Difference between revisions of "Specific impulse/ru"

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(Формула)
(Пример)
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For example liquid fuel engines have the fuel components are [[oxidizer]] and [[liquid fuel]]. When using one [[Rockomax "Mainsail" Liquid Engine]] on the [[launch pad]] at full throttle uses 48.96 units of liquid fuel and 59.84 units of oxidizer with an weight specific impulse of 280.8 seconds and a thrust of 1.5 MN. This gives a conversion factor between 9.81873052&nbsp;m/s and 9.8205356&nbsp;m/s, assuming that the density of liquid fuel and oxidizer is 5&nbsp;kg per unit. By reducing the engine's weight specific impulse it is possible to get higher mass flow rates improving the conversion factor to a value between 9.81994836&nbsp;m/s and 9.82006181&nbsp;m/s by using a thrust of only 85&nbsp;kN and a weight specific impulse of 1 second for all pressures.<ref>Values determined from [[:File:Isp conversion factor.png]].</ref> The value isn't exact, because the exact mass flows aren't known. It can be assumed that the conversion factor is about 9.82&nbsp;m/s² making the engines a bit more efficient than expected.<ref>In [[:File:10X Xenon.png]] 10 [[PB-ION Electric Propulsion System]]s are running at full power and consuming a lower value that 10× the theoretical value calculated with 9.81 m/s².</ref>
 
For example liquid fuel engines have the fuel components are [[oxidizer]] and [[liquid fuel]]. When using one [[Rockomax "Mainsail" Liquid Engine]] on the [[launch pad]] at full throttle uses 48.96 units of liquid fuel and 59.84 units of oxidizer with an weight specific impulse of 280.8 seconds and a thrust of 1.5 MN. This gives a conversion factor between 9.81873052&nbsp;m/s and 9.8205356&nbsp;m/s, assuming that the density of liquid fuel and oxidizer is 5&nbsp;kg per unit. By reducing the engine's weight specific impulse it is possible to get higher mass flow rates improving the conversion factor to a value between 9.81994836&nbsp;m/s and 9.82006181&nbsp;m/s by using a thrust of only 85&nbsp;kN and a weight specific impulse of 1 second for all pressures.<ref>Values determined from [[:File:Isp conversion factor.png]].</ref> The value isn't exact, because the exact mass flows aren't known. It can be assumed that the conversion factor is about 9.82&nbsp;m/s² making the engines a bit more efficient than expected.<ref>In [[:File:10X Xenon.png]] 10 [[PB-ION Electric Propulsion System]]s are running at full power and consuming a lower value that 10× the theoretical value calculated with 9.81 m/s².</ref>
 
== Пример ==
 
== Пример ==
The [[Kerbal X]] has six [[LV-T45 Liquid Fuel Engine]]s with a specific impulse of 320 s in atmosphere and one [[Rockomax "Mainsail" Liquid Engine]] with a specific impulse of 280 s. The average specific impulse of all engines is then:
+
У [[Kerbal X/ru|"Kerbal X"]] есть 6 [[LV-T45 Liquid Fuel Engine/ru|ЖРД "LV-T45"]] с удельным импульсом в 320 с. в атмосфере и 1 [[Rockomax "Mainsail" Liquid Engine/ru|ЖРД "Грот"]] с удельным импульсом в 280 с. Средний удельный импульс всех двигателей составляет:
 
:<math>I_{sp} = \frac{6 \cdot 200 \text{kN} + 1500 \text{kN}}{6 \cdot \frac{200 \text{kN}}{320 \text{s}} + \frac{1500 \text{kN}}{280 \text{s}}} = 296.47 \text{s}</math>
 
:<math>I_{sp} = \frac{6 \cdot 200 \text{kN} + 1500 \text{kN}}{6 \cdot \frac{200 \text{kN}}{320 \text{s}} + \frac{1500 \text{kN}}{280 \text{s}}} = 296.47 \text{s}</math>
To convert this value into a physical usable value. Note that the conversion factor used here is the KSP relevant value of 9.82&nbsp;m/and not the 9.81&nbsp;m/used in real world science.
+
Преобразуем это значение в физически понятную величину. Note that the conversion factor used here is the KSP relevant value of 9.82&nbsp;м/с² and not the 9.81&nbsp;м/с² used in real world science.
 
:<math>I_{sp} = g_{I_{sp}} \cdot 296.47 \text{s} = 2911.34 \frac{\text{m}}{\text{s}}</math>
 
:<math>I_{sp} = g_{I_{sp}} \cdot 296.47 \text{s} = 2911.34 \frac{\text{m}}{\text{s}}</math>
 
This value can then be used to calculate the fuel consumption:
 
This value can then be used to calculate the fuel consumption:

Revision as of 07:27, 16 September 2014

Удельный импульс (англ. "specific impulse") определяет эффективность двигателя. Он связан с тягой и расходом топлива. Его единицы измерения это либо метры в секунду, либо просто секунды.

Формула

Где:
  • - это удельный импульс в метрах в секунду;
  • - тяга в Ньютонах;
  • - расход топлива в кг/с

Пи перемножении этого значения с g0 можно изменить единицы измерения исключительно на секунды, избегая проблем преобразования между единицами СИ и обычными единицами измерения. Значение g0 ведет себя в качестве коэффициента преобразования и не изменяется, при изменении силы тяжести для космического аппарата. Обычно оба значения называют удельным импульсом и обозначают Isp. Названия Isp, g0 используются здесь только для того, чтобы разъяснить, что оба значения - это не одно и то же. Это значение иногда вызывают весовым удельным импульсом.

Где:
  • - это удельный импульс в секундах;
  • - это гравитация на поверхности в требуемых единицах измерения (обычно 9.81 м/с2<sup />).</div>

Для формулы, использующей это (например, для Δv) нужно определить, в каких единицах измерения это действительно ожидается, и, если значение указано в других, тогда необходимо преобразование.

Несколько двигателей

Где:
  • - это удельный импульс в м/с;
  • - это удельный импульс каждого двигателя в м/с;
  • - это тяга каждого двигателя в Ньютонах;
  • - это расход топлива в кг/с.

Когда расход топлива в этой формуле не используется, тогда важно только, чтобы у всех значений тяги были одинаковые единицы измерения (например килоНьютоны), и у удельных импульсов - также одинаковые единицы измерения (например секунды). Тогда результат будет получен в тех же единицах измерения, что и удельные импульсы двигателей. Если у всех двигателей будет одинаковый удельный импульс, то получившийся удельный импульс будет таким же.

Влияние физических законов

In KSP the fuel consumption on most engines depend on the atmospheric pressure with the lowest consumption in vacuum. So the specific impulse is at the highest point in the vacuum. In the real world this is usually reversed: The fuel consumption stays always the same but the thrust is increasing over time, because it is easier to have a steady fuel flow. Because a higher thrust with the same fuel consumption it is more efficient the specific impulse also rises. The specific impulse can only be calculated using this method for reaction engines and not jet engines as those work on another principle.

Although the unit of the specific impulse is a velocity it is lower than the exhaust speed usually, because some of the fuel consumed isn't used for propelling directly, but runs the turbopumps to fuel the engine.

Коэффициент преобразования

To convert the specific impulse between the handy weight specific impulse and the physical usable specific impulse it had to be converted with g0. It appears that this value isn't 9.81 m/s² which is used in real world. To determine the factor the following formula can be used:

Где:
  • is the thrust of the engine
  • is the mass flow of the fuel components
  • is the density of the fuel components
  • is the weight specific impulse

For example liquid fuel engines have the fuel components are oxidizer and liquid fuel. When using one Rockomax "Mainsail" Liquid Engine on the launch pad at full throttle uses 48.96 units of liquid fuel and 59.84 units of oxidizer with an weight specific impulse of 280.8 seconds and a thrust of 1.5 MN. This gives a conversion factor between 9.81873052 m/s and 9.8205356 m/s, assuming that the density of liquid fuel and oxidizer is 5 kg per unit. By reducing the engine's weight specific impulse it is possible to get higher mass flow rates improving the conversion factor to a value between 9.81994836 m/s and 9.82006181 m/s by using a thrust of only 85 kN and a weight specific impulse of 1 second for all pressures.[1] The value isn't exact, because the exact mass flows aren't known. It can be assumed that the conversion factor is about 9.82 m/s² making the engines a bit more efficient than expected.[2]

Пример

У "Kerbal X" есть 6 ЖРД "LV-T45" с удельным импульсом в 320 с. в атмосфере и 1 ЖРД "Грот" с удельным импульсом в 280 с. Средний удельный импульс всех двигателей составляет:

Преобразуем это значение в физически понятную величину. Note that the conversion factor used here is the KSP relevant value of 9.82 м/с² and not the 9.81 м/с² used in real world science.

This value can then be used to calculate the fuel consumption:

Because the engines use liquid fuel and oxidizer with a density of 5000 kg/m³ it is possible to calculate the volume consumed.

Of course this values of the craft are valid for Kerbin's atmosphere. Because the air gets thinner with altitude the efficiency is rising and the fuel consumption is falling. Also because of the staging pattern engines will be dropped until reaching vacuum and thus changing the efficiency again. This time the efficiency lowers, because the higher efficient engines drop first leaving only the Mainsail engine with the lowest efficiency of all engines on the craft.

Обратите внимание

Примечания

  1. Values determined from File:Isp conversion factor.png.
  2. In File:10X Xenon.png 10 PB-ION Electric Propulsion Systems are running at full power and consuming a lower value that 10× the theoretical value calculated with 9.81 m/s².