Could the Bf 109 E really out-turn the Spitfire Mk I?

[Holtzauge]

(Sorry, don't know if this has already been answered)

How that time were they able to measure (to verify the calculated data) the actual turning radius in flight? And how could one determine the altitude and speed where the tightest circle was possible?

This is a good point, and I have not seen any WW2 era measurements on turn radius. However, what we have, is data from multiple sources stating turn times.

But there is also calculated data from WW2 on both turn rate and turn radius. And for my turn model validation of the Bf 109, I've used two German sources (TB-Nr 18/40, Die Kurven-wendigkeit der Me-Typen III. Teilbericht, and a Messerschmitt AG calculation for the instantaneous turn performance of the Bf 109 K-4). In addition there are two comprehensive reports by the RAE, one on the Spitfire Mk I's turn performance as affected by flaps and altitude, RAE R&M 2349, and one assessing the Bf 109 E's handling and maneuverability, RAE R&M 2361.

But actual flight trials from the time measuring turn radius then no, I don't believe such data exists, much for the reason you mentioned, i.e. it was at the time quite difficult to measure accurately.

Regarding the altitude at which the tightest turn radius was possible, that would from a theoretical perspective be at sea level for both the Bf 109 E and Spitfire Mk I.

 

[Galahad]

This is a good point, and I have not seen any WW2 era measurements on turn radius. However, what we have, is data from multiple sources stating turn times.

But there is also calculated data from WW2 on both turn rate and turn radius. And for my turn model validation of the Bf 109, I've used two German sources (TB-Nr 18/40, Die Kurven-wendigkeit der Me-Typen III. Teilbericht, and a Messerschmitt AG calculation for the instantaneous turn performance of the Bf 109 K-4). In addition there are two comprehensive reports by the RAE, one on the Spitfire Mk I's turn performance as affected by flaps and altitude, RAE R&M 2349, and one assessing the Bf 109 E's handling and maneuverability, RAE R&M 2361.

But actual flight trials from the time measuring turn radius then no, I don't believe such data exists, much for the reason you mentioned, i.e. it was at the time quite difficult to measure accurately.

Regarding the altitude at which the tightest turn radius was possible, that would from a theoretical perspective be at sea level for both the Bf 109 E and Spitfire Mk I.

Ah, thanks! Would love to see your great simulations for the K-4 or FW 190 D-9 against its competitors (for example P-51D, Tempest, Griffon Spitfire etc).

 

[Shortround6]

(Sorry, don't know if this has already been answered)

How that time were they able to measure (to verify the calculated data) the actual turning radius in flight? And how could one determine the altitude and speed where the tightest circle was possible?

It was possible. It was also very difficult and only worked at low altitudes. You need ground observers (multiple) and modified surveying instruments. Ane there are limits.
There were also recording G meters (pens recording on paper strips/cylinders) but these did not line up very well with ground observations. That is ground observers didn't know what the airplane was pulling for Gs at any given time.
With a data base they could figure out if airplane was doing a 360 degree turn in 22 seconds and was doing about the same speed at the end as it was at the beginning (or of they knew the speed change) they could look at the charts and figure things out.
Not all planes (in fact most) tested did not have calibrated "test" instruments. Some the test instruments were big and heavy enough to require the removal or relocation of radios/other equipment.

Problem with actual test flights trying to measure the tightest radius is that they have to be done at low altitudes for the best accuracy (ground observers) and if the plane/pilot stalls how much room does he have to recovery before hitting the ground?
If the lower G tests were tracking with the calculated values that was probably good enough.
Stalling speeds could be measured with cameras. Cameras were sometimes used for measuring landing distances. Again, once a data base had been established many flight tests were done without the elaborate test set ups. Unless something out of the expected started happening.


the 109 used a higher wing loading than the Spitfire (and Hurricane) and while the 109 did use more sophisticated high lift devices it was trying to make up a fair amount in wing loading.
109 needed to make up over 25% in coefficient of lift. That is badly stated, the 109s wing in total, needs to generate about 25% more lift than the Spitfire's wing. Not every sq ft of wing is generating the same amount of lift due to airfoil, and airflow over each part of the wing. But figuring that out is very hard.
2nd part is how much drag is wing making to generate the desired lift? If we are looking at CL of 1.3 and higher we have very high angles of attack.
We also have different parts of the wing operating under different conditions. Somebody has already mentioned the Spitfire wing having washout and the outer wing is not operating at the same angle of attack as the inner/mid wing and thus is not generating the same lift per sq ft. But once the 109 (or any other airplane) starts to low flaps to gain an increase that increase is only for the wing part/s that the flap is acting on. Not the area that the ailerons are located at. Unless we are dealing with drooping ailerons and extreme flap deflections.
The 109s slats do help but here again, they are not full span slats and only affect part of the wing. On the 109 only about 1/3 of square footage of wing is affected by the slats due to the wing taper. The Slats keep the outer wing from stalling. If they are fully out the inner wing is stalling and loosing lift.
Difference between airfoil tests in a wind tunnel and the plane actually flying. If you want the best coefficient of lift you need to juggle which parts of the wing are doing what because it may not be uniform across the span and for a 360 degree turn of around 20 seconds the high coefficient of lift means a much higher coefficient of drag.

 

[Simon Thomas]

"We also have different parts of the wing operating under different conditions."
Very true. For the 109, the chord tapers from root to tip and the airfoil thickness tapers from 14.2% T/C at the root to 11/11.35% T/C at the tip. This means that every slice of the wing has a different CL for a set AoA.
The NACA chart for the 2R1 aerofoil is for a single T/C ratio and a single Reynold's number. To determine CL at a different T/C and/or Renold's number requires correction.
Designing a wing is a very complicated exercise, particularly in the 1930's.
Then the actual wing behaves differently again due to elastic deformation under loading, fuselage/wing interactions, wing tip losses and the real wing having gaps, seams, etc.
A flight sim model will never simulate the real aeroplane with 100% accuracy.

 

[Mfezi]

It was possible. It was also very difficult and only worked at low altitudes. You need ground observers (multiple) and modified surveying instruments. Ane there are limits.

and

Problem with actual test flights trying to measure the tightest radius is that they have to be done at low altitudes for the best accuracy (ground observers)

Shortround, do you have a citation where they describe measuring turn radius with ground observers? I have never heard of or seen it done this way and it seems to me it would be extremely inaccurate.

Steady turn performance tests give you both turn rate and turn radius, since the two are kinematically related and that relation is exact for any circular flight path. You only need one to determine the other, but turn rate is much, much easier to measure directly. We always did it this way (point 4 is how you then get an accurate turn radius):

1. Perform a steady level turn (see methods below). How long a steady condition is held depends on instrumentation, technique and some other things that may be specific to the aircraft.
2. Calculate the turn rate (omega) in rad/s or measure the load factor if equipped with a g-meter. The latter is particularly useful for front-side tests (see below).
3. Convert the speed to TAS: IAS -> CAS -> EAS -> TAS
4. Use the kinematic relationships for a circular path to determine turn radius: R = V_t/omega (V_t is the tangential velocity in the circle, equal to the TAS) or use R = V_t^2 / (g * sqrt(n_zw^2 -1)) if load factor was known.

There are additional calculations involved if you want to correct to standard day conditions and compensate for sensor offsets from the aircraft's center of mass (if relying on FTI), but conceptually that is how it is done.

There are typically three test techniques used these days to determine sustained turn performance, depending on the part of the envelope in which you are flying:
1. Front side of the load factor vs airspeed curve (higher speeds): Stable g method
2. Back side (lower speeds): Constant airspeed method, using bank angle to maintain altitude
3. Lower speeds where the load factor is lower than 2: Timed turn method.

Turn performance can also be predicted quite accurately from a level acceleration test, which is very useful as you get a lot of data from one test, but it requires a polar and engine model, so usually only used for aircraft that are already well characterized.

The ground obseerver method for measuring turn radius is new to me - I would appreciate it if you can point me to some reading material. It doesn't really make sense to me, considering how much easier and more accurate the above methods are.

 

[Holtzauge]

Ah, thanks! Would love to see your great simulations for the K-4 or FW 190 D-9 against its competitors (for example P-51D, Tempest, Griffon Spitfire etc).

The next book (Volume 2) I'm planning to do after this one will probably be just that: A comparison of the P-51 and the Fw 190/Ta 152 series.

But to do a fair comparison, I think the P-51's huge internal fuel capacity poses a problem: How much fuel should the P-51 be assumed to be carrying compared to the German fighters?

For the Spitfire Mk I and Bf 109 E comparison, fuel load was not an issue, since they both had about the same internal fuel capacity and fuel consumption, but what weights to assume for the Fw-190 D-9 versus P-51D comparison?

I'm leaning towards a fair comparison being a fuel load for equal endurance, OTOH one could argue that to get an assessment of how a P-51D would fare against a Fw-190 D-9 over Germany, the P-51 WOULD probably be laden with more fuel since it needed this in order to get back to its base in the UK, so this would maybe be a more "realistic" comparison.

 

[Holtzauge]

the 109 used a higher wing loading than the Spitfire (and Hurricane) and while the 109 did use more sophisticated high lift devices it was trying to make up a fair amount in wing loading.
109 needed to make up over 25% in coefficient of lift. That is badly stated, the 109s wing in total, needs to generate about 25% more lift than the Spitfire's wing. Not every sq ft of wing is generating the same amount of lift due to airfoil, and airflow over each part of the wing. But figuring that out is very hard.
2nd part is how much drag is wing making to generate the desired lift? If we are looking at CL of 1.3 and higher we have very high angles of attack.
We also have different parts of the wing operating under different conditions. Somebody has already mentioned the Spitfire wing having washout and the outer wing is not operating at the same angle of attack as the inner/mid wing and thus is not generating the same lift per sq ft. But once the 109 (or any other airplane) starts to low flaps to gain an increase that increase is only for the wing part/s that the flap is acting on. Not the area that the ailerons are located at. Unless we are dealing with drooping ailerons and extreme flap deflections.
The 109s slats do help but here again, they are not full span slats and only affect part of the wing. On the 109 only about 1/3 of square footage of wing is affected by the slats due to the wing taper. The Slats keep the outer wing from stalling. If they are fully out the inner wing is stalling and loosing lift.
Difference between airfoil tests in a wind tunnel and the plane actually flying. If you want the best coefficient of lift you need to juggle which parts of the wing are doing what because it may not be uniform across the span and for a 360 degree turn of around 20 seconds the high coefficient of lift means a much higher coefficient of drag.

And the simulation model I use is designed to capture all those effects you mention: The wing loading, wing profile effects, the wing twist, the Re effects, the slats, and that the flaps only cover part of the wing.

Now how accurately it does that, can of course always be argued: But the proof is in the pudding as they say: If your model produces results that are consistent with flight trials (or IMHO, RAE and Messerschmitt calculations from the era) then you have a good enough model.

I will shortly post another longer video on YouTube with a more detailed comparison of the Spitfire Mk I's versus Bf 109 E's turn performance, and in which how the simulation model was validated will be covered in more detail. To me, the model seems to generate results that are good enough, but I'll leave that up to the viewers to decide.

In my book, I have this quote by the late British statistician George Box which I think captures the problems with simulations quite well: "Essentially, all models are wrong, but some are useful".

 

[Holtzauge]

"We also have different parts of the wing operating under different conditions."
Very true. For the 109, the chord tapers from root to tip and the airfoil thickness tapers from 14.2% T/C at the root to 11/11.35% T/C at the tip. This means that every slice of the wing has a different CL for a set AoA.
The NACA chart for the 2R1 aerofoil is for a single T/C ratio and a single Reynold's number. To determine CL at a different T/C and/or Renold's number requires correction.
Designing a wing is a very complicated exercise, particularly in the 1930's.
Then the actual wing behaves differently again due to elastic deformation under loading, fuselage/wing interactions, wing tip losses and the real wing having gaps, seams, etc.
A flight sim model will never simulate the real aeroplane with 100% accuracy.

And this is why full scale wind tunnel measurements, or flight tests with properly calibrated speed measurements are so important: Because this captures all the effects you mentioned. And the Clmax is just a dimensionless mathematical representation of all this.

So if you have a correct Clmax either from flight trials or full scale wind tunnel tests, you can calculate very accurate turn performance figures. And there is really nothing strange about this, since it's pretty much an established science in aeronautics: If you have an accurate Cl/Cd polar, you can calculate speed, climb and turns with good accuracy. However, this is only half of the puzzle, since you still need to do a good model of the engine, the propeller, and the exhaust thrust. And that is just as big a (if not even a bigger) challenge.

But as was said before, even if you have this base to work from, the next step of mapping this lift and drag on "panels" in the flight simulation engine (wings, propeller blades etc.) is difficult to get right, and which is why current flight simulations sometimes generate very strange effects.

 

[Jaivan]

(Sorry, don't know if this has already been answered)

How that time were they able to measure (to verify the calculated data) the actual turning radius in flight? And how could one determine the altitude and speed where the tightest circle was possible?

I've never seen a report measuring radius in flight. It's usually computed from measured speed and load factor.

In fact, detailed reports on turn performance measured in flight are equally rare for WW2 types. I've only seen two: NACA ACR 3I30 on a Brewster F2A, and Messerschmitt AG VB 110 13 L 42 Kurvenleistung Me 110 F.

In the latter, it is mentioned that they didn't have an experimental procedure to determine turn performance in flight with enough precision until then. In addition to the standard instrumentation, they fitted Me 110 F W.Nr. 3914 with the following extra equipment:
- a Junkers air log to measure true airspeed
- a photoelectric sensor to determine turn time from the Sun's position
- an accelerometer in the cockpit (also with a recorder)
The pilot carried out 20 turns (compare with the +260 done on the F2A!) trying to maintain speed, height and load factor, at heights between 2,100 and 3,500 m, speeds between 190 and 450 km/h IAS and accelerations between 1.1 and 3.75 g, out of which only 6 were considered as "best turns". Data was plotted and corrected to standard take-off weight and normal conditions at 0 m without flaps, giving the following results:
* tightest turn: 24 s, radius 283 m @ 280 km/h IAS and climb rate of -6 m/s
* fastest turn: 19 s, radius 307 m @ 370 km/h IAS and climb rate of -22 m/s
* sustained turn: 30 s, radius 300 m @ 250 km/h IAS

They noted that:
- above 370 km/h, full turn performance was not possible due to high elevator forces and slat deformation
- Cl max decreased with dynamic pressure due to elastic deformation of wing, loss of propeller slipstream overpressure and higher control forces
- in general, best turn performance was obtained at those achievable Cl max without elevator buffeting

 

[Steamed_Banana]

Does anyone know how the Soviet sustained turn time tests were done?

 

[GregP]

It was possible. It was also very difficult and only worked at low altitudes. You need ground observers (multiple) and modified surveying instruments. Ane there are limits.
There were also recording G meters (pens recording on paper strips/cylinders) but these did not line up very well with ground observations. That is ground observers didn't know what the airplane was pulling for Gs at any given time.
With a data base they could figure out if airplane was doing a 360 degree turn in 22 seconds and was doing about the same speed at the end as it was at the beginning (or of they knew the speed change) they could look at the charts and figure things out.
Not all planes (in fact most) tested did not have calibrated "test" instruments. Some the test instruments were big and heavy enough to require the removal or relocation of radios/other equipment.

Problem with actual test flights trying to measure the tightest radius is that they have to be done at low altitudes for the best accuracy (ground observers) and if the plane/pilot stalls how much room does he have to recovery before hitting the ground?
If the lower G tests were tracking with the calculated values that was probably good enough.
Stalling speeds could be measured with cameras. Cameras were sometimes used for measuring landing distances. Again, once a data base had been established many flight tests were done without the elaborate test set ups. Unless something out of the expected started happening.


the 109 used a higher wing loading than the Spitfire (and Hurricane) and while the 109 did use more sophisticated high lift devices it was trying to make up a fair amount in wing loading.
109 needed to make up over 25% in coefficient of lift. That is badly stated, the 109s wing in total, needs to generate about 25% more lift than the Spitfire's wing. Not every sq ft of wing is generating the same amount of lift due to airfoil, and airflow over each part of the wing. But figuring that out is very hard.
2nd part is how much drag is wing making to generate the desired lift? If we are looking at CL of 1.3 and higher we have very high angles of attack.
We also have different parts of the wing operating under different conditions. Somebody has already mentioned the Spitfire wing having washout and the outer wing is not operating at the same angle of attack as the inner/mid wing and thus is not generating the same lift per sq ft. But once the 109 (or any other airplane) starts to low flaps to gain an increase that increase is only for the wing part/s that the flap is acting on. Not the area that the ailerons are located at. Unless we are dealing with drooping ailerons and extreme flap deflections.
The 109s slats do help but here again, they are not full span slats and only affect part of the wing. On the 109 only about 1/3 of square footage of wing is affected by the slats due to the wing taper. The Slats keep the outer wing from stalling. If they are fully out the inner wing is stalling and loosing lift.
Difference between airfoil tests in a wind tunnel and the plane actually flying. If you want the best coefficient of lift you need to juggle which parts of the wing are doing what because it may not be uniform across the span and for a 360 degree turn of around 20 seconds the high coefficient of lift means a much higher coefficient of drag.

The function of the slats was not to keep the outer wing from stalling, though it delayed the outter wing stall, yes. The actual intent and function, according to former Luftwaffe pilots and Messerschmiit employees was to keep the airflow attached to the ailerons to maintain roll control at or around the stall ... the non-slatted portion of the wing's stall. that is. From reports, it did that and the Bf 109 maintained roll control nicely unless it got slow enough or at a high enough angle of attack to fully stall the outer wings. Then it just stalled and maybe spun, like any other non-slat wing does, depending on slip or skid at the time of full stall.

Not intending to say you are wrong above, Shortround, just saying the design intent was to maintain roll control around the stall regime of flight. In practice, it did that quite well.

VERY certainly better than the stall behavior of the Fw 190 series ever did. It's basically why the top aces were VERY relucant to switch airplanes when the Fw 190 becaome available. Nothing wrong with the Fw 190, but it did not exhibit good stall behavior and had very little stall warning before dropping from the sky at stall. To be good in it, you had to go up to altitude and wring it out for feel around the stall before trying to pull hard at low altitude.

 

[Holtzauge]

The function of the slats was not to keep the outer wing from stalling, though it delayed the outter wing stall, yes. The actual intent and function, according to former Luftwaffe pilots and Messerschmiit employees was to keep the airflow attached to the ailerons to maintain roll control at or around the stall ... the non-slatted portion of the wing's stall. that is. From reports, it did that and the Bf 109 maintained roll control nicely unless it got slow enough or at a high enough angle of attack to fully stall the outer wings. Then it just stalled and maybe spun, like any other non-slat wing does, depending on slip or skid at the time of full stall.

Not intending to say you are wrong above, Shortround, just saying the design intent was to maintain roll control around the stall regime of flight. In practice, it did that quite well.

VERY certainly better than the stall behavior of the Fw 190 series ever did. It's basically why the top aces were VERY relucant to switch airplanes when the Fw 190 becaome available. Nothing wring with the Fw 190, but it did not exhibit goos stall behavior and had very little stall warning before dropping for the sky at stall. To be good in it, you had to go up to altitude and wring it out for feel around the stall before trying to pull hard at low altitude.

Yes, I think that was the original purpose of the slats on the bf 109: To improve handling (roll control) close to stall. And the Bf 109 has almost all the design features of the Bf 108 Taifun sporting plane: The adjustable stabilizer with struts, the two control wheels in the cockpit to change the flap and stabilizer angle, the trapezoidal wing planform and the flap and slat arrangement. The Bf 109 is basically and adjustment of the Bf 108 to make it a one-seater and handle a bigger engine. I don't know if anyone can say with certainty that this was the case, i.e. that this was what they did, but the similarities are remarkable.

Then about the Fw 190: Yes, AFAIK it was said to have OK stall warning in power off conditions and at lower speeds, but as I understand it, at higher speeds and when under g-load, it would stall and flick out of a turn with no warning.

 

[Holtzauge]

Does anyone know how the Soviet sustained turn time tests were done?

No, AFAIK this is not documented. But the value of the Soviet era data from for example the TSAGI book Russian aircraft construction 1917 to 1945 is spotty: Some is good, but other data is questionable.

 

[bf109xxl]

Does anyone know how the Soviet sustained turn time tests were done?

Soviet sources do not specify a standard method for measuring turn time, and all the proposed methods - whether using data from onboard recorders of angular velocity and g-force or stopswatch measurements - yield values with a fairly high degree of uncertainty (no less than 1 s, and in reality even more). The books Aircraft Flight Tests, published in 1941 and 1951, contain no references on using ground observation data to determine turn time.

 

[Shortround6]

1. Front side of the load factor vs airspeed curve (higher speeds): Stable g method

very few 1930s or early 40s aircraft had G meters of any sort.
What the pilot thought he was doing vs what he was actually doing could very different.
The NACA was doing a lot of research and put recording G meters in some aircraft in the 1930s or early 30s (?). One test had several pylon racing planes do a 180 degree turn of 10 seconds for an estimated 2 g turn. The actual Gs being pulled at any moment in time from the graph varied from a high of about 6 Gs to a low of -0.something. Ground observers thought the turns looked smooth. The G meter (recording on graph paper) was behind the seat and the pilot/s could not see it in flight.
The planes entered the turn at about 220mph but exited at about 180mph. Pilots had to ease off on the controls in order to avoid tightening the turn too much. If the elevator is below the normal "line" for even a fraction of a second the plane is doing negative Gs for that fraction of a second.
WW II fighters had enough power to maintain a 2 G turn at most operational altitudes (or at least under 20,000ft early in the war) but in tight turns or high speed turns the ability to bank, hold the bank and maintain a constant turn rate with a fixed (or close to it) elevator deflection is very hard.
You can average things out.
Not all testing was the same. An air force wants to know the capability of an airplane/fighter. A national institute or manufacturer wants to know how something is done or what modifications give what results.
Most WW II pilots had the turn and bank indicator and the airspeed indicator for turn. Instruments were primitive compared to a 1970-80s light plane.
US WW II fighters started getting G meters in 1944 (?).
Soviet WW II fighters got G meters when?

 

[Mfezi]

I think I might have missed your point, Shortround, or maybe you missed mine. The methods that I described are selected based on what instrumentation is available both in the cockpit and via the FTI. I made no suggestion that the stable g method was necessarily used in WW2 and, even today, it is only used in front side measurements and when the aircraft is appropriately instrumented. The method consists of stabilizing at different load factors, usually starting at Vmax, but not for complete circles. Although a pilot can write down or photograph/video the indications, suggesting full FTI is not strictly required, at the very least it requires a cockpit g indicator and I never suggested otherwise. In fact, let me quote myself again:

There are typically three test techniques used these days to determine sustained turn performance...

...I was clearly pointing out how we do it in the modern era. In the WW2 era, and depending on whether these were quick tests or part of a fully instrumented test program, other techniques would be used as appropriate. The timed turn method is probably the easiest and I have personally used it in everything from light aircraft to jets, but obviously not for high load factors. On the other hand, if you have a g indicator and the necessary FTI recording equipment, you can use the stable g method on any aircraft for the high speed / high g test points - it works quite well if you have an experienced test pilot to accurately set up and hold the points.

However, note that regardless of the test technique used, the principle for determining turn radius remains the same: You measure turn rate or load factor along with sufficient information to calculate true airspeed, and then calculate the turn radius from there, using the kinematic relationships. You don't measure the turn radius directly, which brings me back to my original request to you:

Shortround, do you have a citation where they describe measuring turn radius with ground observers? I have never heard of or seen it done this way and it seems to me it would be extremely inaccurate.

In your earlier post, you made the suggestion in the two parts that I quoted that you had evidence that a technique involving ground observers was in use to measure turn radius. I simply asked for some reading material, as I'm geniunely interested as I have never heard of this technique and haven't encountered it in my collection of notes from various flight test schools. There are other flight test techniques that traditionally involve ground observers, but I have not seen it for turn radius, therefore my question. I'm not trying to argue at all: I'm geniunely interested in a technique that I haven't encountered in my own flight test experience or heard of being used by others.

 

[Steamed_Banana]

Do we have any data on stall speed for different aircraft while pulling increasing G loads? Does it scale up from stall speed in level flight in a predictable way?

 

[ThomasP]

re

Do we have any data on stall speed for different aircraft while pulling increasing G loads? Does it scale up from stall speed in level flight in a predictable way?

In theory and in general for practical application - yes. However, in practical application the effective stall speed may be affected by the shape of the wing (both the airfoil section and the planform), and by other factors such as surface finish for example.

Relative to the needed coefficient of lift the theory is that lift will increase in a linear manner with the increase in g load, though different airfoils may generate the needed lift at different AOA from one another and the specific airfoil lift slope may not be linear. For a given g load the needed coefficient of lift will be the g load times the lift coefficient need to maintain level 1g flight at a given speed. So for a given aircraft, if the stall speed is 70 mph IAS, and the needed coefficient of lift is 0.46, then if the pilot wants to pull 2g he will have to increase his lift coefficient to a minimum of (2 x 0.46 =) 0.94 - which in turn will require an increase in AOA - and in order to sustain the 2g he will have to increase his speed as well.

Relative to stall speed for a given g load the theory is that the this will increase with the square-root of the g load. So if the stall speed is 70 mph IAS when in level 1g flight, for the same aircraft pulling 2g the minimum speed required would increase to (70 x square-root of 2 =) 99 mph IAS, for pulling 3g the required minimum speed would increase to (70 x square-root of 3 = ) 121 mph IAS, etc - assuming no other oddities are involved.

One example of oddities that I found mention of involved the Hurricane. With the 'A' & 'C' wing gun ports sealed and with reasonable surface finish the stall lift slope and stall speed were almost exactly per basic physics formula upto any practical AOA. With the ports unsealed the metal 'A' wing variants had a slightly lower stall speed at typical g loads than with the ports sealed, while the metal 'C' wing with 4-cannon protruding had the stall speed increased at lower AOAs. In theory this was caused by disturbances in the airflow over the wing caused by the open gunports for the 'A' wing (which created slight vortices) and increased the effective lift behind the guns, while the protruding cannon of the 'C' wing caused too much disturbance over the wing behind the guns which decreased the lift in that area. The effect on the 'C' wing aircraft was to increase the stall speed at low speeds - most noticeably in landing configuration. At higher AOA the 'C' wing with the protruding cannon had little or no effect on stall speed vs the 'A' wing variants.

The differences in effective lift and stall speeds were relatively small for the Hurricane - the 8-gun wing effect (about 2-3 mph decrease) was noticed in flight tests and by pilots that had significant time on the Hurricane, but was not noticed by the average pilot. The increased stall speed (4-5 mph) of the 'C' wing variant was enough that line pilots noticed the difference during landing when flying the different aircraft, and specific mention was made during flight training.

Bleh! I think I explained this correctly and hopefully clearly. If not, let me know and I will try to clarify.

NOTE edited to remove unrealistic values. I used small values of coefficient of lift to keep the math simple, but they were not realistic for a Hurricane. So I have changed the values to a theoretical aircraft with unspecified weight and wing area.

 

[Steamed_Banana]

I wonder if we could build a chart from that relatively simple math for various (level flight) stall speeds and what that translates to turns at 2G, 3G, 4G, 5G, 6G etc.

So per your example, a Hurricane I stalls at 70 mph (clean), and that goes to 99 mph for 2G, for 3G it's 121 mph, 4G it would be 140 mph, 5G would be 156 mph, 6G - 171 mph, and 7G would be 185 mph.

So if a Hurricane IIC stalls at 75 mph then it's stall speed in a 2G turn is 106, 3G is 130 mph, 4Gis 150 mph, 5G is 167 mph, 6G is 183 mph, and 7G is 198 mph

Is that right?

And is this ratio for one particular type of wing shape? Would the progression be different for a Spitfire or a Bf 109?

(is there already a NACA chart for this?)

 

[Greg Boeser]

I wonder if we could build a chart from that relatively simple math for various (level flight) stall speeds and what that translates to turns at 2G, 3G, 4G, 5G, 6G etc.

So per your example, a Hurricane I stalls at 70 mph (clean), and that goes to 99 mph for 2G, for 3G it's 121 mph, 4G it would be 140 mph, 5G would be 156 mph, 6G - 171 mph, and 7G would be 185 mph.

So if a Hurricane IIC stalls at 75 mph then it's stall speed in a 2G turn is 106, 3G is 130 mph, 4Gis 150 mph, 5G is 167 mph, 6G is 183 mph, and 7G is 198 mph

Is that right?

And is this ratio for one particular type of wing shape? Would the progression be different for a Spitfire or a Bf 109?

(is there already a NACA chart for this?)

I've seen them in the pilot's manual for the B-26. Of course it cuts off at the G-limit.