What is the total wing surface area of the A320?

Question

I was trying to calculate the total area of an A320, and in this link I found the wing area and tail area. But here I read that the wing area is just the 2D projection of the wing. So if I wanted to calculate the total surface of the wing I should consider the wing area (122.4 m) and multiply by two, which would be an approximation.

By doing this, and considering the fuselage to be a cylinder, I get a total area of 847 square meters for an Airbus A320, which is close to the 900 square meters reference I found in this article.

So, is it correct to say that the surface area of a wing is approximately the wing area multiplied by two?

Answer 1

As I'm not sure whether you were only looking for the methodological answers provided earlier, this is a more detailed answer to the calculation problem you were trying to solve in the first place, providing an answer to the question posed in the title of your question. It is based on the A320 Airport and Maintenance Planning Manual, which provides approximate dimensions of the aircraft.

For the wings and wing-like surfaces, details are as follows:

• Wing top surface: $99.7 m^2$ (excluding wingtips devices)
• Wingtip devices (normal, non-sharklet A320, both sides): $1.8m^2$
• Horizontal tailplane top surface: $27 m^2$
• Vertical tailplane (both sides): $43 m^2$

Counting horizontal wing and tailplane surfaces twice (upper and lower), that yields a total of $298.2m^2$. This does not properly account for thickness (using the factor $1.07$ mentioned by Daniel yields $319.074 m^2$) and movables (high-lift devices, control surfaces, etc).

For the fuselage and nacelles, only top surfaces are listed. Modelling these as simple cylinders therefore seems the best way to go. Based on a fuselage diameter of $4.14 m$ and a length of $37.57m$, that yields a surface area of about $488m^2$. Of course, the fuselage is not strictly cylindrical, but I'm assuming here that is offset by the fact that I'm not explicitly including the front and rear surfaces (of a closed cylinder). Nacelle dimensions are not specified (probably as that somewhat depends on engine type), but based on drawings, I'm estimating a length of $5 m$ and a diameter of $2.5m$, resulting in a total surface (again: cylindrical approximation) of $78.5 m^2$ for the two engines. For the pylons, lets add another $5m^2$ per side.

In total, that adds up to $872 m^2$ (or $902.874 m^2$ with the 1.07 thickness approximation). That corresponds nicely with the $900m^2$ you found online - and also shows your own calculation wasn't too far off (some 3%).

Answer 2

The answer depends on the method used.

For airliners, the two most important methods are the Wimpress and the Airbus method (the Wimpress being used by Boeing). The difference is the triangles you get by extending the wing's leading and trailing edges forward into the fuselage for Wimpress versus connecting the points where the leading and trailing edges meet the fuselage on both sides by two straight lines for Airbus. This discussion on airliners.net lists a comparison of the wing areas you get with both methods for a range of models.

Wing area methods in comparison. The shaded are is covered by the fuselage and determined differently; creating different areas for the same wing.

Note that the specifics of the method used is irrelevant for the purpose: This wing area serves as the reference area of most aerodynamic coefficients and either method is good enough for the purpose. Consistency is more important than precision here.

Both methods use the projected area of the clean wing in the x-y-plane, because that is the area relevant for lift. Divide by the cosine of the dihedral angle if you feel the projected area is not good enough.

For the wetted area you need to subtract the fuselage, divide by the cosine of the dihedral angle and the cosine of the incidence angle, and also add a factor to account for the wing's thickness. For this, the approximation $1 + 2\cdot\delta$ has proven to be useful, with $\delta$ being the relative thickness of the wing. And then, of course, you need to double that result in order to account for both sides of the wing.

One of your links calculates the area of a wing that needs to be painted: This should include the forward section of the Fowler flaps which are covered by the spoilers in the clean configuration.

Answer 3

As an addition to all previous answers, there are some more detailed estimation methods for the wing wetted area in literature. For instance, here's a method by Torenbeek (1976):

$S_{wet} = 2S_{exp}\left(1+0.25(t/c_r)\frac{1+\tau\lambda}{1+\lambda}\right)$

Where $S_{exp}$ is the exposed part of the wing reference area, $\lambda = c_t/c_r$ and $\tau = (t/c)_t/(t/c)_r$. Note that the root is taken as the wing-fuselage intersection in this case. These kind of methods are especially useful when estimating aircraft parameters such as the drag coefficient using statistical values given by a certain author (Torenbeek, Raymer, Roskam etc.), since these values were derived using certain definitions of the geometrical parameters.

Another more simple method (I can't find the source anymore) suggests $S_{w_{wet}} = 1.07 * 2 * S_{w_{exp}}$. The factor of 1.07 is added to account for the thickness of the wing.

Answer 4

Wing area is usually expressed based on total span x chord, including the area covered by the fuselage.

The fuselage is given a bit of credit as a semi-lifting body. There is a similar credit-for-lifting-body effect when you add floats. The floats generate enough lift, or almost enough lift, to support their own weight, so when floats are added there is usually a fairly small reduction, or sometimes no reduction, in useful load.

Same with the fuselage itself, so the area of fuselage between the wing roots is assumed to be part of the total wing area. Hence total span x chord (or mean chord for a tapered wing, based on the taper extended to the fuselage centerline).