Are the fuselage bottom, elevators and ailerons part of the total surface area or not?

From : Don Stackhouse

We got that same question a while back in the "Ask Joe and Don" section of our website. The specific URL for my answer is:

http://www.djaerotech.com/askjd/wingcalc.html

However, while you're there you might also want to browse some of the other articles in AJ&D, you might find answers to other questions as well. There's approx. 200 different articles in AJ&D now, plus a search engine for searching the articles by keyword.

The convention in most aircraft is to use the area of the wing only, not the tail. In most conventional aircraft the tail contributes very little lift in the vast majority of flight conditions, so we don't count it in the wing loading computations. However, the area of the ailerons, flaps, and the portion of the wing inside the fuselage (because the pressure field on the top and bottom of the wing tends to spread across the fuselage at that location, causing that part of the fuselage to generate lift) DO help support the airplane, so they are included in the wing area.

The concept that someone else mentioned of including the area of the stab but not the elevators would probably be based on the idea of "stick-free" behavior in full-scale aircraft. For those, where a human's hand on the stick is what tries to hold the elevators still, an increase in the aircraft's pitch attitude causes an increase in angle of attack on both the wing and the stab, and a corresponding increase in their lift coefficients. The lift coefficient in the tail was probably low and in most cases slightly negative to begin with, so the stab still isn't contributing much to the aircraft's total lift. However, it does see a change in lift coefficient, even if it's only a change form negative to slightly less negative. Meanwhile, the elevators, which tend to trail in the airflow (unless Arnold Schwartzenegger is holding the stick, with his elbows braced against the seat back), see less of a change. In most normal flight, the stick is only held loosely by the pilot, leaving the elevators even more free to float with the airflow. From a stability standpoint this leads to the difference between "stick fixed" and "stick-free" stability. In stick-fixed stability the area of the movable parts of the tail (such as the elevators) is contributing to the aircraft's stability, but with the stick "free" those now mostly free-floating movable surfaces contribute little. In any case however, the tail is not contributing significantly to the aircraft's support, and so it is not counted in the wing loading computation.

The idea of stick-free vs. stick-fixed does not usually apply to models. Our control surfaces are connected as rigidly as possible to servos, and servos are not supposed to allow the surfaces to move by themselves in response to air loads. In fact, we usually go to a great deal of trouble to make sure they don't! Because of this, control surfaces on models normally behave in a "stick-fixed" mode all the time. However, the tail surfaces still contribute little, if anything, to the overall support of the aircraft, so we don't include the tail surfaces in the wing loading calculation.

In deltas and other tailless designs that use reflexed airfoils (including ones that use non-reflexed basic airfoils but then have the elevons rigged slightly "up", thereby supplying the reflex needed for stability), sometimes the reflexed portion of the wing is left out of the wing loading calculation, for the same reasons given above for conventional tail surfaces. Some folks do include it. Likewise, the tips of some swept flying wings with washout are lifting downwards, so sometimes those areas are treated like tail surfaces and left out of the wing loading calculation. Other folks include all these areas. The conventions are less clear in these cases. Then there's the whole issue of 3-D flow and vortex lift on swept and delta wings, and the effects of that on both lift and drag. In those cases the whole concept of "wing loading" as a means of comparison quickly loses its meaning.

In the case of canards the forward surface is helping support the aircraft, so it is usually included. However, a good case could be made for leaving it out, since its downwash does hurt the lifting ability of the main wing, and the need to make sure that the canard stalls first means that some of the lift-making ability of the wing must be held in reserve. Once again, the conventions are less clear.

In general, the methods for conventional tails are well established. For unconventional layouts, there are no really solid conventions. Which approach you take in those cases depends primarily on how you're going to use that wing loading number, and on how the lift coefficients for the wing are determined. Ultimately you're trying to come up with an indicator of how much load the wing can aerodynamically support, and so the way you figure wing loading should be the method that gives you the most honest depiction of how that particular airplane's lifting ability compares to other aircraft.

Don Stackhouse
DJ Aerotech