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Will the same glider have higher glide ratio if its bigger in proportion or smaller in proportion?

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    $\begingroup$ Please allow at least 24 hours before choosing an answer to give all people around the globe a chance to come up with an answer 🖖 $\endgroup$
    – sophit
    Jul 24, 2023 at 20:16

3 Answers 3

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It depends. If you simply scale an aircraft up and down, most of the aerodynamics behave the same (or at least approximately so).

In order to get perfect scaling behavior, you need to match Mach and Reynolds number. This is our clue to the answer.

Gliders will likely be relatively slow, so we can consider them to operate in incompressible flow and we can ignore any Mach effects.

As you increase the aircraft's scale, Reynolds number will increase. Note that the length term in Re is to the first order.

We'll look at the skin friction coefficient's behavior with Reynolds number.

enter image description here

At high Reynolds number, flow will be turbulent. In this regime, Cf will decrease as you increase Re (make the aircraft bigger). Decreasing Cf will mean lower friction drag and improved L/D.

At very low Reynolds number, flow will be laminar. Likewise, in this regime, Cf will decrease as you increase Re. So a larger aircraft will mean better L/D.

In the middle, things are complicated.

At intermediate Reynolds number, whether you get laminar or turbulent flow depends on the details of your design. How smooth is your surface? Were your airfoils designed for laminar flow? Is the aircraft maintained in meticulous clean condition? If the answer is yes, then you can operate on the laminar skin friction coefficient curve -- which is much lower than the turbulent skin friction in this area.

High performance sailplanes are one of the only kinds of aircraft that can successfully operate in this region (i.e. with significant laminar flow when turbulent flow is possible or prevalent).

In this area, increasing size will decrease skin friction coefficient and will improve L/D. Up to the point where it becomes impossible to maintain laminar flow. At that point, transition to turbulent flow will occur and the skin friction coefficient will rapidly increase.

Keep in mind, this chart is on a log-log scale. The X-Axis scale represents four orders of magnitude change in Reynolds number. To achieve this with scale alone, you would start with a chord of 1cm at Re of 10^4, and each successive vertical line on the chart would represent 10cm, 1m, 10m, 100m. So the change in aircraft size considered here is enormous!

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    $\begingroup$ We're gonna need a bigger boat^H^H^H^Hplane. $\endgroup$ Jul 24, 2023 at 21:55
  • $\begingroup$ Gliders will likely be relatively slow great now i want to see a supersonic glider... $\endgroup$
    – Michael
    Jul 26, 2023 at 17:05
  • $\begingroup$ am i off in thinking a 5km wide saucer shaped "mothership" would glide supersonically quite well? $\endgroup$
    – Michael
    Jul 26, 2023 at 17:08
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    $\begingroup$ @Michael, nasa.gov/sites/default/files/styles/full_width/public/… $\endgroup$
    – prl
    Jul 27, 2023 at 6:10
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The aerodynamics stay largely the same, and the best glide ratio does not change much. It does, however, occur at a higher airspeed as the aircraft gets larger.

But simply scaling an aircraft up is not really practical. If you scale an aircraft by a factor $a$, the wing area scales as $a^2$, while the weight scales as $a^3$. Structurally, the wing roots needs to be able to hold the entire weight of the aircraft plus its payload times the maximum load factor it is rated for. Since the structural strength of parts of the airframe scale as $a^2$ while the weight is scaling as $a^3$, the aircraft is getting structurally weaker.

Increasing the scale also increases the best glide speed Vg due to the higher wing loading, while decreasing Vno and Vne. The aircraft becomes progressively less flyable as Vg and Vne get closer together. Additionally, the minimum sink rate (which is more important for soaring than the glide ratio) increases due to the higher wing loading and required airspeed to maintain flight.

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    $\begingroup$ "If you scale an aircraft by a factor $a$, the wing area scales as $a^2$, while the weight scales as $a^3$" an airplane is not a solid cube, the structural efficiency actually increases with the size: a GA airplane can have an empty weight fraction as high as 0.7 while a big military cargo as low as 0.35 i.e. twice as much structurally efficient despite being 2 orders of magnitude bigger. $\endgroup$
    – sophit
    Jul 24, 2023 at 20:13
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    $\begingroup$ @sophit This is true, because larger airplanes are not just scaled-up versions of smaller ones. $\endgroup$
    – Chris
    Jul 24, 2023 at 20:21
  • $\begingroup$ Well, I suppose the question is not really clear then... $\endgroup$
    – sophit
    Jul 24, 2023 at 20:23
  • $\begingroup$ @sophit The OP specified "the same glider". Clearly that's not technically possible, but the intent seems clear to me - this is an "all things being equal" type question. $\endgroup$
    – MikeB
    Jul 25, 2023 at 7:09
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    $\begingroup$ @MikeB: I'd interpret it as a simple "external surface" scale, otherwise the chosen answer wouldn't be correct rather your comment would: "clearly that's not technically possible". But the OP is happy with the chosen answer and that's the important thing 😉 $\endgroup$
    – sophit
    Jul 25, 2023 at 7:22
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The glider will have a higher glide ratio if larger in proportion. The attached illustration is an extract of figure 3.2 in the cited report, below. Shown is the influence of the scale effect caused by increasing Reynolds number on a wing of aspect ratio 20. Such an increase is accomplished by increasing physical dimensions of the wing, increasing flight velocity to optimize lift and minimize drag, or otherwise by flight within a dense atmosphere under optimum flight conditions. One should note that flow over the wing becomes increasingly dominated by viscosity of the atmosphere below a Reynolds number of about 400,000. At lower Reynolds numbers, aspects of flow separation and flight performance become more difficult to address in a practical way. The other provided answers give sufficient details for an explanation of these effects.

National Research Council/NAS Publication NMAB-495, Uninhabited Air Vehicles. National Academy Press, Washington, D.C. 2000. 108pp.

enter image description here

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