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

enter image description here

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

enter image description here

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?

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  • $\begingroup$ The question seems to be downplaying the importance of parasitic drag. The root of the question seems to be "why doesn't the desire for maximum surface area for solar collection drive the design of solar-powered aircraft toward a lower aspect ratio than we see in practice." $\endgroup$ – quiet flyer Jun 9 at 15:38
  • $\begingroup$ @quietflyer yes I think you could summarize my question as such, but how much of a role does parasitic drag really play? Considering solar panels can provide ~1kw per square meter isn't that enough power to compensate for the added drag? $\endgroup$ – YAHsaves Jun 9 at 15:40
  • $\begingroup$ It's an interesting question-- consider the Solar Impulse-- they could collect enough power to fully charge the batteries after a night of slowly-descending gliding-- it's not clear how more chord would have helped them-- the wing loading was already very low and more chord might have had unacceptable consequences in turbulence and more batteries might have been needed to benefit from the extra cells-- anyway it is a good question and I'm not sure I have a specific suggestion for improvement here. $\endgroup$ – quiet flyer Jun 9 at 15:44
  • $\begingroup$ @quietflyer actually your mention of batteries might explain it. It's not so really how much power these planes can produce in full sun, but the performance of the aircraft when flying at night on batteries. Batteries are heavy, and I think these projects are more about all round performance, than just daytime. $\endgroup$ – YAHsaves Jun 9 at 15:49
  • $\begingroup$ It is not clear to me what is your main question here. Do you want to know why your "flying rectangle" is a bad idea? Or just what are the drivers for the aspect ratio chosen for these projects? It does seem like you understand the role of aspect ratio in the drag equation, so if your question is the first one, could you edit the rest out? $\endgroup$ – AEhere Jun 11 at 8:24
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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.


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.

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    $\begingroup$ “200 - 300W range”: 300 Watt per elefant? Or per potato? Or? $\endgroup$ – Jan Hudec Jun 11 at 20:33
  • $\begingroup$ @JanHudec I deserved that sass. Fixed. $\endgroup$ – AEhere Jun 11 at 20:37
  • $\begingroup$ Thank you for drawing this out on paper, it helps to see the numbers. One thing I didn't understand though, is I mentioned in my question how the induced drag doesn't actually increase with cord length. Are you suggesting the answer I linked to is incorrect? $\endgroup$ – YAHsaves Jun 11 at 20:38
  • $\begingroup$ @Peter Kämpf tends to be right so listen to him. Maybe II can make the answer clearer... or maybe I´m wrong and need to go back to school. Do note that Peter's calculation is for two wings of the same span, so he can allow one to have twice the surface of the other. Since span and area are the usual variables that are set by outside requirements, that approach makes a lot of sense. If you want to compare two wins of the same surface area, things change. $\endgroup$ – AEhere Jun 11 at 20:51
  • $\begingroup$ Note that intensity of Sun light is around $1\ \mathrm{kW}\cdot\mathrm{m}^{-2}$, so $300\ \mathrm{W}\cdot\mathrm{m}^{-2}$ is 30% (at perpendicular insolation; don't forget to multiply with appropriate cosine as wings have to be approximately level to support the aircraft and the panels can't therefore be turned towards the Sun), which is actually pretty good efficiency. IIRC green plants manage only about 4%. $\endgroup$ – Jan Hudec Jun 11 at 20:52
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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.

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    $\begingroup$ The simple answer is: If you add area, do it at the tips as well. $\endgroup$ – Peter Kämpf Jun 12 at 5:05
  • $\begingroup$ "It decreases $C_{D0}$ with increasing chord" I can't see that from the equation presented, it seems to me $C_{D0}$ is a coefficient multiplied by $S$. For an equal span an increase in chord will increase $S$ and thus the contribution of the parasite term. $\endgroup$ – AEhere Jun 12 at 7:15
  • $\begingroup$ @AEhere have added into the answer. $\endgroup$ – Koyovis Jun 12 at 7:43
  • $\begingroup$ @Koyovis fair enough, I didn't think you were operating on the airfoil itself. The pedant in me does want to point out that this might not be a general solution: at low $Re$ adding to the chord may trip the boundary layer and raise drag, but I don't have any numbers handy to argue how much of an impact this has compared to the relative thickness reduction. $\endgroup$ – AEhere Jun 12 at 7:50
  • $\begingroup$ @Koyovis Wouldn't "S" and "weight" be increased no matter what? If the aircraft needs x amount of power to fly, and you need more solar cells to reach x, increasing the the span will still effect both these properties. I'm not familiar with how to solve for "e", but I guess the cord changes it enough to be significant? $\endgroup$ – YAHsaves Jun 13 at 1:16
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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)

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    $\begingroup$ Yes I agree you could scale everything up while keeping the dimensions proportional. However that has it's own problems, 1) longer spans are harder to store/find landing for ect.... 2) weight is a product of volume which is multiplied by 3 directions, while surface area is a product of 2 directions. Which means weight scales faster than surface area. So keeping the geometry the same, but scaling things up will get heavy. I guess I'm asking could you offset these potential negatives using the geometry proposed in my answer? $\endgroup$ – YAHsaves Jun 9 at 15:37
  • $\begingroup$ A wider wing is certainly stronger. And you can even consider 2 wings! Yes, lifting capacity would have to match weight, so greater chord and thicker scale up is possible. Desired cruising speed is another very important consideration. $\endgroup$ – Robert DiGiovanni Jun 9 at 16:21
  • $\begingroup$ @YAHsaves a design you may look into is the RB-57 Canberra. $\endgroup$ – Robert DiGiovanni Jun 9 at 19:28

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