# Perfect Data

Well . . . OK . . . not perfect data, but data that’s close enough.

What we need at this juncture is a set of data points off of a published polar curve. Luckily the Caesar Creek Soaring Club in Waynesville, OH (A big shout-out of thanks to them!) has published the spec sheet on the ASK-21. You can view it here.

Here’s what I did:

1. do a screen capture of the polar graph and save it as a .jpg file
2. open the .jpg file in a graphics editor that will give me image coordinates
3. record the image coordinates and their corresponding real values along each axis
4. fit a line to each coordinate pair giving equations that will translate pixel position to graph values
5. measure pixel coordinates off of the polar curves and translate them back to graph values.

Yes, that’s a lot of work and here’s what it looks like taken a step at a time. First the screen capture:

and what it looks like in the graphics editor (this is the first dash on the 5.3 lbs/sqft line:

So where does that dash really begin? There’s obviously room for error and or interpretation here and we’ll see the effects of that in a second.

We need a way of translating the pixel coordinates (73.062, 122.75) into graph coordinates (around (67.5, 0.67)). Since two points form a straight line if we measure the pixel coordinates at (60,0) and (200,0) along the airspeed axis and (60, 0) and (60, 3.2) along the sink axis we can fit straight lines to each pair. This will give us functions that translate pixel values back to graph values. Here’s a screen shot of a spreadsheet that does this:

The top portion of the spreadsheet contains the two axis measurements and the bottom portion, columns that allow you to enter the pixel coordinates in the first two columns and formulas built from the slopes and intercepts that calculate the graph value. The “Measured Airspeed px” and “Measured Sink px” are the pixel coordinates for (80, 0.2), (90, 0.4), (100, 0.6), (110, 0.8), and (120, 1.0). As you can see in the “Calculated airspeed” and “Calculated sink” columns there is a bit of jitter – not bad though.

NOTE: before someone points it out in the comments, I’m well aware of the fact that the initial x values for the “Airspeed pixel” and “Sink pixel” are different and should be the same. I could of substituted one or the other and made them the same but it matters little to the calculated results (Can you measure your airspeed to the nearest tenth or hundredth of a knot?) and is indicative of a typical measurement error using this method. Live with it.

Now we have a method of generating reasonably accurate data. I measured the pixel coordinates at the left edge of each of the dashes on the 5.3 lbs/sqft curve and entered them in the spreadsheet giving the following data (which, unlike Dick Johnson, I’ll be glad to share here):

Measured Airspeed px Measured Sink px Calculated airspeed Calculated sink
72.333 122.667 67.3232228915663 0.713724174095438
85.667 121.667 70.1346084337349 0.705334032511798
99.333 120.667 73.0159939759036 0.696943890928159
112.667 120.333 75.8273795180723 0.694141583639224
126 120.667 78.6385542168675 0.696943890928159
139.333 122 81.4497289156626 0.70812794965915
153.667 123.667 84.4719578313253 0.722114315679077
166.667 125 87.212921686747 0.733298374410068
180 127.667 90.0240963855422 0.755674882013634
191.333 130.333 92.4135843373494 0.778042999475616
199.667 132.667 94.1707530120482 0.79762558993183
206 134.333 95.5060240963855 0.811603565810173
218.667 137.667 98.1767771084337 0.839576297850026
231.333 142.333 100.847319277108 0.878724698479287
244 147 103.518072289157 0.917881489250131
256 152 106.048192771084 0.959832197168327
268.333 157.667 108.648524096386 1.00737912952281
281.333 164 111.389487951807 1.060513896172
292.667 169.333 113.779186746988 1.10525852123755
304.667 174.667 116.309307228916 1.15001153644468
316.667 181.667 118.839427710843 1.20874252753015
327.333 188 121.08828313253 1.26187729417934
339.333 195.667 123.618403614458 1.3262045097011
351.333 202.667 126.148524096386 1.38493550078658
362.333 209.333 128.467801204819 1.44086418458311
373 217.667 130.71686746988 1.51078762454116
384.333 225 133.106355421687 1.57231253277399
395.333 232.333 135.42563253012 1.63383744100682
406.333 240.667 137.744909638554 1.70376088096487
416.333 248 139.853343373494 1.76528578919769
427.333 256 142.172620481928 1.83240692186681
438.333 265 144.491897590361 1.90791819611956
449 273.667 146.740963855422 1.98063555322496
459.333 281.667 148.919608433735 2.04775668589407
470 290 151.168674698795 2.11767173571054
480 299.333 153.277108433735 2.19597692711065
490 307.333 155.385542168675 2.26309805977976
500 316.333 157.493975903614 2.33860933403251
510 325.667 159.602409638554 2.4169229155742
520.333 335 161.781054216867 2.49522810697431
529.333 344 163.678644578313 2.57073938122706
539 353.667 165.71686746988 2.6518468799161
549.333 363.333 167.895512048193 2.73294598846356
558.333 373.333 169.793102409639 2.81684740429995
567 382.667 171.620481927711 2.89516098584164
576.667 392 173.658704819277 2.97346617724174
586.333 401.667 175.69671686747 3.05457367593078
596.333 411.333 177.80515060241 3.13567278447824
605.333 420.667 179.702740963855 3.21398636601993
614.667 430.667 181.670753012048 3.29788778185632
623.667 440 183.568343373494 3.37619297325642
633.333 449.667 185.606355421687 3.45730047194546

Now that we have some raw data to work with, in the next posting, I’ll delve into the mysterious, arcane, and sometime weird world of R.