Wing Loading / climb rate

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?

Thanks
Chris

On Wednesday, February 1, 2017 at 1:15:05 PM UTC-5, Chris Davison wrote:
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?

Thanks
Chris

No.

best,
Evan

On Wednesday, February 1, 2017 at 10:15:05 AM UTC-8, Chris Davison wrote:
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?

Thanks
Chris

Not if their polars have different sink rates in a bank at min sink speed and the same wing loading. If they were the same it would be a coincidence.

To convince yourself of this imagine two 15/18M gliders of the same type - identical in every way except one has 15M tips and the other has 18M tips. They are ballasted to the same wing loading. In the thermal they are in identical lift. Beyond this the only difference is that the 18M glider has spoilers deployed. Will one glider climb faster? Yes!

Okay, I think your question probably assumes both gliders keep spoilers closed and are identical in every other way, but the same basic idea holds. The 18M glider has different span, aspect ratio and wetted area and therefore a different mix of form and induced drag at any given speed and lift coefficient. Go get a polar for a 15/18M glider and do the ratio of the square root of the wing loadings transformation to equalize the wing loading and you'll see the polars are still different. The 18M ought to have a lower sink rate because of lower induced drag attributable to the higher aspect ratio.. Above a certain speed the polars may cross over as form drag goes up with V-squared. There's actually a lot more going on than just these simple effects, but that ought to give you a basic understanding.

Shorter answer: There's a lot more to aerodynamics and aircraft performance than just wing loading.

Andy Blackburn
9B

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.

--
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

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.

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