# What is the wing span in aspect ratio's calculation?

We all know that the aspect ratio of an airplane is calculate as: $$AR=\frac{b^2}{S}$$

Where:

$$AR=$$ Aspect ratio

$$b=$$ Wingspan

$$S=$$ Wing's area

In an airplane, wing span is the distance from tip to tip of the wing. That means the fuselage also calculated. Below are two picture of two different kind of airplane: Boeing and Cessna. As you see, the wing is placed in different position. The Boeing is below of the fuselage so it look like integrated to the wings. But the Cessna is placed on top of the fuselage, make the fuselage is like the separator of the two wings rather the integrator.

But in another time, what we call as wing is a wings part that are attached to the fuselage, both the left and the right side. The picture below shows what the wing span is. The fuselage itself is NOT considered as part of wing.

To avoid miscalculation, I would like to know what is exactly b in that equation. For this case, just consider the wing shape is fully rectangle. Appreciate if with reference.

b is the width of the wing's projection on the horizontal plane, from tip to tip. The wing's vertical position on the fuselage does not influence b. This may or may not include winglets and ideally should be clarified when b is specified.

Calling one half of the wing a wing is sloppy use of language. Ideally, a wing half should be called that, and not be confused with a wing.

• Appreciated if you may elaborate more detail. To be honest, still very hard for me to get the point, especially whit this: Where the wing is relative to the fuselage does not influence b. Commented Dec 15, 2018 at 2:37
• @AirCraftLover, whether the wing is high or low on the fuselage doesn't matter for such calculations. The wing is considered as a whole. In essence, simply by convention. If you think of it, the 'Cessna' (high) wing is even more 'integrated' than the Boeing one, given that it is the top surface that creates the most lift, so to speak.
– Zeus
Commented Dec 17, 2018 at 1:57
• @Zeus, do you have a reference for that "integrated calculation", please? Appreciated if you have. Commented Dec 17, 2018 at 2:50
• @AirCraftLover, not at hand. It is a general (academic) knowledge that high wing normally has less negative (and in fact, often positive) wing/fuselage interference than other designs. Explaining why is worth a separate question. But anyway, this is not directly relevant to your question: in all cases (in aircraft design and aerodynamics) "wing span" is defined as the total span, tip to tip, including the fuselage or whatever is in between.
– Zeus
Commented Dec 17, 2018 at 4:58
• In calculating the area, we know that the wing and the fuselage are not flat, should I project the surface area seen from above parallel (or in line) to gravity? Or should I do separate calculus integral do find the surface area of all the airplane's parts? Commented Dec 17, 2018 at 7:33

In aeroplanes, the wing is actually one complete, uninterrupted structure, and the fuselage has holes in it to allow the wing to be placed. The middle part of the wing has the highest bending moments, a cut in the wing structure here would pose large structural engineering problems. You can attach two half wings like in the old picture, but only to a centre structure that can absorb all bending moments and torques. The wing central structure, part of the wing.

In birds, the situation is different. There are clearly two wings on a bird, both hinged and independently moveable via muscles.

But for both aeroplanes and birds, the wingspan is from wingtip to wingtip.

• Quote: "In aeroplanes, the wing is actually one complete, uninterrupted structure." I can understand this. In the very beginning, Wright brother had their plane with an integrated wing. But if so, with the modern aero plane like the Boeing and Cessna as I mentioned above, what about the front side and aft side of the fuselage, shouldn't we need to consider them as wing as well? Commented Oct 2, 2023 at 15:36
• We could. Structurally it would make no sense, aerodynamically the situation creates interference problems either way. Also,, in the times when aerodynamic computations were researched (no computers yet!) the wings on biplanes were not interrupted by the fuselage. So the wing span from tip to tip was chosen. Commented Feb 28 at 23:29

All the reference quantities for a wing are just that -- reference. They typically refer to a simplified and idealized trapezoidal wing similar (but not exact) in planform to the real wing.

Transport wings often have trailing edge extensions (Yehudi) and winglets that are omitted from the reference wing.

The reference wing continues to the aircraft center line -- it is not broken up by the fuselage.

The reference wing is used to calculate Sref, b, AR, and other quantities.

• What do you mean with Sref? Commented Oct 2, 2023 at 21:11
• Reference wing area, used for calculations. Commented Oct 2, 2023 at 22:10