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Why does the delta v calculation have 9.81 in it?


ineon
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The calculation is 

dv = ln(MStart / MEnd) * ISP * 9.81

But why is that 9.81 in there? I assume that it is the acceleration due to gravity on Kerbin and Earth (or it could just be a 1-in-100 coincidence). Is the calculation different on Jool (or Mars?) where the acceleration due to gravity is completely different?

Is there a reason that the specific impulse isn't just quoted as 9.81 times higher and then we just drop the "* 9.81" from the equation?

Edited by ineon
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Isp is actually quoted in seconds in real life too and the reason for this is again those silly Americans. Basically if the entire world used metric then you would simply quote exhaust velocity in m/s. But since US still like to measure speed in fps (feet per second), and US is kind of big in rocketry it would be useful if we can quote the efficiency of rocket engines in a unit that does not care if you use meters or feet. So people decided to divide the exhaust velocity by standard gravity (9.81m/s2 or 32.2fps2, whichever system you work in it doesn't affect Earth's mass!) and the result is a number with the unit of seconds. And since Americans and rest of the world are in agreement over how long a second is we can then compare engine performance directly without messing with unit conversion.

Divide exhaust velocity by standard gravity gives you specific impulse. The "specific" part refers to the fact that this is specific to Earth's standard gravity. Specific impulse does have a physical interpretation, I believe it's "the number of seconds the engine (assuming massless) can hover over Earth's surface holding up a 1kg weight while being supplied with 1kg of fuel", or alternatively "the number of seconds the engine (assuming massless) can hover over Earth's surface holding up a 1pound weight while being supplied with 1pound of fuel". As you can clearly see with the physical interpretation, your unit of mass is irrelevant, only your engine exhaust velocity makes a difference.

Edited by Temstar
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Great question! :)

No, it's the same everywhere. The number is there because KSP uses Isp numbers that are "normalized" to Kerbin gravity.

The "real" rocket equation doesn't use a "specific impulse" in seconds, it uses exhaust velocity in m/s (i.e. how fast is the exhaust gas going when it comes out of the nozzle.) That's a pretty big number, typically a few km per second. Squad wanted smaller numbers that are easier to relate to, so they divided by Kerbin gravity, which gives a number in units of seconds.

It's not a completely arbitrary thing to do; I believe it's a not uncommon practice by rocket engineers IRL.

Edited by Snark
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17 minutes ago, Snark said:

Great question!

No, it's the same everywhere. The number is there because KSP uses Isp numbers that are "normalized" to Kerbin gravity.

The "real" rocket equation doesn't use a "specific impulse" in seconds, it uses exhaust velocity in m/s (i.e. how fast is the exhaust gas going when it comes out of the nozzle.) That's a pretty big number, typically a few km per second. Squad wanted smaller numbers that are easier to relate to, so they divided by Kerbin gravity, which gives a number in units of seconds.

It's not a completely arbitrary thing to do; I believe it's a not uncommon practice by rocket engineers IRL.

Im not 100% confident, so people are welcome to correct me.

As I understood it, the specific impulse is there for normalization between metric and imperial units. When people used the exhaust velocity back in the day, they used meters per second or feet pers second or pinky fingers per coint toss or ... This lead to confusion. If you multiply it by g in the appropriate unit system, it comes down to the same value.

Don't get me wrong, I don't condone this, it's kinda stupid. Just use exhaust velocity in metric, and everything is fine. You even have a measurable property right there, instead of some arbitrary number! However, it's a historic thing and that's why it stuck around.

 

Here's what wikipedia says about it: https://en.wikipedia.org/wiki/Specific_impulse#Units

Edited by Kobymaru
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13 minutes ago, Dfthu said:

That's the gravity on Kerbin. Its different on other planets,

Hence my question. It is the gravity for Kerbin - why does it appear in the dV equation for when you are on Minmus (or anywhere else)?

Edited by ineon
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50 minutes ago, Dfthu said:

That's the gravity on Kerbin. Its different on other planets,

Gravity is indeed different on other planets.  However, that's completely irrelevant for dV calculations, because the Isp numbers that are listed for KSP engines have units that are normalized to Kerbin gravity.

38 minutes ago, ineon said:

Hence my question. It is the gravity for Kerbin - why does it appear in the dV equation for when you are on Minmus (or anywhere else)?

Because the "9.81" is not there because of local gravity.  It's there because the Isp numbers have been rigged to Kerbin gravity.

The "real" rocket equation looks like this:

dV = ln(Mstart / Mend) * ve

...where ve is the exhaust velocity of the rocket.  The exhaust velocity of a Poodle in vacuum, for example, is 3433.5 m/s.  That exhaust velocity depends only on the engine itself, not on where it is.  A Poodle in vacuum has the same exhaust velocity regardless of whether it's in LKO, or on Minmus, or on Tylo, or anywhere else; local gravity doesn't affect how fast the gas comes out of the rocket nozzle.

You'll notice, though, that if you go to the parts tab in the VAB and look at the Poodle, it doesn't list an exhaust velocity.  It only lists an Isp value in seconds.  Where did they get that number from?  They got it by dividing the exhaust velocity by Kerbin gravity.  3433.5 m/s divided by 9.81 m/s2 gives you 350 seconds.

As to why they report numbers that way:  see the above posts by @Temstar and @Kobymaru.  It's what happens if you let those darn engineers get into the act, instead of physicists;)

 

 

Edited by Snark
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42 minutes ago, ineon said:

Hence my question. It is the gravity for Kerbin - why does it appear in the dV equation for when you are on Minmus (or anywhere else)?

It's there for the purpose of unit conversion for Isp, as mentioned by other posters.

dV is a measure of change in speed and to convert the seconds of Isp to an exhaust velocity, you need to use g of Kerbin/Earth, because that's the g that was used to convert the original exhaust speed into seconds in the first place.

Edit: @Snark beat me with a more detailed explanation.

Edited by Val
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39 minutes ago, Temstar said:

...the reason for this is again those silly Americans.

You're absolutely right, no argument there.  Being more of a physics type than an engineering type, I get frustrated by non-metric numbers whenever they poke their noses into calculations.

However, I'm just gonna go ahead and leave this here, 'coz if I don't, someone else will.  ;)

Spoiler

1d9460cbaf32f1e0cd94dda7ad386a75.jpg

(...at least for a little while longer...)

 

Edited by Snark
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8 hours ago, Snark said:

However, I'm just gonna go ahead and leave this here, 'coz if I don't, someone else will.  ;)

  Reveal hidden contents

1d9460cbaf32f1e0cd94dda7ad386a75.jpg

(...at least for a little while longer...)

 

Countries that have landed on the Moon, in chronological order: Soviet Union, US, China. Two out of three use metric, and the third uses it for their space program now.

Other posters have covered the fact that g0 is used as a constant to convert speed units into time units, and why this is done (Imperial vs Metric). I'd add the reason why g0 was chosen: It's a constant that every engineer and rocket scientist already has memorized.

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Another explanation for strange unit is like this:

Specific impulse = (received impulse)/(propellant mass) = Thrust*(Burn Time)/(propellant mass)=Thrust/(Fuel consumption)

As long as you take thrust in Newtons and fuel consumption in kg/s, as physicists do, you'll end up with meters per second.

But then there are engineers who like expressing thrust in kilograms...

 

And here KSP has quite an inconsistency - listing thrust in kilonewtons (while tons are OK for practical application in TWR calculations), but ISP in seconds (while it needs to be converted to m/s to find delta v)

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