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:
- do a screen capture of the polar graph and save it as a .jpg file
- open the .jpg file in a graphics editor that will give me image coordinates
- record the image coordinates and their corresponding real values along each axis
- fit a line to each coordinate pair giving equations that will translate pixel position to graph values
- 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.
Next: Are? R? Arrrrr . . .?
Walt's Miscellaneous Ramblings 