Using Wing Cube Loading instead of Wing Loading

[Air-headed Aviator]

I learned about the concept of Wing Cube Loading from watching Tail Heavy Productions on Youtube. WCL is a dimensionless value that intends to describe how an aircraft design gains and loses energy. WCL is an adaptation of Wing Loading, but intends to consolidate the variations seen from different scales and different masses. The point of WCL is best illustrated by comparing the wing loading of say an RC EDF jet and a full scale Piper J-3 Cub. By the numbers the RC Jet has less mass for every equivalent area of wing then the J-3 Cub, but no one would describe the way the Jet flies as "floaty" or the Cub as "heavy". At the different sizes and weights of these two aircraft wing loading becomes less effective at communicating how energy is lost or gained between the two. WCL serves to standardize the potential values.

Wing Cube Loading is not technical a standardized scale, and still works off some subjectivity with its scaling. Below is the scale I adopted from Tail Heavy Productions and RC CAD VR:

This scale is intended to be usable for any size of RC aircraft design within reason, though at certain masses the ability to achieve lower values reduces.

For calculating the WCL, utilize this Formula below:

I've switched to using WCL over Wing Loading in plane design specifically because it provides a more reliable metric in deciding how an aircraft will "feel" to fly. Higher values can create sharper feeling aircraft with quick responding controls/ lower values can produce forgiving aircraft that resist stalls and fly at low speeds. However it is important to note that WCL is an ingredient to aircraft design, not the core. For instances while a very low WCL could supposedly create a high retention, slow speed aircraft, if it possessed an airfoil with a low coefficient of lift, then it will stall at those slow speeds. If an aircraft design with a very high WCL possesses a complex wing design that maintains lift well, then it could potential fly slower than what its WCL suggests. In aircraft design all the puzzle pieces together contribute to the whole picture; Wing Cube Loading is a well defined piece to more precisely build with.

 

[FoamyDM]

I wish i saw this before i recorded Episode 109 of the AviationRCNoob Podcast

 

[Piotrsko]

Hmmm. What does the formula do with variable geometry surfaces, or do you run the equation for each point of change then draw a graph? Not a lot of wind tunnel data for flaps

 

[Air-headed Aviator]

Hmmm. What does the formula do with variable geometry surfaces, or do you run the equation for each point of change then draw a graph? Not a lot of wind tunnel data for flaps

If the wing is a variable sweep type the WCL doesn't technically change, but sweep does shift the effective speed range up. For an equivalent speed a wing with more sweep has less overall energy, and acts as though it will lose energy more quickly.

Wings with flaps shift their maximum coefficient of lift up so I like to think of them as the opposite of sweep; they don't technically change the WCL but they do shift at what speed the aircrafts energy state is, in this case lower.

 

[cyclone3350]

I do large scale golden age era type planes. I find that U can use this fornula on the full scale to see how it compares to the scale size. For example, when I did the J-3 using its gross weight of 1220 lbs, I came up with a WCL of 10.9 oz. When I did my 1/4, I was concerned that I came in at just over 18lbs. The WCL on that one is 10.3 oz. Sure eneogh, it flies nice and slow just like the full size. A club member did a 1/3 BUSA Pup that came in close to 35lbs, but when we did the WCL, it matched the full scale and that thing flies slower than my Cub. BTW the full Pup is at 6.5 0z and his came in at 4.9oz.

 

[telnar1236]

Hmmm. What does the formula do with variable geometry surfaces, or do you run the equation for each point of change then draw a graph? Not a lot of wind tunnel data for flaps

Wing cube loading is fundamentally a scaling approach - it's intended to make the small plane look about the same as the big plane/fly at a scale speed, so if you have scale flaps, then I think the idea is they should work about the same as on the full scale.
That said, I don't really like wing cubic loading personally. It's definitely an established method and a lot of people like to use it, but it doesn't really tell you much about your RC plane as an RC plane. If you want a plane to look scale, it's great, but mostly I'm more concerned with if my plane can successfully operate off my field's runway. Also, to your point, it doesn't address changes in lift coefficient coming from flaps, or for that matter from changes to the airfoil. An RC plane with a Clark Y airfoil will create twice as much lift as an RC plane with a scale supersonic airfoil and therefore fly 40% slower.
Basically, wing loading tells you how your plane will fly, while wing cubic loading tells you how your plane will look while it flies

 

[telnar1236]

If the wing is a variable sweep type the WCL doesn't technically change, but sweep does shift the effective speed range up. For an equivalent speed a wing with more sweep has less overall energy, and acts as though it will lose energy more quickly.

Wings with flaps shift their maximum coefficient of lift up so I like to think of them as the opposite of sweep; they don't technically change the WCL but they do shift at what speed the aircrafts energy state is, in this case lower.

What do you mean by energy in this context?

 

[Air-headed Aviator]

What do you mean by energy in this context?

What I mean is that trade off between speed and lift. Designs of high WCL don't transition their forward speed into lift as readily as designs with low WCL. That means that in maneuvers the high WCL aircraft will preserve their speed for longer at the expense of lift development while the low WCL aircraft create lift more readily at the expense of maintaining their speed. When I think about the effect flaps have on wings, raising the maximum CL, I think of them as improving the wings ability to tern forward motion into lift. Similar with sweep; the CL isn't technically changed but sweep reduces the amount of air normal to the airfoil of which ever wing design. It makes the wing act like its moving slower than it is, which reduces the effect of its forward energy, reducing the effectiveness of producing lift. At least in my peerspective.

 

[telnar1236]

What I mean is that trade off between speed and lift. Designs of high WCL don't transition their forward speed into lift as readily as designs with low WCL. That means that in maneuvers the high WCL aircraft will preserve their speed for longer at the expense of lift development while the low WCL aircraft create lift more readily at the expense of maintaining their speed. When I think about the effect flaps have on wings, raising the maximum CL, I think of them as improving the wings ability to tern forward motion into lift. Similar with sweep; the CL isn't technically changed but sweep reduces the amount of air normal to the airfoil of which ever wing design. It makes the wing act like its moving slower than it is, which reduces the effect of its forward energy, reducing the effectiveness of producing lift. At least in my peerspective.

Makes sense. What are your thoughts on how lift to drag ratio comes into this? A "dirty" plane with flaps and gear down has a lot more lift available for a given speed but it also has a lot more drag. Think trying to do a loop with an EDF jet with full flaps - probably won't end well at any speed

 

[Air-headed Aviator]

Makes sense. What are your thoughts on how lift to drag ratio comes into this? A "dirty" plane with flaps and gear down has a lot more lift available for a given speed but it also has a lot more drag. Think trying to do a loop with an EDF jet with full flaps - probably won't end well at any speed

I suppose that becomes one of the moments where WCL can only be an ingredient to the dynamics of a design and not the whole picture. It turns out WCL is a real unit so there must be a way to quantify that with the values of Lift and Drag; primarily it can only be that measure of how well or poorly the wing turns a planes momentum into lift. If things like drag or efficiency or even altitude vary then I suppose it should be looked at as those elements taking a piece of the pie of the total available energy. Less drag in a design will make an aircraft act like it has a much lower WCL then the numbers suggest.

 

[telnar1236]

I suppose that becomes one of the moments where WCL can only be an ingredient to the dynamics of a design and not the whole picture. It turns out WCL is a real unit so there must be a way to quantify that with the values of Lift and Drag; primarily it can only be that measure of how well or poorly the wing turns a planes momentum into lift. If things like drag or efficiency or even altitude vary then I suppose it should be looked at as those elements taking a piece of the pie of the total available energy. Less drag in a design will make an aircraft act like it has a much lower WCL then the numbers suggest.

I think you might enjoy looking into energy maneuverability theory - it's pretty much a formal description of what you're describing

In terms of wing cubic loading having units, this is true, but it isn't necessarily all that meaningful from a dynamics perspective - it's basically a way to measure the density of the airplane - you can express it as WCL = k*airplane density where k is a constant for some particular airplane.

This might be a bit too much math, but you can express drag as
D=1/2*rho*u^2*s*Cd
where rho is air density, u is air speed, s is wing area, and Cd is coefficient of drag.
And energy as
E = 1/2*m*u^2 + m*g*h
Where m is the aircraft mass, u is still airspeed (if energy is calculated in a reference frame where the air is still), g is gravity, and h is the altitude of the plane.
If the airplane is at a constant altitude, energy is only dependent on speed. You can then calculate how quickly the plane gains or loses speed with respect to time using Newton's second law F = ma which is equivalent to a = F/m. I'm also going to use Q = 1/2*rho*u^2 in the equation so I don't have to write out the expression for dynamic pressure every time.

So
du/dt = a = (T- D)/m = (T - Q*S*Cd)/m
where T is thrust and the other variables are as use before. So, the rate at which speed and therefore energy changes is dependent only on thrust, speed, wing area, coefficient of drag, and the weight of the plane. If you want to calculate how many G the plane can pull you can express drag as L*Cd/Cl where lift is also dependent on wing area (L=Q*S*Cl).

In energy maneuverability theory, this is typically expressed in terms of excess power instead of in terms of excess acceleration since this is a more direct expression of the way the energy state changes.

A short summary on Wikipedia:

Energy–maneuverability theory - Wikipedia

en.wikipedia.org

And the now public original paper on it from the national archives:

https://www.archives.gov/files/declassification/iscap/pdf/2011-052-doc1.pdf

With wing cubic loading, you're normalizing to the scale of the airplane, so an airplane half the size can pull twice as many g for a given airspeed or in other words turn in half the radius for a given speed or fly at about 70% of the speed of the larger one. So it's much more about how a plane looks flying, then about the dynamics of how it actually flies