Kerbal Space Delta V Map How to Read

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Kerbal Space Program rocket scientist's cheat sheet: Delta-5 maps, equations and more than for your reference so you can become from here to at that place and back again.

Contents

• 1 Mathematics
  • 1.1 Thrust-to-weight ratio (TWR)
  • one.2 Specific Impulse (I_sp)
  • 1.3 Delta-five (Δv)
    • i.iii.one Basic adding
    • 1.3.ii True Δv of a stage that crosses from atmosphere to vacuum
    • 1.3.3 Maps
    • 1.3.4 Maximum Δv nautical chart
• 2 Math examples
  • two.1 TWR
  • 2.ii I_sp
  • 2.3 Δv
  • 2.4 Maximum Δv
  • ii.5 Truthful Δv
• 3 Run into besides

Mathematics

Thrust-to-weight ratio (TWR)

→ Meet also: Thrust-to-weight ratio

How hard exercise your engines button UP? That's "thrust".

How difficult does gravity pull Downward? That's "weight".

The ratio of those two is, surprisingly, the "thrust-to-weight" 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 "thrust-to-weight" ratio, or TWR, in a nutshell.

${\displaystyle {\text{TWR}}={\frac {F_{T}}{m\cdot g}}>ane}$

If TWR is less than one, and then your rocket will non exist going into space. You will need more engines, or maybe MOAR BOOSTERZ!

If TWR is significantly to a higher place, say, 2.0, your rocket will ZOOM! Simply it might ZOOM likewise hard for your poor Kerbalnauts. Most rockets, direct off the launch pad, will use a TWR between 1.5 and ii.0.

Specific Impulse (I_sp)

→ Run across too: Specific impulse

Specific impulse measures the efficiency of a detail engine. Because this depends on the force per unit area of a rocket's surroundings, this can change between Body of water Level and Vacuum (in space). Almost engines are designed for optimal operation either at Sea Level (the big ones that drive your first stage and boosters, which take lots of thrust!) or Vacuum (where they won't burn down equally much propellant, but tin be VERY efficient).

Specific impulse is used in of import equations like THE ROCKET EQUATION (see next department) to determine how much oomph (or "delta-vee") you can get out of a given amount of propellant. The college the specific impulse, the more than efficient an engine is!

In real life, specific impulse is governed past things similar combustion chamber force per unit area and propellant free energy (hydrogen/oxygen is more efficient than kerosene/oxgyen). Fortunately for Jebediah, our honey Kerbals only accept one make of fuel to worry nigh.

Delta-v (Δv)

Bones calculation

→ Come across also: Tutorial:Advanced Rocket Blueprint

Basic calculation of a rocket'due south Δv. Use the atmospheric and vacuum thrust values for atmospheric and vacuum Δv, respectively.

${\displaystyle \Delta {v}=ln\left({\frac {M_{starting time}}{M_{cease}}}\right)\cdot I_{sp}\cdot 9.81{\frac {thou}{s^{2}}}}$

True Δv of a stage that crosses from temper to vacuum

Torso	Δvout
Kerbin	2500 m/south
other bodies' data missing

Calculation of a rocket stage'due south Δv, taking into account transitioning from atmosphere to vacuum. Δv_out is the amount of Δv required to leave a body'southward atmosphere, non attain orbit. This equation is useful to figure out the bodily Δv of a stage that transitions from temper to vacuum.

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

Maps

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

KSP Visual Calculator, online tool that determines delta-five required for multiple checkpoint missions

• https://ksp-visual-figurer.blaarkies.com

Subway mode Δv map (KSP i.ii.one):

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'southward Δv Map for KSP 1.0.4

• http://i.imgur.com/q0gC9H7.png

Maximum Δv chart

This nautical chart is a quick guide to what engine to utilise for a unmarried stage interplanetary send. No affair how much fuel yous add you volition 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/south)	Engines	Remarks
250	5249	O-ten "Puff"	Monopropellant (max total/empty mass ratio = viii.five)
290	6249	LV-1R "Spider" 24-77 "Twitch"
300	6464	KR-1x2 "Twin-Boar"
305	6572	CR-seven R.A.P.I.Eastward.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-North "Nerv"
4200	58783	Ix-6315 "Dawn"	Xenon (max full/empty mass ratio = 4.167)

(Version: 1.6.i)

Math examples

TWR

• Copy template:

TWR = F / (one thousand * g) > 1

I_sp

1. When I_sp is the aforementioned for all engines in a stage, then the I_sp is equal to a single engine. And then half dozen 200 I_sp engines yet yields simply 200 I_sp.
2. When I_sp is different for engines in a single stage, and then utilise the following equation:

• Equation:

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

• Simplified:

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

• Explained:

I_sp = ( Force of thrust of 1st engine + Force of thrust of 2d engine...and then 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... )

• Case:

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

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

• Equation:

${\displaystyle \Delta {v}=ln\left({\frac {M_{start}}{M_{dry out}}}\right)\cdot I_{sp}\cdot nine.81{\frac {m}{south^{two}}}}$

• Simplified:

Δv = ln ( Mstart / Mdry ) * I_sp * chiliad

• Explained:

Δv = ln ( starting mass / dry mass ) Ten Internet access provider X 9.81

• Instance:

Single phase 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 × nine.81m/s² = Total Δv of 503.0152618 m/s

Maximum Δv

Simplified version of the Δv calculation to find the maximum Δv a arts and crafts with the given ISP could hope to reach. This is done by using a magic 0 mass engine and not having a payload.

• Equation:

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

• Simplified:

Δv =21.576745349086 * I_sp

• Explained / Examples:

This calculation only uses the mass of the fuel tanks and and then the ln ( Mstart / Mdry ) office of the Δv equation has been replaced by a constant as Mstart / Mdry is ever ix (or worse with some fuel tanks) regardless of how many fuel tanks you utilise.

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 × ix.81m/s² = Maximum Δv of 8199.1632327878 m/s

Δv = 2.1972245773 × 380 seconds I_sp × ix.82m/s² = Maximum Δv of 8199.1632327878 m/southward (Replaced the log of mass with a abiding every bit the ratio of total mass to dry out mass is constant regardless of the number of tanks used every bit there is no other mass involved)

Δv = 21.576745349086 × 380 seconds I_sp = Maximum Δv of 8199.1632327878 one thousand/s (Reduced to its well-nigh simple class by combining all the constants)

Truthful Δv

1. How to summate the Δv of a rocket stage that transitions from Kerbin atmosphere to vacuum.
2. Assumption: Information technology takes roughly 2500 thousand/south of Δv to escape Kerbin'southward atmosphere before vacuum Δv values take over for the stage powering the transition (actual value ranges between 2000 thousand/s and 3400 m/s depending on ascent). Note that, as of KSP 1.iii.1, effectually 3800 1000/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 authentic."

• Equation for Kerbin atmospheric escape:

${\displaystyle \Delta {5}_{T}={\frac {\Delta {v}_{atm}-\Delta {v}_{out}}{\Delta {v}_{atm}}}\cdot \Delta {v}_{vac}+\Delta {five}_{out}}$

• Simplified:

Truthful Δv = ( ( Δv atm - 2500 ) / Δv atm ) * Δv vac + 2500

• Explained:

True Δv = ( ( Total Δv in atmosphere - 2500 1000/s) / Total Δv in temper ) X Total Δv in vacuum + 2500

• Example:

Single phase with total atmospheric Δv of 5000 one thousand/due south, 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 Lath: A library of tutorials and other useful information

bergspectlemeded1971.blogspot.com

Source: https://wiki.kerbalspaceprogram.com/wiki/Cheat_sheet

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