Why don't solar powered aircraft use wings with more surface area

Question

I was looking at some solar aviation projects, and I noticed they appear to follow the designs of a glider.

The Helios drone above is basically a flying wing with a high aspect ratio.

And the solar impulse above is a textbook glider with minimal cord length and a long wing span.

I understand the idea is a wing with a high aspect ratio reduces parasitic drag by decreasing its surface area, however in this case don't you want the most wing surface area possible?

This answer shows that induced drag is unaffected by the wings aspect ratio, so if it's only parasitic drag we're trying to combat here, why not keep the wing span the same, but make it's cord longer?

Won't the added solar panels you could fit on a wing make up for any friction drag caused by the longer cord?

Taking this to the extreme could you make some kind of solar powered rectangle that has a width (span) comparable to the gliders above, but a length (cord) twice as long as the span?

Surely you'll have enough power to make the aircraft fly, so are there other design considerations that factor in when choosing the cord length of these solar powered projects?

Answer 1

First, because solar panels are pretty mediocre sources of power per area. An industry average found via quick Google search is in the 200 - 300 Watt per square meter range, so let us be very optimistic and take the higher value, $300W/m^2$, for a round of math. If you want the details, solar irradiation on the surface is about $1kW/m^2$ and the best experimental photo-voltaic cell efficiencies by year are graphed here.

Using the ASH 26 motor glider as a case study, we can see if solar powering an aircraft is as trivial as the OP suggests.

Assuming our panels are made of fairy dust we can further decide their weight is negligible and that we can perfectly cover the $11.68\,m^2$ of wing area this glider has and that it will operate as though under normal incidence (Sun at 90° to the panel) all the time. Thus, $3.5\,kW$ of free energy... which sadly is only $9.4\,\%$ of the power supplied by the Wankel engine used on the real glider, and with which it attains a very humble $4\,m/s$ climb rate. This is before even considering that batteries are also very inefficient sources of energy per unit of mass when compared to hydrocarbons.

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Now, for the second part of the OP´s query, how about enlarging the chord of the wing to increase the area? This also happens to fall flat for different reasons. The drag coefficient: $$ C_D =C_{D0} + \frac{(C_L)^2}{\pi e AR} $$ has the aspect ratio ($AR = {b^2 \over S}$) of the wing in the denominator of the second term, the so called induced drag (because it is induced by the lift, note the coefficient of lift itself appears in the numerator).

This equation quickly illustrates why gliders have long wings: a higher AR provides a lower induced drag term. The other term, the parasitic drag, is either indifferent to the chord or slowly grows with it due to boundary layer transition in laminar airfoil designs.

We can arrive at the conclusion that for a given surface, a higher-AR wing will be the less draggy solution.

Therefore, the current attempts at solar powered aircraft all attempt to add area by extending the wings, and are limited by structural constraints like bending moment at the root, which you can clearly see them try and alleviate by spacing out the engines into the wings, providing some relief at the expense of increased roll inertia.

Answer 2

Adding chord to an existing wing does the following:

• It increases wing area S
• It reduces aspect ratio A
• It increases weight.

These three factors influence each other and should all be considered.

Drag D of a sub-sonic fixed wing aeroplane is $$D = C_D \cdot \frac{1}{2} \rho V^2 \cdot S = \left( C_{D0} + \frac{{C_L}^2}{\pi A e }\right)\cdot \frac{1}{2} \rho V^2 \cdot S \tag{1}$$

Lift L = weight W (a valid approximation at stationary flight at small angles): $$L = W = C_L \cdot \frac{1}{2} \rho V^2 \cdot S => C_L = \frac{2 \cdot W}{\rho V^2 \cdot S} \tag{2}$$

Substitute (2) into (1): $$D = C_{D0} \cdot \frac{1}{2} \rho V^2 \cdot S + \frac{2 W^2}{\pi A e \cdot \rho V^2 \cdot S} \cdot \tag{3}$$

With:

• S = wing area
• A = aspect ratio = $b^2 / S$ with $b$ = wing span
• e = Oswald factor, accounting for varieties in profile drag, lift distribution, interference.

Substitute $A \cdot S = b^2$ in (3):

$$D = C_{D0} \cdot \frac{1}{2} \rho V^2 \cdot S + \frac{2 W^2}{\pi e \cdot \rho V^2 \cdot b^2} $$

So now we can see what increasing chord does while keeping span the same

• It increases S with increasing chord
• It increases weight with increasing chord
• It decreases e with increasing chord
• It decreases $C_{D0}$ with increasing chord if only chord is added to the wing profile and thickness stays the same - relative thickness decreases and $c_d$ decreases. $C_{D0}$ remains the same if both chord and thickness are increased proportionally.

Three out of four factors above increase drag with weight being a quadratic factor, and we're hoping to offset the increase in drag with more propulsive power. We're increasing drag, weight, complexity, cost...

Prudent aircraft design would be contrary to this.

Answer 3

You definitely could add chord to the wings, but it is the same question of efficiency. Rarely do you sacrifice aerodynamic efficiency to carry more weight.

But in this case the benefits of adding chord to increase surface area have merit, although keeping aspect ratio the same and simply making the whole wing bigger may be a choice as well. And let's not forget the possibility of adding area to the tail too.

Another possibility is to scale up the size of the aircraft, as weight per surface area increases with size. Improving the efficiency of the solar cells and the charge carrying capacity of the batteries also helps.

Also, take note of the span loading benefits of the NASA aircraft. (a little more weight on the ends may have been an improvement)