Tailless Aircraft - Reflex and other design issues

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Aesquire

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If span is not constrained, but stall speed is, then increased AR allows lower area.

Correct me on that, please.

Or.... Increased L/D allows lower area?

Either assertion fits the facts if you look at wing area on modern hang gliders. http://www.moyesusa.com/products.html

These are all roughly the same planform, a flying wing. The Malibu has a thinner airfoil and much more exposed structure than the other 3, more twist, so if you prefer to keep it as oranges to oranges, just consider the 3 models with the buried cross spar.

None of these is as efficient as an ideal wing. Laminar flow is very limited, as the first seam in the upper surface trips the flow, if near imperceptible span wise ripples haven't already. The exposed pilot can be more than half the total parasitic drag. However, as a side by side comparison, those factors are about equal.
 

Himat

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If span is not constrained, but stall speed is, then increased AR allows lower area.

Correct me on that, please.
No, area and coefficient of lift do set the stall speed.

Or.... Increased L/D allows lower area?
In some cases, yes. An increased L/D, or rather Cl/Cd make it possible to operate at a higher Cl for the same Cd. If power constrained, the airplane can then have a smaller wing
 

Himat

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Everything above is correct, however you said constant span, but not constant speed.
What I said (maybe not clearly enough) is that at the same span the high A/R wing will reach it's maximum L/D at a higher speed with (possibly) less induced drag than the low A/R wing. The exact speed of max L/D depends on the parasite drag, but if the fuselage is very clean (as in: sailplanes) you get not only lower overall drag, but also lower induced drag at max L/D for the high A/R wing. As i said before at any given speed the low A/R wing will have less induced drag. That is trivial, of course.

In your initial post you didn't contrain airspeed. If your requirements are indeed span and (low) airspeed, then at some point you'll have to increase area which means lowering A/R. No surprise either.
Evaluated at constant span and equal speed the formula for induced drag can be rearranged to:

Cdi = k*Cl^2*AR

If the airplanes are built to equal standards the only drag part that reduces with aspect ratio is the skin friction. This will change with the area that follow:

Area = constant / AR

If the high aspect ratio airplane does achieve a higher Cl/Cd than a low aspect ratio airplane then depend on if the skin friction at some point get larger than the induced drag. This at least at speeds below where wave drag gets significant.

My conclusion is that increasing the aspect ratio work by reducing span loading. In some ways the dimensionless aspect ratio number mask this.
 

BJC

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Evaluated at constant span and equal speed the formula for induced drag can be rearranged to:

Cdi = k*Cl^2*AR
Not exactly. That is a formula for a non-dimensionalized induced drag coefficient, not the induced drag. If you work with actual induced drag, you will see that it depends on span, not aspect ratio.


BJC

edit. I’m a big proponent of always carrying / showing units with formulas and calculations. Doing so helps avoid confusing a coefficient with a physical quantity.
 

Himat

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Not exactly. That is a formula for a non-dimensionalized induced drag coefficient, not the induced drag. If you work with actual induced drag, you will see that it depends on span, not aspect ratio.


BJC

edit. I’m a big proponent of always carrying / showing units with formulas and calculations. Doing so helps avoid confusing a coefficient with a physical quantity.
Yes, imprecise of me, I should have said induced drag coefficient.

Edit:
Dimensionless numbers are fine when scaling designs, but in the case of the induced drag coefficient I am not sure. The trouble to me is it is not really scaling a design or comparing two similar designs. Used for design it alter the design and mask the change in physics between the designs. The difference in span loading.
 
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Aesquire

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Digging through the intraweb, I found a glider I mentioned much earlier in this thread.

a19780263000cp2.jpg

valkyrieDRAWNG.jpg

Short coupled little beast, and marginal in pitch stability. I wonder how I would have reacted to it if I'd had much more experience with short chord wings, as I later had. I might have kinder words to say. But performance wasn't all that impressive, no matter how much my adrenals were squirting at the time.
 
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