If I recall correctly, the best competition gliders have a L/D ratio as high as 60:1. What imposes this limit? Is there a maximum theoretical L/D ratio, or could sufficiently advanced materials allow a glider with a L/D ratio of, say, 200:1?
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asked Apr 1, 2015 at 19:32
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2$\begingroup$ For lighter-than-air craft, there is no such maximum. Buoyancy goes like the third power of the linear dimensions, but weight and drag go only like the second power. $\endgroup$– user7915Apr 1, 2015 at 21:08
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$\begingroup$ @BenCrowell that may well be, but I don't think lighter-than-air craft count as gliders $\endgroup$– raptortech97Apr 1, 2015 at 21:10
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2$\begingroup$ @BenCrowell: Weight also goes up like third power. $\endgroup$– Jan HudecApr 2, 2015 at 7:12
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2$\begingroup$ @JanHudec: The weight of a balloon is proportional to its surface area, not its volume. $\endgroup$– user7915Apr 2, 2015 at 12:42
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$\begingroup$ @Jan Hudec nice to see some of your vintage commentary. Surprised that it was not surmised that "weight" = (density x volume of aircraft) - (density x volume atmosphere) - lifting force generated from motion. Drag is friction from motion. Buoyancy is insignificant for most aircraft, yet a pressurized cabin weighs a bit more at altitude. Was trying to calculate ton miles per gallon for Graf Zeppelin. Of course a motionless balloon has infinite lift to drag, but how much would it's volume effect drag once underway? $\endgroup$– Robert DiGiovanniFeb 7, 2019 at 10:42
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5 Answers
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With current technology the L/D might go up to 70 or 75, and going higher would require an almost impractically large wing span. Gliders need to fly in tight circles to use updrafts, and the larger the wingspan becomes, the bigger the speed difference between inner and outer wing will be. Also, landing such a wide wing without dropping a wingtip will be very hard. Smaller wings with a high aspect ratio will have a low chord length, leading to smaller Reynolds numbers, which translates into a steep increase of friction drag if the aspect ratio is increased without increasing wing area. Therefore, only adding wing span will help, and this runs into a soft wall beyond the 30 m of designs like the Eta. In addition, the current mass limit of 850 kg will make bigger aircraft unattractive for competition pilots.
The Concordia (pdf!) is claimed to have an L/D approaching 75, but I have learned over the years to see theoretical predictions as invariably optimistic, and realistic performance, with bugs on the wing and all, will never quite measure up to the hoped-for ideal.
Werner Pfenniger proposed to use boundary layer laminarisation by suction (pdf!) to reduce friction drag and proposed glider designs with L/D ratios in excess of 100. Turbines at the wingtips would drive the suction pumps, so these would still be unpowered aircraft. But so far nobody has dared to turn his visions into reality.
While laminarisation avoids the increase in friction drag of a turbulent boundary layer, a moving wall would eliminate viscous losses altogether. Now the friction generation is between the moving wall (this could be a taut foil running between two cylinders at the forward and aft end of the wing) and the fixed structure. With current materials there is no hope of reducing drag this way, but who knows what tricks will be possible in the future.
A glide ratio of 100 or more looks rather unlikely in the next 50 years.
answered Apr 1, 2015 at 20:37
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$\begingroup$ Ah, I forgot that gliders have to circle updrafts. $\endgroup$ Apr 1, 2015 at 20:39
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1$\begingroup$ Is there a theoretical limit though? Kind of like a speed-of-light for L/D? $\endgroup$ Apr 2, 2015 at 2:31
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3$\begingroup$ No, there is no thoretical limit: anything which produces some lift whilst drag tends to zero will tend towards an infinite L/D ratio. $\endgroup$– user7979Apr 2, 2015 at 11:20
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$\begingroup$ @thepowerofnone So what's the plan to eliminate skin friction? I want to get rich. :-) $\endgroup$– CalphoolApr 2, 2015 at 15:38
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2$\begingroup$ @raptortech97: Yes, correct on both counts. Ideally, the forward location of both cylinders should move with the angle of attack, such that the stagnation point is exactly between the two. Quite a challenge! $\endgroup$ Apr 2, 2015 at 21:54
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With any measure of aircraft performance, we must begin with the airfoil section. All reasonable real-world airfoils start at about a 120:1 best L/D. This is because with a testable airfoil you typically have an optimal combination of Cl = 1.2 & Cd = 0.10; hence the L/D of 120:1 (read "Abbott and Von Doenhoff" for more theoretical and practical considerations).
As you add the drag of extraneous components to your airplane like: cockpits, wheels, control surfaces, dirt, doors, screw heads, antennas, wing tips, ventilation, panel seams, and so on; you chip away at the best achievable configuration L/D. For airplanes like the Space Shuttle you'll end up with a L/D of less then 5:1 (hence the phrase "Flying Brick"). A typical general aviation aircraft on the other hand, has about a 9:1 L/D. For a sophisticated sailplane where extreme attention is made to the details, the configuration suffers only a 50% performance loss and achieves the aforementioned 60:1 L/D. Higher performance is certainly possible, but is likely to be incremental in nature.
The starting point in designing an airplane often sets the initial configuration such that wing-skin friction drag is equal to the mathematical lift-induced drag. Following that calculation, we start adjusting things until an acceptable configuration emerges. The more realistic the first guess, the sooner the configuration emerges.
When evaluating advanced concepts like boundary layer suction or blowing, the performance cost of powering the air pumps is often ignored in testing; as is the reality that many microscopic pores quickly clog and are rendered ineffective, so be careful about taking the boundary layer control performance data at face value.
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$\begingroup$ In your first paragraph, is that meant to read Cd=0.01, perhaps? otherwise the ratio is off by factor 10 $\endgroup$– bukwyrmSep 6, 2019 at 10:47
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Loosely speaking, L/D ratio is limited by the aspect ratio of the wing (its length to its chord width) and the friction of the wing surface (which is why frost/ice on the wing is a bad thing -- it dramatically increases wing friction).
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Yes, you can have a L/D as high as you'd like. But I don't think you'd enjoy flying in milliKelvin liquid helium superfluid which has zero viscosity...
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The lift and drag coefficient are defined with a fixed and uniformed pressure. Therefore, gravity and Archimedes' principle should not be involved in this topic. The maximum lift-drag-ratio is obtained with infinite wings. 2D airfoil optimization with genetic algorithm give the following optimization for the lift/drag ratio: 1/0.00166/0.002=300 000
https://optimization.mccormick.northwestern.edu/index.php/Wing_Shape_Optimization
This is a theoretical limit of course....which do not have some much sense in the present real world with finite wings, clear-air turbulence, surface roughness, water on wings,etc...
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$\begingroup$ The 300000 is definitely the genetic algorithm exploiting a software bug or assumption. $\endgroup$ Jan 9, 2022 at 9:31