Difference between revisions of "Cheat sheet"

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(I made the delta V calculation easier by using Isp in m/s rather than in s. I also removed gravity from the calculation as that gave the incorrect answer. I also added an Isp formula to find Isp in m/s using the data given in game.)
(Undo revision 95557 by Dooby (talk) (Edit had good intentions but using a different definition of I_sp will horribly confuse new users))
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{{See also|Tutorial:Advanced Rocket Design}}
 
{{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.
 
Basic calculation of a rocket's Δv. Use the atmospheric and vacuum thrust values for atmospheric and vacuum Δv, respectively.
{{Formula|math=\Delta{v} = ln\left(\frac{M_{start} }{M_{end} }\right) \cdot I_{sp}|where=* <math>\Delta{v}</math> is the velocity change possible in m/s
+
{{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
 
* <math>M_{start}</math> is the starting mass in the same unit as <math>M_{end}</math>
 
* <math>M_{start}</math> is the starting mass in the same unit as <math>M_{end}</math>
 
* <math>M_{end}</math> is the end mass in the same unit as <math>M_{start}</math>
 
* <math>M_{end}</math> is the end mass in the same unit as <math>M_{start}</math>
* <math>I_{sp}</math> is the specific impulse of the engine in m/s}}
+
* <math>I_{sp}</math> is the specific impulse of the engine in seconds}}
It should be noted that the I<sub>sp</sub> needed for this calculation isn't the same as the I<sub>sp</sub> of engines shown in game after right-clicking on the parts as that value isn't taken from the weight of the fuel but rather the units of fuel.
 
 
 
==== I<sub>sp</sub> calculation ====
 
The I<sub>sp</sub> needed for this calculation can easily be found with:
 
{{Formula|math=I_{sp} = \frac{F_T \cdot U_f}{\dot u \cdot m_f}||where=* <math>F_T</math> is the force of the thrusters in N
 
* <math>U_f</math> is the number of units of fuel in the tanks being used during that stage
 
* <math>\dot u</math> is the rate of fuel consumption of the engines in units/s
 
* <math>m_f</math> is the mass of the fuel being used during that stage in kg (full tank mass - empty tank mass)}}
 
  
 
==== True &Delta;v of a stage that crosses from atmosphere to vacuum ====
 
==== True &Delta;v of a stage that crosses from atmosphere to vacuum ====

Revision as of 22:24, 18 February 2020


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.

Where:
  • is the thrust of the engines
  • the total mass of the craft
  • the local gravitational acceleration (usually surface gravity)

Combined specific impulse (Isp)

→ See also: Specific impulse

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:

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.

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 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.

Maps

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

Subway style Δv map (KSP 1.2.1):

Δv to all bodies in the Kerbol System


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:

  • 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 values.
  2. For vacuum Δv value, use vacuum values.
  3. Use this equation to figure out the Δv per stage:
  • Equation:

  • 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:
  • 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:

  • 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