Is wing loading important to thermaling performance?

Bernard (btfraser@direct.ca) asks:

I heard recently that planes with more wing area and wing loading don't necessarily thermal better than planes with less even if they weigh the same. If this is true how can this be so. A friend and me have been trying to figure this out and can't seem to.

Bernard, there's a lot involved in thermalling performance, and wing loading is actually one of the less important items.

One of the main factors in thermalling performance is drag. There are two general categories of drag, parasite and induced. Induced drag is the drag that comes as a natural by-product of producing lift; parasite drag is everything else that isn't the result of making lift. At high speeds, parasite drag is the dominant factor. At max L/D, parasite drag and induced drag are exactly equal. At low speeds, such as thermalling, induced drag is by far the biggest factor.

So what controls induced drag? Essentially it's a function of the amount of lift being made (weight and bank angle), how much air is being influenced by the wing (i.e.: "mass flow"), and how efficiently the wing uses that mass flow. Mass flow depends on the density of the air, the speed of the aircraft, and the wingspan. Note that I did NOT say "aspect ratio". Induced drag is NOT directly a function of aspect ratio. For a fixed wing area, an increase in aspect ratio will improve induced drag, but only because the only way to increase aspect ratio for a fixed wing area is by increasing the span. It's SPAN that controls mass flow, NOT aspect ratio and NOT wing area!

How efficiently the wing uses its span is called "span efficiency". It's determined by the lift distribution, which is mainly a factor of flight condition, planform, twist distribution, and local airfoil characteristics. In general, the highest span efficiency will be found with an elliptical lift distribution, but this does NOT necessarily mean an elliptical planform. In fact, at model Reynolds numbers a perfectly elliptical planform will almost certainly not give you an elliptical lift distribution, because of the effects of Reynolds number variations along the wing. There's another article in "Ask Joe & Don that discusses this in more detail.

For a fixed span class like hand-launch or two meter, the only way to improve induced drag is by reducing weight, increasing speed, or by improving span efficiency. In your question you specified that weight of the models being compared was the same. This means that their induced drag is likely to be very similar. On the other hand, you didn't specify that their spans were the same; if one was larger than the other, then there's a good chance the larger span one has lower induced drag than the shorter one.

If you increase speed you also hurt the turning radius, which makes it harder to stay in the core of the thermal. Virtually everything in aircraft design ends up being some sort of compromise!

Span efficiency does offer the possibility of significant improvements, but it requires careful balancing of a number of different factors to achieve it.

Airfoil selections have a sgnificant influence on eficiency, but these must be matched to the twist and planform, and the non-uniform flow field the wing sees in a thermal turn (which is another whole subject of its own!). All of this requires good analysis tools, and the experience to use them effectively.

Note that none of the above directly involves wing area! Wing area does indirectly influence some things, such as chord (and therefore the local Reynolds numbers), and the maximum amount of lift the wing can make at a given airspeed before stalling. However, all of the wing area and wing loading related effects are too indirect for them be used alone as accurate predictors of thermalling performance. It's very possible to make a truly horrible design from almost any set of initial parameters! What really matters in the end is how well you match all the different parameters to each other, and to the needs of the mission.

Don Stackhouse @ DJ Aerotech