# Could higher aspect ratio actually reduce gliding efficiency of a smaller glider?

I have been building 1 meter wingspan 100g class free flight mono wing gliders with a chord of around 10 cm and a flying speed of approximately 3 meters per second. So far glide ratios of around 10:1 have been achieved. The wing thickness is 1.2 centimeters. The airfoil has maximum thickness at 3.5 cm from leading edge. The bottom is flat, but only covered 6 cm from leading edge, leaving an undercambered area the remaining 4 cm to the trailing edge (this design grew out of thin undercambered wings).

So, is there a maximum aspect ratio (possibly based on Reynolds number calculations and/or "pressure leakage" due to the small scale or low speed)? Or do we continue to go for as high an aspect ratio as structurally possible.

Reynolds number for airfoils = Vc/v where V = 3 m/s, chord = 0.1 meter, kinematic viscosity at sea level = 1.460 × 10 minus 5th power = 20,548 for my model.

A response by Peter Kampf June 22, 2018 to "Is it best to use a thick airfoil or an undercambered airfoil for for slow speed flight" mentioned the Daedelus airfoils DAE 11, DAE 21, DAE 31, so it seems to be on the right track.

I am getting ready to start a build, would there be an optimal aspect ratio for this new aircraft?

• The rule that gliding performance increases with aspect ratio is under assumption that the wing area is the same. But you have fixed span and trying to vary the area, so it does not apply. Sep 22, 2019 at 21:26
• @JanHudec I submit area can vary somewhat because the lift/drag ratio is being considered. There is a weight constraint, so your point has some validity. May 23, 2021 at 13:06

With again thanks to other writers who have inputted valuable information, it has been found that excessive aspect ratio, by way of Reynolds Number, can effect gliding efficiency of a smaller, slower glider negatively as follows:

Reynolds number = Vc/v. Slower speed and shorter chord reduce Reynolds number. Kinematic viscosity of air v does not change.

Using Airfoil Tools, Coefficient of Lift/Coefficient of Drag at various Alpha was evaluated using a range of Reynolds Numbers from 50,000 to 1,000,000 for the Bleriot Eiffel 428 (thin undercambered) and the Wortmann FX 60 126 (thicker, less under camber).

It was found that Clift/Cdrag is significantly greater, at higher Reynolds number, particularly in a "sweet spot" around 6 degrees AOA. In this region, drag seems to "plateau", while Clift continues to rise.

At very low Reynolds Numbers, the Eiffel 428 showed a slightly better Clift/Cdrag ratio, but in ALL cases higher Reynolds number improved Clift/Cdrag ratio up to around 500,000 (will vary depending on air foil type), after which the polars seemed much more consistant.

First do the essential numbers:

Wing span is 100 cm, chord is 10 cm. So your wing area is 0.1 m². I assume standard atmospheric density, assuming you live close to sea level. This makes your lift coefficient with 100 g of mass and 3 m/s $$c_L=\frac{2\cdot m\cdot g}{\rho\cdot v²\cdot S}=\frac{1.96}{1.1025}=1.78$$ while the Reynolds number is only 20,534. This doesn't fit together – not even Airfoiltools goes that low. Your speed is most likely higher (the other possibility is flight somewhere in Siberia, which I discount for now).

More than a $$c_L$$ of 1.2 at those Reynolds numbers is unlikely. This would be reached at 3.65 m/s and Re = 25,000. Your best glide will be at this lift coefficient with an aspect ratio of 10 and a zero-lift drag of 0.05 (let's for now use a classical model airfoil). If you follow the Airfoiltools results, even at twice the Reynolds number the E387 has a large, laminar upper side separation bubble that requires the use of a turbulator. At Re = 25,000 the maximum lift coefficient is well below 1.2 and drag rises from 0.03 at $$c_L$$ = 0.6 to 0.07 at $$c_L$$ = 1.1. I smoothed the Airfoiltools coordinates for the E387, increased camber and thickness a bit to come as close to the airfoil you describe and placed a forced transition at 30% of chord on the upper side. Still, its high drag would give a best gliding lift coefficient of around 0.9 at the Reynolds number of 29,000 that this lower lift coefficient would suggest.

You are most likely better off with a bird-like airfoil of less thickness and more camber. With what you have the aspect ratio of 10 looks too high, which is confirmed by the lower aspect ratio of all smaller birds. Using $$c_L$$ = 0.9 and $$c_{D0}$$ = 0.035, the aspect ratio to make this point that of best glide is only $$AR=\frac{c_L^2}{c_{D0}\cdot\pi\cdot\epsilon}=\frac{0.81}{0.1045}=7.75$$

• Re "which is confirmed by the lower aspect ratio of all smaller birds" -- consider swifts? May 23, 2021 at 17:40
• @quietflyer yes, and seagulls. They fly a lot faster (hence the name) which shifts their Reynolds numbers up considerably. This in turn increases the optimum aspect ratio, too. May 23, 2021 at 19:19

From your description, your glider is squarely in the laminar flow regime, barring any unintended turbulator due to manufacturing.

From an aerodynamic perspective, you'll be trading off skin friction drag with induced drag. Induced drag is characterized by: $$C_{D_i}=\frac{C_L^2}{\pi e A}$$, whereas skin friction drag is: $$C_{D_f} \approx 2\frac{1.328}{\sqrt{Re_c}}$$ (source: Anderson, Fundamentals of Aerodynamics). $$A$$ is aspect ratio, $$S$$ is wing area, $$Re_c=\frac{\rho V c}{\mu}$$ is the characteristic Reynolds number of the wing.

Assume the simplest case of a rectangular wing, characteristic chord is $$c=\frac{S}{b}=\sqrt{\frac{S}{A}}$$. You can use a spreadsheet to find out where an increase in aspect ratio begins to increase your drag, assuming surface area remains the same.

The structural perspective is harder to nail down. I would imagine that the structural members are minimum gauge (i.e. sized not for strength but for manufacturability) even for the smaller aspect ratios. But as you increase in aspect ratio, there will be a weight impact.

• "barring any unintended turbulator due to manufacturing", I had heard balsa gliders (and frisbees) actually benefit (on their scale) from a little surface roughness. There is something about "tripping" the flow or "energizing" it that helps with efficient lift creation (golf ball dimples too). Sep 22, 2019 at 12:11
• “where an increase in aspect ratio begins to increase your drag, assuming surface area remains the same”—the question clearly states span is 1 m, so the area is the variable here. Slightly different calculations are called for! Sep 22, 2019 at 21:19