For maximum glide range, should I minimize glide angle or AoA?

Question

I'm currently taking an aeronautical engineering course in school. For an upcoming project, we're going to build balsa toss gliders and we have to design our own wings. The program we're using (Aery32) provides information about how the model will fly, including CoD, AoA, and glide angle. I already know that using long, tapered wings will provide the most efficiency, however, to further optimize the design, I need to know which item I should minimize- AoA or glide angle. Obviously in a perfect world I would do both however I don't have a large amount of time. To summarize- I'd like to know if reducing the angle of attack or decreasing the glide angle will provide a further glide.

Answer 1

The furthest glide is by definition the lowest glide angle! So if that is one of your design inputs, you should definitely go for that.

But seriously, reducing weight and form drag gets you the furthest.

1. General glide distance theory

With glide angle $\bar\gamma$ = -$\gamma$:

$\quad C_D \cdot \frac{1}{2} \rho V^2 \cdot S = W \cdot \text{sin }\bar\gamma \tag{1}$

$\quad C_L \cdot \frac{1}{2} \rho V^2 \cdot S = W \cdot\text{cos }\bar\gamma \tag{2}$

Division yields: tan $\bar\gamma$ = $C_D/C_L$, and both $C_D$ and $C_L$ are a direct function of Angle of Attack.

For the drag coefficient the following parabolic approximation can be used to incorporate induced drag: $$C_D = C_{D_0} + \frac {C_L^2}{\pi A e}$$ Minimal $\bar\gamma$ will be at maximal $C_L/C_D$, which will be found at $\frac{1}{2} \sqrt{\frac{\pi A e}{C_{D0}}}$. For the lowest glide angle, find the lowest form drag factor $C_D$ and the highest wing aspect ratio A. Longer span & narrower chord will get you further.

2. Toss glider particulars.

They Take Off by an arms throw, and upon release are thrown up with a lot of excess speed and let it exchange speed for extra altitude. After which the glide starts into the trimmed state: speed, AoA and $\bar\gamma$ (thx to @Zeus for pointing this out).

The graph above is from Low Speed Airfoil Data by M. Selig, page 68, and depicts $C_L, C_D$ and $\alpha$ at very low design Reynolds numbers. As can be seen:

1. $({c_l/c_d})_{max}$ of the wing profile, at Re > 300,000, occurs at $\alpha$ = 1°. So wing AoA should be kept close to this angle in flight.
2. The trimmed speed must be such that Re > 300,000 to reach the minimum $c_d$ at $c_l$ = 0.6. From this Re follows the wing chord, and from equation (2) above then follows $$V_{launch} = \sqrt{\frac{2W}{C_L \rho S}} \tag{3}$$

Weight follows from the maximum energy W/S should be chosen such that it follows from a comfortable throw.

Answer 2

Well, well, well. Time to go to ... the well.

"Balsa toss gliders" can be a lot of things, but they are a great place to start. If they are thrown for distance design criteria will be different from flown from a height such as from a hill or tall building.

Reynolds number is a very important consideration for slow glider models. No, they are not replicas of larger full scale gliders. Studying lift to drag graphs at airfoiltools.com should get you off to a good start on selection of airfoil and AoA to use.

Design. The Wright Brothers? They started with kites, essentially tethered free flight models. Airfoil in the back, flat plate in the front. Why?? Above a certain airspeed the cambered airfoil begins to generate a stronger suction peak above the wing forcing the nose down, reducing AoA$^2$.

Though their "canard" design made stall recovery more difficult$^1$, it makes the aircraft less likely to pitch up and stall due to a gust!. So ... for both applications (throw and hill) ... unsweep Suzanne's$^3$ wings! ... or perhaps ... the "F-14" Suzanne (swing wing with canards).

As with all wings, optimal Lift/Drag AoA will give you optimal range, or Vbg. Practice will make perfect here, as proper aspect ratio and drag reduction are needed to take 1st prize. Strength, stability and crosswind performance are important too.

Before you jump into the build, do some homework on similarly sized gliders. Good luck.

$^1$ The Wrights led the aviation world when sustained powered flight and turning a circle were state of the art. Once aviators "went vertical": climbing with more powerful engines, difficulties recovering from the "power on stall" doomed their design, opening the way for the classic tractor/rear tail design we see today.

$^2$ The upper wing suction peak strengthens as velocity increases. This is why Lift/Drag ratio improves with higher Reynolds number.

$^3$ Suzanne is the "Paper Airplane Guy's" record throwing design.