Stretch Machine Calculations

When I bought my splits machine, I had no way to easily calculate the angle of the machine. So I dialed in a visual 90° angle and started looking for convenient ways to measure the machine’s leg length. I measured a leg length of 28 to the screws at the end of the leg, and then measured the “base” of the triangle between the opposite leg’s screws. I discovered a measurement of 39.5, which gave 89.717°. Measuring from the absolute ends of the machine legs show a leg length of 29 and a base (spread distance) of 41, for a result of 89.996°. This was very accurate and since it was round numbers I was happy with the results.

I would then use an on-line triangle calculator to determine the angle of my splits for the session by measuring the distance between the legs.

Months later it occurred to me that I could just measure the distance between the legs and use that to index a previously calculated figure. So I re-measured 180cm from end to end at 180°, and then 125cm end to end for 90°. The implication being that the factor is about 1.6° per cm as you go from 125cm to 180cm. To test this I dialed in a visual 135° using the tiles on the floor and measured 164cm. This is an extra 39cm, and I expected only an additional 27cm. So the figure gets more accurate as you get closer to 180°. What would be better, likely then, is to do a table of expected results based on the leg length and not rely on a formula.

However while doing the table I kept coming back to highly accurate visual results indicating that a leg length of 29 (88cm) was very accurate between 90° to 180°. It became simply too convenient to use this number. Yet, when measuring at 180° we got 180cm, so perhaps using a leg length of 90cm would be a bit more accurate.

As it turned out, a leg length of 90cm provided greater than a very careful visual tuning of the angle. At 135° and 90°, observed error was attributable to human error. For example, I tried to make the machine 135° and measured a 165cm spread from pad-end to pad-end. This would give us 132.9°. But when I went to visually check the degree I found it to be slightly inside 135°. Meaning, closer to 132.9°. Thus the leg length of 90° was adopted and used to key spread lengths to spit angles.

Table 1: Spread Length to Angle

Spread Length Expected Angle
180cm 180°
175cm 153°
170cm 142°
165cm 133°
160cm 125°
155cm 119°
150cm 113°
145cm 107°
140cm 102°
135cm 97°
130cm 92°
125cm 88°

Table 2: Required Spread Length for Angle

Angle Spread Length
180cm 180cm
170° 179cm
160° 177cm
150° 174cm
140° 169cm
130° 163cm
120° 156cm
110° 147cm
100° 138cm
90° 127cm

More later.

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