Guide to calculating turn rates of aircraft

GregP · Mar 12, 2018

We did have a guy in here who insisted that the slats on the Bf 109 improved the airfoil to a CL of something like 1.94 or so, as I recall. I countered that the slats were only across about some 1/3 of the wing and they were there to keep the ailerons effective near and through stall, not to make it turn tighter. He didn't buy it, but we have a Hispano Ha.1112 and a Bf 109E at the museum, so I measured the slats. They are across only about 23% of the outer span.

So, the effective wing area would have normal CL plus some small addition at the outer edges. Since the wing tapers, the outer 23% is NOT 23% of the wing area, but less. Net result was not all that much, but it DID keep the Bf 109 hanging in there near the stall, fully controllable with ailerons. That is in contrast to SOME fighters that tip-stalled, and could hang in there until near the stall, at which point the stick would not raise a wing if stalled.

Not surprisingly, the Bf 109 had some very good dogfighting characteristics, and some that were not so good. Go figure ... it was a compromise, as were all the fighters. To be sure, it was a good one, but not perfect. The other great European fighter of the ETO, the Spitifre, was also a compromise. Surprise. In some situations, the Bf 109 had the advantage. In others, no so.

I'd say the pilot who knew his mount, inside and out, had an advantage that would be hard to lose, regardless of which one he was flying.

Ivan1GFP · Mar 12, 2018

Hello GregP,

Thanks for the insight. I really had not thought about how long the slats actually were.
It should still increase the CL, but from your measurements, maybe not enough to make a great deal of difference.
My understanding was that when a wing dropped at the stall, the proper recovery technique was with the rudder and not the ailerons though I am in no position to test whether stick or rudder is appropriate.

- Ivan.

GregP · Mar 12, 2018

The proper reaction to a wing drop IS rudder, but some planes also retain aileron effectiveness through stall. The Bf 109 was one of those.

In the modern era, we also have the Mitsubishi-Mooney Mu-2 series. There was a short one and a long one. Both have spoilers as primary roll control. Since spoilers only reduce lift, they were not effective at all near, at, or below stall, and rudder was the ONLY effective control. I have read, but have never confirmed that using aileron (nee ... spoiler) at stall made the wing drop worse. The Mu-2 had a bad accident rate at first. It was proven that proper training made that go away. Today, you can fly an Mu-2, but will pay a LOT of insurance unless you get and maintain proper training in the aircraft. It has a good safety record with properly-trained pilots.

I don't know of any military aircraft with just spoilers as primary roll control.

DarrenW · Mar 12, 2018

Dean did some calculating of his own regarding the turn radius of various US fighters in America's Hundred Thousand. He basically was looking at two factors, wing loading and maximum wing CL, under the assumption that the aircraft had enough power to sustain the turn and not sink in altitude. With this information he placed the FM-2 as best of the eleven fighters, giving it an arbitrary 100%, and ranked the others in comparison to it accordingly.

For instance, the P-63 came in second at being able to achieve 124% of the FM-2's radius, followed by the P-61 at 133%, then the F6F at 138%, the P-51 at 179%, and so on. Even more surprising to me than the Black Widow's ranking was the placement of the F4U in dead last. Dean surmises that the relatively lower maximum CL, due to the spoiler on the right wing, was the culprit and apparently NACA testing supports this notion.

I figure that turn radius is just as important as turn rate, because if you can't turn tight enough to bring your guns to bear on an enemy than being able to turn at a high rate of speed really amounts to nothing.

Shortround6 · Mar 12, 2018

The thing is you would be trading off a very momentary advantage of angle for an even faster bleed off of speed. As an extreme example say you are doing 375mph in the 109 when you start to pull a 6 G turn. Stalling speed at 6 "G"s (at 12,000ft) is around 275mph. Now you can try to pull a 7 "G" turn, but just yanking on the stick is probably not going to change the angle of attack to a point where the slats pop out at 75-100mph faster than the stall speed.
Since lift goes up with the square of the speed going 350mph gives you just under 16% more lift than 325mph let alone the difference of 300mph vs 375mph.

SOme of the people who seem to be advocating this extra few degrees of angle of attack seem to forget that both the area of the wing and the area of the fuselage (and horizontal stabilizer) are all going to be merrily traveling along tilted up about 15-17 degrees from the aircraft's actual line of travel. In other words, even if the airplane isn't technically stalling it sure isn't making the smallest possible turn either. The slats may add 2-3 degrees to the angle of attack (figures going into the 20 degree angle of attack range are for full span slats)

The other point is that the coefficient of drag is rising faster than the coefficient of lift at these high angles of attack and deliberately pulling the plane into an near accelerated stall is just a little bit dangerous.

BiffF15 · Mar 12, 2018

DarrenW said:
Dean did some calculating of his own regarding the turn radius of various US fighters in America's Hundred Thousand. He basically was looking at two factors, wing loading and maximum wing CL, under the assumption that the aircraft had enough power to sustain the turn and not sink in altitude. With this information he placed the FM-2 as best of the eleven fighters, giving it an arbitrary 100%, and ranked the others in comparison to it accordingly.

For instance, the P-63 came in second at being able to achieve 124% of the FM-2's radius, followed by the P-61 at 133%, then the F6F at 138%, the P-51 at 179%, and so on. Even more surprising to me than the Black Widow's ranking was the placement of the F4U in dead last. Dean surmises that the relatively lower maximum CL, due to the spoiler on the right wing, was the culprit and apparently NACA testing supports this notion.

I figure that turn radius is just as important as turn rate, because if you can't turn tight enough to bring your guns to bear on an enemy than being able to turn at a high rate of speed really amounts to nothing.

View attachment 485744

DW,

You are speaking of two fights and discounting one unnecessarily. The two fights are rate (degrees per sec) and radius AKA a knife fight or min radius. Yes you must be able to bring your nose to bear however it can be done in many ways. The Guy who turns more degree per second has an advantage if used properly. Same for the radius fighter. Both have uses and merits, as well as drawbacks. I have won many a fight by being faster, turning more degrees per sec, all while flying a bigger circle. The geometry of two mismatched circles means one guy will eventually bring his nose to bear / allow weapons employment.

Cheers,
Biff

DarrenW · Mar 12, 2018

Thanks BiffF15 for your first hand knowledge of the subject, sometimes being there makes all the difference. And I can see how both methodologies are useful, depending on the circumstances one finds himself in.

Stig1207 · Mar 13, 2018

BiffF15 said:
DW,

You are speaking of two fights and discounting one unnecessarily. The two fights are rate (degrees per sec) and radius AKA a knife fight or min radius. Yes you must be able to bring your nose to bear however it can be done in many ways. The Guy who turns more degree per second has an advantage if used properly. Same for the radius fighter. Both have uses and merits, as well as drawbacks. I have won many a fight by being faster, turning more degrees per sec, all while flying a bigger circle. The geometry of two mismatched circles means one guy will eventually bring his nose to bear / allow weapons employment.

Cheers,
Biff

That's something I struggle to get my head around, as often the difference in turn rate is a mere second or two. Assumnig that the combatants start of on equal terms, then it's going to take awhile before the aircraft with 1 or 2 secs advantage can capitilise on it. That may work out alright in a 1-on-1 situation; but in a multi participant engagement, it seems a bit risky.
Are there some other factors I'm missing, when turn rates are compared?

Shortround6 · Mar 13, 2018

I keep referring to these charts when discussion of turning come up.
http://www.spitfireperformance.com/spit109turn.gif

They are calculated and not the result of test flights and may be based of at least one wrong assumption but they illustrate many of the differences we are talking about.
For example if you take the time to turn 360 degrees of 20 seconds ( right hand side of chart) and run it across to the stall line you find the 109 is doing just about 3 Gs, has a radius of 870 ft (calculated) and is doing about 190mph (or just a bit more?) but cannot maintain height.

The Spitfire, also taking 20 seconds to turn 360 degrees is pulling just under 2.5 "G"s and has a radius of about 696ft because it is flying at 150mph. It can maintain height. Please note there are, in theory, quite a number of speeds, radiuses and G loadings that will give a 20 second turn time. Many are not practical in combat.

Please note that this chart was calculated for the 109E and the 109F and due to a much lower drag the F had more power available to sustain a turn. It might not have been able to turn any tighter at stall (or maybe it could, I don't know) but it could turn much tighter than the E IF both planes were trying to maintain altitude.

They charts do show the wide variations possible in turning. They also show only one altitude and one power to weight ratio for each airplane.

Ivan1GFP · Mar 13, 2018

I believe part of what is missing from this discussion is what happens after the initial maximum rate turn.
My comment to Laurelix97's method which also applies to DarrenW's quote from Francis Dean's book is that neither comparison takes into account the energy loss from profile drag, induced drag, etc. and also don't take into account how much of that energy can be replaced by engine thrust.

Two aeroplanes may both enter the same 6G turn at the same speed. Perhaps one CAN pull more G but the pilot probably can't handle it and still do anything useful. Initially the limit may be aircraft structural strength or pilot endurance rather than maximum lift or stall speeds.
One has to consider what happens after the first 90 degrees or 180 degrees.
One aeroplane may have much more drag or less engine thrust and the speeds are no longer the same and the slower aeroplane may not be able to pull as much G as the faster aeroplane.
The time to execute a 360 degree turn is a useful data point, but it really does not show even close to the entire picture.
Knowing the entrance and exit speeds also helps because without it, what we are really comparing is a couple airshow or figure skating performances.
This is why I was stating that whenever drag and engine thrust are not taken into account, it is really a measure of instantaneous and not sustained turn performance. I am by no means stating that this is a useless comparison because it is not, but one must keep its meaning in perspective.

- Ivan.

BiffF15 · Mar 13, 2018

Stig1207 said:
That's something I struggle to get my head around, as often the difference in turn rate is a mere second or two. Assumnig that the combatants start of on equal terms, then it's going to take awhile before the aircraft with 1 or 2 secs advantage can capitilise on it. That may work out alright in a 1-on-1 situation; but in a multi participant engagement, it seems a bit risky.
Are there some other factors I'm missing, when turn rates are compared?

Stig1207,

You are right on both accounts. With 1-2 degrees per second advantage it could take considerable time and fuel to end a fight. However look at it under a couple of different scenarios. First you are defensive but are the player with the 1-2 degree advantage. You would sustain what you are doing until you can leave the fight (as long as you are not about to die), reverse and go offensive or get a friend to join in. The slower offender will: change the fight to force you to err as to gain position to employ, will call in his buddy to help or go home / leave.

In a pristine environment you can fight for as long as you want, or gas allows, or get kill removed. When training the pristine set up is best for learning as it's a building block approach. As skill increases so does the tactical problems and more options become available as do variables.

In a large force event you don't want to turn much if possible in a dirty environment (hostile laden) as you can easily get whacked from a guy doing the "unobserved" entry. If you do anchor you do what's required to survive if defensive or quickly kill if offensive. Wing flashes, flares, explosions are all like blood in the water and the sharks will show up rather quickly.

Cheers,
Biff

swampyankee · Mar 13, 2018

GregP said:
The proper reaction to a wing drop IS rudder, but some planes also retain aileron effectiveness through stall. The Bf 109 was one of those.

In the modern era, we also have the Mitsubishi-Mooney Mu-2 series. There was a short one and a long one. Both has spoilers as primary roll control. Since spoilers only reduce lift, they were not effective at all near, at, or below stall, and rudder was the ONLY effective

I don't know of any military aircraft with just spoilers as primary roll control.

P-61. I believe its small ailerons were to provide feel.

swampyankee · Mar 13, 2018

DarrenW said:
Dean did some calculating of his own regarding the turn radius of various US fighters in America's Hundred Thousand. He basically was looking at two factors, wing loading and maximum wing CL, under the assumption that the aircraft had enough power to sustain the turn and not sink in altitude. With this information he placed the FM-2 as best of the eleven fighters, giving it an arbitrary 100%, and ranked the others in comparison to it accordingly.

For instance, the P-63 came in second at being able to achieve 124% of the FM-2's radius, followed by the P-61 at 133%, then the F6F at 138%, the P-51 at 179%, and so on. Even more surprising to me than the Black Widow's ranking was the placement of the F4U in dead last. Dean surmises that the relatively lower maximum CL, due to the spoiler on the right wing, was the culprit and apparently NACA testing supports this notion.

I figure that turn radius is just as important as turn rate, because if you can't turn tight enough to bring your guns to bear on an enemy than being able to turn at a high rate of speed really amounts to nothing.

View attachment 485744

I'm looking at some of the lift coefficients shown, and I'm not believing them. While there are specialized airfoils with unflapped max lift coefficients in the range of 2+, like the Liebeck airfoils, they're very much one-point designs. Clmax of 1.6 to 1.7 would be plausible.

ssnider · Mar 13, 2018

http://www.dtic.mil/dtic/tr/fulltext/u2/a800883.pdf

more then I can understand for F2A3

DarrenW · Mar 14, 2018

swampyankee said:
I'm looking at some of the lift coefficients shown, and I'm not believing them. While there are specialized airfoils with unflapped max lift coefficients in the range of 2+, like the Liebeck airfoils, they're very much one-point designs. Clmax of 1.6 to 1.7 would be plausible.

I can understand your skepticism and respect your knowledge on the subject. But would you at least agree that the order of highest to lowest Clmax is correct, does this at least look plausible to you? I'm asking this because the figures for maximum lift coefficient given in the book were only used for ranking each aircraft according to their minimum achievable turn radius and not for calculating other aerodynamic qualities of the aircraft.

swampyankee · Mar 14, 2018

DarrenW said:
I can understand your skepticism and respect your knowledge on the subject. But would you at least agree that the order of highest to lowest Clmax is correct, does this at least look plausible to you? I'm asking this because the figures for maximum lift coefficient given in the book were only used for ranking each aircraft according to their minimum achievable turn radius and not for calculating other aerodynamic qualities of the aircraft.

I don't think the relative rankings are too far off, but I would probably move the Corsair up with n the rankings.

GregP · Mar 15, 2018

Hi Swampyankee.

Yes, but it did HAVE small ailerons which would function if the spoilers failed, so it wasn't an all-spoiler aircraft like the Mu-2 is.

ODonovan · Mar 15, 2018

I see a lot regarding sustained turns and initial 360 turns, but I see nothing about turns which were not circular. I doubt many pilots did circular 360s, at least after the first few seconds. That's been my experience in simming, anyway. It would be "pull it in tight, lose some speed, relax the turn to gain back a bit of speed, then pull it in tight again," so most sustained turns would be more like a series of ovals.

For pure turning, even the Dauntless could out-turn the Zero in a dogfight simply because the Zero couldn't go above six Gs without ripping the wings off and the Dauntless could go as high as 12 Gs. Once the Dauntless pulled a firing solution on the zero, the pilot could take a shot then relax his turn to conserve speed and altitude, knowing the Zero didn't have that powerful of an engine and would have to swing a bit wide to keep E as well.

Before I get tons of "you have to be kidding" responses, this actually happened in real life.

"Swede" Vejtasa was a true badazz pilot. All I know is that I wouldn't have wanted to have been his gunner, that day. When they landed, he was probably three inches shorter in height than he was when they took off. The Navy (in effect) said to Vejtasa, "if you're such a hotshot in a Dauntless, let's see what you can do in a fighter," so they transferred him into Wildcats. He proceeded to get seven kills in one day, and that was in a Wildcat, not even a Hellcat. Bad to da bone!

-Irish

DogMD11 · Mar 15, 2018

Hi GregP,

Another Mitsubishi product, the Mu-300 Diamond jet, has only spoilers for roll control. I flew the Air Force version of this aircraft, the T-1 Jayhawk, for 11 years. If you take a look at the wing, it sure looks like it has ailerons, but they are in fact only trim tabs; they do not move with the spoilers. The spoilers are manually powered, which give a slow roll rate and heavy feel, a desired attribute since the T-1 is used to train heavy pilots. The spoilers are effective throughout the airspeed range, even in the stall, and they also double as speed brakes--but are not very effective in this aspect.

Stig1207 · Mar 15, 2018

ODonovan said:
"Swede" Vejtasa was a true badazz pilot. All I know is that I wouldn't have wanted to have been his gunner, that day. When they landed, he was probably three inches shorter in height than he was when they took off. The Navy (in effect) said to Vejtasa, "if you're such a hotshot in a Dauntless, let's see what you can do in a fighter," so they transferred him into Wildcats. He proceeded to get seven kills in one day, and that was in a Wildcat, not even a Hellcat. Bad to da bone!

Claimed or was credited with that number of kills, but was that what the Japanese lost in those encounters?

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