How to calculate Spacecraft Delta-V In Space

[Nendra]

Hey guys, i want to ask. We all probably know how to calculate the Delta-V in Earth . https://wikimedia.org/api/rest_v1/media/math/render/svg/f7b5f1134cca290884b493ab8b676936e0d995b3

But it is for calculating Rocket Or Spacecraft's Delta-V Inside Earth, because the Gravity Standart Is 9.8 m/s'2. But how to calculate when the Rocket or Spacecraft is in Orbit around the earth or Sun Or other Planet (Outside the atmosphere). Please help me on how to calculate that.

 

 

Thanks

[AHHans]

You just keep using the standard 9.81 m/s². This isn't really used because the acceleration happens in Earth's (or Kerbin's) gravity field, but because it was used when defining how I_sp is calculated.

Edited February 8, 2020 by AHHans
formatting

[bewing]

Are you sure you want to calculate it? Or would you be happy enough to just figure it out experimentally? I usually find it's faster just to create a savegame, cheat the craft into a very high orbit, note the orbital velocity, burn every bit of fuel on board, note the new velocity, and subtract. Then restore the savegame.

 

[AHHans]

3 minutes ago, bewing said:

Are you sure you want to calculate it? Or would you be happy enough to just figure it out experimentally? I usually find it's faster just to create a savegame, cheat the craft into a very high orbit, note the orbital velocity, burn every bit of fuel on board, note the new velocity, and subtract

Hmmmm... For me just typing some values into a python shell is faster. (And I often include the stored ore in my fuel calculations, so the built-in dV calculation also doesn't always work.)

[bewing]

OK, OK, I think it's more fun to do it experimentally!

[Neilski]

1 hour ago, AHHans said:

because it was used when defining how I_sp is calculated

Indeed. I have always wondered why Isp isn't simply quoted as a velocity, which would make far more sense to me (and, I would suggest, everyone). At least, if I ever found out the reason, I've since forgotten it!

1 hour ago, bewing said:

I usually find it's faster just to create a savegame, cheat the craft into a very high orbit, note the orbital velocity, burn every bit of fuel on board, note the new velocity, and subtract.

Umm, I must be confused here. Once you've launched and done any staging, the dv calculation in the GUI would surely mean there's no need to actually do the burn. Then again, the same calc in the VAB would mean much the same. So I am pretty certain I'm misunderstanding your point.

Personally I do tend to use a quick calc when the built-in dv calc isn't doing what I need (especially when asteroids are involved, cos the burns can take a veeeerrryyy long time).
If you simply type something like "350*9.81*ln(96/36)" into google, it does it instantly with no faff.

[AHHans]

55 minutes ago, bewing said:

OK, OK, I think it's more fun to do it experimentally!

Well, I can see that. I tend to disagree, but I can see that some people think this is fun.

19 minutes ago, Neilski said:

I have always wondered why Isp isn't simply quoted as a velocity, which would make far more sense to me (and, I would suggest, everyone).

You and me both! It may have something to do with how it is actually measured, but I haven't yet ruled out that this was done in WW2 by the allies to confuse the Germans!

[GluttonyReaper]

1 hour ago, Neilski said:

I have always wondered why Isp isn't simply quoted as a velocity, which would make far more sense to me (and, I would suggest, everyone).

I could be entirely wrong, but I believe it was to do with it being more universal - Isp only has the units of seconds, which has always been accepted as the standard unit of time for everyone. Velocity however would often be quoted in feet/second by one certain country, and in metres/second by everyone else. Not the best reason, but it is what it is.

I totally agree though, velocity is much more convinient measure - it actually gives you a little more info  

[AHHans]

2 hours ago, GluttonyReaper said:

I could be entirely wrong, but I believe it was to do with it being more universal - Isp only has the units of seconds, which has always been accepted as the standard unit of time for everyone. Velocity however would often be quoted in feet/second by one certain country, and in metres/second by everyone else. Not the best reason, but it is what it is.

Na! I stick with the "ploy to confuse Germans" explanation. That make more sense to me!

[bewing]

11 hours ago, Neilski said:

Umm, I must be confused here. Once you've launched and done any staging, the dv calculation in the GUI would surely mean there's no need to actually do the burn. Then again, the same calc in the VAB would mean much the same. So I am pretty certain I'm misunderstanding your point.

That would depend entirely on which version of the game that you are running. Not everyone is running something recent.

[Zhetaan]

On 2/8/2020 at 6:38 AM, Nendra said:

Hey guys, i want to ask. We all probably know how to calculate the Delta-V in Earth . https://wikimedia.org/api/rest_v1/media/math/render/svg/f7b5f1134cca290884b493ab8b676936e0d995b3

But it is for calculating Rocket Or Spacecraft's Delta-V Inside Earth, because the Gravity Standart Is 9.8 m/s'2. But how to calculate when the Rocket or Spacecraft is in Orbit around the earth or Sun Or other Planet (Outside the atmosphere). Please help me on how to calculate that.

Thanks

Others have given the reason, and I have nothing to add to that answer.

On 2/8/2020 at 9:45 AM, Neilski said:

Indeed. I have always wondered why Isp isn't simply quoted as a velocity, which would make far more sense to me (and, I would suggest, everyone). At least, if I ever found out the reason, I've since forgotten it!

I do have something to add to this.  Here's the technical (that means long) explanation:

Spoiler

 

When you derive the rocket equation from first principles with respect to masses and momenta of a rocket moving through free space, you do get a velocity.  That velocity is equal to the rocket nozzle exhaust velocity (approximately, at least, because of variation due to engine design, external pressure, and other factors).  However, there are other ways to consider the nozzle exhaust, and one is in terms of thrust.

Thrust is typically measured in newtons (in SI units, of course), which is also the unit of force.  However, one should note that this was not always so:  in the United States customary system, the avoirdupois pound is used for both mass and force, giving rise to such unlikely units as pounds-mass and pounds-force.  There is a unit of mass called the slug, which is that mass that is accelerated by one foot per second per second by a one-pound force.  Under standard gravity, this mass weighs a bit over 32 pounds.  In terms of practical application, it is almost never used; the convention is to assume that a mass that weighs one pound (pounds-force, in this case) on Earth has one pound-mass of mass.

Comparatively, exhaust velocity is more difficult to measure than thrust.  There is the practical-minded option of licking your finger and sticking your hand in the engine nozzle to see how fast the exhaust is blowing out of it, but that method is plagued by problems:  it's inaccurate, for one thing, and you can only do it twice at most, for another.  Contrariwise, thrust can be measured directly with a strain gauge, or indirectly by other means.

Propellant consumption is also easy to measure:  provided that the propellant can be piped or pumped to the engine, the tanks can be placed on calibrated scales so that their mass is measured.  Given accurate-enough scales and good timekeeping, the amount of propellant consumed over the time of the test burn is also straightforward to measure--especially when the engine is always run at full throttle.

Ultimately, this gives rise to a situation where the rocket engine's thrust is measured against its propellant consumption.  At this point, it is more helpful to give an example:  let's pretend that the LV-909 'Terrier' engine is a real engine and that its KSP performance is the same in reality.  This would, actually, make it a terrible engine, but in KSP, it's one of the most efficient, with a vacuum I_sp of 345 seconds and a thrust of 60 kilonewtons.  Multiplying the I_sp by g₀ (9.80665 m/s²) gives 3383.29 m/s, the exhaust velocity.  Dividing 60,000 newtons by 3383.29 m/s gives 17.734 kg/s, the mass flow rate for the engine.

However, in an actual testing scenario, we wouldn't begin with the I_sp; instead, we'd have only the numbers that are easy to measure:  the mass flow rate of propellant and the thrust of the engine.  Let's assume that these are the only numbers we have to work with.  In U.S. customary units, the thrust is 13,488 lbf. (that's pounds-force) and the propellant mass flow rate is 39.097 lb./s (that's pounds-mass per second).  Divide the thrust by the flow rate to get 344.99 pound-seconds per pound, or 344.99 seconds.  The missing hundredth is a rounding error, so we can call it 345 seconds.

The issues with measurement plague the metric system, too.  Remember also that the newton is part of SI, which was introduced in 1960, and which was not even named as a unit until 1948.  Prior to that, German rocket scientists used the kilogram-force, which has essentially the same relationship to the kilogram-mass as the pound-force to the pound-mass (it still sees limited use:  as a case in point, note that people give their metric weights in kilograms, not newtons).  In other words, the Terrier would be considered under this convention to have 6,118.3 kilograms of thrust and 17.734 kilograms per second of propellant flow.  Dividing 6,118.3 by 17.734 yields 345 kilogram-force seconds per kilogram-mass, which again simplifies to 345 seconds.  (As an aside, please note that if you divide 60,000 N by 17.734 kg/s, then you get 3383.3 m/s, which is the exhaust velocity.  Acknowledgement of thrust as a force independent of weight will yield results that work more intuitively with the rocket equation.)

You would not be wrong to now object to this assumed equivalence of units of mass to units of force:  issues surrounding this confusion are part of the reason why the newton was defined as a unit.  At the same time, the reason that the measurement of specific impulse in seconds includes an otherwise-unnecessary inclusion of a one-gee acceleration should also be apparent:  the distinction between mass and force is that force also includes an acceleration.  When assuming mass-force equivalence with a unit of weight, the acceleration is that due to gravity.  Thus, one will carry the gravitational acceleration factor into any calculation made with that unit.  However, because the assumption of mass-force equivalence is made with units whose difference is in respect to weight on Earth, it is Earth's gravity that becomes the conversion factor.  It has nothing to do with the local gravitational field:  an analogous example is that although the Celsius temperature scale is defined to range from 0 to 100 over the standard-pressure freezing point to the boiling point of water, the temperature value doesn't change when you're measuring a substance other than water.

I admit that I find it interesting to see how that conversion would work with other substances, though:  for example, iron is a liquid from 1,538 to 2,862 degrees Celsius.  If we re-scale that temperature range (1,324 degrees Celsius) to be one hundred units in size and then convert room temperature (20 degrees Celsius) to the new scale, then room-temperature iron is at a temperature of approximately -114.7 iron-Celsius degrees (properly, this should be called something like 'liquid-phase centispans') compared to its melting point.  That is extraordinarily cold relative to iron's melting point, but it has no useful meaning or physical application, because the point of the temperature scale is not to show thermal energy relative to a substance's own intrinsic properties, but rather to show the thermal energy relative to other thermal energies.  This is part of the reason why Kelvin is an objectively better temperature scale for that sort of thing:  zero Kelvin is zero thermal energy (technically, this means that 22.1 iron-kelvin is a marginally more useful temperature than -114.7 iron-Celsius, but it really only tells us that most things are cold compared to molten iron--and even then only because we already know 22.1 kelvin to be extremely cold).  In like kind, avoiding mass-force equivalence is an objectively better way to compare rocket performance, because it avoids many or most of the historical artefacts of a unit's creation that relate to the environmental conditions within which it was originally defined.  Thus, the performance of an engine is compared, not to other gravitational conditions, but to other engines, which is as it should be.

To conclude, the reason that specific impulse is not given in terms of velocity is pragmatic:  it is easier to measure the factors that give rise to seconds.  However, the physicists involved were perhaps too pragmatic and took a shortcut in the calculation that people today would find distastefully cavalier, if not sloppy.

 

 

Edited February 10, 2020 by Zhetaan

[AHHans]

1 hour ago, Zhetaan said:

However, one should note that this was not always so:  in the United States customary system, the avoirdupois pound is used for both mass and force, giving rise to such unlikely units as pounds-mass and pounds-force.

I knew it! It was made to confuse Germans! _SCNR

 

Thanks for the explanation. It's kind of what I had expected.

[pmborg]

On 2/8/2020 at 11:38 AM, Nendra said:

Hey guys, i want to ask. We all probably know how to calculate the Delta-V in Earth . https://wikimedia.org/api/rest_v1/media/math/render/svg/f7b5f1134cca290884b493ab8b676936e0d995b3

But it is for calculating Rocket Or Spacecraft's Delta-V Inside Earth, because the Gravity Standart Is 9.8 m/s'2. But how to calculate when the Rocket or Spacecraft is in Orbit around the earth or Sun Or other Planet (Outside the atmosphere). Please help me on how to calculate that.

 

 

Thanks

Hello ,

Delta-V: Formula is what you wrote on your first comment is correct

Δv = VE * ln(ML / ME)

Where: Δv = Final velocity (Δv) of the rocket in meters per second or feet per second.

VE: Velocity of the rocket's exhaust in meters per second or feet per second.
ML: Total mass of the rocket fully loaded (with payload, propellant, etc).
ME: Empty mass of the rocket at burnout with all propellant expended.

Computing Exhaust Velocity from ISP:
VE = ISP * 9.81 m/sec2 (metric),      =9.81 is standard gravity, not the earth gravity, besides earth gravity is also 9.81!

 

The formula don't exchange in vacuum besides our 9.81 earth g, the only thing that you don't have in vacuum is the atmospheric drag that will slow you down.

What change is the value of ISP in vacuum.

 

nice to meet you

 

 

[RizzoTheRat]

11 hours ago, AHHans said:

I knew it! It was made to confuse Germans! _SCNR

 

Thanks for the explanation. It's kind of what I had expected.

 

Then of course there's the Troy pound, which is traditionally used to measure precious metals and gemstones...and gunpowder so in theory calculating ISP of early SRBs would be even more complicated
 

Spoiler

 

There are 24 grains to the pennyweight, 20 pennyweights to the troy ounce, and 12 troy ounces to the troy pound.

Meanwhile there are 16 avoirdupois ounces in an avoirdupois pound, but while a troy ounce is heavier than an avoirdupois ounce, a troy pound is lighter than an avoirdupois pound.

So a good pub quiz question is "Which is heavier, a pound of feathers or a pound of gold?", as few people will realise that a pound of feathers is about 453g while a pound of gold is about 373g.