Wing Loading / climb rate

Whoops
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

I have had a similar question, with a small difference, for many years.

My question is:

"Using only s single glider and changing only the max flying weight - adding ballast shot bags, whatever - will that glider give its pilot a greater potential thermal climb rate when heavier or lighter?"

I am aware that higher weight will alter airspeeds but that is not my curiosity - other than a higher weight will raise stall speed some - which may add difficulties for the heavier glider using very narrow thermals - turn radius varies as the square of true airspeed, etc.

At 23:39 02 February 2017, Jim wrote:
I have had a similar question, with a small difference, for many years.

My question is:

"Using only s single glider and changing only the max flying weight -
addin=
g ballast shot bags, whatever - will that glider give its pilot a greater
p=
otential thermal climb rate when heavier or lighter?"

I am aware that higher weight will alter airspeeds but that is not my
curio=
sity - other than a higher weight will raise stall speed some - which may
a=
dd difficulties for the heavier glider using very narrow thermals - turn
ra=
dius varies as the square of true airspeed, etc.



For any glider increasing the weight will reduce it's climb rate.

On Friday, February 3, 2017 at 11:15:04 AM UTC+3, Tom Claffey wrote:
At 23:39 02 February 2017, Jim wrote:
I have had a similar question, with a small difference, for many years.

My question is:

"Using only s single glider and changing only the max flying weight -
addin=
g ballast shot bags, whatever - will that glider give its pilot a greater
p=
otential thermal climb rate when heavier or lighter?"

I am aware that higher weight will alter airspeeds but that is not my
curio=
sity - other than a higher weight will raise stall speed some - which may
a=
dd difficulties for the heavier glider using very narrow thermals - turn
ra=
dius varies as the square of true airspeed, etc.



For any glider increasing the weight will reduce it's climb rate.

The concept is pretty simple :-)

If you double the weight of a glider you increase all the speeds, including the sink rate, by 40%. So maybe you go from 100 fpm sink to 140 fpm.

If the lift is strong enough that an unballasted glider climbs at 10 knots then the ballasted one will climb at 9.5 knots or so. Maybe worse. Maybe 9 knots. So 5% or 10% slower climb.

But then it gets to run 40% faster at the same glide angle.

You need to factor in the increased thermal speed and larger diameter circles. Unless the core of the thermal is large the climb rate is reduced significantly more than just the glide calculations predict. In the "real world" higher wing loading gives an advantage, but not as much as many think unless you are flying mostly on streets. In the mountains I often do better with a 9.5 to 10 pound wing loading because I can maneuver better and work small diameter thermals.

My curiosity has been about the effect of just gross weight vs. wing loading on the

For example, let's stipulate a thermal providing a vertical force ( I avoid using newtons as the SI unit for force. I've never managed to get comfortable with it.) that would provide +5 kt lift to a glider with a gross weight of 800 lbs and a wing loading of 10 lbs / sqft.. I'm just making this stuff up. I am not trying to be realistic!

Now let's invent another glider with a wing loading of just 5 lbs / sqft. but with the same gross weight as the first glider.

Would the second glider, with a wing loading of just 5 lbs / sqft, get a better climb rate than the first glider since it appears it would need only half the lifting force per square foot of wing than would the first glider?

On Friday, February 3, 2017 at 10:19:00 AM UTC-7, Jim wrote:
My curiosity has been about the effect of just gross weight vs. wing loading on the

For example, let's stipulate a thermal providing a vertical force ( I avoid using newtons as the SI unit for force. I've never managed to get comfortable with it.) that would provide +5 kt lift to a glider with a gross weight of 800 lbs and a wing loading of 10 lbs / sqft.. I'm just making this stuff up. I am not trying to be realistic!

Now let's invent another glider with a wing loading of just 5 lbs / sqft. but with the same gross weight as the first glider.

Would the second glider, with a wing loading of just 5 lbs / sqft, get a better climb rate than the first glider since it appears it would need only half the lifting force per square foot of wing than would the first glider?

Unfortunately it is not that easy. The short answer is the lighter wing loading glider will climb better, just as the heavier will run better. The long answer is they won't fly at the same speed so the lighter wing loading glider has the advantage additionally of working a tighter core.