Buckaroo's Flightgear Projects
Guide To YASim: Contents

Induced Drag and YASim

By Gary "Buckaroo" Neely

What is Induced Drag?

In flight, air doesn't simply flow over and under the wing, there is also a spanwise movement of air under the wing, around the wing tips, and spilling over to the top of the wing. The lower pressure above the wing causes air under the wing to flow around the wingtip to the top of the wing. The reduced pressure differential causes an almost total loss of lift at the wingtip. The effect gets smaller as measured toward the wing root and is known as the "spanwise pressure gradient". This disrupts the flow over the wing, causing nasty vortices which reduce lift. To compensate, you can increase the angle of attack to gain more lift. But this tilts the wing's lift vector backwards slightly. Though most of the lift force is still upwards, a portion is now generating a force that tugs rearward on the wing. This is induced drag.

Induced drag is proportional to the square of the lift, which also means it's inversely proportional to the square of airspeed. Essentially, the slower you go and the more you increase AoA, the more induced drag you get. If you had a wing of infinite span, you'd get no induced drag because there are no wingtips to allow air to escape around to the topside. We can't build infinitely long wings, but high-aspect wings still produce less induced drag because wingtip vortex effects are reduced on long wings. In effect, induced drag is inversely proportional to aspect ratio (though technically it's more a function of span loading). Washout or twist also plays a role by proportionally generating more lift toward the inboard wing segments. It's been found that elliptical wing configurations are best for reducing induced drag, which is why aircraft like the Spitfire and P-38 had such curvy wing shapes. But elliptical configurations are difficult and expensive to make, so designers compromise by building tapered wings and playing tricks with the wingtips to divert vortices away from the wing.

Note that induced drag is not the same as parasitic drag, which is generated by bodies moving through the airstream and rises geometrically with airspeed. Induced drag is of particular importance to the takeoff, climb, and landing regions of a flight profile, where it can be more than 20% of the total drag forces, and at take off might be as high as 70% for some planes.

Induced Drag and YASim

Back to Flightgear's YASim. The YASim document states: "In general, low aspect wings will generate less induced drag per-AoA than high aspect (glider) wings." Whoever wrote this was probably sleepy. High-aspect wings diminish the effects of induced drag as explained above. A major reason that sailplanes have long wings is because they reduce induced drag.

In the YASim code, induced drag is more guestimate than calculation. The idrag attribute is a multiplier on this internal guestimate, which makes idrag a guestimate factoring a guestimate. This puzzles me, since it doesn't seem unreasonable for YASim to use the standard approximation for induced drag: CDi = Coefficient of Lift^2/(Pi x Aspect Ratio x e). Internally everything is known or could be calculated except e, which estimates how close a wing comes to the theoretical best-case elliptical wing. Typical values for e are between 0.7 and 0.9. The internal YASim guestimate value is 0.7, but there's no indication that this is related to the standard CDi approximation. The internal code documentation reads, "70% is a magic number that sorta kinda seems to match known throttle settings to approach speed." The code seems meant to circumvent more complicated (and realistic) lift calculations.

Incidentally, because YASim does not actually model loss of lift due to tip vortices (at least I've seen nothing relevant in the code base), this implies that YASim's calculations based on wing geometry are on the liberal side, giving full benefits for the entire span at all airspeeds and angles of attack. Since vortices spoil some lift especially during takeoff and landing, this suggests some possible improvements in the code. In the meantime, for this reason alone I'd advise erring on the short side for wing spans.

Using the "idrag" Attribute

The default idrag value is 1, which essentially leaves the internal guestimate unmodified. For most general aviation aircraft with conventional wings, I suggest omitting the idrag attribute, if for no other reason than to simplify your initial FDM attempts.

As currently defined in YASim, decreasing the value of idrag actually /increases/ induced drag. This is the opposite of what you might expect and what the documentation says. Conversely, increasing idrag decreases induced drag. I have verified this by careful testing on many different Flightgear models. YASim induced drag test results

I've not validated the cause yet but I strongly suspect the problem is due to an inadvertant placement of a factor of -1 in the calculations. So until there is a fix:

to reduce induced drag: set idrag > 1
to increase induced drag: set idrag < 1

After you get a good solution from your FDM, if you want to experiment with idrag try these ideas:

If your aircraft has a particularly good method for reducing wingtip vortices, consider a 10-20% reduction of induced drag by setting idrag to 1.1 or 1.2. Most modern wings have some wingtip modification to reduce vortex effects, for without them some of the outboard wing lift is lost. (The original OV-10 Bronco design had no wingtip mods, not even Hoerner wingtips, and the designers later lamented that if they had employed a good wingtip mod, they could have shaved off a considerable portion of the outboard wingspan.)

If your aircraft has significantly tapered wings, and especially if it has elliptical wings (Spitfire, P-38, Lockheed Constellation, etc.), consider increasing the idrag value. (Remember, increasing idrag reduces induced drag.) For taper values greater than 0.5, try a 5% reduction (1.05). For those of 0.5 or less, try 10% (1.1). For elliptical wings, try 15% (1.15).

If your aircraft has long high-aspect wings like most sailplanes, consider reducing induced drag considerably, 20% to 40% or more, depending on your research and flight tests. If your aircraft has short delta wings or no wingtip anti-vortex modifications, consider raising the induced drag by reducing idrag to 0.9 or smaller.

Combine any of the above as seems reasonable. Fly the results. The effects may be subtle and hard to notice but should be more observable at low airspeeds with high angles of attack (typical of takeoff, climb, and approach profiles). When testing, make sure you always fly the same flight profile. The generic autopilot is your friend here, just make sure to give it time to let the numbers settle.

If your aircraft employs a stabilator rather than the conventional stabilizer-elevator, you might consider reducing the idrag of the stabilator hstab. As the wing AoA increases, the stabilizer incidence will decrease to compensate for the wing's tendency to pitch down (at least with a cambered airfoil), therefore the stabilator will be at a lesser AoA with respect to the wing and have less induced drag. YASim can't simulate this due to YASim's exclusive internal control of hstab incidence, but you can reduce the hstab's induced drag as a kludged step in that direction. This is speculation on my part; I'd be interested if anyone experiments with this.