Wing Loading / climb rate

On Thursday, February 2, 2017 at 5:12:27 AM UTC+3, Eric Greenwell wrote:
Chris Davison wrote on 2/1/2017 10:14 AM:
A questions that I should know the answer to but don't...in a
thermal, all things being equal, will a 15m glider and an 18m glider
with the same wing loading climb at the same rate?

I'm told thermal climb rate is related to "span loading" (weight/span),
while high speed performance is related to wing loading (weight/wing
area). In your example, the 18m glider will climb better.

Told by who, I wonder? :-)

Span is important to minimize induced drag, but that's a waste of time unless you have enough wing area to give an acceptable coefficient of lift or AoA at desired circling speeds and radii.

There is probably an intermediate cruising speed range where the dominant factor is wing loading / wing area / wetted area / span*chord. At a guess that might be from midway between min sink and best L/D speeds out to maybe 1.4 or 1.5 times best L/D speed.

At higher speed I'd have thought the dominant factor would be minimizing span*wing thickness, i.e. frontal area. That's what kills the 1960s 40:1 ships at high speed -- or newer short span ones such as the PW5.

On Wednesday, February 1, 2017 at 8:42:35 PM UTC-8, Bruce Hoult wrote:
On Thursday, February 2, 2017 at 5:12:27 AM UTC+3, Eric Greenwell wrote:
Chris Davison wrote on 2/1/2017 10:14 AM:
A questions that I should know the answer to but don't...in a
thermal, all things being equal, will a 15m glider and an 18m glider
with the same wing loading climb at the same rate?

I'm told thermal climb rate is related to "span loading" (weight/span),
while high speed performance is related to wing loading (weight/wing
area). In your example, the 18m glider will climb better.

Told by who, I wonder? :-)

Span is important to minimize induced drag, but that's a waste of time unless you have enough wing area to give an acceptable coefficient of lift or AoA at desired circling speeds and radii.

There is probably an intermediate cruising speed range where the dominant factor is wing loading / wing area / wetted area / span*chord. At a guess that might be from midway between min sink and best L/D speeds out to maybe 1.4 or 1.5 times best L/D speed.

At higher speed I'd have thought the dominant factor would be minimizing span*wing thickness, i.e. frontal area. That's what kills the 1960s 40:1 ships at high speed -- or newer short span ones such as the PW5.

In classical aerodynamics, induced drag dominates at low speeds (high lift coefficients), and that is inversely proportional to aspect ratio. However if you work through the math, area and wing loading cancel the wing chord out, hence the term span loading (which normalizes for wing loading in effect).

At high speeds profile (and parasitic) drag is dominant. Wing thickness is loosely related to profile drag, but the main thing that kills the 60's ships is the bad behavior of the laminar flow, not the thickness per se. Fuselages have gotten a little cleaner, but it is the wing sections and understanding of laminar flow that is the biggest difference I think.

On Thursday, February 2, 2017 at 9:47:29 AM UTC+3, jfitch wrote:
On Wednesday, February 1, 2017 at 8:42:35 PM UTC-8, Bruce Hoult wrote:
On Thursday, February 2, 2017 at 5:12:27 AM UTC+3, Eric Greenwell wrote:
Chris Davison wrote on 2/1/2017 10:14 AM:
A questions that I should know the answer to but don't...in a
thermal, all things being equal, will a 15m glider and an 18m glider
with the same wing loading climb at the same rate?

I'm told thermal climb rate is related to "span loading" (weight/span),
while high speed performance is related to wing loading (weight/wing
area). In your example, the 18m glider will climb better.

Told by who, I wonder? :-)

Span is important to minimize induced drag, but that's a waste of time unless you have enough wing area to give an acceptable coefficient of lift or AoA at desired circling speeds and radii.

There is probably an intermediate cruising speed range where the dominant factor is wing loading / wing area / wetted area / span*chord. At a guess that might be from midway between min sink and best L/D speeds out to maybe 1.4 or 1.5 times best L/D speed.

At higher speed I'd have thought the dominant factor would be minimizing span*wing thickness, i.e. frontal area. That's what kills the 1960s 40:1 ships at high speed -- or newer short span ones such as the PW5.

In classical aerodynamics, induced drag dominates at low speeds (high lift coefficients), and that is inversely proportional to aspect ratio. However if you work through the math, area and wing loading cancel the wing chord out, hence the term span loading (which normalizes for wing loading in effect).

Could you run through that math for me?

As I see it, wing area equals span times (average) chord. Wing loading equals weight divided by wing area, so weight/(span*chord). Not sure I see how chord cancels out of that?

Certainly I agree that for a given wing area and wing loading, more span and less chord is better. 10 sqm has been the traditional benchmark wing area for a single seater, getting smaller with time. Ka6 and Cirrus are both about 12; Std Libelle, Discus, LS8, even PW5 about 10; Diana 2 is 8. If you could build a single-seater with 50m span and 200mm chord (and no more than 20 - 30 mm thickness) without it breaking then it would probably go pretty well in a straight line.

So span loading is a useful figure if you hold the wing loading constant.

But you can't just pick a span loading you like and then reduce or increase the chord to whatever you feel like. A single seater with 15m span with 500mm - 800mm average chord works. 200mm or 2000m would be ridiculous, assuming you want to fly in the speed ranges we fly gliders in. 200mm chord might be interesting if you didn't mind a 70 knot stall speed and 90 knots thermalling :-)

I worked some math out on page 15 of this PDF. The section is called drag.

http://spekje.snt.utwente.nl/~roeles/maccready.pdf

On Thursday, February 2, 2017 at 11:33:07 AM UTC+3, wrote:
I worked some math out on page 15 of this PDF. The section is called drag.

http://spekje.snt.utwente.nl/~roeles/maccready.pdf

The requested URL /~roeles/maccready.pdf was not found on this server.

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Make that
http://spekje.snt.utwente.nl/~roel/maccready.pdf

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Make that
http://spekje.snt.utwente.nl/~roel/maccready.pdf

On Thursday, February 2, 2017 at 11:33:07 AM UTC+3, wrote:
I worked some math out on page 15 of this PDF. The section is called drag..

http://spekje.snt.utwente.nl/~roeles/maccready.pdf

Ok, good. What exactly do you wish to point to there?

I see that in general there are a lot of approximations, assuming small angles etc. I didn't check if that always looks like a good simplification, but this did jump out at me:

"Using this formula we can calculate both CD0 and e if we know some data
about the best L/D point of the polar. Since at this point the induced drag
should equal the parasitic drag"

That is certainly wrong.

It's true that in practice where you are looking for a minimum of two different ways to lose, the minimum is likely to be at a point where they are roughly equal, but it's only very rough. The two things could easily be different by, say, a factor or two, or more.

What *is* true at the minimum is that the *derivatives* of the two things are equal in magnitude, and opposite in sign.

Take, for example, the (positive) minimum of 1/x + x^2 (which is something similar in form to induced plus form drag). They are equal when x = 1, and both halves are 1 (so the total is 2).

But the minimum is at x = 1/cubeRoot(2) ~= 0.793701. At this point 1/x is 1.26 and x^2 is 0.63. So in fact the "induced drag" is twice the "form drag" at the minimum.

As you'll know, the derivative of 1/x is -1/x^2, while the derivative of x^2 is 2x. So at x = 0.793701 the derivatives are -1.5874 and +1.5874 (cube root of 4) -- equal and opposite.

At the minimum of a sum, the *slopes* are equal (and opposite), not the *values*.

Thanks for the comments. I'll reply by email later on, as not to spoil the thread.

People were referring to the equations regarding drag,in turns .
Therefore I pointed to the drag formula in the pdf.

Bruce Hoult wrote on 2/1/2017 8:42 PM:
On Thursday, February 2, 2017 at 5:12:27 AM UTC+3, Eric Greenwell wrote:
Chris Davison wrote on 2/1/2017 10:14 AM:
A questions that I should know the answer to but don't...in a
thermal, all things being equal, will a 15m glider and an 18m glider
with the same wing loading climb at the same rate?

I'm told thermal climb rate is related to "span loading" (weight/span),
while high speed performance is related to wing loading (weight/wing
area). In your example, the 18m glider will climb better.

Told by who, I wonder? :-)

Aerodynamics people (Dan Somers and Greg Cole, I recall), and people
intent on handicapping a range of gliders.


Span is important to minimize induced drag, but that's a waste of time unless you have enough wing area to give an acceptable coefficient of lift or AoA at desired circling speeds and radii.

The OP did specify "same wing loading", so we know they both have
"enough" area, even if the area isn't optimum for other reasons.

There is probably an intermediate cruising speed range where the dominant factor is wing loading / wing area / wetted area / span*chord. At a guess that might be from midway between min sink and best L/D speeds out to maybe 1.4 or 1.5 times best L/D speed.

At higher speed I'd have thought the dominant factor would be minimizing span*wing thickness, i.e. frontal area. That's what kills the 1960s 40:1 ships at high speed -- or newer short span ones such as the PW5.

The 18 m ship could choose to fly at a higher wing loading while
retaining a climb equal to the shorter span glider, then reap the
benefits of the higher wing loading the cruise.

--
Eric Greenwell - Washington State, USA (change ".netto" to ".us" to
email me)
- "A Guide to Self-Launching Sailplane Operation"

https://sites.google.com/site/motorg...ad-the-guide-1
- "Transponders in Sailplanes - Dec 2014a" also ADS-B, PCAS, Flarm

http://soaringsafety.org/prevention/...anes-2014A.pdf