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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.

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.

\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)

→ 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:

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 Δvout
Kerbin 1000 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:

Δv to all bodies in the Kerbol System


Total Δv values

Δv change values

Δv nomogram

Δv with Phase Angles

Precise Total Δv values

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 ) = 130.89 seconds Isp

Δv

  1. For atmospheric Δv value, use atmospheric thrust values.
  2. For vacuum Δv value, use vacuum thrust 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 503.2 m/s

True Δv

  1. How to calculate the Δv of a rocket stage that transitions from Kerbin atmosphere to vacuum.
  2. Assumption: It takes approximately 1000 m/s of Δv to escape Kerbin's atmosphere before vacuum Δv values take over for the stage powering the transition.
  3. Note: This equation is an guess, 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 - 1000 ) / Δv atm ) * Δv vac + 1000
  • Explained:
True Δv = ( ( Total Δv in atmosphere - 1000 m/s) / Total Δv in atmosphere ) X Total Δv in vacuum + 1000
  • Example:
Single Stage with total atmospheric Δv of 5000 m/s, and rated 6000 Δv in vacuum.
Transitional Δv = ( ( 5000 Δv atm - 1000 Δv Required to escape Kerbin atmosphere ) / 5000 Δv atm ) X 6000 Δv vac + 1000 Δv Required to escape Kerbin atmosphere = Total Δv of 5800 m/s

See also