Stall speed of some aircraft

[Brooke]

I recently got the pilot's manuals for most US fighters and was looking at stall speeds with full flaps and gear down.  I got curious and tested several models in AH, and some of the aircraft (such as the F4U) seem different from what is listed in the manuals.  Maybe I'm doing something wrong, or the pilot's manuals are not accurate in their stall-speed values, but here is what I did.

I took each aircraft up to about 400 ft (+/- 100 ft) and put on the autopilot and opened the E6B.  I then slowed down, dropped full flaps and gear and adjusted the throttle to that I was flying steadily with the stall horn just starting to sound.  I then smoothly reduced throttle to zero and noted the speed from the E6B where the nose made its sharper drop (a little after the buffetting sets in, of course).  I reapeated it a bunch of times to make sure I was getting the correct number, as the speed is decreasing in the course of doing this test.  I am pretty sure, though, I'm getting the number when the nose makes its sharp drop.

I then looked in the pilot's manuals for stall speed with full flaps, gear down, and power off.  I corrected for the fuel load and ammo load in Aces High (by looking at the E6B to get fuel load, hangar to get ammo load, looking in America's Hundred Thousand for the gross weight of the aircraft at similar loads and correcting for the difference in weight of fuel load by 6 lbs/gallon and ammo at 249 lbs per 800 rounds .50 cal and 92 lbs per 150 rounds of 20 mm, and using either the chart in the pilot's manual or correcting the stall speed with vstall_at_new_weight = sqrt(new_weight/ref_weight) * vstall_at_ref_weight).  I corrected for IAS vs. corrected air speed by using the charts in the pilot's manuals (so that when the manual gave stall speed in IAS, I corrected to corrected airspeed).  And I converted everything when in knots to mph.

For the F4U-1, in AH, I get stall at 71 mph (+/- about 2 mph).  From the pilot's manual, I get 86 mph.

For the P-38J, in AH, I get a stall at 83 mph (+/- about 2 mph).  From the pilot's manual, I get 89 mph, so reasonably close.

For the F6F, in AH, I get a stall at 74 mph (+/- about 2).  The manual is somewhat inconsistent on what the flaps-down, gear-down stall speed is (as two values are inconsistent, and one graph does not say if the y axis is IAS or corrected airspeed).  It could be 72 mph (which is quite close, but perhaps not correct), 83 mph (which is perhaps the most likely value from the manual), or 92 mph.

[Schatzi]

Im not 100% sure here Brooke, but i think when buffetting sets in, youre way past stall speed already.

To me, stall speed is the point where you cannot hold level flight anymore. That point is a little earlier, at the onset of stall horn buzzing.
That would explain why your numbers are a little low consistently.

[Pyro]

Using the auto-pilot will give low results because it can't hold level flight at slow speed and you'll be in a pretty good descent.   It's a pain to do but it has to be flown manually.  It's not easy though, I have a tough time trying to do it even with specialized flight-testing debug versions.

[Brooke]

Originally posted by Pyro
Using the auto-pilot will give low results because it can't hold level flight at slow speed and you'll be in a pretty good descent.   It's a pain to do but it has to be flown manually.  It's not easy though, I have a tough time trying to do it even with specialized flight-testing debug versions.

The stall speed should, I think, be nearly identical.  The reason is that, if the plane is going level at stall, the stall happens at the lowest velocity where L = W, which is the following, where rho is air density, v_stall_level is the stall speed in level flight, C_L_max is the maximum coefficient of lift of the aircraft, S is the wing area, and W is the weight of the plane:

0.5 * rho * v_stall_level^2 * S * C_L_max = W

If the plane is not going level, but is in a descent of theta degrees (where theta = 0 means it's going level), where v_stall_descent is the airspeed at which the stall happens in this configuration, the stall happens at:

0.5 * rho * v_stall_descent^2 * S * C_L_max = W * cos(theta)

When I look at the rate of descent during the autopilot method, it is about 750 fpm descent.  Even at a rate of descent of 1000 fpm at stall, 1000 ft/min = 11 mph, so if the airspeed is 70 mph at stall, theta = atan(11 / 70) = 9 degrees.  cos(9 deg) = 0.988.  Then, v_stall_descent^2 / v_stall_level^2 = 0.988, and v_stall_descent = sqrt(0.988) * v_stall_level = 0.994 * v_stall_level.

To double check, I took up the F4U-1 and did it manually, keeping the rate of descent as close to zero as I can manage (which is reasonably close to zero at stall), I get about 70 +/- 2 mph indicated, about the same as the autopilot method.

[Brooke]

Originally posted by Schatzi
Im not 100% sure here Brooke, but i think when buffetting sets in, youre way past stall speed already.

To me, stall speed is the point where you cannot hold level flight anymore. That point is a little earlier, at the onset of stall horn buzzing.
That would explain why your numbers are a little low consistently.

Howdy, Schatzi.  Buffetting (for airplanes that feel buffetting -- there are some that just go from smooth flight to stall, depending on the characteristics of their wings and location of the elevators) starts when airflow starts its separation from the surface of the wing.  Buffetting gets worse and worse until the airflow completely separates from the surface of the wing, which is the stall.  At that point, there is a rapid and large breakdown of lift.

Different airplanes hit stall at slightly different angles of attack, but generally WWII-type airplanes stall at about 12-16 degrees angle of attack.  On civilian planes like Cessna 152's, a stall horn is typically set to start sounding at a particular angle of attack and to get louder as the angle of attack increases to give a graded warning as you approach the angle of attack of stall.  Buffetting is a more-direct indication of stall as it is happening because of the start of separation of airflow and gets worse as more and more airflow separates.

However, the amount of pre-stall buffetting is dependent on the airplane.  Some have a coefficient of lift vs. angle of attack that has a rolloff from linear well in advance of stall and a tail behind the wing that is in the path of the turbulence rolling back from the wings.  For those, buffetting is a good indication of impending stall, with a good amount of warning and with buffetting getting stronger as the stall is approached.  Others have a very linear coefficient of lift vs. angle of attack until the stall angle is hit, and then there is the rapid dropoff -- i.e., the separation occurs suddenly and all at once, not in any graded way, so there is not much buffetting in advance of the stall.  Others have a tail that isn't in the way of the turbulence from separation off the wing, and they don't feel the buffetting in the stick, for example (although they still might feel its effect on lift and resultant shaking of the plane).

Hitech has said that the buffetting in AH is modelled as starting at a particular angle of attack.  So, all airplanes get it, and it is kind of an approximation of real buffetting.

As for ability to fly level, what you are talking about is probably more an effect of velocity.  The lift equation is:

L = 0.5 * rho * v^2 * S * C_L

where rho is air density, v is the airspeed, S is the wing area, and C_L is the coefficient of lift (which depends on the angle of attack of the wing).  C_L increases with angle of attack up to just before stall then falls off upon stall.  The maximum is C_L_max.  But even at C_L_max, there are velocities that are low enough that L is less than W the weight of the aircraft, and so you cannot maintain level flight.  That doesn't mean you are in a stalled condition in the aircraft, though -- you can still have a lower angle of attack than stall and still have flow attached over your wings at any speed.

[Brooke]

Originally posted by Brooke
Even at a rate of descent of 1000 fpm at stall, 1000 ft/min = 11 mph, so if the airspeed is 70 mph at stall, theta = atan(11 / 70) = 9 degrees.

Hmm.  Actually, it should be theta = asin(11 / 70), although that's still theta = 9 degrees.

[Brooke]

HiTech just posted elsewhere that the buffet in Aces High is in fact adjusted to be the moment of stall, or specifically the peak of coefficient of lift.  So, buffet is not slightly before stall, but right at stall.

This makes testing a lot easier and more repeatable.  I will retest under the above conditions but using buffet as the indication of stall instead of nose drop.  The data is going to be the same, I believe, as the nose drop and buffet occur a fraction of a second apart, and the speed I read from the E6B is going to be the same to within the margin of error of my ability to read it.

[Brooke]

I've redone my study of F4U-1 stall speed in Aces High vs. the stall speeds listed in the F4U-1 pilot's manual for clean, power off; clean, power on; dirty, power off; and dirty, power on. I find excellent agreement between the manual and Aces High.

I did some math to figure out a technique that would be repeatable, that would allow steady-state measurements (which are much easier to take), and that would allow reasonably easy avoidance of changing g loads on the aircraft.

My results and analysis are posted here:

http://www.electraforge.com/brooke/flightsims/aces_high/stallSpeedMath/stallSpeedMath.html

If anyone finds errors with my analysis or data, please let me know. I've checked it a couple of times, but that doesn't mean there aren't errors, and it would be better if the analysis and data stands the test of being looked at by others.

There is a discussion of stall speeds in another thread here:

http://forums.hitechcreations.com/forums/showthread.php?s=&threadid=197316

which is the more appropriate place.

[Brooke]

So, my first tests were, I now believe, not good for finding the stall speed in Aces High.  The problem, I think, was that the first tests were not careful about g load on the aircraft (i.e., accelerations in the directions of lift an weight).  Steady-state descent or ascent is OK, but accelerations in those directions can have a big impact on where stall happens.  The new method gets around accelerations.

[FBplmmr]

I like the blue planes:)