Difference between revisions of "Cheat sheet"

Revision as of 00:09, 25 January 2019

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.

{\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 (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:

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

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.

\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	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.

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

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

http://www.skyrender.net/lp/ksp/system_map.png

Δv change values

http://i.imgur.com/duY2S.png

Δv with Phase Angles

http://i.imgur.com/dXT6r7s.png

Precise Total Δv values

http://i.imgur.com/UUU8yCk.png

WAC's Δv Map for KSP 1.0.4

http://i.imgur.com/q0gC9H7.png

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:

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

Simplified:

I_sp = ( F1 + F2 + ... ) / ( ( F1 / I_sp1 ) + ( F2 / I_sp2 ) + ... )

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 $I_{sp}$ values.
For vacuum Δv value, use vacuum $I_{sp}$ values.
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 ) * 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:

\Delta {v}=21.576745349086\cdot I_{sp}

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:

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

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

@@ Line 69: / Line 69: @@
 | 250 || 5249 || O-10 "Puff" || Monopropellant (max full/empty mass ratio = 8.5)
 |-
-| 290 || 6251 || LV-1R "Spider" <br /> 24-77 "Twitch" ||
+| 290 || 6249 || LV-1R "Spider" <br /> 24-77 "Twitch" ||
 |-
-| 300 || 6466 || KR-1x2 "Twin-Boar" ||
+| 300 || 6464 || KR-1x2 "Twin-Boar" ||
 |-
-| 305 || 6574 || CR-7 R.A.P.I.E.R. <br /> Mk-55 "Thud" ||
+| 305 || 6572 || CR-7 R.A.P.I.E.R. <br /> Mk-55 "Thud" ||
 |-
-| 310 || 6682 || LV-T30 "Reliant" <br /> RE-M3 "Mainsail" ||
+| 310 || 6680 || LV-T30 "Reliant" <br /> RE-M3 "Mainsail" ||
 |-
-| 315 || 6790|| LV-1 "Ant" <br /> KS-25 "Vector" <br /> KS-25x4 "Mammoth" ||
+| 315 || 6787|| LV-1 "Ant" <br /> KS-25 "Vector" <br /> KS-25x4 "Mammoth" ||
 |-
-| 320 || 6898 || 48-7S "Spark" <br /> LV-T45 "Swivel" <br /> RE-I5 "Skipper" ||
+| 320 || 6895 || 48-7S "Spark" <br /> LV-T45 "Swivel" <br /> RE-I5 "Skipper" ||
 |-
-| 340 || 7329 || KR-2L+ "Rhino" <br /> T-1 "Dart" ||
+| 340 || 7326 || KR-2L+ "Rhino" <br /> T-1 "Dart" ||
 |-
-| 345 || 7436 || LV-909 "Terrier" ||
+| 345 || 7434 || LV-909 "Terrier" ||
 |-
-| 350 || 7544 || RE-L10 "Poodle" ||
+| 350 || 7542 || RE-L10 "Poodle" ||
 |-
-| 800 || 17244 || LV-N "Nerv" ||
+| 800 || 17238 || LV-N "Nerv" ||
 |-
-| 4200 || 58803 || IX-6315 "Dawn" || Xenon (max full/empty mass ratio = 4.167)
+| 4200 || 58783 || IX-6315 "Dawn" || Xenon (max full/empty mass ratio = 4.167)
 |}
 (Version: 1.6.1)

Difference between revisions of "Cheat sheet"

Revision as of 00:09, 25 January 2019

Contents

Mathematics

Thrust-to-weight ratio (TWR)

Combined specific impulse (I_sp)

Delta-v (Δv)

Basic calculation

True Δv of a stage that crosses from atmosphere to vacuum

Maps

Maximum Δv chart

Math examples

TWR

I_sp

Δv

Maximum Δv

True Δv

See also

Navigation menu

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Views

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Difference between revisions of "Cheat sheet"

Revision as of 00:09, 25 January 2019

Contents

Mathematics

Thrust-to-weight ratio (TWR)

Combined specific impulse (Isp)

Delta-v (Δv)

Basic calculation

True Δv of a stage that crosses from atmosphere to vacuum

Maps

Maximum Δv chart

Math examples

TWR

Isp

Δv

Maximum Δv

True Δv

See also

Navigation menu

Search

Combined specific impulse (I_sp)

I_sp