F4U Wing Area Discrepancy?

[Stoney]

Gents,

Sgt Pappy and I were discussing some lift/drag stuff via PM which led me to start some research.  I stumbled upon this document:  http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20050081862_2005071383.pdf on the NASA Tech Reports Server (located here: http://ntrs.nasa.gov/search.jsp).

Anyway, I've always used the 314 ft^2 wing area from Dean for the F4U series when running aero formulas on the aircraft.  However, when I added the wing, aileron, and flap area in this report, I came up with 331 ft^2 instead of 314 ft^2.  The aircraft in the test is a F4U-4, and Dean doesn't note any additional wing area being added to the 4-Hog.  Did Dean miss something, or am I just imagining things?

From the report:

Wing area:  276.3 ft^2
Flap area:  36.4 ft^2
Ailerons:  18.1 ft^2

=330.8 ~ 331 ft^2

I tried to think about the flap assembly and how Dean may not have counted any flap area that was covered when retracted, but the only part that's covered is the radiused area around the torque tube.  The actual wetted surface of the flap is always exposed, regardless of its position.  Perhaps the Navy didn't figure the area correctly?  Is this showing the actual area when the 3D gull-wing affect is considered instead of the 2D planform?

I'll almost be relieved to hear I haven't considered something.
 

[Wmaker]

Just checked that the 314sqft is across the fuselage so that isn't it either (and it would have been too small of a difference to include the fuse).

I may be wrong, but my guess is that Dean hasn't calculated the area himself but referenced some primary source document.

[Pyro]

314 is used in all the other docs I've seen as well as being what falls out of wing loading calculations in various documents.  An interesting thing about the document that you linked to is that the wing area figure of 276.3 is circled with a note saying "Wing area is this?"   Then there is also what appears to be a "314" written below that.  I can't make out the other note to the left.

<edited for clarity as my brain ran ahead of my fingers when I typed this>

[Pyro]

The note to the left appears to read "wing - included fus. area" with a "37.7" written above that. 

276.3 + 37.7 = 314

[Stoney]

314 is used in all the other docs I've seen as being what falls out of wing loading calculations in various documents.  An interesting thing about the document that you linked to is that the wing area figure of 276.3 is circled with a note saying "Wing area is this?"   Then there is also what appears to be a "314" written below that.  I can't make out the other note to the left.

Yeah, I noticed that and tried to zoom in on it for a better look.  But, I assumed that they counted the wing area separate from the aileron and flaps given its much lower number than what I was expecting.  The reference they noted was a 3-view drawing.

I love the irony of a document such as this simply muddying the waters further...

[Pyro]

The note to the left appears to read "wing - included fus. area" with a "37.7" written above that.  

276.3 + 37.7 = 314

That also explains why they have an invalid aspect ratio listed.  They calculated it off of the 276.3 area instead of 314 giving an incorrect figure of 6.08 instead of 5.35.  

[SgtPappy]

Hah wow. That almost sparked something. Good finds, Stoney. I had the same report but never had the time to read it. 

[Stoney]

That also explains why they have an invalid aspect ratio listed.  They calculated it off of the 276.3 area instead of 314 giving an incorrect figure of 6.08 instead of 5.35.  

I didn't even catch that one...  Keep this one in my back pocket when someone wants to talk about the infallibility of test flight documents...   

[Charge]

"That also explains why they have an invalid aspect ratio listed.  They calculated it off of the 276.3 area instead of 314 giving an incorrect figure of 6.08 instead of 5.35."

Fuselage is calculated in the aspect ratio too? How come?

-C+

[Stoney]

Fuselage is calculated in the aspect ratio too? How come?

The portion of the fuselage that "covers" the wing in the center is traditionally not deducted from the wing area.  The total planform of the wing,   including the area as the wing passes through the center of the plane is what is used in determining span and area.  Therefore, aspect ratio, at:

b^2 / S where b = span and S = area

includes the fuselage portion.  Other calculations, such as computing the skin friction drag of the wing, only use the "wetted" area of the wing and discount the area "within" the fuselage.

[SgtPappy]

This makes me believe that every time we've read official figures of wing area for aircraft, we have also included the fuselage wing area for those other aircraft.

I.e. 242 sq. ft. of wing area for a Spitfire includes the area contained within the fuselage? Though this is a little strange as the Spitfire wings, like other aircraft, were attached onto the plane and there technically was no wing area 'in' the fuselage. I suppose this inner wing area is a calculated value if it applies for all aircraft wing area figures.

[Stoney]

This makes me believe that every time we've read official figures of wing area for aircraft, we have also included the fuselage wing area for those other aircraft.

I.e. 242 sq. ft. of wing area for a Spitfire includes the area contained within the fuselage? Though this is a little strange as the Spitfire wings, like other aircraft, were attached onto the plane and there technically was no wing area 'in' the fuselage. I suppose this inner wing area is a calculated value if it applies for all aircraft wing area figures.

Yes, the wing area always includes the fuselage unless, again, it is being referenced in terms of "wetted" area.  For the purposes of most aerodynamic equations, you use it all.  There are ways to approximate fuselage affects on the wing, but that's a whole different ball of wax entirely.

[Charge]

I don't know if this sounds stupid but what is the effective wing area for a plane with an angled wing? Is it the wing area you can calculate from e.g. a planform picture from above or is it the exact length of those two sections from fuselge to bend and from bend to wing tip? I mean if you calculate the wing area from a 2D planform picture it will be less than using the actual lengths of those two parts of the wing. From that question we get to aspect ratio. What is the effective aspect ratio for such wing. The 2D projection from above or is it more complicated due to its 3D nature?

-C+

[Stoney]

I don't know if this sounds stupid but what is the effective wing area for a plane with an angled wing? Is it the wing area you can calculate from e.g. a planform picture from above or is it the exact length of those two sections from fuselge to bend and from bend to wing tip? I mean if you calculate the wing area from a 2D planform picture it will be less than using the actual lengths of those two parts of the wing. From that question we get to aspect ratio. What is the effective aspect ratio for such wing. The 2D projection from above or is it more complicated due to its 3D nature?

-C+

For most straight wings, you don't need to account for dihedral and its affect on span length, but given, using the gull-wing of the hog for example, that the curved section would hold a substantial amount of wing area, I would think you'd have to account for it.  That being said, I don't know if the 314 ft^2 of the Corsair wing area accounts for it or not.

[FLS]

If span is the straight line distance between wingtips instead of the length of the wings plus fuselage width it's likely to skew a few calculations. Interesting question.