Is 1,5 meters the optimum span for a DLG? - RC Groups
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Dec 08, 2017, 12:00 PM
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Is 1,5 meters the optimum span for a DLG?

Make sure you open the post en click on the read more to see the all pages. Otherwise you will see page 8 as last page, and not page 16.

O previously posted some analysis on DLG design in this Blog. After some discussions about smaller than 1.5 meter wing span DLG's possibly outperforming the full size ones on the last WC in the Ukraine, I dug up my old analysis, and worked on it a little to find out if I could derive the theoretical optimum span for a DLG. That is to say: optimum for maximum airtime in still air at a fixed launch speed.

It turns out that actually the current launch speed determines the optimum terminal velocity to design the plane for. So making the plane faster or slower with respect to this terminal velocity would lower the total airtime for this launch speed. A terminal velocity of only 60% of the launch speed would be the optimum design speed for obtaining maximum airtime.

Secondly, the maximum airtime itself can be expressed in the L/D ratio and the launch speed only! So, basically speaking, just optimise L/D and you will optimise maximum airtime (for the optimum design speed that is). The expression is quite simple:

t_(flight,max) ≈ 2 / 3g ∙ (L/D)_optimum ∙ √((L/D)_optimum ) ∙ v_launch

When entering an L/D of 12 to 20, and a v_launch of 40 m/s, the still air time will be between 115 and 245, with an average 180 seconds.

Finally, the question I started with. The expression for terminal velocity that you can find in the analysis can be rewritten to determine the optimal span, by replacing the terminal velocity by the 60% of launch velocity, which gives us for the span b:

b = 4,56∙√m∙(L/D)_optimum/v_launch

Entering the same figures, and a mass of 250 grams, gives an optimum span of 1,53 meters.

Well, how surprising! For the current normal build of a DLG of about 250 grams AUW, the actual size of 1.50 m IS the optimum, when launching at 40 m/s.

If you can throw faster, or build lighter, it would increase airtime if you would lower the span!! But make sure you don't lose L/D by lowering the span. You will loose the advantage again.

And this is where the actual limits kick in. Lowering the span will almost certainly lower the L/D, since it will lower the Reynolds numbers. And we are already on the edge with the 65.000 we are at.

All the formulas and derivations are in the attachement pages. Part of them are a mere copy of the ones in the other blog, but some small improvements have been made in the text here and there, so I included all for download in this post.

The last page contains the formulas used in this abstract.

Have Fun and Just Fly!
Last edited by l shems; Dec 12, 2017 at 12:54 PM.
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