A polar calculation question for you number crunching enthusiasts out there

[ES]

I'm trying to use Paul Remde's very handy "Reichmann to Cambridge and SeeYou" spreadsheet to derive some usable SeeYou polar numbers for my Diana-1. But I'm having a heck of a time picking three speed/sink-rate pairs from the data set that result in Max L/D and Best Glide Speed numbers that pass the sniff test.

For example, I can enter 3 pairs of values from early, middle, and late in the data set, and it tells me I have a max L/D of 49 (wouldn't that be nice!) at ... 38 km/h. Uh, that's well below stall speed!

Is there any conventional wisdom on this?

Are there any other tools available that can take a set of sink rates (hopefully more than 3) and produce some decent numbers?

Wishing the flight computers would just start with lookup tables,

tuno/ES

[Tim Taylor]

Ted,

Does the rest of the curve look like a reasonable match to the polar? If so that is likely good enough. You are not going to use a speed to fly to fly too slow. You will only fly down to best l/d speed anyway.

If you really want to force the lower portion of the curve you need to use more pairs of points and likely will need to go to a third or fourth order polynomial. The problem is most flight software is designed around the second order fit.

Tim

[Eric Greenwell]

Put in the values for an ASW 27. If after flying a few flights that
seems to pessimistic, put in the values for the next step up. Accuracy
in the polar isn't important to success.

--
Eric Greenwell - Washington State, USA (change ".netto" to ".us" to
email me)

[ES]

<Accuracy in the polar isn't important to success.>

Your position is stipulated -- my OP is ONLY about the accuracy of the polar.

[Martin Gregorie]

On Sun, 23 Feb 2014 15:49:16 -0800, ES wrote:

> Are there any other tools available that can take a set of sink rates
> (hopefully more than 3) and produce some decent numbers?
>

Does your flight computer accept polars in the Winpilot format?

If so, are the numbers for an SZD-56-2 Diana-2 of any use, either
directly or for use as a starting point? If so the SZD-56-2 polar is
included on the LK8000 polars database.

> Wishing the flight computers would just start with lookup tables,
>

Well, both XCsoar and LK8000 do just that and both load polars from
Winpilot format polar files, - but neither currently has a polar for the
SZD-56-1 Diana-1.


--
martin@ | Martin Gregorie
gregorie. | Essex, UK
org |

[ES]

I'm using SeeYou Mobile with an LXNAV V7. Both take polars in the same form: stall speed, A, B, and C coefficients, min (wing) loading, min weight, max weight, empty weight, and pilot weight.

I'm also confused about the weights. If "pilot weight" is provided, then I can only assume "empty weight" means just the glider without the stick actuator, but why would the computer care about that? Why not just "dry take-off weight"?

[anderson....@gmail.com]

On Monday, February 24, 2014 5:15:14 AM UTC-8, ES wrote:
> I'm using SeeYou Mobile with an LXNAV V7. Both take polars in the same form: stall speed, A, B, and C coefficients, min (wing) loading, min weight, max weight, empty weight, and pilot weight.
>
>
>
> I'm also confused about the weights. If "pilot weight" is provided, then I can only assume "empty weight" means just the glider without the stick actuator, but why would the computer care about that? Why not just "dry take-off weight"?

Hmmm...

Do they have provision for different pilot profiles to fly the glider?

[Mike the Strike]

You could also throw Dick Johnson's polar test data into an Excel spreadsheet and do a curve fit - that might be a good starting point.

Mike

[anderson....@gmail.com]

On Sunday, February 23, 2014 3:49:16 PM UTC-8, ES wrote:
> I'm trying to use Paul Remde's very handy "Reichmann to Cambridge and SeeYou" spreadsheet to derive some usable SeeYou polar numbers for my Diana-1. But I'm having a heck of a time picking three speed/sink-rate pairs from the data set that result in Max L/D and Best Glide Speed numbers that pass the sniff test.
>
>
>
> For example, I can enter 3 pairs of values from early, middle, and late in the data set, and it tells me I have a max L/D of 49 (wouldn't that be nice!) at ... 38 km/h. Uh, that's well below stall speed!
>
>
>
> Is there any conventional wisdom on this?
>

I took a look at the spreadsheet. It uses the normal formulas for solving a quadratic fit to three points as near as I can tell. I built my own just because I like knowing what the assumptions are. Depending on what points you pick, values for L/D and sink outside those three points might be inconsistent with the actual polar - especially at the low end where the actual polar can be quite non-quadratic. If you care about speeds below best L/D you'll need to pick a point off the actual polar at that speed - it's probably a good idea so you don't get unrealistic advice if you set Mc=0 on a glide (not a great idea, but I know people do it). Keep in mind that the quadratic will go exactly through the three points you pick - all other points will depend on how close the factory polar is to quadratic in behavior - it's very glider-specific.

9B

[anderson....@gmail.com]

I should add that this is all predicated on the assumption that the factory polar is how the actual glider performs. Nothing like a few long final glides to see how good the polar really is.

[Dan Marotta]

If I understand your question correctly you need to have your polar curve
plotted on a grid which has an origin, e.g., (0,0). You get min sink speed
by drawing a horizontal line from the Y (vertical) axis which is tangent to
the curve. Record the speed and sink at that point. You get best L/D by
drawing a line from the origin (0,0) which is tangent to the curve. Record
that speed and sink rate. Pick your third point at a reasonable cruise
speed, say 80 kts and pick the sink rate off the Y axis for that speed.

I don't mean to insult you with the above, I just don't know if you know.

"ES" <tedcw...@gmail.com> wrote in message
news:16906844-3579-49e1...@googlegroups.com...

[Mike the Strike]

Based on Dick Johnson's test data, minimum sink (~ 100 ft/min)was at the lowest tested airspeed, just below 40 knots. Maximum glide was about 50:1 at around 55 knots, a plateau. A second plateau in the polar occurred between about 75 to 85 knots with a sink speed of around 250 ft/min. The best-fit quadratic equation fits the very low-speed and high-speed data well and goes through the middle of the second plateau, but over-estimates sink rate a bit in the low-speed plateau.

I wouldn't sweat the difference.

[mattm...@gmail.com]

The conventional wisdom goes back to Reichmann's Cross Country Soaring textbook.
Remember that his "day" job was teaching math! In the book, he describes using
a quadratic equation to estimate the sink rate at any speed. This is a pretty
good method since the drag on a sailplane is dominated by the parasite drag in
the range of speeds you'll use for final glide, and parasite drag is
proportional to v**2. There are some noted weaknesses with the approach:
drag at lower speeds has a larger amount of induced drag, and flapless
gliders have more drag at higher speeds than predicted by the quadratic
(a result of the optimization of the airfoil for climb).

I've gone through the exercise a number of times. (At one point I had a cool
PostScript program that would print out one of those circular sliderule
glide computers, but alas the diskette containing it was bad!) Picking the
3 speeds is more crucial than you think. It helps to make a spreadsheet
that shows the difference between measured and computed sink rates, and
the resulting l/d, and then try picking different sets of points to
generate the quadratic.

In general the range you should use is best l/d speed up through the fastest
you'd expect to fly final glide. Lower speeds include too much induced drag,
and higher speeds stray into the drag bucket. For my ASW-19 I used 55-85kts
as the range. Best L/D is about 39 at 50kts, but only drops off to 38.5 at
55kts.

[ES]

What I *really* wish is that SeeYou Mobile and the L7 would take polars in the Cambridge/GNII format: max glide ratio; the speed at max glide (V1); and the speed at sink = -2 m/s (V2). Those figures generalize a polar a lot better than 3 coefficients which go all over the place depending on what data points you choose.

O/T: my FM lists a factory W&B empty weight of 180kg, but does not say whether that is with or without the main batteries. I know the Diana batteries are pretty much right on the CG reference point, but is it normal for "empty weight" to include batteries?

[anderson....@gmail.com]

On Monday, February 24, 2014 2:31:51 PM UTC-8, ES wrote:
> What I *really* wish is that SeeYou Mobile and the L7 would take polars in the Cambridge/GNII format: max glide ratio; the speed at max glide (V1); and the speed at sink = -2 m/s (V2). Those figures generalize a polar a lot better than 3 coefficients which go all over the place depending on what data points you choose.
>
>
>
> O/T: my FM lists a factory W&B empty weight of 180kg, but does not say whether that is with or without the main batteries. I know the Diana batteries are pretty much right on the CG reference point, but is it normal for "empty weight" to include batteries?

Empty weight does not include batteries in my experience, nor does it include a full complement of instruments. Best way to confirm is to do an actual W&B on scales.

It's possible to derive a set of coefficients based on the GNII approach. I think you are just taking the derivative of the quadratic and setting the values at the relevant speeds to 0 for min sink speed and best L/D for max glide speed. I'd have to go back to my high school differential calculus to figure out the formula.

9B

[David Salmon]

To add to what Martin says, LK8000 (don't know about XCS), has the facility
to add the wing area field to the polar file. You can then set your wing
loading, for actual flight, and the polar will be adjusted automatically.
Dave

[Bryan Searle]

Use the excellent polar spreadsheets buy Paul Remde here:
http://www.cumulus-soaring.com/soarmn/soaring_files.htm
Tables are not used by LK8000, and the quadratic approximations are not a
great way to do it, look-up would be much better!

[ES]

The best solution, I think, was to take Paul's "Remde_Polar_Cambridge_to_Reichmann_and_SeeYou.xls" spreadsheet and enter the E1 (Max Glide Ratio), V1 (Best Glide Speed) and V2 (speed at sink = -2m/s) directly off of Dick Johnson's test results (E1=45, V1=99km/h, V2=171km/h). The resulting graph fits the test data nicely, and I have my SeeYou polar coefficients.