Preface:
     This is revised, updated and added information from the CWL section "Wing Cube Loading (WCL)" in the article "One Way of Selecting a Brushless Outrunner Electric Motor for a Radio Controlled (RC or R/C) Sport Plane or Sport Scale Plane Using ANR26650M1 (A123 Systems NanophospateTM lithium ion) 2300mAh Cells", by Ken Myers, December 2007

     "Wing loading is a lousy way to compare models with each other and with full-scale airplanes, because wing loading varies with the size of the plane. The problem is that we are dividing weight, a cubic-like function (weight is proportional to volume which we measure in cubic feet) by area, a squared function measured in square feet. We should be, and many modelers are, comparing planes by their wing cube loading, which is independent of size because both the numerator and the denominator are cubic."
Francis Reynolds, Model Builder, September 1989
(Bold font created by KM for emphasis.)

     Wing Cube Loading (WCL) provides a comparative value which can be used as an indicator, or a rule of thumb, for grouping radio controlled, miniature, aircraft by similar flight characteristics and "flyability". As Mr. Reynolds notes in his article, some people feel that it is a better "flyability" indicator than wing area loading (WAL) expressed in oz./sq.ft. of wing area. The WCL comparative value, or even WAL, has little to do with the aerodynamics needed to get the model to fly at various sizes/scales in real, un-scaleable air.

     As Mr. Reynolds points out, the term weight, as we commonly use it, is really a cubic function based on the volume of a mass.

     "Mass is commonly confused with weight. The two are closely related, but they measure different things. Whereas mass measures the amount of matter in an object, weight measures the force of gravity acting on an object. The force of gravity on an object depends on its mass but also on the strength of gravity. If the strength of gravity is held constant (as it is all over Earth), then an object with a greater mass also has a greater weight."
Matter-Mass-and-Volume

     "Volume is a measure of the amount of space that a substance or an object takes up. The basic SI unit (International System of Units - KM) for volume is the cubic meter (m³), but smaller volumes may be measured in cm³, and liquids may be measured in liters (L) or milliliters (mL). How the volume of matter is measured depends on its state."
Matter-Mass-and-Volume

     The "tricky" part about understanding the concept of wing cube loading (WCL) is that it not a directly measurable value, like the wing area loading (WAL).

     To create the WCL value, the wing area is mathematically manipulated to create a volume. The weight, which in final analysis is a cubic volume, is then divided by the mathematically manipulated cubic volume of the wing area yielding a comparative value.

     For me, the WCL comparative value seems to be more useful than the more commonly used wing area loading (WAL).

     As previously stated, the common wing area loading uses the ready to fly (RTF) weight in ounces (oz.) related to the wing area in square feet (sq.ft.). In Imperial units the wing loading is given as ounces per square foot (oz./sq.ft.). This is a real world value based on physically measurable objects. A scale of some type can "weigh" the plane. The actual wing area can be computed with physical measurements.

     Using the wing cube loading (WCL) comparative value, because it is not "size" dependent, makes it easier to comprehend the possible "flyability" of a plane and the skill required to fly the plane as an RC model. If a person states that their aircraft has a WCL of 8, no other mental calculations need to be performed, That plane will fly in a similar manner to other aircraft with a WCL of about 8 without regard to its actual size. The actual wing area does not have to be taken into account when the wing cube loading (WCL) value is stated. It provides a single step, comparative number.

     Using wing area loading (WAL) is a two step process to understand how a given plane might fly. If someone says that their model has a 20 oz./sq.ft. wing loading, then the actual wing area of the model must also be taken into consideration. A plane with a 400 sq.in. wing with a 20 oz./sq.ft. wing area loading will fly very differently from a similar plane with a 1200 sq.in. wing with the same 20 oz./sq.ft. wing area loading. Both the wing area loading and the actual wing area must be known by the experienced modeler to determine the possible flight characteristics when using the wing area loading method. That is two steps.

     The importance of the WCL comparative value is that it also indicates the relative ease of flying, or skill level, required to fly various RC model aircraft and allows for the pilot's ability level to be linked to the "flyability" groupings of these aircraft.

     As previously noted, it appears that when two aircraft, with the same wing loading, are sized or scaled differently, they fly differently. A "giant scale" model of 1200 sq.in. with a 32 oz./sq.ft. wing loading seems to fly, subjectively, much differently, and seems to the pilot, more easily, than a 400 sq.in. model with the same 32 oz./sq.ft. wing loading.

     The wing cube loading (WCL) comparative value attempts to handle this apparent difference in "flyability" using a mathematical manipulated wing area. The resultant mathematical volume is not related to the real, measurable, volume of the three-dimensional wing. The WCL comparative value does not take into consideration the actual airfoil or aerodynamics required to get the plane to fly at a given size or scale in "real" air. It simply applies an ease of flight VALUE for grouping and comparing aircraft by possible flight characteristics and skill levels.

     Creating mathematical models is not unusual. We create useful mathematical models to help us understand many things. Electrically powered model builders and fliers are aware of and use these types of mathematical models a lot. An example would be when trying to determine the power loss through an electrically powered motor system. Factors such as Io, Rm, K_v, amps and volts are put into a mathematical formula yield an answer that approximates what the output power might be.

One way that the WCL can be used - An Example:

     The example model has a ready to fly (RTF) weight of 60 ounces and a wing area of 500 sq.in.

     That aircraft has a wing area loading of 60 oz. / (500 sq.in. / 144 sq.in.) = 17.28 oz./sq.ft.
The 500 sq.in. wing area is divided by 144 sq.in. because there are 144 sq.in. in a square foot.
The result yields the wing area in square feet.
500 sq.in. / 144 sq.in. = 3.4722222 sq.ft.
60 oz. / 3.4722222 sq.ft. = 17.28 oz./sq.ft.

     The wing cube loading (WCL) = 60 oz. / ((500 sq.in. / 144 sq.in.)^1.5)Ê
The 500 sq.in. wing area is divided by 144 sq.in. because there are 144 sq.in. in a square foot. The result yields the wing area in square feet.
500 sq.in. / 144 sq.in. = 3.4722222 sq.ft.
Raising that result by a factor of 1.5 yields a cubic result.
3.47222^1.5 is 6.47
When a number is raised to the 3rd power it is called cubing the number, which is the number times the number times the number.
That previous result, by raising to the 1.5, is exactly the same as finding the square root of 3.47222 sq.ft. and then cubing it.
The square root of 3.47222 is 1.86339. (A simple calculator yields this result.)
1.86339 cubed, or raised to the 3rd power, is 6.47.
That is the same value as 3.47222 raised to the 1.5.

     Again, it is important to keep in mind that the mathematical manipulated cubic result has nothing to do with the actual volume of the wing.

How is using the wing cube loading (WCL), instead of the wing area loading (WAL) in ounces per square foot, useful to us?

     A similarly designed plane, to the example plane, with a 250 sq.in. wing is not half of the size of the 500 sq.in. wing used for the example. Actually it is only about 30% smaller.

     To scale wing area, it needs to be changed to a linear value. That is done by finding the square root of the area value.
The square root of 500 sq.in. is 22.36068 in.
The square root of 250 sq.in. is 15.81138 in.
15.81138 in. divided by 22.36068 in. = 0.7071068
Thus the 250 sq.in. model is about 71% of the size of the 500 sq.in. model.

     For the smaller model, with a 250 sq.in. wing, to have similar flight characteristics, providing it is designed properly to fly at the reduced scale, it would have to have the same WCL of 9.27 as the larger model. It should weigh, (250/144)^1.5 * 9.27 = 21.2 oz. ready to fly (RTF). The wing area loading of the 250 sq.in. would be, 21.2 oz. / (250 sq.in. / 144 sq.in.) = 11.65 oz./sq.ft. That is quite different from the 500 sq.in. model's wing area loading of 17.28 oz./sq.ft.

     Even though the wing area loadings are over 30% different for the two models, with the appropriate power system and aerodynamics, the 250 sq.in. plane would have much the same "feel" and flight characteristics as the 500 sq.in. model because they both have a WCL of 9.27.

     A 1000 sq.in. wing, based on the example plane, for the same type/task aircraft is about 30% larger than the 500 sq.in. plane. Using the same cubic wing loading (CWL), yields a RTF weight of (1000 / 144) ^1.5 * 9.27 = 169.64 oz. Its wing loading would be 169.64 / (1000/144) or 24.42 oz./sq.ft. Again, the 1000 sq.in. model would have the same "feel" and flight characteristics as the other two sizes, given the proper power and aerodynamics.

     In the April 2014 issue of the Ampeer, I presented the data for two similar designs in different scales. See "Scaling the ElectroFlying Fusion"

Steve Pauly's Electro Flying Fusion design from a kit:
RTF Weight: 74.615 oz.
Wing area: 558.45 sq.in.
WAL: 19.24 oz./sq.ft.
WCL: 9.77

Ken Myers' Fusion 380 scratch build:
RTF Weight: 40.6 oz.
Wing Area: 375.5 sq.in.
WAL: 15.57 oz./sq.ft.
WCL: 9.64

     The "flyability" "feels" almost identical for the two planes as well as the skill level required to fly them both. There is about a 20% difference between the wing area loadings (WAL) of the two planes but only about a 1% difference in wing cube loadings (WCL).

     Yes, the statement about "flyability" and "feels" is subjective, but it is true for me. With decades of RC flight experience, it has also proven true for a whole range of different RC aircraft types and sizes.

Continuing With the Example Plane:

Another way to look at it.

     If the 250 sq.in. plane had a wing area loading of 24.42 oz./sq.ft., like the 1000 sq.in. plane, it would weigh 42.4 oz. Flying a 250 sq.in. model at this weight is challenging.

     The WCL indicates why.
WCL = 42.4 / (250 / 144)^1.5 = 18.54. A WCL of 18.54 is for experts only. Why that is true is illustrated later in this article.

     Wing area loading (WAL) forms a straight line on the graph. The wing cube loading (WCL) creates a curved line.

     The wing area loading for the graph is 17.28 oz./sq.ft. The WCL is 9.27. Both values are based on the Example plane of 500 sq.in.

     The graph shows, that for a small range of wing areas, the WAL or the WCL can be used to compare planes with equally useful results, but as the wing area differences approach the extremes, there is a much greater difference between the WAL and WCL predictive useful results.

     This graph demonstrates what happens when the WCL is set to reach the predictive value of a 1000 sq.in. wing at a RTF weight of 120 oz. based on a WAL of 17.28 oz./sq.in.

     Using 17.28 oz./sq.ft. changes the WCL to 6.56 because the weight of the 1000 sq.in. plane is now only 120 oz. 120 oz. / (1000 sq.in. / 144 sq.in.)^1.5 = 6.56

     The WCL line on the graph indicates that for the plane scaled to 500 sq.in., to fly in a similar manner, it should weigh about 42.43 oz. ready to fly. That would be a WAL of 12.22 oz./sq.ft.

     The WCL line on graph also indicates that for the plane scaled to 250 sq.in., to fly in a similar manner, it should weigh about 15 oz. ready to fly. That would be a WAL of 8.64 oz./sq.ft.

     With all of this taken into account, I believe that the WCL factor IS the valid indicator of flight characteristics, even more so than the traditional wing area loading.

     The three different size examples of the same plane, using wing area loadings of 11.65 oz./sq.ft., 17.28 oz./sq.ft. and 24.42 oz./sq.ft., all would have pretty much the same "feel" to the pilot and exhibit close to the same flight characteristics, but their wing area loadings are very different, especially if the smallest, 250 sq.in wing area version, with an 11.65 oz./sq.ft. WAL, is compared to the biggest, 1000 sq.in. wing area version, with a 24.42 oz./sq.ft WAL.

     Over the decades, one anecdotal comment by RC pilots, has always been, "Bigger flies better." Using WCL, partially explains this subjective observed phenomenon. The WCL line on the first graph also indicates this. Of course there are other factors involved as well.

     In Getting Started In Backyard Flying by Bob Aberle, Bob chose to group model types using weight, wing area and wing area loading. When the comparative value of WCL is used instead of wing area loading in oz./sq.ft., some interesting things come to light.

     Bob created several groups (p.64, p.65);

Ultra Micro: Up to 2 oz., wing area 50-100 sq.in., wing loading up to 5 oz./sq.ft.
Sub Micro: 2-3 oz., wing area 75-125 sq.in., wing loading up to 5 oz./sq.ft.
Micro: 3-8 oz., wing area 125-300 sq.in., wing loading up to 5 oz./sq.ft.
Parking Lot & Backyard: 8-14 oz., 300-600 sq.in., wing loading up to 8 oz./sq.ft.
Speed 400: 14 oz. and up, 300 sq.in. and up, wing loading 8-10 oz./sq.ft.

     Here's another way to look at them with one specific example from each group.

Ultra Micro: Lite Flyer, 1.6 oz., 68 sq.in., 3.4 oz./sq.ft, WCL 4.93
Sub Micro: DJ Aerotech Roadkill Series, 2.8 oz, 80 sq.in., 5 oz./sq.ft., WCL 6.76
Micro: GWS Pico Stick, 7.7 oz., 238 sq.in., 4.7 oz./sq.ft., WCL 3.62
Parking Lot & Backyard: Merlin, 17 oz, 511 sq.in., 4.9 oz./sq.ft., WCL 2.54
Speed 400: Miss-2, 29 oz., 390 sq.in., 10.8 oz./sq.ft., WCL 6.5

     None of these planes would be considered "hard to fly" by an experienced R/C pilot.