P-40 turn rate/Flight model check

[Venturi]

Example A (from in game testing)

155km/h = √((2*3760kg*9.81m/s²) / (1.225kg/m³*21.92m²*CLmax)) 

  155km/h=√(73771.2kg*m/s² / 26.852kg/m*CLmax)

  1854m²/s²=(2747m²/s²)/CLmax

 

  gives aircraft CLmax of 1.48

 

 

Example B (from Boscombe trials)

145kph = √((2*3760kg*9.81m/s²)/(1.225kg/m³*21.92m²*CLmax))

  145km/h=√(73771.2kg*m/s² / 26.852kg/m*CLmax)

  1622m²/s²=(2747m²/s²)/CLmax

 

  gives aircraft CLmax of 1.69

Edited December 29, 2016 by Venturi

[JtD]

They were tested in real life at 3850kg, according to parts 8 and 10 of the report. Standard weight in game is 3819kg, according to the developers.

 

Please take a look at the position error curve given in figure 3 of the report, part 17. It only goes down to 120, but if I was to extrapolate it to 90, I'd end up at 6-7 mph. Compared to that, Kai_Lae's testing has confirmed, that in game we have no position error.

If you were to follow my 6-7mph position error correction, we'd have essentially the same lift coefficients from in game and real life tests, in the region of 1.5. Which is incredibly high.

 

Given the difficulties of keeping the plane exactly level near the stall, I suppose lift coefficient at least in game is lower than calculated right now. The same problem occurred with other in game stall tests.

[Venturi]

Alright, the PEC is giving a correction to ASI of -5mph by my read, but TAS according to Kai Lae's in game tests matches IAS. 

 

The question is, is this PEC being done for all aircraft, if IL2 does not model PEC? If not, and it is being applied as a penalty to the P40, that is a relative error that needs to be fixed.

 

The other thing is, what altitude was the test conducted at? That affects air density. As I know the one in game is at sea level, however the one in real life? I understand stall testing usually was done at 5,000' or 10,000'.

 

 

Edited December 29, 2016 by Venturi

[JtD]

Real life stall speed 90 indicated, position error 5-7 -> 95-97 calibrated air speed. In game, 95-96 indicated, no position error -> 95-96 calibrated air speed. It is the same result. At least it appears to be at a first glance.

 

WRT altitude, stall occurs at the same calibrated air speed at any altitude (unless you're stalling at near Mach speeds, then you'll have to take a few more things into account ). The reduced air density is compensated with a higher true air speed for the same calibrated stall speed.

Edited December 29, 2016 by JtD

[Venturi]

I think altitude affects PEC. 

 

Up to 10,000' it appears constant on this - although speed is increasing which would tend to argue that PEC is in fact, decreasing for the same airspeed.

 

The term for air density will change on altitude.

Edited December 29, 2016 by Venturi

[JtD]

No, that's not it. If you look at the position error curve in figure 3 part 17 you'll see that the numbers in your table are exactly matching the curve, except for the 118 and 113, which are extrapolated, as the curve ends at 120.

What changes is the compressibility error correction, but that does not matter at speeds near stall speed. Position error correction is typically given as a function of indicated speed, and thus depends on that speed, not altitude or density.

If you stall at 100 indicated at sea level, you'll stall at 100 indicated at 20k.

 

I don't know the topic in detail - if the test reports I'm referring to haven't been posted/linked already, please say so.

Edited December 29, 2016 by JtD

[Venturi]

Yes you're right, I was looking at TAS. Sorry it's late and I'm on a cell phone. I was wondering if the nature of the PEC was affected by altitude but no, only speed . OK.

 

Four points jump out at me still, after all this .

I, what altitude was the stall test at Boscombr done at? Altitude will affect air density and CLmax in the equation. It is a big variable in the denominator. This makes it impossible to compare in game and real life testing, if we don't know the altitude for the real life test. Unless I am missing something.

2. Aircraft CLmax is what we should be using... since the tail makes lift... and so does the wing roots... and the fuselage... not just the wing.

3. Is PEC correction artificially factored into every FM in IL2, since it is not modeled? If so then Ok, if not... there is still a relative error

4. The P40 has a higher CLmax than the BF109 even with slats open (should be 1.4 for 109E aircraft CLmax). Aircraft does not behave this way, at low speeds, however...

Edited December 29, 2016 by Venturi

[Farky]

Real life stall speed 90 indicated, position error 5-7 -> 95-97 calibrated air speed. In game, 95-96 indicated, no position error -> 95-96 calibrated air speed. It is the same result. At least it appears to be at a first glance.

 

 

Position error is minus 5-7 mph -> 83-85 calibrated air speed.

[JtD]

About point 1 - you either look at true air speed and factor density, or indicated/calibrated/equivalent air speed. Since the trials refer to indicated air speed, you don't need density.

 

The formula you've been using in the above posts is actually for true air speed, but it works fine because true air speed at sea level density is the same as calibrated/equivalent and indicated plus/minus position error correction. So, if you were to reduce density to factor in higher altitude, you'd in the same manner need to increase the speed in that formula. You'd still arrive at the same cl's.

 

About point 2 - aircraft clmax is what everyone uses, but it also relates to a reference area that typically is larger than the real wing area, since it typically uses an approximation that for instance includes the fuselage between the wings.

 

About point 3 - typically, you'd do the calculations in true air speed, factor in density to calculate aircraft behaviour, and in the animation of the speed gauge needle add a position error. It is totally irrelevant for anything related to the actual flight physics.

 

About point 4 - the 1.5 we have should be taken with a grain of salt. I consider it too high. The interesting point is that it matches a real life test. Dev data indicates they are using around 1.35, which imho is perfectly reasonable.

[JtD]

Position error is minus 5-7 mph -> 83-85 calibrated air speed.

Bloody hill, that's true. Thanks for catching that.

 

Apparently there's either some information missing, or the P-40 was the first aircraft to implement anti gravity technology.

[unreasonable]

I thought I did, but offhand, I can't find it at the moment. 

 

Is the math correct above for clmax?

 

The maths is fine, although it is easier to see why the CLmax is sensitive to the Vmin figure if you reorder the equation to solve for CLmax -  the Vmin (only) is squared so any change or error is magnified. You can check yourself with the CLmax calculator I posted earlier.

 

Basically a 6.6% change in  Vmin generates a 13.6% change in CLmax, which will have large effects in game, as we have seen with the Fw190 issue which seems very similar as discussed elsewhere. This magnitude change is what caused all the grief.

 

In that case we know why the developers choose to make their changes and why they are going to redo them, it would be interesting to know exactly what the thought process is in this case since the P-40 numbers look odd at first glance. I think it may be to do with the idea that the plane is beyond the critical AoA in three point attitude, which is why you have to wheel it in, so you end up with a rather high stall speed, especially if the game IAS has no PEC, but that is speculation.

 

(And no, this has nothing to do with PC floating point error )

[JG13_opcode]

Baloney.

 

Don't be so childish if you clearly don't understand how computers work.

 

All numbers are represented on your computer as a binary integer.  The IEEE or Institute of Electrical and Electronics Engineers defines a number of different standards for translating that integer into a floating point (decimal) number.

 

Some decimal numbers simply cannot be represented because your computer has a fixed number of digits.  Example:  the quantity 1/3 cannot be represented on any computer, because to do so in decimal notation you need an infinite number of decimal places.

 

Here is some simple C++ code that demonstrates the problem.  Thinking logically, the loop should iterate exactly 5 times. In fact, it never terminates. You can compile it and run it yourself if you don't believe me. What does this mean?

 

It means that on your computer, (0.01 + 0.01 + 0.01 + 0.01 + 0.01) does not equal 0.05!

 

#include <iostream>

int main(int argc, char** argv) {

  float i = 0.0;

  while ( i != 0.005 ){
    i = i + 0.001;
    std::cout << i << std::endl;
  }
  
  return 0;
}

 

Maybe try educating yourself before running your mouth, huh?

Edited December 30, 2016 by JG13_opcode

[ACG_KaiLae]

To answer the questions about the testing done, the stall tests were done in instant mission with 100% fuel and ammo, and at 3000m. The IAS/TAS checking was done at 1000m but the mission creator set the atmospheric conditions to be at sea level. 

 

So, what value of clmax does the plane in game use? I've seen several numbers thrown around. Also, the weight at stall testing was max so that should be 8480 pounds or 8500 pounds, depending on source. Assume 8480, which works out to 3846kg - I haven't seen anyone using that weight?

 

Where is the information that at full load the P-40 weighs 3819 kg? I'm not sure where that would come from?

Edited December 29, 2016 by Kai_Lae

[unreasonable]

To answer the questions about the testing done, the stall tests were done in instant mission with 100% fuel and ammo, and at 3000m. The IAS/TAS checking was done at 1000m but the mission creator set the atmospheric conditions to be at sea level. 

 

So, what value of clmax does the plane in game use? I've seen several numbers thrown around. Also, the weight at stall testing was max so that should be 8480 pounds or 8500 pounds, depending on source. Assume 8480, which works out to 3846kg - I haven't seen anyone using that weight?

 

You should do the stall test at the same height as your IAS/TAS check in the same mission, otherwise the speed and air density have to be recalibrated to the new height which is a bit of a pain. If you do it in the test mission we can assume IAS=TAS and standard air density: less room for error.

[Venturi]

Position error is minus 5-7 mph -> 83-85 calibrated air speed. I thought about this, but was too tired last night to make a run at it. That means instead of 6% error, there is 12% error in stall speed, which means that there is a even larger difference in CLmax... on the order of 20+%....

 

 

About point 1 - you either look at true air speed and factor density, or indicated/calibrated/equivalent air speed. Since the trials refer to indicated air speed, you don't need density. 

The formula you've been using in the above posts is actually for true air speed, but it works fine because true air speed at sea level density is the same as calibrated/equivalent and indicated plus/minus position error correction. So, if you were to reduce density to factor in higher altitude, you'd in the same manner need to increase the speed in that formula. You'd still arrive at the same cl's. This answers my question.

 

About point 2 - aircraft clmax is what everyone uses, but it also relates to a reference area that typically is larger than the real wing area, since it typically uses an approximation that for instance includes the fuselage between the wings. My understanding from previous conversations here is that wing CLmax is what people are referring to, which may be actually somewhat different than aircraft CLmax. I think, especially for a PC program, that it is more important to get the summation of an aircraft's CLmax as empirically tested, than to do it piecemeal by adding up wing, tailplane, fuselage, etc lifts - all of which must interact aerodynamically as well. 

 

About point 3 - typically, you'd do the calculations in true air speed, factor in density to calculate aircraft behaviour, and in the animation of the speed gauge needle add a position error. It is totally irrelevant for anything related to the actual flight physics. Well it is only irrelevant if the PEC correction is being applied to ALL aircraft's CLmax, rather than only one or two, and leaving "unfavorable" PEC corrections to CLmax out, by for instance, using only theoretical CLmax from wing data on some aircraft. "There are three kinds of lies: Lies, damn lies, and statistics." Bottom line is, we don't know if the devs are using aircraft CLmax or theoretical wing CLmax.

 

About point 4 - the 1.5 we have should be taken with a grain of salt. I consider it too high. The interesting point is that it matches a real life test. Dev data indicates they are using around 1.35, which imho is perfectly reasonable. I think that empiric data from actual aircraft is more useful than theoretical wing CLmax, for the above reasons. I don't think a 0.15 drop in CLmax is reasonable as it induces a very large change in aircraft handling. My calcs below show that actually the difference is more like 0.5! I think we have to acknowledge that the real world data is contradicting theory here - in other words, the science is showing that the aircraft CLmax is much higher than just the wing CLmax.

 

 

The maths is fine, although it is easier to see why the CLmax is sensitive to the Vmin figure if you reorder the equation to solve for CLmax -  the Vmin (only) is squared so any change or error is magnified. You can check yourself with the CLmax calculator I posted earlier. Yep

 

Basically a 6.6% change in  Vmin generates a 13.6% change in CLmax, which will have large effects in game, as we have seen with the Fw190 issue which seems very similar as discussed elsewhere. This magnitude change is what caused all the grief. It is actually closer to 13% off in Vmin, now.

 

In that case we know why the developers choose to make their changes and why they are going to redo them, it would be interesting to know exactly what the thought process is in this case since the P-40 numbers look odd at first glance. I think it may be to do with the idea that the plane is beyond the critical AoA in three point attitude, which is why you have to wheel it in, so you end up with a rather high stall speed, especially if the game IAS has no PEC, but that is speculation. It might be. The aircraft was supposed to be a two wheel lander, and maybe the new gear shock absorbing mechanics will make this possible. I like the phrase "trust the devs, but verify". 

 

(And no, this has nothing to do with PC floating point error ) ha!

 

 

To answer the questions about the testing done, the stall tests were done in instant mission with 100% fuel and ammo, and at 3000m. The IAS/TAS checking was done at 1000m but the mission creator set the atmospheric conditions to be at sea level. 

 

So, what value of clmax does the plane in game use? I've seen several numbers thrown around. Also, the weight at stall testing was max so that should be 8480 pounds or 8500 pounds, depending on source. Assume 8480, which works out to 3846kg - I haven't seen anyone using that weight? I can run it at exact weights. I did not use the exact weight from the devs source but rather, weights I found from other sources. I can use 3846kg. That would give:

 

GAME (no PEC correction)

155km/h = √((2*3846kg*9.81m/s²) / (1.225kg/m³*21.92m²*CLmax)) 

  155km/h=√(75459kg*m/s² / 26.852kg/m*CLmax)

  1854m²/s²=(2810m²/s²)/CLmax

 

  gives aircraft CLmax of 1.52

 

BOSCOMBE (minus 10kph for PEC correction - assuming Farky is correct)

135kph = √((2*3850kg*9.81m/s²)/(1.225kg/m³*21.92m²*CLmax))

  135km/h=√(75537kg*m/s² / 26.852kg/m*CLmax)

  1406m²/s²=(2813m²/s²)/CLmax

 

  gives aircraft CLmax of 2.00

 

 

Where is the information that at full load the P-40 weighs 3819 kg? I'm not sure where that would come from? Nevermind, I used the dev's numbers above for the in game testing, and the Boscombe weight for their testing. It is a large difference.

 

 

 

Don't be so childish if you clearly don't understand how computers work. I'm not being childish, you brought floating decimal points into a straightforward algebra equation, and I called you on it. By the way, I didn't use sig figs for my calcs, because the final result (CLmax) is only 3 sig figs... this is not quantitative analytical chemistry level stuff..

 

Maybe try educating yourself before running your mouth, huh? OK..

 

Edited December 29, 2016 by Venturi

[Venturi]

Just for fun, here is a math test of the Me109E-7 CLmax, using the dev's numbers for wing area and loaded weight:

 

Example A (from in game testing)

165kph = √((2*2614kg*9.81m/s²)/(1.225kg/m³*16.4m²*CLmax))

  165km/h=√(51286.7kg*m/s² / 20.09kg/m*CLmax)

  2100.4m²/s²=(2747m²/s²)/CLmax

 

  gives aircraft CLmax of 1.31

 

Example B (from British tests June 1940 of Bf109E-3)

154kph = √((2*2531kg*9.81m/s²)/(1.225kg/m³*16.17m²*CLmax))

  154km/h=√(49658.2kg*m/s² / 19.81kg/m*CLmax)

  1830m²/s²=(2507m²/s²)/CLmax

 

  gives aircraft CLmax of 1.37

 

Note that the Bf109E-7 has 83kg more weight than the Bf109E-3, per the dev's notes - somehow also gained 0.23m² of wing area. Nevertheless CLmax matches pretty closely...

 

I welcome someone to do better stall testing on the Bf109E-7, my stalls were done only a few times. If you get a lower (more precise) stall speed than I did at 165kph, the CLmax will increase, and I bet it will be very close to 1.37...

Edited December 29, 2016 by Venturi

[ACG_KaiLae]

I think we need more than one source for the real aircraft. I know others were looking into it? The clmaxes thrown around here seem...a bit high, from my limited understanding, to be typical. While Unreasonable is right that the stall test probably should be redone using the speed mission parameters, the stall information that I got also matches the information on the stats page by 1CG, so there is good reason to think it's right. Which, again, leads to real airplane stalling at slower speed than in game P-40. There is a cause for that.

Edited December 29, 2016 by Kai_Lae

[Venturi]

I think the question is, are the "typical" numbers being thrown around theoretical "wing only" CLmax or whole aircraft CLmax? If the aircraft body is producing lift then you will get a higher CLmax if you are only using the wing area in the calculation.

 

However, if that extra lift is not taken into account in the game, it also explains why the aircraft behaves differently in real life than in the game. Which is why we should use aircraft CLmax and not just wing CLmax.

 

But you're right, the more data the better.

[JG13_opcode]

I'm not being childish, you brought floating decimal points into a straightforward algebra equation, and I called you on it.

Any high school student knows that "straightforward algebra" doesn't mean you can't have decimal points.

 

"Called me on" what, exactly? I think you are quite confused.

 

By the way, I didn't use sig figs for my calcs, because the final result (CLmax) is only 3 sig figs... this is not quantitative analytical chemistry level stuff..

Sig figs are not relevant to what I'm talking about here.

[unreasonable]

I think we need more than one source for the real aircraft. I know others were looking into it? The clmaxes thrown around here seem...a bit high, from my limited understanding, to be typical. While Unreasonable is right that the stall test probably should be redone using the speed mission parameters, the stall information that I got also matches the information on the stats page by 1CG, so there is good reason to think it's right. Which, again, leads to real airplane stalling at slower speed than in game P-40. There is a cause for that.

 

I should have said that to calculate in game CLmax it is easier if the stall speed is tested at standard conditions - to compare with a RL test then it is best to try to make your test conditions identical to the RL test as you did.

 

I do wonder about the weights as mentioned: in RL life tests the plane must have been considerably lighter than fully loaded weight.

 

 

I think the question is, are the "typical" numbers being thrown around theoretical "wing only" CLmax or whole aircraft CLmax? If the aircraft body is producing lift then you will get a higher CLmax if you are only using the wing area in the calculation.

 

However, if that extra lift is not taken into account in the game, it also explains why the aircraft behaves differently in real life than in the game. Which is why we should use aircraft CLmax and not just wing CLmax.

 

But you're right, the more data the better.

 

If you calculate CLmax using a test of a plane (RL or game) then by definition you are calculating a whole aircraft CLmax - if you want wing CLmax that would have to come from a wind tunnel test of the wing only. The lift in all the tests discussed above must be of the whole plane, since at level stall lift = weight. The wing reference area is an approximation that assumes that the net lift of all the other "non-wing" areas is zero, which is reasonable since the fuselage might provide a little but the horizontal stab, for instance, is usually producing negative lift by design.

 

The difference between wing and plane CLmax is less to do with the reference area and more the extra drag produced by gun ports, wheel wells and so on that is typically not captured in wing tests.

 

The devs are definitely interested in whole plane CLmax - from Davrick's DD 140 he discusses the whole plane CLmax - although whether this number is an input into the FM or a calculated output is unknown to us.

 

When we were working on Fw-190 A-3 we didn't have data that could allow us to pinpoint its stall speed and maximum lift coefficient, two directly linked values. We didn't have its wind tunnel data and the maximum lift coefficient calculated from the wing profile somewhat differs from its value on the real aircraft. Also, its stall speed wasn't clearly given in the reports we had. For example, the flight manual mentioned the landing speed with flaps and a rough estimate of its landing speed increase without flaps, but these values can give only an approximate stall speed. The stall speed was mentioned in the British report on captured aircraft flight tests - but the mass of the aircraft, an important parameter for calculating the maximum lift coefficient using the stall speed, was omitted from that report. 

Edited December 30, 2016 by unreasonable

[unreasonable]

Sig figs are not relevant to what I'm talking about here.

 

Not wanting to get into your argument, but I also find the idea that a 5% difference here could be due to floating point errors implausible.  Using spreadsheets with large numbers for years the only situations I can think of off-hand that might lead to that high an error are if the quantities are expressed to very few significant digits, so rounding error is large - but you say that is not what you are talking about.

 

You might get that indirectly if you subtract two similar numbers that very close, as in calculating a very low profit margin for instance. If you do this in a time series and then calculate the change in the margin over time you can get significant rounding error again, but only because you have reduced the number of significant digits from say 10 to 2.

 

Obviously the developers are balancing a complex model using approximations of physics to try to get close to RL data points (that are themselves approximate measurements!) so it would be silly to expect a perfect fit, but given the sensitivities involved  a 5% error in Vmin leads to quite severe consequences, so if this really is due to an insolvable technical floating point issue I would like to know how this can possibly arise.

[JG13_opcode]

Not wanting to get into your argument, but I also find the idea that a 5% difference here could be due to floating point errors implausible.  Using spreadsheets with large numbers for years the only situations I can think of off-hand that might lead to that high an error are if the quantities are expressed to very few significant digits, so rounding error is large - but you say that is not what you are talking about.

I never attributed 5% to floating point error. Please go back and read what I wrote.

 

What I wrote is that 0% error is strictly impossible (Venturi disagrees because he doesn't understand computers). Even with perfect test data in perfect conditions with perfect instrumentation and measurement systems, there is still some amount of error that is introduced by representing real physical processes on a computer, due to the way numbers are represented in binary (among other reasons).

 

The ramifications are thus: When calculating physical quantities (which Venturi somehow thinks doesn't involve decimal points because it's "straightforward algebra"), relations that normally hold true when done with paper and pencil don't always work on the computer because the right side won't necessarily equal the left side.

 

Back in university I wrote an iterative numeric solver for hyperbolic differential equations. In a nutshell, it basically does guess-and-check because you can't really solve for X to get the answer. But with IEEE-compliant floating-point numbers, the left hand side of the equation will never equal the right-hand side of the equation, so I had to write an algorithm that would home-in on the right solution and stop when it got "close enough".

 

Because of this, we must accept some amount of error. What anyone's individual threshold of acceptability is is up to them. Stall speed being off by 6.6% seems acceptable to me. IIRC Oleg's threshold for the old sim was within 10% of RL figures.

Edited December 30, 2016 by JG13_opcode

[Venturi]

Let us assume I hold your point true, that floating point calculation errors are of a meaningful amount in CLmax calculations... 

 

Even if so, aircraft CLmax is a fixed value, once the decision is made as to what the value should be. What we are discussing here is what that fundamental value should be, because an aircraft's CLmax must be basically correct, if an aircraft's performance is also to be simulated as basically correct. As has been stated over and again here, errors in CLmax are compounded such that small differences have large impacts.

 

It is incorrect to argue that because the computer's calculations may be imprecise (you do not state the actual size of your proposed errors in calculation), that it is also acceptable that the underlying terms in the equation can be allowed to be incorrect.

 

On the contrary, your assumption that the calculation may be somewhat imprecise argues that the underlying terms must be MORE accurate, to avoid compounding inaccuracies in both the terms and then subsequently the calculation. I would expect anyone with any real experience with precision mathematics would understand this..

 

In any case, I do not think it is relevant to this discussion.

Edited December 30, 2016 by Venturi

[Venturi]

I do wonder about the weights as mentioned: in RL life tests the plane must have been considerably lighter than fully loaded weight. They specify exactly the weight of the aircraft, without which they could not calculate CLmax.

 

If you calculate CLmax using a test of a plane (RL or game) then by definition you are calculating a whole aircraft CLmax... yes, obviously

 

If you want wing CLmax that would have to come from a wind tunnel test of the wing only. Many people are referring to wing polars as being "the holy grail", but as you point out, it is not, for a PC simulation of a whole plane

 

The lift in all the tests discussed above must be of the whole plane, since at level stall lift = weight. The wing reference area is an approximation that assumes that the net lift of all the other "non-wing" areas is zero, which is reasonable since the fuselage might provide a little but the horizontal stab, for instance, is usually producing negative lift by design. Really? That would induce a very, very large nose up angle for most aircraft, in fact Kurt Tank talks of increasing the tailplane area for more tail lift to balance out wing area increase in production models of Fw190, so that the lift balance is maintained of original design..

 

The difference between wing and plane CLmax is less to do with the reference area and more the extra drag... no, there is no term for drag... what CLmax tells us, only - is when the plane will stall for any given airspeed at (x) Gs. Drag is another set of equations and this is more difficult to determine.

[unreasonable]

I never attributed 5% to floating point error. Please go back and read what I wrote.

 

What I wrote is that 0% error is strictly impossible (Venturi disagrees because he doesn't understand computers). Even with perfect test data in perfect conditions with perfect instrumentation and measurement systems, there is still some amount of error that is introduced by representing real physical processes on a computer, due to the way numbers are represented in binary (among other reasons).

 

The ramifications are thus: When calculating physical quantities (which Venturi somehow thinks doesn't involve decimal points because it's "straightforward algebra"), relations that normally hold true when done with paper and pencil don't always work on the computer because the right side won't necessarily equal the left side.

 

Back in university I wrote an iterative numeric solver for hyperbolic differential equations. In a nutshell, it basically does guess-and-check because you can't really solve for X to get the answer. But with IEEE-compliant floating-point numbers, the left hand side of the equation will never equal the right-hand side of the equation, so I had to write an algorithm that would home-in on the right solution and stop when it got "close enough".

 

Because of this, we must accept some amount of error. What anyone's individual threshold of acceptability is is up to them. Stall speed being off by 6.6% seems acceptable to me. IIRC Oleg's threshold for the old sim was within 10% of RL figures.

 

I read exactly what you said:

 

"Look, the nature of floating point mathematics in x86 processors ensures that it is 100% impossible to ever get an exact match. 

 

Some error is strictly unavoidable due to the way computers represent numbers internally. 

 

At some point we need to accept a result as reasonable. 6.6 % error in stall speed between the game and historical tests is acceptable in my book. "

 

Of course there is error in a model - as my post also points out, but this is primarily due to measurement error plus the fact that the equations used are approximations, not because of floating point error.  personally I think a 6.6% error in stall speed is a little over the limit of what is acceptable given the team's own high standards, since it implies a 13.6% error in CLmax but that is a matter of taste.

 

What your first post clearly implies, and is repeated in your reply, ("because of this")  is the implication that floating point error could be a significant contributor to this 6.6%. If it is not - it is all measurement error and model approximation - then I am not sure why you raised it. If it is, then I am still curious to know specifically how this could happen in the context of an FM, especially if as you say this is not a matter of significant digits. 

[ACG_KaiLae]

To me the amount of error seems to be making the aircraft behave in a nonhistoric way. This is when it matters, otherwise we wouldn't be here. Of course there are other factors, but I'd like to get a definitive difference between what the BOS plane has and what the RL plane has, so a determination on what the major component is can be determined. 

[unreasonable]

 

I do wonder about the weights as mentioned: in RL life tests the plane must have been considerably lighter than fully loaded weight. They specify exactly the weight of the aircraft, without which they could not calculate CLmax.

 

If you calculate CLmax using a test of a plane (RL or game) then by definition you are calculating a whole aircraft CLmax... yes, obviously

 

If you want wing CLmax that would have to come from a wind tunnel test of the wing only. Many people are referring to wing polars as being "the holy grail", but as you point out, it is not, for a PC simulation of a whole plane

 

The lift in all the tests discussed above must be of the whole plane, since at level stall lift = weight. The wing reference area is an approximation that assumes that the net lift of all the other "non-wing" areas is zero, which is reasonable since the fuselage might provide a little but the horizontal stab, for instance, is usually producing negative lift by design. Really? That would induce a very, very large nose up angle for most aircraft, in fact Kurt Tank talks of increasing the tailplane area for more tail lift to balance out wing area increase in production models of Fw190, so that the lift balance is maintained of original design..

 

The difference between wing and plane CLmax is less to do with the reference area and more the extra drag... no, there is no term for drag... what CLmax tells us, only - is when the plane will stall for any given airspeed at (x) Gs. Drag is another set of equations and this is more difficult to determine.

 

 

Wiki says: 

 

"Another role of a longitudinal stabilizer is to provide longitudinal static stability. Stability can be defined only when the vehicle is in trim;^[5] it refers to the tendency of the aircraft to return to the trimmed condition if it is disturbed.^[6] This maintains a constant aircraft attitude, with unchanging pitch angle relative to the airstream, without active input from the pilot. Since obtaining static stability often requires that the aircraft center of gravity be ahead of the center of lift of a conventional wing, a stabilizer positioned aft of the wing is then often required to produce negative lift."

 

There was an article by Lednicer of a computer analysis of Fw190 lift etc, which IIRC showd the horizontal stab also showing negative lift. Unfortunately I cannot find the link.

 

I am sure this is situation specific though, probably a bit OT.

 

As for the drag: if you increase surface roughness or add gun ports etc you reduce the CLmax as shown in the various NACA reports. I do not think this is all or mostly lost lift as such. I think drag is relevant because a draggy plane has to maintain the same speed to provide lift for level flight -  and cannot use extra power in a power off stall test - and the only way it can do that is by reducing its AoA. I.e. it will stall out at a higher speed other things being equal that it's shiny brother. (Just do not ask me to put any of that into maths )

Edited December 30, 2016 by unreasonable

[Holtzauge]

The turn time figure of 19 s in the TSAGI table in post #2 looks really strange and as JtD pointed out already it does not make sense given the P-40 power and weight loading from a physics standpoint. In addition, while the figures in TSAGI document in general are in line with other sources there are some anomalies in it like the turn time for the Me-109 E3 for example being stated as 23.9 to 26 s which is way too high. So with this in mind I would treat the figure of 19 s for the P-40E with some caution……

 

My estimate of the turn time for the P-40E at a weight of 3840 Kg  at 1km altitude assuming a low Mach Clmax of 1.35 and 1150 hp is 25.1 s. Not saying that that is the right answer but I have modeled a number of different aircraft in my C++ simulation and in general the number tab up pretty well with historical sources. So if the BoM P-40E is stated to target 24+ s this seems pretty reasonable IMHO.

[303_Kwiatek]

Sorry for offtopic but what about turn time 109 F-2 in BOS.  I actually found that according to developers data it got 23.6 sec turn time at sea level comparing to F-4 ( 20.3 s )  and G-2 (22.2 s).  What i thought F-2 should be best in sustained turn at sea level from all these three. ( VVS test cofirmed these).   But  in BOS it looks that is the worst?  Holtzauge what is your calculation for F-2?

[Venturi]

Sustained turn is not the same as CLmax, obviously. But CLmax has bearing upon sustained turn times, because nearing the aircraft's stall point in a turn, as in a max effort turn, will increase drag, reduce velocity, and therefore increase turn time. So a reduced CLmax will reduce the Gs (and therefore the deg/sec which can be achieved) before the aircraft encounters higher drag conditions. The lost velocity in that turn from higher drag, would then have a proportionally larger effect on an aircraft with a relatively lower power to weight ratio, as the P40E.

 

So CLmax does have a role to play.

 

I have yet to hear why we cannot extrapolate aircraft CLmax from the real-life tested and position error corrected stall speed and weight, which gives CLmax of 2.0 for the P-40E from the Boscombe trials. Using these same methods we get the correct CLmax for the Bf109E, as I posted above.

 

BOSCOMBE (minus 10kph for PEC correction)

135kph = √((2*3850kg*9.81m/s²)/(1.225kg/m³*21.92m²*CLmax))

  135km/h=√(75537kg*m/s² / 26.852kg/m*CLmax)

  1406m²/s²=(2813m²/s²)/CLmax

 

  gives aircraft CLmax of 2.00

Wiki says: 

 

"Another role of a longitudinal stabilizer is to provide longitudinal static stability. Stability can be defined only when the vehicle is in trim;^[5] it refers to the tendency of the aircraft to return to the trimmed condition if it is disturbed.^[6] This maintains a constant aircraft attitude, with unchanging pitch angle relative to the airstream, without active input from the pilot. Since obtaining static stability often requires that the aircraft center of gravity be ahead of the center of lift of a conventional wing, a stabilizer positioned aft of the wing is then often required to produce negative lift."

 

There was an article by Lednicer of a computer analysis of Fw190 lift etc, which IIRC showd the horizontal stab also showing negative lift. Unfortunately I cannot find the link.

 

I am sure this is situation specific though, probably a bit OT.

 

As for the drag: if you increase surface roughness or add gun ports etc you reduce the CLmax as shown in the various NACA reports. I do not think this is all or mostly lost lift as such. I think drag is relevant because a draggy plane has to maintain the same speed to provide lift for level flight -  and cannot use extra power in a power off stall test - and the only way it can do that is by reducing its AoA. I.e. it will stall out at a higher speed other things being equal that it's shiny brother. (Just do not ask me to put any of that into maths )

 

Negative lift may make sense, although I understand that many fighters were actually quite longitudinally unstable, which gives good turning performance (more rearward CG actually increases CLmax). The P39 and Spitfire being good examples. The P40E also perhaps being an example (it would "tumble" - but not spin - per veteran pilots, I have already posted these remarks on this forum). But it is another reason to consider whole-aircraft CLmax rather than wing CLmax, because any negative lift would then be incorporated into the equation inherently.

 

"Draggy" parts on a wing reduce CLmax, when testing "pre" vs "post" modifications to an airframe - yes, because you reduce wing lift by disturbing the boundary layer over the wing. This will also increase the speed at which the 1g stall occurs, so this lift loss is already encapsulated in the empiric derivation of aircraft CLmax. But drag does not otherwise enter into the equation to derive CLmax when using empiric methods, by just a examination of the equation.

 

Aircraft CLmax is encapsulated by "overall lift" of the aircraft which takes into account the gun barrels, bulges, and much more including the extremely complex interaction of all the lifting surfaces of the aircraft. It is again another reason to distinguish empiric aircraft CLmax vs theoretical wing CLmax, and to use empiric aircraft CLmax for a PC simulation. Again, we don't know how the devs actually implement CLmax for these planes, etc.

Edited December 30, 2016 by Venturi

[ZachariasX]

So, another Clmax discussion? The last one was (surprisingly) productive in the end.

 

And opcode still seems to suffer from Pentium-bug bites...

[unreasonable]

 

 

Aircraft CLmax is encapsulated by "overall lift" of the aircraft which takes into account the gun barrels, bulges, and much more including the extremely complex interaction of all the lifting surfaces of the aircraft. It is again another reason to distinguish empiric aircraft CLmax vs theoretical wing CLmax, and to use empiric aircraft CLmax for a PC simulation. Again, we don't know how the devs actually implement CLmax for these planes, etc.

 

Yes I agree with that, indeed that is what much of my last thread (CLmax calculator) on the Fw190 was all about !

 

As to the drag issue, obviously I agree it is not in the equation to calculate CLmax from a set of data but it does affect the aircraft flying the test from which the data is taken.

Suppose you had an aircraft and tested it, then installed a small light-weight drogue chute, thus increasing drag slightly but not affecting lift or weight.  My question is would this affect the Vmin? My guess is that it would, and therefore the CLmax, but I suppose it could just increase the deceleration to the to the same Vmin when the power is turned off. This is a bit OT - sorry OP! 

[Venturi]

Suppose you had an aircraft and tested it, then installed a small light-weight drogue chute, thus increasing drag slightly but not affecting lift or weight.  My question is would this affect the Vmin? My guess is that it would, and therefore the CLmax

 

 

You are talking horizontal vectors, and I am talking vertical vectors. Not the same.

 

Look at the equation:

 

V(g) = √( 2*W*g / ρ*S*CLmax ) 

Where,

V(g) = Stall Speed at (x)g

W = Weight of the aircraft

g = acceleration at (x)g, for 1g it is 9.81 m/s²

ρ = Density of Air

S = Wing Area

CLmax = Coefficient of Lift at Stall

 

CLmax is the property of the aircraft which determines when the aircraft stalls out at a given speed and g force. It is only a variable in the equations we have been talking about previously, insofar that that I am backwards-solving for it as an unknown from all the other knowns in the equation. 

 

In reality, it is a fixed quality of an aircraft and determines at what speed an aircraft will stall for any given "g" force, or conversely, at what "g" force the aircraft will stall if at a certain speed.

 

Speed is only important insofar that it, in combination with the CLmax of the aircraft, determines how much lift the aircraft can produce.

 

It's an instantaneous value and only tells you what the aircraft will do at one moment in time, IE, the maximum Coefficient of Lift or CLmax.

Edited December 30, 2016 by Venturi

[ZachariasX]

Yes I agree with that, indeed that is what much of my last thread (CLmax calculator) on the Fw190 was all about !

 

As to the drag issue, obviously I agree it is not in the equation to calculate CLmax from a set of data but it does affect the aircraft flying the test from which the data is taken.

Suppose you had an aircraft and tested it, then installed a small light-weight drogue chute, thus increasing drag slightly but not affecting lift or weight.  My question is would this affect the Vmin? My guess is that it would, and therefore the CLmax, but I suppose it could just increase the deceleration to the to the same Vmin when the power is turned off. This is a bit OT - sorry OP!

 

If the "chute" doesn't affect airflow over the lifting parts of the aircraft, it doesn't affect Clmax or Vmin on a noticeable way. It just makes it faster to get there.

 

In a glider, you would notice your extra drag as proportionally increased sink rate. You use this to make your approach. (If you use the airbrakes as a mean to decrease your speed, you'll be short lived.) The rest of the parameters are unaffected for practical purposes until you exert a lot of drag. This very much to the convenience of the pilot.

[Holtzauge]

Sorry for offtopic but what about turn time 109 F-2 in BOS.  I actually found that according to developers data it got 23.6 sec turn time at sea level comparing to F-4 ( 20.3 s )  and G-2 (22.2 s).  What i thought F-2 should be best in sustained turn at sea level from all these three. ( VVS test cofirmed these).   But  in BOS it looks that is the worst?  Holtzauge what is your calculation for F-2?

 

It seems my estimates are a bit more optimistic: I get a turn time of 20.2 for the G2 and 19.7 for the F4. I Don’t have the F2 modeled but isn’t that quite close in both wing- and power loading? If it is I don’t see why they should not be on par in term of sustained turn rate? Anyway, if the F2 in BoM takes 23.6 s to do a 360 at SL that sounds way to pessimistic.

 

OTOH both the F4 and G2 climb way better than they should in BoX AFAIK: I started a thread about that a while back and AFAIK both the G2 and F4 climb too well in IL-2 at the moment. The figure in post #1 shows this and can be used to compare with the IL-2 climb rates and if the F2 and F4 are close together in powerloading they should also be close in turn rate.

 

Sustained turn is not the same as CLmax, obviously. But CLmax has bearing upon sustained turn times, because nearing the aircraft's stall point in a turn, as in a max effort turn, will increase drag, reduce velocity, and therefore increase turn time. So a reduced CLmax will reduce the Gs (and therefore the deg/sec which can be achieved) before the aircraft encounters higher drag conditions. The lost velocity in that turn from higher drag, would then have a proportionally larger effect on an aircraft with a relatively lower power to weight ratio, as the P40E.

 

So CLmax does have a role to play.

 

I have yet to hear why we cannot extrapolate aircraft CLmax from the real-life tested and position error corrected stall speed and weight, which gives CLmax of 2.0 for the P-40E from the Boscombe trials. Using these same methods we get the correct CLmax for the Bf109E, as I posted above.

 

BOSCOMBE (minus 10kph for PEC correction)

135kph = √((2*3850kg*9.81m/s²)/(1.225kg/m³*21.92m²*CLmax))

  135km/h=√(75537kg*m/s² / 26.852kg/m*CLmax)

  1406m²/s²=(2813m²/s²)/CLmax

 

  gives aircraft CLmax of 2.00

 

Negative lift may make sense, although I understand that many fighters were actually quite longitudinally unstable, which gives good turning performance (more rearward CG actually increases CLmax). The P39 and Spitfire being good examples. The P40E also perhaps being an example (it would "tumble" - but not spin - per veteran pilots, I have already posted these remarks on this forum). But it is another reason to consider whole-aircraft CLmax rather than wing CLmax, because any negative lift would then be incorporated into the equation inherently.

 

"Draggy" parts on a wing reduce CLmax, when testing "pre" vs "post" modifications to an airframe - yes, because you reduce wing lift by disturbing the boundary layer over the wing. This will also increase the speed at which the 1g stall occurs, so this lift loss is already encapsulated in the empiric derivation of aircraft CLmax. But drag does not otherwise enter into the equation to derive CLmax when using empiric methods, by just a examination of the equation.

 

Aircraft CLmax is encapsulated by "overall lift" of the aircraft which takes into account the gun barrels, bulges, and much more including the extremely complex interaction of all the lifting surfaces of the aircraft. It is again another reason to distinguish empiric aircraft CLmax vs theoretical wing CLmax, and to use empiric aircraft CLmax for a PC simulation. Again, we don't know how the devs actually implement CLmax for these planes, etc.

 

Yes I agree to most of this but the Clmax will determine the P-40 stationary turn rate at low altitudes: You get it at the intersection of the lift- and power limited turn rates. It’s only at high alt you get the better sustained turn rates at a lower Cl than that. However, there seems to be something off with the Boscombe figures: There is no way you will have any WW2 fighter plane that will have a no-flap Clmax of 2. As has been already said, given the NACA 2209 to 2215 used on the P-40 you should expect to see a reference area based Clmax in the order of 1.3 to 1.4. On the P-40 at 3840 Kg with a wing reference area of 21.92 that gives stall speed of 102 mph at SL assuming a Clmax of 1.35 which AFAIK is not too far off from the IL-2 stall speed? Anyway a stall speed in the order of 85 mph sounds way too low. But sometimes you get these kind outliers in measured data: The G2 climb thread I started was to show that 24 m/s climb rate for the G2 measured by the Finns was off the charts and the 85 mph stall speed for the P-40 seems to be in the same category IMHO. Are there no other sources when it comes to the P-40 stall speed we can compare with?

Edited December 30, 2016 by Holtzauge

[Holtzauge]

Yes I agree with that, indeed that is what much of my last thread (CLmax calculator) on the Fw190 was all about !

 

As to the drag issue, obviously I agree it is not in the equation to calculate CLmax from a set of data but it does affect the aircraft flying the test from which the data is taken.

Suppose you had an aircraft and tested it, then installed a small light-weight drogue chute, thus increasing drag slightly but not affecting lift or weight.  My question is would this affect the Vmin? My guess is that it would, and therefore the CLmax, but I suppose it could just increase the deceleration to the to the same Vmin when the power is turned off. This is a bit OT - sorry OP! 

 

I would say it would not affect the power off stall speed (i.e. Clmax) but simply bring you there faster after you power down. However, it would affect the sustained turn rate since it would "lower" the power limited turn rate curve leading to a lower deg/s figure resulting in a longer time to do a 360 deg turn.

[unreasonable]

OK guys I get the point - I think I was confused by the language in the NACA reports which discuss how increases in drag on a wing - roughness, gun ports etc - reduce CLmax.

 

It would be clearer to say that sticking irregularities on wings can increase drag and reduce lift considered as two distinct forces, and it is the effects on the lift force that implies the reduced CLmax result. The effect on drag is to increase the power required to achieve a given speed/lift configuration.

 

Thanks for the clarification - always an education hanging around here!  

[ACG_KaiLae]

It seems my estimates are a bit more optimistic: I get a turn time of 20.2 for the G2 and 19.7 for the F4. I Don’t have the F2 modeled but isn’t that quite close in both wing- and power loading? If it is I don’t see why they should not be on par in term of sustained turn rate? Anyway, if the F2 in BoM takes 23.6 s to do a 360 at SL that sounds way to pessimistic.

 

OTOH both the F4 and G2 climb way better than they should in BoX AFAIK: I started a thread about that a while back and AFAIK both the G2 and F4 climb too well in IL-2 at the moment. The figure in post #1 shows this and can be used to compare with the IL-2 climb rates and if the F2 and F4 are close together in powerloading they should also be close in turn rate.

 

 

 

Yes I agree to most of this but the Clmax will determine the P-40 stationary turn rate at low altitudes: You get it at the intersection of the lift- and power limited turn rates. It’s only at high alt you get the better sustained turn rates at a lower Cl than that. However, there seems to be something off with the Boscombe figures: There is no way you will have any WW2 fighter plane that will have a no-flap Clmax of 2. As has been already said, given the NACA 2209 to 2215 used on the P-40 you should expect to see a reference area based Clmax in the order of 1.3 to 1.4. On the P-40 at 3840 Kg with a wing reference area of 21.92 that gives stall speed of 102 mph at SL assuming a Clmax of 1.35 which AFAIK is not too far off from the IL-2 stall speed? Anyway a stall speed in the order of 85 mph sounds way too low. But sometimes you get these kind outliers in measured data: The G2 climb thread I started was to show that 24 m/s climb rate for the G2 measured by the Finns was off the charts and the 85 mph stall speed for the P-40 seems to be in the same category IMHO. Are there no other sources when it comes to the P-40 stall speed we can compare with?

The aircraft's own pilot manual lists 90 mph. This is repeated multiple times in several documents. 85 comes from how they are interpreting the PEC information.

[Holtzauge]

The aircraft's own pilot manual lists 90 mph. This is repeated multiple times in several documents. 85 comes from how they are interpreting the PEC information.

 

OK, does the manual specify the weight for the 90 mph stall?

[unreasonable]

 

 

 As has been already said, given the NACA 2209 to 2215 used on the P-40 you should expect to see a reference area based Clmax in the order of 1.3 to 1.4. 

 

As you suggest, this is exactly what you get in Il-2, if you use the DD's robot in-game test stall speeds as per my post 137:

 

     In-game stall speeds are 153-176 kph  (95 - 109mph) IAS  (F+G up) over the range of weights they use, (see DD 123) compared to the two estimates of 90 and 92 given in Farky's post.

 

     I take the minimum stall speed in DD 123  153 kph as being at the minimum weight: 3264 kg, > CLmax of 1.32

     At maximum stall speed - 176 kph I assume "maximum takeoff weight"  4414 kg. > CLmax 1.35

    Somewhere in the middle, "standard weight"  3819kg, speed (153+176)/2 = 165kph > CLmax  1.34

 

My hypothesis for the discrepancies are a) that the RL tests were actually at lower weights than we have assumed, since I am not sure how you can stall test a fully loaded aircraft without warming it up and climbing to altitude and b) that the RL tests (and game tests by players) were pilot eyeballed from the altimeter and not quite at level flight, unlike the in game robot tests which were. In addition the RL PEC at the stall speed is negligible - two out of three of Farky's sources suggest this.

 

If that is the case the game is fairly accurate in this respect, so perhaps the issues people have with it are down to the engine limitations more than the CLmax.

Edited December 30, 2016 by unreasonable