse measures the efficiency of a particular engine. Because this depends on the pressure of a rocket's surroundings, this can change between Sea Level and Vacuum (in space). Most engines are designed for optimal performance either at Sea Level (the big ones that drive your first stage and boosters, which have lots of thrust!) or Vacuum (where they won't burn as much propellant, but can be VERY efficient).
Specific impulse is used in important equations like THE ROCKET EQUATION (see next section) to determine how much oomph (or "deltavee") you can get out of a given amount of propellant. The higher the specific impulse, the more efficient an engine is!
In real life, specific impulse is governed by things like combustion chamber pressure and propellant energy (hydrogen/oxygen is more efficient than kerosene/oxgyen). Fortunately for Jebediah, our dear Kerbals only have one brand of fuel to worry about.
Deltav (Δv)
Basic calculation
 → See also: Tutorial:Advanced Rocket Design
Basic calculation of a rocket's Δv. Use the atmospheric and vacuum thrust values for atmospheric and vacuum Δv, respectively.
Where:
 is the velocity change possible in m/s
 is the starting mass in the same unit as
 is the end mass in the same unit as
 is the specific impulse of the engine in seconds
True Δv of a stage that crosses from atmosphere to vacuum
Body  Δv_{out} 

Kerbin  2500m/s 
other bodies' data missing 
Calculation of a rocket stage's Δv, taking into account transitioning from atmosphere to vacuum. Δv_{out} 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.
Maps
Various fanmade maps showing the Δv required to travel to a certain body.
KSP Visual Calculator, online tool that determines deltav required for multiple checkpoint missions
Subway style Δv map (KSP 1.7.3):
Total Δv values
Δv change values
Δv with Phase Angles
Precise Total Δv values
WAC's Δv Map for KSP 1.0.4
Maximum Δv 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 ΔV without staging to shed mass or using the slingshot maneuver. (These calculations use a full/empty fueltank mass ratio of 9 for all engines except those noted.)
ISP(Vac) (s) Max Δv (m/s) Engines Remarks 250 5249 O10 "Puff" Monopropellant (max full/empty mass ratio = 8.5) 290 6249 LV1R "Spider"
2477 "Twitch"300 6464 KR1x2 "TwinBoar" 305 6572 CR7 R.A.P.I.E.R.
Mk55 "Thud"310 6680 LVT30 "Reliant"
REM3 "Mainsail"315 6787 LV1 "Ant"
KS25 "Vector"
KS25x4 "Mammoth"320 6895 487S "Spark"
LVT45 "Swivel"
REI5 "Skipper"340 7326 KR2L+ "Rhino"
T1 "Dart"345 7434 LV909 "Terrier" 350 7542 REL10 "Poodle" 800 17238 LVN "Nerv" Mark 1 fuselage tanks, others have differing mass ratios 4200 57099 IX6315 "Dawn" Xenon (max full/empty mass ratio = 4.0)
(Version: 1.12.5)
Math examples
TWR
 Copy template:
 TWR = F / (m * g) > 1
I_{sp}
 When I_{sp} is the same for all engines in a stage, then the I_{sp} is equal to a single engine. So six 200 I_{sp} engines still yields only 200 I_{sp}.
 When I_{sp} is different for engines in a single stage, then use the following equation:
 Equation:
 Simplified:
 I_{sp} = ( F1 + F2 + ... ) / ( ( F1 / I_{sp}1 ) + ( F2 / I_{sp}2 ) + ... )
 Explained:
 I_{sp} = ( Force of thrust of 1st engine + Force of thrust of 2nd engine...and so on... ) / ( ( Force of thrust of 1st engine / I_{sp} of 1st engine ) + ( Force of thrust of 2nd engine / I_{sp} of 2nd engine ) + ...and so on... )
 Example:
 Two engines, one rated 200 newtons and 120 seconds I_{sp}; another engine rated 50 newtons and 200 seconds I_{sp}.
 Isp = (200 newtons + 50 newtons) / ( ( 200 newtons / 120 ) + ( 50 newtons / 200 ) = 130.4347826 seconds I_{sp}
Δv
 For atmospheric Δv value, use atmospheric values.
 For vacuum Δv value, use vacuum values.
 Use this equation to figure out the Δv per stage:
 Equation:
 Simplified:
 Δv = ln ( Mstart / Mdry ) * I_{sp} * g
 Explained:
 Δv = 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_{sp}.
 Δv = ln ( 23 Tons / 15 Tons ) × 120 seconds I_{sp} × 9.81m/s² = Total Δv of 503.0152618 m/s
Maximum Δv
 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.
 Equation:
 Simplified:
 Δv =21.576745349086 * I_{sp}
 Explained / Examples:
 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.
 The following example will use a single stage and fuel tanks in the T100 to Jumbo 64 range with an engine that outputs 380 seconds I_{sp}.
 Δv = ln ( 18 Tons / 2 Tons ) × 380 seconds I_{sp} × 9.81m/s² = Maximum Δv of 8199.1632327878 m/s
 Δv = 2.1972245773 × 380 seconds I_{sp} × 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)
 Δv = 21.576745349086 × 380 seconds I_{sp} = Maximum Δv of 8199.1632327878 m/s (Reduced to its most simple form by combining all the constants)
True Δv
 How to calculate the Δv of a rocket stage that transitions from Kerbin atmosphere to vacuum.
 Assumption: It takes roughly 2500m/s of Δv to escape Kerbin's atmosphere before vacuum Δv values take over for the stage powering the transition (actual value ranges between 2000m/s and 3400m/s depending on ascent). Note that, as of KSP 1.3.1, around 3800m/s of Δv is required to reach an 80km orbit from the KSC.
 Note: This equation is a guess, an 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:
 Simplified:
 True Δv = ( ( Δv atm  2500 ) / Δv atm ) * Δv vac + 2500
 Explained:
 True Δv = ( ( Total Δv in atmosphere  2500 m/s) / Total Δv in atmosphere ) X Total Δv in vacuum + 2500
 Example:
 Single stage with total atmospheric Δv of 5000 m/s, and rated 6000 Δv in vacuum.
 Transitional Δv = ( ( 5000 Δv atm  2500 Δv required to escape Kerbin atmosphere ) / 5000 Δv atm ) X 6000 Δv vac + 2500 Δv required to escape Kerbin atmosphere = Total Δv of 5500 m/s
See also
 Tutorials
 Terminology
 The Drawing Board: A library of tutorials and other useful information