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Old 06-10-2018, 08:36 PM
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rickoff rickoff is offline
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Join Date: May 2008
Location: Maine, USA
Posts: 3,366
An angle relationship study for the 3/4-inch build

Today I decided to make a graph showing the angle relationships for the lay angle of 3/4-inch PVC pipes against the 90 degree elbows of adjacent pipes in order to determine what angles would be achieved at specified distances from the wheel's center point. This was drawn to actual scale, though the photo taken of the drawing may appear smaller than noted. As shown in the photo below, I drew a vertical radian line at the right side of the drawing, and another radian line angled 60 degrees from the vertical. Along each of the radian lines, I measured out inch markings from the convergence point (center point of the wheel), beginning at 3-inches and ending at 10-inches. At each of these measured inch marks, I drew a circle. The circles on the vertical radian line were drawn to the actual outside dimension of the PVC pipe, which is 1.050-inches, while the circles drawn along the 60 degree radian were drawn same size as the PVC elbow's outside diameter, which is 1.318-inches. I then drew lines from the bottom of each circle on the vertical radian line to the top of each circle on the 60 degree radian line to represent how the PVC pipe would actually lay upon the elbow at each measured distance. Once drawn, I was then able to measure each of the angles precisely using my True Angle layout tool. Here is the photo showing the results, with each angle marked at the right side.

While some of the lines in this drawing appear not to be straight, and the vertical and horizontal lines appear not to intersect at quite a 90 degree angle, this appearance is caused by the camera lens and the actual lines and angles were drawn very accurately.

As can be seen, the lay angle that would be achieved if the bore hole centers were set at 3-inches from the wheel's center point would be 85 degrees, which is very close to horizontal. If bored at that location, water would not flow outward in a pipe until it's bore hole was nearly at the 12-o'-clock position. In comparison, a pipe with a lay angle of 68 degrees would transfer water outward at a point 30 degrees before its bore hole reaches the 12-o'-clock position, and this is why I believe that a 68 degree angle would be ideal.

Notice how the angle at the 4-inch bore hole narrows to 78 degrees, a 7 degree difference from the 3-inch angle, but at each successive bore hole, moving upwards, the degree change becomes smaller and smaller, until the degree change between the seventh and eighth bore hole is just 3/4 (0.75) of a degree. At this rate, we don't achieve the desired 68 degree angle unless we mark the center of our bore holes at slightly less than 9 inches outward from the wheel's center point. Of course this would mean that we would have to either use round cut wheels of 20.5-inches in diameter, or build two dodecagon wheels, and it also means that the vertical support arms would have to be made somewhat higher than those needed for the current build.

I do plan to complete the current build as is, as I do feel confident that the wheel will self-rotate, but will also begin planning for a corrected 3/4-inch build based upon the above drawing factors. I think it should prove interesting to see what difference there may be in performance level when comparing the two different angles. I had guessed that my current wheel may have an angle of about 72 degrees, but the drawing would prove that the actual angle is somewhere closer to 73.75 degrees.

As a side note of some interest, it occurred to me, after reviewing the drawing, that if each of the lay lines was extended several inches beyond the circles on the 60 degree radian line, they would very likely intersect at the same convergence point.
"Seek wisdom by keeping an open mind to alternative realities, questioning authority, and searching for truth. Only then, when you see or hear something that has 'the ring of truth' to it, will it be as if a veil has been lifted, and suddenly you will begin to hear and see far more clearly than ever before." - Rickoff

Last edited by rickoff; 09-17-2018 at 09:55 PM. Reason: updated for accuracy
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