Cheat sheet
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.
Contents
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.
- is the thrust of the engines
- the total mass of the craft
- the local gravitational acceleration (usually surface gravity)
Combined specific impulse (I_{sp})
- → See also: Specific impulse
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:
Delta-v (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.
- 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 | 2500 m/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 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
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 T-100 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 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.
- 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