Wing Loading and Different Sized Airplanes

By Ed Moorman

We normally use an airplane's wing loading, the number of ounces weight of the plane per square foot of wing area, as one indication of how an RC plane will fly. As a general rule, somewhere in the low 20's oz/sq. ft. makes for a good performing airplane. Get up close to or over 30 oz/sq. ft. and the plane begins to feel heavy and must be landed faster. Many scale planes, especially warbirds are in this range of wing loading. Landing with flaps are common to offset the high wing loading. If a flier has been used to calculating wing loading and he builds a giant, he is in for a surprise. A plane he expects to be in the low 20 oz/sq. ft. may have a wing loading in the low 30 oz/sq.ft. or even higher, up near 40 oz/sq.ft. He expects it to be a bear to fly, but finds out it is a real pussycat. Why is this?

The answer is that wing loading does not work well in comparing airplanes of different sizes. Other aerodynamic factors, such as Reynolds number, are dependent on wing size and aircraft speed. "Bigger is better," as the giant fliers say, is really true. Well, if wing loading is not a good way to compare planes, what parameter can we use for comparison? One answer is cubic loading, a number which attempts to include the overall size or volume of the plane in the equation. Francis Reynolds, in his July 1989, Model Builder magazine article, "Cubic/Displacement Loading" presented formulas for cubic loading, displacement loading and a performance rating, combining all of the loading factors.

Rather than go into the details of his math, let's look at some results for planes of three different sizes, a .40 sized plane with a 600 square inch wing area, a small giant for Super Tigre 3000 or Moki 1.8 with 1200 sq. in. & a large giant of 1800 sq. in. area, approximately like a Stinger.

For the baseline, I'll use an original sport giant design of mine, the Hawk, which has 1200 sq. in. area and weighs in at 15 lbs. The design has been built by several different people. It is an easy flier and may be landed by touching the tail wheel first, then the main gear. This indicates it is not a heavily wing loaded plane, rather one which might be compared to a lightly loaded, sport plane. However the wing loading is 28.8. If I had this wing loading on a .40 sized plane, it would probably feel heavy and I would have to be careful on landing.

Now let's compare all three different size planes with their weights adjusted to give a wing loading of 28.8.

Our .40 plane with 600 sq. in. weighs 7.5 pounds, pretty heavy. It would probably be a fairly fast landing plane. We would expect a good, light .40 sized plane to weigh in somewhere in the 5-6 pound range. The 1200 sq. in. Hawk, I have already told you feels lightly loaded and can be dragged in on landing. Our larger 1800 sq. in. Stinger-sized plane would feel fairly light at 22.5 pounds and probably be a floater.

Now take a look at the cubic loadings. They are 14.11, 9.98 and 8.15. These figures indicate the .40 sized plane to be the heaviest loaded of the three, which we know from experience to be true-the 7.5 lb., 600 sq. in. area, .40 sized plane will not be a slow lander. Cubic loading, then, seems to give a better method of comparison than wing loading.

To further check out cubic loading, here are a second set of calculations with weights adjusted to give the same cubic loading. I have used the cubic loading of the Hawk for the baseline since I know its performance.

With the same cubic loading, the weight of the .40 sized plane comes down to 5.3 pounds, more in line with a lightly loaded, good performing plane. The wing loading of just over 20 oz. per sq. in. also shows this is a lightly loaded plane. On the very large size, note the wing loading of the 1800 sq. in. plane. It is over 35, a figure which we would consider very heavy for a small plane. This figure would not be heavy for a plane this large.

Finally, let's look at the figures adjusted for the heavier cubic loading corresponding to the 28.8 wing loading on the .40 sized plane.

We already know a 7.5 pound, .40 sized plane would feel heavy. I know from many years of flying my Hawk design, 21 plus pounds would be heavy. Having flown Stingers, I can also say, 39 pounds would also be very heavy.

So having looked at wing loading for the three planes and their cubic loading both at the light range and the heavy range, cubic loading seems to me to gives us a better and more accurate method of comparing airplanes of different sizes.

Now that cubic loading looks good, how do we calculate it? There are a couple of ways to do it both of which come out with reasonable figures. The one I normally use is the weight in pounds divided by the product of the area in square feet times the square root of the area in square feet. This results in ounces per cubic foot.

CL= Wt / [Area x sqr(area)]

You'll need a calculator which has a square root on it. Most of them except for the real cheapies or the business calculators have this.

Let's go through the .40 sized example above.

7.5 lbs x 16 = 120 ounces

600 sq. in. / 144 = 4.16667 sq. ft.

Sq root 4.16667 = 2.04124 ft.

4.16667 x 2.04124 = 8.50517 ft cubed

120 oz. / 8.50517 ft cubed = 14.10906 oz/cu ft