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Old 10-07-2015, 04:56 PM   #1
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Default CLmax and wing design of the FW-190D9

Several months ago there was a discussion on the CLmax of the FW-190.

http://forums.eagle.ru/showpost.php?...0&postcount=83

http://forums.eagle.ru/showthread.php?t=136596&page=9

This not a "call to action" to have DCS make any changes that I am aware of to the Dora. It is simply to fulfill my promise of posting Focke Wulf GmbH determination of the CLmax of the aircraft.

First of all, let's talk about how engineers determine CL max of an airfoil. Simply put, the 2 dimensional cross section of the airfoil gives us our CL max. When we mathematically turn that 2D airfoil into a 3 dimensional wing, the CL max remains the same but the angle of attack data is shifted as a function of drag due to lift production.

In the FW-190 we find two different airfoils used and some aerodynamic twist. The airfoils selected are the NACA 5 digit series both of which were popular with designers of the day. In fact, Grumman used both of these airfoils or variations of in their fighters designs in World War II.

http://m-selig.ae.illinois.edu/ads/aircraft.html

These airfoils have two different purposes. The root airfoil, NACA 2015.3 determines the stall point or when the aircraft reaches Vs and the wing no longer produces enough lift required to keep the aircraft in normal flight.

The wingtip airfoil, NACA 23009 modifies the stall characteristics leaving the pilot with some lateral control and softening the stall characteristics ensuring the wingtips remain in flight so that the airplane remains controllable and does not posses a dangerous stall.

We will examine the NACA 2D data for both of the airfoils and gain some insight into what it is telling us and range of possible Clmax's each can produce.

First we need to understand the concept of Reynolds number (RN). Simply put, RN is a measurement of the "stickiness" of the air.

RN is used primarily as a scaling factor. It allows the engineer to make a tiny sized model and then predict how the full sized aircraft will act.

RN = (Velocity* Chord)/ kinematic viscosity of air

Rearranging the basic RN formula:

Velocity = (RN*kinematic viscosity of air)/ Chord

Now, we do not have all the information we need to make an exact velocity determination because we lack the data required to make a good wind tunnel correction for the conditions the data was determined. That is ok. We are not looking for specifics we just need an idea of what is plausible. We can tell enough to say the FW-190 cannot achieve this RN or this RN is probably well above stall speed of the aircraft to see the range of coefficients of lift the airfoil can produce. It gives a sense of the plausibility Focke Wulf's determination of CLmax.

In other-words, is the CLmax used by Focke Wulf reasonable and since they are the experts in their own design....correct. Of course it is but some readers will never be convinced of that fact.

Here is the root airfoil data. Granted, it is not the 15.3% chord of the FW-190 but it is close enough to gauge possibility. We need specifics, Focke Wulf GmbH had those specifics and already did that legwork for us.

Immediately, and engineer will notice the shape of the polar. The abrupt loss of lift coefficient at the stall tells us this airfoil has a sharp and violent stall.



If we run the math on the RN and ballpark the scale it to find the velocity the FW-190 would have to achieve to achieve the CLmax range of the 2D airfoil we find:

Velcoity = (8900000*.000156927)/2 = 698 fps or 475mph

At an RN of 8900000, our 24 inch airfoil has to be traveling at ~475mph to achieve a Clmax of 1.7.

The FW-190 with its wing chord of 5.95 ft would have to travel at 234 mph. That is well above stall speed. Windtunnel corrections change that speed specific speed.

Will call that our high speed realm.

The next RN is 2600000 and delivers a CLmax of 1.5.

Velcoity = (2600000*.000156927)/2 = 408 fps or 139 mph.

Our speeds work out to 139 mph for our 24 inch airfoil section and 46 mph for the FW-190 wing at an RN of 2600000.

Well, the FW-190 cannot fly at 46 mph so that is our low speed value.

So we can say with certainty the 2D airfoil could produce a CLmax ranging from 1.5 to 1.7 and the 1.5 lower end is not representative of the FW-190 wing's CL max. The CLmax in all probability lies somewhere in the middle!

Now that we have our plausible range for the FW-190's CLmax, lets look at the angle of attack the root airfoil stalls.

The NACA 2015 series stalls at about 18 degrees. Note that as it will be very important later.

Now lets look at the tip airfoil, NACA 20009.



Right away, we can see the polar shows us this airfoil also has the characteristic violent stall of the NACA 230XX 5 digit series.

First the speeds were are looking at on the polar.

At an RN of 826000 our 30 inch airfoil needs to travel at 353mph and our FW190 wing at 217mph.

It is our high speed realm.

At an RN of 3850000 our 30 inch airfoils needs to travel at 163mph and our FW-190 wing at 69mph.

Well again, the FW-190 cannot fly at 69mph.

We will call that our low speed realm.

Putting it together, the NACA 2009 delivers a CL max range of 1.45 to 1.57 or so.

Looking at the polar we see the stall angle of attack occurs between 18.5 and 21 degrees.

So, the FW-190 wing is comprised of two airfoils which deliver a CLmax range of 1.5 to 1.7 at the root and 1.47 to 1.57 at the tip.

The CLmax of the wing will be the result of calculus based on each of the wing section airfoils.

Fortunately we do not have to guess or do the math based on incomplete knowledge of the design. Focke Wulf did that math for us and is it listed on the cut sheet used by the firms engineers.



The CLmax of the FW-190 series wing is 1.58. In examining the 2D data, their determination is not only plausible, it is most likely correct.

Caution is advised for transferring aerodynamic coefficients from one system to another especially for drag. However, because wing CL max is simply taken from the 2D airfoil data and represents our 1G power off CLmax, it has a good chance of transferring easily form one system to the next. Aircraft performance calculations are predicated on this fact.

A CLmax of 1.58 gives a 4270Kg FW-190D9 a 1G stall speed of 109mph.

It also gives excellent agreement with flight testing results in both Allied and Axis test's.

Now, lets take a look at the airfoils stall angle of attack data so see how Focke Wulf and Grumman put together two airfoils with very harsh stall characteristics into a wing with a gentle 1G stall.

The NACA 2015 series stalls at about 18 degrees on a fairly consistent basis. Looking at the NACA 23009 airfoil the stall angle of attack occurs between 18.5 and 21 degrees.

Focke Wulf used a common practice to add two degrees of twist to the wing. In principle this means the root airfoil will always be at 2 degrees angle of attack higher than our wing tip airfoil. So when the root stalls at 18 degrees, the tip airfoil will only be at 16.5 degrees angle of attack. Since our root airfoil no longer allows the wing to produce enough lift to increase the angle of attack in 1G flight, our wing tip airfoil will never reach stall angle of attack.

Since only part of the wing is stalled, the entire wings stall characteristics are changed from the harsh stall of the 2D data into something exactly like this:



Here the entire aircraft was placed in a truss in a wind-tunnel in France at wind-speed of 20 mph and the polar constructed. It was not to measure CLmax but to gauge the stall characteristics of the aircraft.

Immediately, the engineers sees the gentle 1G stall characteristics of the wing.

It was done both with and without a propeller mounted as well as with power on.

Last edited by Crumpp; 11-08-2015 at 11:13 AM. Reason: Removed a simplification error
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Old 10-07-2015, 06:41 PM   #2
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There are two very strange points in your conclusions: the stall speed of 109 mph (174 kph) looks like a stall speed for a landing with FULL FLAPS.
20 mph = 36 kph = 10 m/s(!) - is not a typical speed in the wind tunnel. As far as I remember it was about 36 m/s that is very close to the Re of stall speed for the full-scale plane.

And 1.5 from the wind tunnel is very close to 1.58 in the German table.

The well know tendency for CL vs Re - is to grow with Re.
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Old 10-07-2015, 08:01 PM   #3
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Quote:
There are two very strange points in your conclusions: the stall speed of 109 mph (174 kph) looks like a stall speed for a landing with FULL FLAPS.
Unstick speed is 150-160kph IAS...

The wing has to be producing a CL of 2(+) with take off flaps to achieve that.

I will post some good data from the RAE, too.
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Old 10-07-2015, 08:05 PM   #4
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Quote:
And 1.5 from the wind tunnel is very close to 1.58 in the German table.
9 PS is not the zero drag with propeller mounted at 180kph...it is more like the 9 m/s and 13 m/s I read in the report.

http://forums.eagle.ru/showpost.php?...9&postcount=37


Quote:
The well know tendency for CL vs Re - is to grow with Re.

Exactly, I just proved it to cut down on the "white noise" and to show readers the purpose of Re.

Last edited by Crumpp; 10-07-2015 at 08:09 PM. Reason: added the link to the polar with power on
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Old 10-07-2015, 10:04 PM   #5
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Good post Crumpp

Unfortunately I don't believe our ingame Fw190 features this CLmax figure. Either that or the P-51 features a windtunnel derived CLmax, i.e. assuming a completely smooth surface for laminar flow, something which was NOT possible in production aircraft, let alone in the field.

A factory fresh condition NACA 6 digit airfoil (i.e. std. roughness) produced a CLmax around 1.3.

By comparison the NACA 23xxx series didn't suffer any negative effects to its Cd or CLmax characteristics under operational surface conditions, as one can observe in NACA tests concerning this specific subject = surface roughness effects on various airfoils.

Last edited by Hummingbird; 10-08-2015 at 12:20 AM.
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Old 10-07-2015, 10:12 PM   #6
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Btw, as an interesting side note one can also observe on the FW tables how the high aspect ratio of the Ta-152H's wing raises the CLmax from 1.58 to 1.7. Coupled with the large reduction in Cdi this results in a highly efficient wing in terms of lift to drag ratio, and thus it is little wonder why this aircraft was considered such a fantastic turning aircraft.
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Old 10-07-2015, 11:11 PM   #7
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Let's look at what our CLmax must be in a know configuration of 13 degrees take off flaps.

Unstick speed is listed in IAS as 150-160kph for the FW-190A5 and FW-190A6 handbuch.



Weight for the FW-190A5 because it is the lightest and will return the most conservative CL range:



Some simple math in the BGS system to see the range of possibility for the Coefficient of Lift required in the FW-190A5 to lift off with 10-13 degrees of flap:

Sea Level on a standard day.

IAS = EAS (we won't both with IAS to CAS because the PEC curve is diminishing CAS is ~6-9mph slower than IAS. It does not matter for this case because slower speeds = higher CL required.)

Weight = 4106Kg = 9052lbs

S = 197ft^2

q = V^2/295 (295 is a correction factor for using Knots in BGS...it works and gives good agreement and is easy to follow)

150kph = 80.9KEAS

q = 80.9KEAS^2/295 = 22.186p/ft^2

CL = Weight/(q*S) = 9052lbs/(22.186p/ft^2*197ft^2) = 2.071

160kph = 86.4KEAS

q = 86.4KEAS^2/295 = 25.3p/ft^2

CL = Weight/(q*S) = 9052lbs/(25.3p/ft^2*197ft^2) = 1.81

Unstick speed or Vmu is the minimum safe lift off speed. It is forward (faster) than stall speed in the take off configuration and represent the slowest safe speed the aircraft will begin to fly.

Adding landing flaps (40 degrees) MUST increase the CL of the wing. It is not going to get smaller with landing flaps.

The Coefficients are easily attainable and closer to what is expected with the split flap design.

It can be said with certainty that a CL of 1.58 cannot represent the CLmax of the wing with Landing Flaps deployed.

What is the stall speed then of a fully loaded FW-190D9 if our wings CLmax is 1.58 as Focke Wulf says in their cut sheet.

4270Kg = 9413lbs

q = 94.4KEAS^2/295 = 30.2p/ft^2

CL = Weight/(q*S) = 9413lbs/(30.2p/ft^2*197ft^2) = 1.58

94.4KEAS * 1.15 = 109mph EAS = 175Kph EAS
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Old 10-07-2015, 11:14 PM   #8
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Quote:
A factory fresh condition NACA 6 digit airfoil (i.e. std. roughness) produced a CLmax around 1.3.
FWIW...

Standard roughness is misleading. To be at the NACA standard roughness, the aircraft would have to be finished in sandpaper.

If the airplane can fly with "standard roughness"....the company won't be getting sued no matter how much the finish deteriorates!

For aircraft performance and design, the airfoils are considered smooth.
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Old 10-08-2015, 12:22 AM   #9
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Quote:
Originally Posted by Crumpp View Post
FWIW...

Standard roughness is misleading. To be at the NACA standard roughness, the aircraft would have to be finished in sandpaper.

If the airplane can fly with "standard roughness"....the company won't be getting sued no matter how much the finish deteriorates!

For aircraft performance and design, the airfoils are considered smooth.
Problem was that even small bulges would ruin the laminar flow airfoils' windtunnel characteristics, where'as this didn't affect the NACA 23xxx series.
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Old 10-08-2015, 12:24 AM   #10
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Quote:
Originally Posted by Crumpp View Post
Let's look at what our CLmax must be in a know configuration of 13 degrees take off flaps.

Unstick speed is listed in IAS as 150-160kph for the FW-190A5 and FW-190A6 handbuch.



Weight for the FW-190A5 because it is the lightest and will return the most conservative CL range:



Some simple math in the BGS system to see the range of possibility for the Coefficient of Lift required in the FW-190A5 to lift off with 10-13 degrees of flap:

Sea Level on a standard day.

IAS = EAS (we won't both with IAS to CAS because the PEC curve is diminishing CAS is ~6-9mph slower than IAS. It does not matter for this case because slower speeds = higher CL required.)

Weight = 4106Kg = 9052lbs

S = 197ft^2

q = V^2/295 (295 is a correction factor for using Knots in BGS...it works and gives good agreement and is easy to follow)

150kph = 80.9KEAS

q = 80.9KEAS^2/295 = 22.186p/ft^2

CL = Weight/(q*S) = 9052lbs/(22.186p/ft^2*197ft^2) = 2.071

160kph = 86.4KEAS

q = 86.4KEAS^2/295 = 25.3p/ft^2

CL = Weight/(q*S) = 9052lbs/(25.3p/ft^2*197ft^2) = 1.81

Unstick speed or Vmu is the minimum safe lift off speed. It is forward (faster) than stall speed in the take off configuration and represent the slowest safe speed the aircraft will begin to fly.

Adding landing flaps (40 degrees) MUST increase the CL of the wing. It is not going to get smaller with landing flaps.

The Coefficients are easily attainable and closer to what is expected with the split flap design.

It can be said with certainty that a CL of 1.58 cannot represent the CLmax of the wing with Landing Flaps deployed.

What is the stall speed then of a fully loaded FW-190D9 if our wings CLmax is 1.58 as Focke Wulf says in their cut sheet.

4270Kg = 9413lbs

q = 94.4KEAS^2/295 = 30.2p/ft^2

CL = Weight/(q*S) = 9413lbs/(30.2p/ft^2*197ft^2) = 1.58

94.4KEAS * 1.15 = 109mph EAS = 175Kph EAS
THis lift off speed does not seem very good to calculate CL because of two factors - ground effect and TO power. The more accurate result would give stall speed in clean configuration (power-off for sure) or touchdown speed (stilll with ground effect though).
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