Is the optimal incidence angle of the wing 0 degrees at the wing root?

(seems like that would make sense!)

From : Don Stackhouse

Good question, but no it isn't. However, I would be interested in hearing why you thought it might be. I'm always looking for alternative points of view, to expand my own thoughts and to better understand the perceptions of others.

The whole issue of incidence is complex and widely overblown but sorely misunderstood by much of the sailplane community.

First of all, there is no such thing as a single "optimum incidence angle". Incidence of the wing does not control stability or handling to any significant degree for most aircraft (with the possible exception of widebodies such as the Super Guppy, where the fuselage generates a significant percentage of the aircraft's total lift). All it normally influences is fuselage L/D. For any given angle of attack of the wing, there is some angle of attack of the fuselage that results in the best possible L/D for the total aircraft, but the difference between those two (the "incidence angle") will be different for each different flight condition. Before you can define an "optimum" incidence angle, you must first define the flight condition you are optimizing for. Since there is a vast continuum of possible flight conditions, all of which are important in one situation or another, the choice of where to optimize incidence is a judgement call at best.

That said, there are some things that will tend to narrow the choices down a bit. Although the fuselage's narrow span makes it a very poor lift producer, the optimum fuselage angle of attack for a given flight condition would still be at a very slight (as in "vanishingly small") amount of positive fuselage lift. The main concern would be to minimize fuselage drag as much as possible. Because it is such an awful lift producer, most of the drag of the fuselage is of the parasite variety, not the induced variety. If you can't make much lift, then you also can't make much induced drag. Our choice of optimums must therefore focus on the flight conditions where parasite drag is a high priority.

Parasite drag is a very low priority in thermalling conditions, because those are dominated by induced drag of the wing. Among full-scale competition sailplane fliers, one of the favorite ways to "show off" the performance of their latest mega-$$$ "glass slipper" supership relative to their rivals is to climb past them in a thermal with their landing gear down. While impressive, it really isn't that significant, just because the induced drag so totally dominates the picture in that particular flight mode. For a slow-flier, where the aircraft spends virtually all of its time at high lift coefficients, it might make sense to optimize incidence for flight at low speed. For most sailplanes it would be a very bad choice.

At first glance, the best L/D flight condition might seem to be a good choice. According to aero theory, there is one discreet operating point for best L/D, the point where induced drag and parasite drag for the entire aircraft are exactly equal. This is because, with one of them decreasing with airspeed and the other increasing, the point where they are equal is also the point where their sum is the lowest. This is for still air of course. Now the $64,000 question: how often do you fly in truly still air? With a tail wind or in lift, the speed for best L/D relative to the ground will be lower, while with a head wind or in sink, the speed for best L/D relative to the ground will be higher.

So what about penetration? Here it starts to make more sense, because at high speed the parasite drag dominates the picture. This gives us a general category, but at what particular airspeed will we be penetrating? This depends on weather and winds, lift conditions, distance between thermals, personal flying style and strategy, and a host of other factors. One thing is virtually certain, we almost never penetrate at the same airspeed twice!

Then there's launch. For the winch-launched classes this means high speed but also high lift coefficient, possibly with large flap deflections, during the towed portion of launch, and near zero lift during the zoom. A launch for an HLG is similar to the zoom portion of a winch launch, with high speeds and near zero lift coefficients. In terms of priority, launch is one of the smallest percentages of total flight time, but the altitude gained during the launch has profound effects on the entire flight.

What we are left with is a delicate balancing act, constructing a weighted average of the model's different flight modes and their relative importance. In my experience, the result usually favors something in the realm of penetration, but there is still a vast range of possible operating points within that range. The characteristics of the model, the probable local terrain and weather conditions, and the expected flying style of the typical customer for that model are only some of the factors that influence the final decision.

Now that we've covered some of the easier basics ("say WHAT??!!!"), now we can look at the more complicated details. Incidence of the wing root relative to the fuselage depends on the detail design of the wing itself. Washout, planform, airfoil characteristics all play an important role. Where you choose to measure angle of attack depends on what the lift distribution for the entire wing looks like. If we're looking at incidence in turning flight, then there's also the distortions due to the curvature of the local airflow as a result of the turn. Once we have a good idea of the wing characteristics (and also the aerodynamics of the fuselage shape at our chosen point of optimization), we can determaine a desired angle of attack for both, then from the washout distribution of the wing we can figure the angle of the wing root (which, due to washout, will probably be different from everywhere else on the wing).

One other thing that plays into this is that there are several different ways to measure that angle. The method commonly used by modelers uses the "chord" line (a straight line between the furthest forward point on the leading edge and the furthest aft point on the trailing edge), but there is also a practice on older models with nearly flat-bottomed airfoils to use a tangent to the lower surface. Then there's the practice on some NACA airfoils of specifying the coordinates of the leading edge radius center relative to the leading edge of the chord line, which means that the leading edge of the chord line might not be the furthest forward point on the leading edge, if the center of the leading edge radius is not located on the chord line (which, for an airfoil with non-zero camber it usually isn't). So here we now have three different ways of specifying the line from which we measure incidence. Guess what - the air doesn't recognize ANY of those! The air is sensitive to what is called the "zero lift line", which for cambered airfoils is quite different. For example, for the popular SD7037 airfoil, depending on the Reynolds number, when the airfoil is a zero lift (i.e.: angle of attack relative to the zero lift line equals zero), the angle of attack relative to the chord line is at anywhere from -1.5 to -3 degrees! When the chord line is at zero degrees angle of attack, the lift coefficient is at about +0.2 to +0.3 ! Add to all this the effects of flap position along the wing on both zero lift line (due to camber change) and the chord line location, and things get very complicated indeed.

Then of course there's the question of the zero lift line for the fuselage, which behaves like a very complex 3-D airfoil itself.

The corresponding incidence for the tail is influenced by even more factors, such as fuselage shape, aerodynamic pitching moments of the wing, tail and fuselage, C/G location, and for power models the charcateristics of the motor, prop and thrustline. The software I use for determining wing and tail incidence is one of the most complex in my entire collection. Considering the complexity involved, for the average scratch-builder, the best method may be to simply build a prototype with easily adjustable wing and tail incidence, then go out and fly it. If you lack the tools and the experience to do it analytically, the old cut-and-try methods will probably involve the fewest simplifying assumptions, and give you the best quality answers of any of the options available. With all my computer analysis I've been able to hit the right combination on the first or second try on most of our recent designs, but I still rely on flight test results to verify the final answer.

Once we've tentatively selected a preferred flight condition for optimization, then gone through all the agonizing required to find an answer for that point, we also have to consider the effects of this choice on all the other flight conditions, and determine if we have unnecessarily compromised any of those in an effort to optimize the primary design point. It may be wise to trade off a little performance at the primary point if it yields bigger improvements at the other points.

Obviously there can be no general conclusions of any value regarding any universal "optimum" incidence angle.

Yes, you can calculate a "magic number" for the "correct" incidence, and it is reasonably certain that this number will be "optimum" at some specific flight condition, and less optimum at other flight conditions. The problem is, who's to say what is the "correct" flight condition? In the end it all comes down to a judgement call, one which cannot be answered with any degree of precision without a lot of detailed information about the specific aircraft design involved.

Don Stackhouse
DJ Aerotech