Cheat sheet

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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.

Mathematics

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. Note that the local gravitational acceleration, which is usually the surface gravity of the body the rocket is starting from, is required.

${\text{TWR}}={\frac {F_{T}}{m\cdot g}}>1$ Where:
• $F_{T}$ is the thrust of the engines
• $m$ the total mass of the craft
• $g$ the local gravitational acceleration (usually surface gravity)

Combined specific impulse (Isp)

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

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

$\Delta {v}=ln\left({\frac {M_{start}}{M_{end}}}\right)\cdot I_{sp}\cdot 9.81{\frac {m}{s^{2}}}$ Where:
• $\Delta {v}$ is the velocity change possible in m/s
• $M_{start}$ is the starting mass in the same unit as $M_{end}$ • $M_{end}$ is the end mass in the same unit as $M_{start}$ • $I_{sp}$ is the specific impulse of the engine in seconds

True Δv of a stage that crosses from atmosphere to vacuum

Body Δvout
Kerbin 2500 m/s
other bodies' data missing

Calculation of a rocket stage's Δv, taking into account transitioning from atmosphere to vacuum. Δvout 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.

$\Delta {v}_{T}={\frac {\Delta {v}_{atm}-\Delta {v}_{out}}{\Delta {v}_{atm}}}\cdot \Delta {v}_{vac}+\Delta {v}_{out}$ Maps

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

Subway style Δv map (KSP 1.2.1):

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 fuel-tank mass ratio of 9 for all engines except those noted.)
ISP(Vac) (s) Max Δv (m/s) Engines Remarks
250 5249 O-10 "Puff" Monopropellant (max full/empty mass ratio = 8.5)
290 6249 LV-1R "Spider"
24-77 "Twitch"
300 6464 KR-1x2 "Twin-Boar"
305 6572 CR-7 R.A.P.I.E.R.
Mk-55 "Thud"
310 6680 LV-T30 "Reliant"
RE-M3 "Mainsail"
315 6787 LV-1 "Ant"
KS-25 "Vector"
KS-25x4 "Mammoth"
320 6895 48-7S "Spark"
LV-T45 "Swivel"
RE-I5 "Skipper"
340 7326 KR-2L+ "Rhino"
T-1 "Dart"
345 7434 LV-909 "Terrier"
350 7542 RE-L10 "Poodle"
800 17238 LV-N "Nerv"
4200 58783 IX-6315 "Dawn" Xenon (max full/empty mass ratio = 4.167)

(Version: 1.6.1)

Math examples

TWR

• Copy template:
TWR = F / (m * g) > 1

Isp

1. When Isp is the same for all engines in a stage, then the Isp is equal to a single engine. So six 200 Isp engines still yields only 200 Isp.
2. When Isp is different for engines in a single stage, then use the following equation:
• Equation:

$I_{sp}={\frac {(F_{1}+F_{2}+\dots )}{{\frac {F_{1}}{I_{sp1}}}+{\frac {F_{2}}{I_{sp2}}}+\dots }}$ • Simplified:
Isp = ( F1 + F2 + ... ) / ( ( F1 / Isp1 ) + ( F2 / Isp2 ) + ... )
• Explained:
Isp = ( Force of thrust of 1st engine + Force of thrust of 2nd engine...and so on... ) / ( ( Force of thrust of 1st engine / Isp of 1st engine ) + ( Force of thrust of 2nd engine / Isp of 2nd engine ) + ...and so on... )
• Example:
Two engines, one rated 200 newtons and 120 seconds Isp ; another engine rated 50 newtons and 200 seconds Isp.
Isp = (200 newtons + 50 newtons) / ( ( 200 newtons / 120 ) + ( 50 newtons / 200 ) = 130.4347826 seconds Isp

Δv

1. For atmospheric Δv value, use atmospheric $I_{sp}$ values.
2. For vacuum Δv value, use vacuum $I_{sp}$ values.
3. Use this equation to figure out the Δv per stage:
• Equation:

$\Delta {v}=ln\left({\frac {M_{start}}{M_{dry}}}\right)\cdot I_{sp}\cdot 9.81{\frac {m}{s^{2}}}$ • Simplified:
Δv = ln ( Mstart / Mdry ) * Isp * 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 Isp.
Δv = ln ( 23 Tons / 15 Tons ) × 120 seconds Isp × 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:
$\Delta {v}=21.576745349086\cdot I_{sp}$ • Simplified:
Δv =21.576745349086 * Isp
• 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 T-100 to Jumbo 64 range with an engine that outputs 380 seconds Isp.
Δv = ln ( 18 Tons / 2 Tons ) × 380 seconds Isp × 9.81m/s² = Maximum Δv of 8199.1632327878 m/s
Δv = 2.1972245773 × 380 seconds Isp × 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 Isp = Maximum Δv of 8199.1632327878 m/s (Reduced to its most simple form by combining all the constants)

True Δv

1. How to calculate the Δv of a rocket stage that transitions from Kerbin atmosphere to vacuum.
2. Assumption: It takes roughly 2500 m/s of Δv to escape Kerbin's atmosphere before vacuum Δv values take over for the stage powering the transition (actual value ranges between 2000 m/s and 3400 m/s depending on ascent). Note that, as of KSP 1.3.1, around 3800 m/s of Δv is required to reach an 80km orbit from the KSC.
3. 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:

$\Delta {v}_{T}={\frac {\Delta {v}_{atm}-\Delta {v}_{out}}{\Delta {v}_{atm}}}\cdot \Delta {v}_{vac}+\Delta {v}_{out}$ • 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