User:Operator873/sandbox/KSP

Thrust-to-weight ratio (TWR)
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)
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:

$$I_{sp} = \frac{(F_1 + F_2 + \dots)}{\frac{F_1}{I_{sp1}} + \frac{F_2}{I_{sp2}} + \dots}$$

Basic calculation
Basic calculation of a rocket's &Delta;v. Use the atmospheric and vacuum thrust values for atmospheric and vacuum &Delta;v, 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 &Delta;v of a stage that crosses from atmosphere to vacuum
Calculation of a rocket stage's &Delta;v, taking into account transitioning from atmosphere to vacuum. &Delta;vout is the amount of &Delta;v required to leave a body's atmosphere, not reach orbit. This equation is useful to figure out the actual &Delta;v 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 &Delta;v required to travel to a certain body.

Subway style &Delta;v map (KSP 1.2.1):

Total &Delta;v values &Delta;v change values &Delta;v with Phase Angles Precise Total &Delta;v values WAC's &Delta;v Map for KSP 1.0.4
 * http://www.skyrender.net/lp/ksp/system_map.png
 * http://i.imgur.com/duY2S.png
 * http://i.imgur.com/dXT6r7s.png
 * http://i.imgur.com/UUU8yCk.png
 * http://i.imgur.com/q0gC9H7.png

Maximum &Delta;v 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 &Delta;V without staging to shed mass or using the slingshot maneuver.
 * {| class="wikitable"

! ISP(Vac) (s) !! Max &Delta;v (m/s) !! Engines 24-77 "Twitch" Mk-55 "Thud" RE-M3 "Mainsail" KS-25 "Vector" KS-25x4 "Mammoth" LV-T45 "Swivel" RE-I5 "Skipper" T-1 "Dart" (Version: 1.2.2)
 * 250 || 5394 || O-10 "Puff"
 * 290 || 6257 || LV-1R "Spider"
 * 290 || 6257 || LV-1R "Spider"
 * 290 || 6257 || LV-1R "Spider"
 * 300 || 6473 || KR-1x2 "Twin-Boar"
 * 305 || 6581 || CR-7 R.A.P.I.E.R.
 * 305 || 6581 || CR-7 R.A.P.I.E.R.
 * 305 || 6581 || CR-7 R.A.P.I.E.R.
 * 310 || 6689 || LV-T30 "Reliant"
 * 310 || 6689 || LV-T30 "Reliant"
 * 315 || 6797|| LV-1 "Ant"
 * 315 || 6797|| LV-1 "Ant"
 * 320 || 6905 || 48-7S "Spark"
 * 320 || 6905 || 48-7S "Spark"
 * 340 || 7336 || KR-2L+ "Rhino"
 * 340 || 7336 || KR-2L+ "Rhino"
 * 345 || 7444 || LV-909 "Terrier"
 * 350 || 7552 || RE-L10 "Poodle"
 * 800 || 21837 || LV-N "Nerv"
 * 4200 || 33751 || IX-6315 "Dawn"
 * }
 * 800 || 21837 || LV-N "Nerv"
 * 4200 || 33751 || IX-6315 "Dawn"
 * }
 * }

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:

$$I_{sp} = \frac{(F_1 + F_2 + \dots)}{\frac{F_1}{I_{sp1}} + \frac{F_2}{I_{sp2}} + \dots}$$
 * 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

&Delta;v

 * 1) For atmospheric &Delta;v value, use atmospheric $$I_{sp}$$ values.
 * 2) For vacuum &Delta;v value, use vacuum $$I_{sp}$$ values.
 * 3) Use this equation to figure out the &Delta;v per stage:

$$\Delta{v} = ln\left(\frac{M_{start}}{M_{dry}}\right) \cdot I_{sp} \cdot 9.81 \frac{m}{s^2}$$
 * Equation:


 * Simplified:
 * &Delta;v = ln ( Mstart / Mdry ) * Isp * g


 * Explained:
 * &Delta;v = 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.
 * &Delta;v = ln ( 23 Tons / 15 Tons ) × 120 seconds Isp × 9.81m/s² = Total &Delta;v of 503.0152618 m/s

Maximum &Delta;v

 * Simplified version of the &Delta;v calculation to find the maximum &Delta;v 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:
 * &Delta;v =21.576745349086 * Isp


 * Explained / Examples:
 * This calculation only uses the mass of the fuel tanks and so the ln ( Mstart / Mdry ) part of the &Delta;v 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.
 * &Delta;v = ln ( 18 Tons / 2 Tons ) × 380 seconds Isp × 9.81m/s² = Maximum &Delta;v of 8199.1632327878 m/s
 * &Delta;v = 2.1972245773 × 380 seconds Isp × 9.82m/s² = Maximum &Delta;v 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)
 * &Delta;v = 21.576745349086 × 380 seconds Isp = Maximum &Delta;v of 8199.1632327878 m/s (Reduced to its most simple form by combining all the constants)

True &Delta;v

 * 1) How to calculate the &Delta;v of a rocket stage that transitions from Kerbin atmosphere to vacuum.
 * 2) Assumption: It takes approximately 1000 m/s of &Delta;v to escape Kerbin's atmosphere before vacuum &Delta;v 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."

$$\Delta{v}_T = \frac{\Delta{v}_{atm} - \Delta{v}_{out}}{\Delta{v}_{atm}} \cdot \Delta{v}_{vac} + \Delta{v}_{out}$$
 * Equation for Kerbin atmospheric escape:


 * Simplified:
 * True &Delta;v = ( ( &Delta;v atm - 1000 ) / &Delta;v atm ) * &Delta;v vac + 1000


 * Explained:
 * True &Delta;v = ( ( Total &Delta;v in atmosphere - 1000 m/s) / Total &Delta;v in atmosphere ) X Total &Delta;v in vacuum + 1000


 * Example:
 * Single stage with total atmospheric &Delta;v of 5000 m/s, and rated 6000 &Delta;v in vacuum.
 * Transitional &Delta;v = ( ( 5000 &Delta;v atm - 1000 &Delta;v required to escape Kerbin atmosphere ) / 5000 &Delta;v atm ) X 6000 &Delta;v vac + 1000 &Delta;v required to escape Kerbin atmosphere = Total &Delta;v of 5800 m/s