A Different Way of Calculating Wing Area and Various Wing Loading Methods Compared

By Ken Myers

We are now in the buy and fly era of model aviation. A large number of people who enter the hobby today just purchase a bind-and-fly (BNF) or ready-to-fly (RTF) model airplane instead of creating their own model airplane.

Once it assembled, they expect it to fly as described in the various reviews; hobby magazines, online (Web site) or video (i.e. YouTube).

The only airframe parameters they are interested in is wingspan and fuselage length. In other words, “Will it fit in my vehicle?” or “How many can I fit in my vehicle?”

With a few more airframe parameters, a person who’s been in the hobby for awhile can compare and predict the flight characteristics of an unknown airframe. The added parameters provide useful information to those who have passed the introductory stage of RC modeling.

Many magazine reviewers provide the ready to fly (RTF) weight. If the RTF weight is given as 5.1 oz. to 5.6 oz. and the wing span is noted as 28.15″, it does provide a little comparative information when comparing it to to another model that has a RTF weight of 2.22 lb. (35.5 oz.) with a wingspan of 65″, but not much.

As a quick mental exercise, try to arrange the following in order from easiest to fly to hardest. All the planes were reviewed in the Winter 2018 issue of “PARKPILOT” magazine.

Horizon Hobby E-Flite UMX Aero Commander 5.6 oz. & 28.15″ – 2.39 oz./ft.
Origin Funter Glider Trainer EP RR 35.5 oz. & 65″ – 6.55 oz./ft.
Hacker Model Pilatus Turbo 890mm EP ARF 7.3 oz. & 35″ – 2.5 oz./ft.
Horizon Hobby Blade UMX F-27 FPV BNF Basic 2.8 oz. & 17″ – 1.98 oz./ft.
Horizon Hobby HobbyZone T-28 Trojan S RTF with SAFE 1.65 oz. & 16.8″ – 1.18 oz./ft.
Horizon Hobby E-flite X-VERT VTOL BNF Basic 7 oz. & 19.85″ – 4.23 oz./ft.
Tough Jets T-15 40 oz. & 31″ 15.48 oz./ft.
Horizon Hobby E-flite UMX Waco BL BNF Basic 3.5 oz. & 21.7″ – 1.94 oz./ft.

This method has an obvious flaw. The Waco is a biplane and only the wingspan of the top wing is noted. That is okay for noting how much space the top wing will require, but not so good for comparative information.

Ounces per linear foot is an oddball way to try the anticipate possible flight characteristics and similarities of flight of various model planes.

Full scale designers, and modelers, have used ounces, or sometimes pounds, per square foot of wing area for generations as a comparative and anticipatory value.

A look at the example planes using ounces per square foot of the wing planform area.

Horizon Hobby E-Flite UMX Aero Commander 5.6 oz. & 93.1 sq.in. – 8.66 oz./sq.ft.
The reviewer did not note the wing area. It is on Horizon Hobby’s Web site.

Origin Funter Glider Trainer EP RR 35.5 oz. & 434 sq.in. – 6.55 oz./sq.ft.
The reviewer did not note the wing area. It is on Tower Hobby[s Web site.

Hacker Model Pilatus Turbo 890mm EP ARF 7.3 oz. & ?? sq.in – ?? oz./sq.ft.
Neither the reviewer nor Tower Hobbies noted the wing area.

Horizon Hobby Blade UMX F-27 FPV BNF Basic 2.8 oz. & ?? sq.in. – ?? oz./sq.ft.
Neither the reviewer nor Horizon Hobby noted the wing area.

Horizon Hobby HobbyZone T-28 Trojan S RTF with SAFE 1.65 oz. & ?? sq.in. – ?? oz./sq.ft.
Neither the reviewer nor Horizon Hobby noted the wing area.

Horizon Hobby E-flite X-VERT VTOL BNF Basic 7 oz. & 120 sq.in. – 8.4 oz./sq.ft.
The reviewer did not note the wing area. It is on Horizon Hobby’s Web site.

Tough Jets T-15 40 oz. & 615 sq.in – 9.37 oz./sq.ft.
Wing area was noted by the reviewer and it is on the Tough Jets’ Web site

Horizon Hobby E-flite UMX Waco BL BNF Basic 3.5 oz. & 132 sq.in. – 3.82 oz./ft.
The wing area was noted by the reviewer and it is on the Horizon Hobby’s Web site

Arranging these planes by ounces per square foot, for comparison purposes is a bit easier, except three of the planes cannot be arranged by wing planform area loading because the wing planform area is not available.

The F-27 and T-28 are somewhat similar, with some of the shortest wingspans in the group, and both are ‘low weight’ models, so they could be expected to fly in a similar fashion. The Hacker Model Pilatus Turbo 890mm EP ARF with a 35″ wingspan and 7.3 oz. weight would fly differently.

Making a ‘Best Guess’
     There is a manual for the Hacker Pilatus.

On p. 6 of the manual it shows the main parts with the wing panels included. There is also a known measurement available on page 1. The wingspan is noted as 890mm, which is (35.03937 inches).

A screen grab can be made of the wing panels and saved. The saved file can be imported into a CAD program, traced and then enlarged based on the given wingspan to give the actual dimensions. That method yielded 434 sq.in. for this model. 7.3 oz. & 434 sq.in. – 2.42 oz./sq.ft.

Using the same method with a bottom view photo from Horizon’s Web site for the F-27 yielded about 83.5 sq.in. 2.8 oz. & 83.5 sq.in. – 4.83 oz./sq.ft.

A top view from the manual for the T-28 Trojan was used in the same manner. The wing area was calculated as 51 sq.in. 1.65 oz. & 51 sq.in. – 4.66 oz./sq.ft.

The method of using CAD is a very convoluted way to estimate the wing area, but it is better than nothing, which is what was provided by both the suppliers and reviewers for these planes. There are many ways that the estimated wing area could be off some, but it should be relatively close.

Luckily, reviewers do have a quite an easy way to calculate the wing area because they have the model “in hand”.

Calculating the Wing Area of a Model “In Hand” if the wing is not rectangular or trapezoidal.
     Calculating the area or a rectangle or trapezoid is pretty straight forward. Sometimes though, you are curious about the wing tip area or the wing or wings have an ‘odd’ shape to them. The following method can be used to include wing tips or when dealing with oddly shaped wings.

Items Required: a scale for weighing relatively light objects, a piece or two of Dollar Tree Foam Board or Ross Foam Board available at Walmart depending on the size of the wing, a single edge razor blade and/or X-ACTO knife with a #11 blade, a pen

Procedure:
1. Weigh the foam board sheet or sheets (I prefer grams.)
2. Calculate the weight per square inch of the foam board.
3. Lay the wing panel, panels, or assembled plane if small, on the foam board.
4. Draw the wing outline onto the foam board.
5. Cut out the wing planform outline.
6. Weigh the wing planform outline.
7. Divide the weight of the foam board wing planform outline by the calculated weight per square inch.
8. The result is the wing area of the wing planform.

My example is for a fairly large wing. Two pieces of foam board are required, as the chord, at its widest point is 10-3/8″ and foam board is only approximately 20″ wide.

Two different brands of foam board were used as a ‘check’ of the method against each other.

The DTFB sheets weighed 0.184g per square in.
The Ross foam board sheets weighed 0.215g per square in.

When the two wing panels were cut out of DTFB, the two panels weighed 107.2 g.
107.2g divided by 0.184g per sq.in. = 582.6 sq.in.
When the two wing panels were cut out of the Ross, they weighed 125.6 g.
125.6g divided by 0.215g per sq.in. = 584.2 sq.in.

I am comfortable in noting the wing area as 585 sq.in.

Using the Wing Cube Loading Value
     Some people believe that the mathematical wing cube loading value is even more useful to make comparative judgements about the flyability of different planes.

There is a lot of information on the EFO Web site about the wing cube loading value. The most recent is “Wing Cube Loading”, By Ken Myers, February 2018.

The formula for a WCL comparative value is:
wing planform area in square inches divided by 144 sq.in. in a square foot raised to the 1.5
That yields a cubic value for the area. It is NOT the wing volume! It is only a value to use instead of a squared value.

The weight, in ounces, is then divided by the cubic value and that yields a comparative value, which is typically, not assigned a unit value.
Weight in ounces / (area in square inches / 1.44)^1.5

Tough Jets example:
WCL = 40 oz. / (615 sq.in. / 144 sq.in.)^1.5
615 sq.in. / 144 sq.in. = 4.27083333333333 sq.ft. rounded to 4.27 sq.ft.
4.27 sq.ft. ^ 1.5 = 8.8261018658529 units have been dropped and rounded to 8.83
40 units dropped / 8.83 = 4.53001132502831 rounded to 4.53
Wing Cube Loading Comparative Value = 4.53

The table compares all three methods for determining comparison factors and flyability of the eight airplanes reviewed in “PARKPILOT.”

In the table, the planes are listed from the lowest value in each column to the highest. That sorts them by their ease of flyability. The wing planform area loading arrangement is somewhat similar to the WCL value arrangement, but not quite.

The Tough Jets T-15 is the most notable example of a change in position when the WCL value is used. The T-15 is also the ‘largest’ of the review models.

It is often said that larger models ‘fly better’. There are many reasons for that, but the WCL value offers a quantified value for that statement. The common wing planform area loading does not take that into account.

The table also shows some subjective comments about the flyability of the reviewed airplanes for comparison to the WCL values. How hard can it be to fly the T-15 when the reviewer notes that it can land at walking-speed when no wind is present, yet wing planform area loading indicates that it should be “the hardest to fly”?

To provide the useful wing planform area, reviewers could use the weight to area method of calculating the approximate wing planform area. For those interested, it could be a helpful indicator.