Atmospheric drag

[Ydoow]

Is the equation for atmospheric drag mentioned anywhere?

[Iskierka]

That is going to depend what aspect of drag you want; what are you trying to do?

[Ydoow]

Oh I just wanted to be able to replicate drag forces graphically. To help find the 'optimal speed' I should shoot for.

I know it changes as you go up, and depends on your ship too.

[Iskierka]

That, unfortunately, can\'t be provided. Optimal airspeed relies on how much lift is being produced, and we don\'t have knowledge of how lift affects drag.

Added to that, lift is fundamentally broken. (it\'s proportional to v, which I\'ve pointed out in the development topic about aerodynamics.) I -think-, with this factor, even ignoring the control surface bugs, the most efficient speed is 'as slow as possible.'

Yeah, not a great answer, unfortunately. If aerodynamics had something that could be considered more than a passing resemblance to what the real world sees, I\'d be happy to help with the theory of cruising flight. (For that matter, I\'d be happy to help Harv sort out how to make it so things match the basic theory, but I don\'t think he\'s currently interested in looking at the aerodynamics.)

[Ydoow]

That\'s unfortunate. So I couldn\'t generally predict it even ignoring lift?

I think he is interested in revising aerodynamics though, or at least is looking into it shortly

[Iskierka]

It would be possible to predict it, but calculating ideals for aircraft is rendered effectively impossible for the current game.

However, while it won\'t work for winglets, which have variable drag, I can give an equation which works with the [tt]maximum_drag[/tt] cfg setting, which is the following:

D = ? * v^2 * m * [tt]maximum_drag[/tt]

Yes, m is a parameter in the drag equation, which I suspect is a bug.

[Ydoow]

m as in mass? Wouldn\'t surface area make more sense?

[Iskierka]

m as in mass, yes. And while the standard drag equation for IRL involves surface area, [tt]maximum_drag[/tt] is intended to represent Cd*A, taking both those parameters out of the equation.

I say intended to, as it\'s actually Cd*A/m, which is where the stray mass term comes from.

[Ydoow]

Aaaah, I see.

So either maximum_drag should include mass, or the equation used in game should be dividing by mass

[closette]

I\'m confused - does the current model include an incorrect dependence of air drag on the part\'s current mass (assuming that\'s what 'm' is, which can change as fuel is used up).

Or is mass correctly canceled out when multiplying the factors together to calculate the force D?

[Hypocee]

The first - Iskierka\'s researched and proven there\'s an erroneous mass term. You can verify it by dropping, say, a full and a burned SRB side-by-side. They behave the same.

[closette]

Thank you, and the test you suggest is definitive proof. I\'m not sure how to do it but I think I can come up with a way.

It\'s going to be interesting when the drag model is improved - we\'ve all been building ships in the current scheme, and they may not work so well with a more accurate model. That could be quite a drastic change compared to previous version updates - just fine by me though since it will make predicting the drag effects easier when designing.

[Guest GroundHOG-2010]

Thank you, and the test you suggest is definitive proof. I\'m not sure how to do it but I think I can come up with a way.

It\'s going to be interesting when the drag model is improved - we\'ve all been building ships in the current scheme, and they may not work so well with a more accurate model. That could be quite a drastic change compared to previous version updates - just fine by me though since it will make predicting the drag effects easier when designing.

I can\'t wait to see everyone elses designs fail.

[closette]

Everyone else\'s? Are your designs immune from aerodynamic drag?

By the way, on another thread, user Kosmo-not took free-fall velocity data to find that the Kerbal atmosphere has an exponential dependence with altitude between 200 and 40 000m, with a scale height of about 4900m. (The absolute value of density depends on the units that 'mass' and 'thrust' are given in).

Link: http://kerbalspaceprogram.com/forum/index.php?topic=5813.msg86098#msg86098 and comments below.

[Guest GroundHOG-2010]

Everyone else\'s? Are your designs immune from aerodynamic drag?

By the way, on another thread, user Kosmo-not took free-fall velocity data to find that the Kerbal atmosphere has an exponential dependence with altitude between 200 and 40 000m, with a scale height of about 4900m. (The absolute value of density depends on the units that 'mass' and 'thrust' are given in).

Link: http://kerbalspaceprogram.com/forum/index.php?topic=5813.msg86098#msg86098 and comments below.

No, every new version I wipe my saves. Also some people use the same design over and over again, while most of my designs are different to each other.

[Iskierka]

Kerbin\'s atmosphere follows said exponential curve from surface to edge, and as I recall HarvesteR stated the scale height was 5 km, though I do also recall a more recent comment that might have changed the scale slightly (4.75 km comes to mind).

Quite a bit of this data has had developer confirmation long ago, though it\'s fun to see the experiments people come up with to determine them.

[closette]

All I could find from a message board search was this from Harv last July: http://kerbalspaceprogram.com/forum/index.php?topic=471.msg4000#msg4000

I don\'t think 4750 m fits the data that Kosmo-not provided, I can get the fitted curve to work as low as 4830 m, but it would be safe to say the scale height is 4900 +/-100 m for the range 200 to 40 000 m.

For a simple isothermal model one could use this to guess the molecular weight of Kerbin\'s atmosphere! (See http://en.wikipedia.org/wiki/Atmospheric_models#Isothermal-barotropic_approximation_and_scale_height). My guess is that it has a high concentration of SF₆ or SeF₆ in place of our Nitrogen component.

And depending on the drag model and mass/thrust units used on the program (say either kg and N or tonnes and kN), the surface density is close to either 0.01 kg/m³ or 10 kg/m³, compared to Earth\'s ~ 1.1 kg/m³. From the presence of grass and liquid water on the planet, I would speculate it\'s closer to 10 (which also matches the densities and masses of things like parachute pods and SRBs compared to real-world values).

[thorfinn]

For a simple isothermal model one could use this to guess the molecular weight of Kerbin\'s atmosphere! (See http://en.wikipedia.org/wiki/Atmospheric_models#Isothermal-barotropic_approximation_and_scale_height). My guess is that it has a high concentration of SF₆ or SeF₆ in place of our Nitrogen component.

I was looking for a way for introducing SF₆ in the 'story' too, you know? And the purpose is not only 'explaining' the high drag that we encounter now with the provisional aero model; I\'d like a good excuse for lowering the speed of sound a bit^(*), since 340 m/s is a LOT on Kerbin. A high concentration of gases with heavy molecular weight would do just that...

(*) I know, it\'s not significant yet. But when it will be, having Mach 1 'scaled' like everything in KSP would be nice, and give more depth for aero designs. Something like 240 m/s on the deck, 210 m/s in the stratosphere? ...

[Iskierka]

SF6 wouldn\'t give nearly those values of a (= speed of sound), but a reduced mach 1 would be a good idea for gameplay. a in pure SF6 is less than 150 m/s.

As for atmospheric scale, an open search of all forums for 'scale height' by HarvesteR turned up this very early post:

KSP uses an exponential decay for atmospheric density, with a scale height of 6.8 (Earth is 7.0). So the curve is a little different than that of earth, but the decay is similar.

That said, the calculations for that (and how that translates to drag) are not 100% yet. It\'s another of the thousand things that still have to be worked on

Cheers

It seems I was correct that the scale height had been reduced when the atmosphere was extended to 69 km, but it had been changed to 5 km, from 6.8 km. 5 km is consistent with what has been stated in other official posts and close to consistent with the data gathered in the other thread, which definitely has the potential to have slight errors.

[closette]

I hadn\'t pondered the implications of the speed of sound, that\'s another great way to compare the mass units we are using with distance units (assuming that 1 Kerbal meter = 1 metric meter).

First, let\'s not quibble but Kosmo-not\'s data in the other thread show that the scale height of the Kerbal atmosphere is definitely less than 5km, but not by much. I find it closer to 4.85km between 0 and 35000 m. I can\'t think of any systematic errors which would throw off this estimate of scale height and yet still allow me to fit an exponential atmosphere model so closely. But I could be wrong, and don\'t have the nice software I used to have to calculate a +/- on that scale height easily, so if it\'s 4.85 +/- 0.15 km we\'ll both be right!

Second, the sea-level densities I provided above apparently had an extraneous factor of 2. Assuming that Harv\'s drag model already includes that factor (which I saw on an old thread it does), the 'correct' sea-level density for Kerbin\'s atmosphere is about 0.0051 Kerbal Mass Units per meter³, where the command module has a mass of 1 Kerbal Mass Unit.

If as I suspect (based on old discussions about Kerbal fuel densities compared to Earth\'s), 1 Kerbal Mass Unit = 1000 kg, that means their sea-level atmospheric density is 5.1 kg/m³.

That\'s what one would expect for SF₆!!! (Molecular mass 146 as opposed to 29 for air).

The speed of sound in a gas (see the Wikipedia article) is given by sqrt (gamma * Pressure / density), where gamma is that pesky ratio of specific heats.

Since gamma = 1.04 for SF₆ and 1.4 for air, that would make the sea-level sound speed at standard temperature and pressure equal to... wait for it... 340 m/s * sqrt(1.04/1.4 * 29/146) = 131 m/s.

Is that low enough for ya? It\'s not much greater than the terminal speed of a falling object in the current model. Of course I think it\'s likely that we\'re over-interpreting the Kerbin model here - a model which will evolve in time and may not be self-consistent, but the data is what it is, and physics is physics on any world.

[thorfinn]

Is that low enough for ya? It\'s not much greater than the terminal speed of a falling object in the current model. Of course I think it\'s likely that we\'re over-interpreting the Kerbin model here - a model which will evolve in time and may not be self-consistent, but the data is what it is, and physics is physics on any world.

More than likely. But the most interesting thing about KSP is how it makes you learn physics (or refresh, in my case) without even realizing sometimes

Anyway, our green friends will need something less inert than SF₆ to breathe, so we can assume that their atmosphere is not 100% hexafluoride And if we start thinking too hard about it, we realize that sulphur hexafluoride is the most potent greenhouse gas known on Earth, so we have either to accept that the star is extremely dim (and the other planets prabbly frozen?) or find some other excuse for Kerbin NOT being a Venus analogue...

[closette]

Very true, thorfinn, and don\'t forget the grass that needs to grow! I\'d also love for a biologist to weigh in on the cellular-level energetics of the Kerbals. (Although we only see them bopping around in their seats, someone must have constructed the launch complex).

A lot hinges on the conversion between Kerbal mass units and kilograms, which gives plenty of room for a mixed atmosphere and a slightly higher sound speed if you want it. It could be that 1 Kerbal Mass Unit (or command module mass) = 500 kg for instance, not 1000 kg as I assumed above.

As for a strong greenhouse effect, we want it! Using properties given on the KSP wiki, an M class star like Kerbol (a bit less massive than Proxima Centauri) has a tiny habitable zone at around 0.03 A.U. from the star, whereas Kerbin orbits at 0.09 A.U. See image attached.

As to why Kerbin\'s day is not tidally locked to its year, that\'s another can of worms!

It\'s incredibly difficult to come up with a self-consistent world limited by 'playability', and all these considerations convince me even more that KSP is a work of pure genius. The fact that we can even have meaningful conversations about the physics is testament to that.

[Iskierka]

I hadn\'t pondered the implications of the speed of sound, that\'s another great way to compare the mass units we are using with distance units (assuming that 1 Kerbal meter = 1 metric meter).

First, let\'s not quibble but Kosmo-not\'s data in the other thread show that the scale height of the Kerbal atmosphere is definitely less than 5km, but not by much. I find it closer to 4.85km between 0 and 35000 m. I can\'t think of any systematic errors which would throw off this estimate of scale height and yet still allow me to fit an exponential atmosphere model so closely. But I could be wrong, and don\'t have the nice software I used to have to calculate a +/- on that scale height easily, so if it\'s 4.85 +/- 0.15 km we\'ll both be right!

One main factor I\'d suggest as a possible source of error is the altimeter. Its behaviour is rather strange - both lagging and predictive. Jumping time warp around in an elliptic orbit can readily show this; at the apses, it\'s easy to see that there\'s a slight delay to its height reading, coming to show the apsis altitude less time before the apsis is reached than it takes to move away after leaving the apsis behind. Jumping the warp down while ascending or descending, it can be observed to jump back a few units, before carrying on as it was. The only explanation I can come up with for the reversal is that the altimeter is moving ahead, trying to be predictive with these high velocities.

This can\'t exactly be proven systematic, but is much more likely to be than the other obvious source of error, which is the limited (1 second) time resolution.

Second, the sea-level densities I provided above apparently had an extraneous factor of 2. Assuming that Harv\'s drag model already includes that factor (which I saw on an old thread it does), the 'correct' sea-level density for Kerbin\'s atmosphere is about 0.0051 Kerbal Mass Units per meter³, where the command module has a mass of 1 Kerbal Mass Unit.

If as I suspect (based on old discussions about Kerbal fuel densities compared to Earth\'s), 1 Kerbal Mass Unit = 1000 kg, that means their sea-level atmospheric density is 5.1 kg/m³.

That\'s what one would expect for SF₆!!! (Molecular mass 146 as opposed to 29 for air).

The speed of sound in a gas (see the Wikipedia article) is given by sqrt (gamma * Pressure / density), where gamma is that pesky ratio of specific heats.

Since gamma = 1.04 for SF₆ and 1.4 for air, that would make the sea-level sound speed at standard temperature and pressure equal to... wait for it... 340 m/s * sqrt(1.04/1.4 * 29/146) = 131 m/s.

Is that low enough for ya? It\'s not much greater than the terminal speed of a falling object in the current model. Of course I think it\'s likely that we\'re over-interpreting the Kerbin model here - a model which will evolve in time and may not be self-consistent, but the data is what it is, and physics is physics on any world.

After going through the maths several times, with an estimated sea-level terminal velocity for a mk1pod of 90 m/s, I get an atmospheric density of ~12 kgm^-3. For this I used the equation in my early post, with a slight modification of being / 2, like the real drag equation is. ( In full, F_D = ( ? * v^2 * m * [tt]maximum_drag[/tt] ) /2 )

Equated to mg and rearranged, the equation I\'m working with is as follows:

? = (2 * g) / (v² * [tt]maximum_drag[/tt])

For v = 90, g=9.81, and drag = 0.2, this works out at 12.1 kgm^-3, again assuming the standard unit is 1 ton, as makes sense thus far.

As for that calculation of speed of sound, while that possibly gives a good value for drag divergence with respect to gameplay, a ? that low results in an utterly pitiful stagnation temperature. Reentry is boring now? Adding realistic heating for that value will be almost as boring. Stagnation temperature is proportional to M², which that value of a makes slightly less than that on earth, and also proportional to the value of (? - 1). Reducing ? from 1.4 to 1.04 means bringing stagnation temperature, and thus reentry heating, to a tenth of what it would be on Earth for the same mach. While that does still mean a fairly high peak flow temperature, at least compared to ambient, and assuming said ambient is about comparable to Earth, peak flow temperature is far, far higher than the heating experienced by a reentering vehicle, due to the sparsity of the atmosphere.

For reference assuming ambient in both cases to be 250K, temperature ratio on Kerbin, with a reentry Mach of 20 (velocity 2600 m/s) would be 9, for peak flow of 2,250 K. On Earth, with a reentry Mach of 25 (typical estimate), temperature ratio is 126, for peak flow temperature of 31,500 K. While there will be some inaccuracy in these values due to gamma reducing with temperature, and peak temperature not being reached near vehicle skin, this demonstrates the disparity between the two situations.

Summary: It\'s kinda hard to make Kerbin fit realistic properties. It\'s already significantly more than twice the density of lead. This has lead to the theories of Kerbin being an inverted dyson shell around a neutron star, which could also explain the lack of tidal locking.

Edit: Slight correction to temperature ratios, which were 1 less than they should\'ve been.

[thorfinn]

First things first: yeah, Kerbin IS a pretty impossible planet. Figuring out why it\'s impossible is fun, though.

That being said... you are making a calculation with a perfect gas model: it\'s completely unusable for space reentry conditions, on Earth at least

There is a very good Wikipedia page on this topic, at http://en.wikipedia.org/wiki/Reentry#Perfect_gas_model

[closette]

First things first: yeah, Kerbin IS a pretty impossible planet. Figuring out why it\'s impossible is fun, though.

Moar physics make closette happy! BWAHAHA!

On the issue of mass density for the bodies (Kerbol\'s density is infinite right now), all we can derive from distances and speeds is the value of GM, not mass M independently, so messing with the gravitational constant G in their universe can bring material densities back into the 'reasonable' range. A neutron star core is fine by me, all the same.

@Iskierka, there are so many uncertainties flying around that a factor of 2 doesn\'t seem that important, but I took the drag model from this thread:

http://kerbalspaceprogram.com/forum/index.php?topic=5623.msg72319#msg72319

written by someone you might know, and it implies that the maximum_drag parameter includes the conventional factor of 1/2 in front of c_dA.

Which is the correct equation used by KSP, and how do you know for sure? It directly affects the average molecular weight of the atmosphere, so the Kerbals (and I) are holding our breath until we know

Oh, and as you are aware we don\'t really know gamma for the atmosphere, it could very well have a bunch of Xenon if you don\'t like SF₆. Would that help any? IMHO less re-entry heating than Earth\'s makes for a more playable KSP, and is in line with the gentler aspects of gravity and atmosphere that make early success in the game easier. (That\'s one reason I haven\'t tried Orbiter in a long time!).