Corsair Turning Ability in AH

[gripen]

Brooke, did you got my email on determining the e? The median system you use is not particularly accurate.

[Brooke]

It's reasonably OK -- I looked at the fit manually.  Best is probably least squares, but median gives correct value +/- about 0.01 or 0.02 or so.

[Brooke]

I just did a quick plug-in of data for the P-38J.  It seems that the P-38J should have higher turning rate than the F4U both with and without flaps (unless I made an error, of course) but a larger turning radius.

I was using, from America's Hundred Thousand:

A = 8.24
S = 327.5 ft^2
BHP = 1600 HP
N = 3000/2.1 = 1429 RPM
D = 11.5 ft
W = 15,500 lbs

From P-38J pilot's manual at W = 15,000 lbs, clean, v_stall = 94 mph ias = 110 mph CAS.  With full flaps, v_stall = 69 mph IAS = 84 mph CAS.  So, C_L_max at 15,500 lbs = 1.5 flaps up and 2.58 with full flaps.

I assumed e = 0.8 for clean and e = 0.9 with full flaps.  I assumed C_D_min = 0.02 clean and 0.09 with full flaps.

Doing all this in the spreadsheet (a link to which is in the my document), I have to correct for T = 2 * (thrust per engine), and I get:

max turn rate with flaps = 22.75 deg/sec, radius = 525 ft
max turn rate flaps up = 20 deg/sec, radius = 875 ft

The spreadsheet I'm using is here:

http://www.electraforge.com/brooke/flightsims/aces_high/stallSpeedMath/turningPerformance-v3.xls

Note that for P-38's, you have to manually modify the T column (add a multiplier of 2 in the formula).

[gripen]

Originally posted by Brooke
It's reasonably OK -- I looked at the fit manually.  Best is probably least squares, but median gives correct value +/- about 0.01 or 0.02 or so.

I got the e value about 0,76 (you got 0,81) for clean condition using least squares from the chart you quoted (it's pretty hard to read). The Cl^2/Cd chart also shows if the curve starts to bend from linear when nearing stall.

[F4UDOA]

You're forgetting about the drag; in order to improve the turn radius and have the same turn rate, you'd need to add as much lift as drag.

Benny,

At low speed drag is not much of a factor only weight.

[Brooke]

Originally posted by gripen
I got the e value about 0,76 (you got 0,81) for clean condition using least squares from the chart you quoted (it's pretty hard to read). The Cl^2/Cd chart also shows if the curve starts to bend from linear when nearing stall.

I digitized the graph.  Here is a table of data.  I get 0.81 and 0.95 or so when I look for best fit of C_D_actual vs. C_D_formula (plotting one vs. the other) for various values of e.

Clean
C_L, C_D

-0.408945687   0.031011236
-0.234504792   0.022921348
-0.064536741   0.019325843
0.015974441   0.019325843
0.074121406   0.019325843
0.172523962   0.019325843
0.253035144   0.021123596
0.423003195   0.031011236
0.575079872   0.043595506
0.731629393   0.060674157
0.932907348   0.085842697
1.111821086   0.11011236
1.27284345   0.138876404
1.366773163   0.155955056
1.402555911   0.164044944

Full flaps
C_L, C_D

-0.230031949   0.101123596
-0.064536741   0.093932584
0.132268371   0.093033708
0.3514377   0.100224719
0.512460064   0.111910112
0.72715655   0.127191011
0.923961661   0.144269663
1.125239617   0.16494382
1.268370607   0.193707865
1.438338658   0.221573034
1.594888179   0.256629213
1.791693291   0.295280899
1.961661342   0.333033708
2.104792332   0.37258427

[Brooke]

I also made a general-purpose spreadsheet (easy to use, I hope) so that folks can estimate the turning performance of any aircraft as long as you know things like prop diameter, HP, wing area, aspect ratio, weight, etc.

Here it is.  It would be interested to see people plug in various other aircraft to see how they compare to performance Aces High.

http://www.electraforge.com/brooke/flightsims/aces_high/stallSpeedMath/turningPerformance-v4.xls

[gripen]

Brooke,
You include nonlinear part of the Cl^2/Cd (below about Cl 0,15) to the calculation and also the part above Cl 1. The wind tunnel data in this case is a bit strange because above Cl 1 the e actually raise, normally it decrease due to separation (this indicates that there might be something wrong in the wind tunnel data corrections). If you look Perkins&Hage, you can see that they don't include nonlinear parts to the slope of the Cl^2/Cd curve and also NACA measured e in range between Cl 0,2-1.

If I use your values at that range (Cl 0,2-1), I got e values around 0,75-0,77 depending what I include to the calculation. Full positive Cl range (including nonlinear parts) gives e value 0,80.

[Brooke]

For most flight modelling (modelling climbs, level flight, etc.), they want the model to fit best at lower C_L's, as that's where the plane is flying.  For this modelling, we want C_D as a function of C_L that works when C_L is higher, as that's the performance regime the system is trying to model. For me, by eye, it looks like a truly great fit with e = 0.8 clean and e = 0.95 with full flaps.

[HoseNose]

I just watched Borat... I'm in absolutely in no condition to even attempt to understand anything beyond common second grade knowledge.

My brain...she burns.

[Knegel]

Originally posted by gripen
The F2A data (Figure 5) shows pretty similar increase in value of the e with flaps. Because the e can be presented as:

e = 1/(pi*AR*K)

And the F2A data gives values of K:

flaps 0deg K = 0,070 => e = 0,78
flaps 22deg K = 0,068 => e = 0,80
flaps 56deg K = 0,057 => e = 0,95

So the same phenomena is there but the output of the engine limits the turn performance more than in the case of the F4U and the flaps system is not particularly effective (there were much more effective setups giving similar drag characters as in the figure from Perkins&Hage posted by dtango in the page two of this thread).

To lower the flaps increase the aspectratio, that will increase e, thats ok, but at same time the wingarea get reduced!! This will even out the + of e, it also result in a less effective thrustline and no all parts of the wing produce the max lift anymore(the parts without flaps never reach its max AoA).

You also ignore in all your calculations that despite the fact that the CL max is higher, the max lift is smaler at so much slower speed(110mph vs 180mph, best turnspeeds for the AH F4U-4), but at both conditions the planes need to overcome the 1G, as result the slower flying plane need to waste more of its lift to stay in a level flight, so it have a smaler "excess lift" than expected. With other words, the plane cant bank as tight, without to lose altitude.

This factors together make a sustained turn, same like the climb less effective with flaps.

[dtango]

Knegel:

Gosh, where do I start??  I'll post a response when I get a chance to pull a few things together.

Tango, XO
412th FS Braunco Mustangs

[Knegel]

Originally posted by HoseNose
I believe that turn rate should only be lower at particular speeds.

At some speeds the initial deployment of flaps and even when the flaps go all the way down, the aircraft will turn at more degrees per second (or turn rate) at slightly lower speeds. If the opposing aircraft (let's say they're both F4U-4's for example) is flying in the speed range without flaps, it will not turn at the same degrees per second. Once the opposing F4U-4 (no flaps) reaches a speed high enough, it will then turn at more degrees per second than the F4U-4 with full flaps.

If we could have a chart with 'degrees per second' on the y-axis and 'mph' on the x-axis for our in-game F4U-4 and perhaps 3 different lines (one indicating F4U at no flaps, one with F4U at maybe 20 degrees and one F4U at 50 degrees) that would help.

We still talk about a sustained turn here. For now noone argue aginst the positive influece of flaps while a decelerated turn(turn with energy lost).

[Knegel]

Originally posted by F4UDOA
Knegal,

As i wrote before, if this climb chart is ok, then the plane must be able to climb at even slower speeds and it must be able to turn at this speed, but in AH it cant. Thats my point.

The F2A test show that no matter if sustained or decelerated, the turn with flaps/no matter what flap position) result in a less good turnrate and radius above speeds of 110mph IAS. Lets say the F4U is more big and so the speed is a bit higher, but flaps simply dont provide more lift at highspeed, the speed where the airflow cant follow the airfoil is very low with flaps and the flaps start to work as leverage below the plane, as result mainly drag get produce and the nose down behaviour start to(at highspeed) occur.
While our AH flaps dont stop to produce more and more lift.

If i remeber right, british testers also fund that the 109 flaps dont brought an advantage regarding the turn radius.

Greetings,

Knegel

[Brooke]

Knegel, are you arguing that the F4U should not turn better with full flaps?

If so, I have the opposite belief.  Unless there is an error in my model (and I am quite confident in it at this point) -- the F4U does turn better with full flaps.

If you want to try the model on the F2A, click on the spreadsheet link here.  You can put in F2A prop diameter, HP, wing area, aspect ratio, etc. and see how it works out.

http://www.electraforge.com/brooke/flightsims/aces_high/stallSpeedMath/turningPerformance-v4.xls