Polar numbers for Discus A

On Saturday, April 16, 2016 at 4:55:01 PM UTC-7, Dan Marotta wrote:
You can make a custom polar in XCSoar and use your own numbers.

thanks, I put 51=1.22 76=2.5 97=5 and we will see.

seeyou I did at 50=1.21 65=1.8 80=3.07

but the Cambridge has only two points. Not sure what to fudge. Took me a week to find a 1995 computer with a serial port. Finally got the down audio to shut up.

I have a Belkin USB to Serial adapter for my laptop. It worked great
with Vista, but doesn't work at all with 8.1. Fortunately for me, I had
an old desktop computer that I dropped off in my hangar.

On 4/16/2016 8:32 PM, xcnick wrote:
On Saturday, April 16, 2016 at 4:55:01 PM UTC-7, Dan Marotta wrote:
You can make a custom polar in XCSoar and use your own numbers.
thanks, I put 51=1.22 76=2.5 97=5 and we will see.

seeyou I did at 50=1.21 65=1.8 80=3.07

but the Cambridge has only two points. Not sure what to fudge. Took me a week to find a 1995 computer with a serial port. Finally got the down audio to shut up.

--
Dan, 5J

On Sunday, April 17, 2016 at 2:32:17 PM UTC+12, xcnick wrote:
On Saturday, April 16, 2016 at 4:55:01 PM UTC-7, Dan Marotta wrote:
You can make a custom polar in XCSoar and use your own numbers.

thanks, I put 51=1.22 76=2.5 97=5 and we will see.

seeyou I did at 50=1.21 65=1.8 80=3.07

but the Cambridge has only two points. Not sure what to fudge. Took me a week to find a 1995 computer with a serial port. Finally got the down audio to shut up.

Cambridge uses only two points, but one of the speeds has two constraints:

1) the L/D at that speed, AND
2) this is *best* L/D speed

Therefore, together with the 2nd speed and sink rate, you have three constraints, same as the other programs. Three constraints uniquely specifies a parabola, which is what virtually all software assumes the polar curve is (at least above min sink):

X*speed^2 + Y*speed + Z = sink

The programs will use the information you input to calculate X, Y, and Z.

For example for your XCSoar numbers 51=1.22 76=2.5 97=5

2601*X + 51*Y + 1*Z = 1.22
5776*X + 76*Y + 1*Z = 2.5
9409*X + 97*Y + 1*Z = 5

Enter these into any linear equation solver, for example at

http://wims.unice.fr/wims/wims.cgi?+...+met hod=coef

x = 0.0014749482401656, y = -0.13611842650104, z = 4.325699378881989

Put those into a spreadsheet and try with 51, 76, 97 and you'll see you get exactly 1.22, 2.5 and 5.

However with 50, 65, 80 you get 1.2071, 1.7097, 2.8759 so the numbers you've put into seeyou are not exactly consistent.

Putting your seeyou numbers into the solver:

2500*X + 50*Y + 1*Z = 1.21
4225*X + 65*Y + 1*Z = 1.8
6400*X + 80*Y + 1*Z = 3.07

x = 0.0015111111111111, y = -0.13444444444444, z = 4.154444444444445

I don't know which of those sets of inputs is best for you. If you use a SVD solver (Singular Value Decomposition) then you can input all six equations (or more!) and get a best fit solution for X, Y, and Z.

Or, we could just say that something between them is close enough. Say:

X=0.001485, Y=-0.135, Z=4.245

These give sink rates different from your inputs by +/- 0.25 fpm at 50&51 knots, +/- 6 fpm at 65&76 knots, and +/- 12 fpm at 80&97 knots.

So, lets work with:

0.001485*speed^2 - 0.135*speed + 4.245 = sink

Cambridge want different kinds of numbers.

Best L/D speed
Best L/D
speed at 2 m/s sink

The L/D is the reciprocal of the glide slope. i.e. if the L/D is 40 then the glide slope is 0.025. If the L/D is 100 then the glide slope is 0.01. etc. We'll work with glide slope for the moment.

Glide slope is sink/speed.

sink = 0.001485*speed^2 - 0.135*speed + 4.245

so

glide slope = 0.001485*speed - 0.135 + 4.245/speed

Best L/D means minimum glide slope, which happens where the 1st derivative of the slide slope is zero.

Remembering high school calculus:

0.001485 - 4.245/speed^2 = 0

= best L/D speed = sqrt(4.245/0.001485) = 53.466

Glide slope at 53.466 = 0.001485*53.466 - 0.135 + 4.245/53.466 = 0.0238

Best L/D = 1/0.0238 = 42.03

For speed at 2 m/s sink, solve:

0.001485*speed^2 - 0.135*speed + 4.245 = 3.88769 (knots)

or

0.001485*speed^2 - 0.135*speed + 0.35731 = 0

Any quadratic equation solver will give 2.73 knots and 88.18 knots. Ignore the answer that is below stall speed :-)

So for Cambridge:

Best L/D speed = 53.466 knots = 99.02 km/h
Best L/D = 42.03
speed at 2 m/s sink = 88.18 knots = 163.3 km/h.

Dan, I have the USB to serial working in modern windows, but the Cambridge software only had ports 1 to 4 as an option. The USB to serial wire was assigned a higher number like 8.

Were you able to reassign the wire to a lower number or find later Cambridge software with a larger selection of port numbers?

Bruce, I did give you garbage. When the xcsoar numbers came out as a parabola I knew I screwed up big time. I guess those are the number generated when you choose discus.

The actual numbers from Johnson show the kink some talk about so I don't expect them to fit a parabola.

So I took my school boy ruler to the little graph on page 3 of the Johnson article and come up with the following. I guess I am looking for a quadratic equation near these numbers except 97 knots. Because of the kink 97 knots should be off the most.

max L/d 42.5 @ 53kts min sink 115 ft/min @ 45kts
50kts 121 ft/min or 1.195kts or .615 m/s
60kts 160 ft/min or 1.58kts or .813m/s
65kts 195 ft/min or 1.925kts or .99m/s
76kts 270 ft/min or 2.666kts or 1.372m/s
80kts 308ft/min or 3.05kts or 1.569m/s
97kts 650ft/min or 6.42kts or 3.3m/s

You gave me enough I should be able to learn some calculus. I was not able to get there this morning, but I will try again.

Is the A,B,C of see you x y and z of a quadratic?

On Monday, April 18, 2016 at 7:18:31 AM UTC+12, xcnick wrote:
Bruce, I did give you garbage. When the xcsoar numbers came out as a parabola I knew I screwed up big time. I guess those are the number generated when you choose discus.

Any three constraints will always give you a parabola. That's just maths. Unless they lie on a straight line. Which you could look at as a section of a veeery flat parabola.

You can of course fit a cubic or higher to those three constraints, but there are an infinite number that will fit, and you've got no basis on which to choose between them. So parabola is the best choice.


The actual numbers from Johnson show the kink some talk about so I don't expect them to fit a parabola.

Yes. The famous Discus "laminar flow drag bucket". Also present in many later designs.

I *think* (without having analysed it) that both the portion below the kink and the portion above the kink correspond very closely to parabolas -- just two different parabolas.

Does any flight optimisation software actually model that? I suspect not. Except in very strong conditions (or final glide), it's the part slower than the kink that you care about.

A bit of a bugger that the CAI software wants the 2 m/s sink speed, as that's past the kink. I reckon the thing to do would be to solve for the parabola from min sink to the kink, and then figure out where 2 m/s sink would occur if the kink didn't happen.


Is the A,B,C of see you x y and z of a quadratic?

Very probably. I don't have seeyou handy. The names don't matter. A,B,C being z,y,x would matter :-) Do the values look similar?

Nick,

I haven't been able to make my USB to Serial interface work since I
upgraded(???) to Windows 8.1. Maybe if I could find Windows 7
installation media... But it's all moot to me now since I'm using a
ClearNav XC vario so I can create my profile, including polar, on my
laptop and copy it to a USB stick which the ClearNav reads directly.

Dan

On 4/17/2016 1:18 PM, xcnick wrote:
Dan, I have the USB to serial working in modern windows, but the Cambridge software only had ports 1 to 4 as an option. The USB to serial wire was assigned a higher number like 8.

Were you able to reassign the wire to a lower number or find later Cambridge software with a larger selection of port numbers?

Bruce, I did give you garbage. When the xcsoar numbers came out as a parabola I knew I screwed up big time. I guess those are the number generated when you choose discus.

The actual numbers from Johnson show the kink some talk about so I don't expect them to fit a parabola.

So I took my school boy ruler to the little graph on page 3 of the Johnson article and come up with the following. I guess I am looking for a quadratic equation near these numbers except 97 knots. Because of the kink 97 knots should be off the most.

max L/d 42.5 @ 53kts min sink 115 ft/min @ 45kts
50kts 121 ft/min or 1.195kts or .615 m/s
60kts 160 ft/min or 1.58kts or .813m/s
65kts 195 ft/min or 1.925kts or .99m/s
76kts 270 ft/min or 2.666kts or 1.372m/s
80kts 308ft/min or 3.05kts or 1.569m/s
97kts 650ft/min or 6.42kts or 3.3m/s

You gave me enough I should be able to learn some calculus. I was not able to get there this morning, but I will try again.

Is the A,B,C of see you x y and z of a quadratic?

--
Dan, 5J

On Monday, April 18, 2016 at 7:18:31 AM UTC+12, xcnick wrote:
Dan, I have the USB to serial working in modern windows, but the Cambridge software only had ports 1 to 4 as an option. The USB to serial wire was assigned a higher number like 8.

Were you able to reassign the wire to a lower number or find later Cambridge software with a larger selection of port numbers?

Bruce, I did give you garbage. When the xcsoar numbers came out as a parabola I knew I screwed up big time. I guess those are the number generated when you choose discus.

The actual numbers from Johnson show the kink some talk about so I don't expect them to fit a parabola.

So I took my school boy ruler to the little graph on page 3 of the Johnson article and come up with the following. I guess I am looking for a quadratic equation near these numbers except 97 knots. Because of the kink 97 knots should be off the most.

max L/d 42.5 @ 53kts min sink 115 ft/min @ 45kts
50kts 121 ft/min or 1.195kts or .615 m/s
60kts 160 ft/min or 1.58kts or .813m/s
65kts 195 ft/min or 1.925kts or .99m/s
76kts 270 ft/min or 2.666kts or 1.372m/s
80kts 308ft/min or 3.05kts or 1.569m/s
97kts 650ft/min or 6.42kts or 3.3m/s

You gave me enough I should be able to learn some calculus. I was not able to get there this morning, but I will try again.

Is the A,B,C of see you x y and z of a quadratic?

About the kink...

If this copy of a Discus polar is roughly accurate ..

http://www.fsglider.de/polaren/pol_dcs.gif

... then you never ever want to fly above the kink (at the lighter weight) unless the MC setting plus current airmass sink is 10 knots or more! In which case you should go straight past the end of the curve to .. I don't know ... whatever point between rough air speed and Vne makes you comfortable?

Meantime, you're only flying slower than the kink if MC plus airmass sink is less than 3 knots.

For every situation between MC=3 and MC=10 (in still air), right on the kink is the only place to be.

(assuming no wind)

Thanks everybody for the help.

I should probably start a new thread, but how do I get the down audio to quit?

I unchecked the box for down audio in the cambridge software and that worked on the ground, but once it went into circling mode in the air the down audio came back.

330 kg 100 and 160 at 42L/D worked pretty well. With McCready at 2 I ran some 30 40 mile runs at a point and it came out close enough. Water for tomorrow.

I would guess that the down audio that you can turn off is for cruise
mode, not circling. Is the vario quiet while running through sink?

On 4/18/2016 8:32 PM, xcnick wrote:
Thanks everybody for the help.

I should probably start a new thread, but how do I get the down audio to quit?

I unchecked the box for down audio in the cambridge software and that worked on the ground, but once it went into circling mode in the air the down audio came back.

330 kg 100 and 160 at 42L/D worked pretty well. With McCready at 2 I ran some 30 40 mile runs at a point and it came out close enough. Water for tomorrow.

--
Dan, 5J

On Tuesday, April 19, 2016 at 8:20:29 AM UTC-7, Dan Marotta wrote:
I would guess that the down audio that you can turn off is for
cruise mode, not circling.* Is the vario quiet while running through
sink?

Down audio works in cruise. I don't mind that too much. But in climb I just have to turn it off.

Got a polar work around. I just loaded the program's polar and then added bugs to make seeyou and xcsoar say the same thing. I could do this in the air.