Cheat Sheet/ru

Шпаргалка (англ. "cheat sheet") ракетного ученого Космической Программы Кербала: карта дельта-v, уравнения и другие ссылки для Вас, так что Вы можете перейти туда и обратно.

Математика

Соотношение тяги к весу (TWR)

→ Смотрите также: Thrust-to-weight ratio/ru

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.

${\text{TWR}}={\frac {F_{T}}{m\cdot g}}>1$

Где:

• $F_{T}$ - тяга двигателей;
• $m$ - общая масса аппарата;
• $g$ - локальное гравитационное ускорение (обычно сила гравитации на поверхности).

Общий удельный импульс (I_sp)

→ Смотрите также: Удельный импульс

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:

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

Дельта-v (Δv)

Основные вычисления

→ Смотрите также: Tutorial:Advanced Rocket Design

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

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

Где:

• $\Delta {v}$ 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

Настоящие Δv ступени, которая движется из атмосферы в вакуум

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. 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.

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

Карты

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

Subway style Δv map:

Total Δv values

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

Δv change values

• http://i.imgur.com/duY2S.png

Δv nomogram

• http://ubuntuone.com/1kD39BCoV38WP1QeG6MtO6

Δv with Phase Angles

• http://i.imgur.com/dXT6r7s.png

Precise Total Δv values

• http://i.imgur.com/UUU8yCk.png

Диаграмма максимальных значений Δv

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.

ISP (s)	Максимум Δv (м/с)	Двигатели
290	6257	LV-1 LV-1R
300	6473	24-77
320	6905	Mark-55
330	7120	Mainsail
350	7552	Skipper 48-7S
360	7768	KS-25X4 KR-1X2
370	7983	LV-T30 LV-T45
380	8199	KR-2L
390	8415	Poodle LV-909 Aerospike
800	17261	LV-N

Математические примеры

TWR

• Copy template:

TWR = F / (m * g) > 1

I_sp

1. 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.
2. 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 ) = 130.89 seconds I_sp

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 ) * 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 503.2 m/s

Максимум 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)

Фактическое значение 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

Обратите внимание

• Руководства;
• Термины и определения;
• Чертежная доска: Библиотека руководств и другой полезной информации.