A polar calculation question for you number crunching enthusiasts out there

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" wrote in message
...
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

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.

On Monday, February 24, 2014 2:20:47 PM UTC-5, Dan Marotta wrote:
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" wrote in message

...

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

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.

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?

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

At 02:58 24 February 2014, Martin Gregorie wrote:
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 |

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

At 10:20 25 February 2014, David Salmon wrote:
At 02:58 24 February 2014, Martin Gregorie wrote:
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 |

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



Use the excellent polar spreadsheets buy Paul Remde he
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!

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.