How to calculate this torque? (steel ball in a spiral tube)

[JBA]

@Baluncore , After all of our work I hardly believe I am posting this.

Last night, I began to consider that I had made an error in my above calculation by using D2*π as the distance the ball traveled for each wrap of the helix in my in my F = E/n/(D2*π) calculation; when, I should have used:
F =E/n/(sqrt((D2*p)^2+H2^2) for that formula.

After making that revision this morning, I appear to have verified its accuracy because with that revision my calculation result for F at 90° is exactly the same as the simple F = Ma*sin(33°) = 16.60N result, (unfortunately I failed to check that for my original calculation after seeing my correlation with your result at 45°).
Obviously, the main issue that creates is that at α = 45°, that revision reduces my original T = .835N-m value to
T = .693N-m and reduces the values in my curve but not its profile and still calculates T = 0 at α= 0°; but, no longer correlates with your results.

Please review this revision and let me know your thoughts.

 

[Baluncore]

I have not yet looked at your revision, but the agreement between our numbers was close to numerically perfect.

Pitch angle 33.995 °
Torque at a = 45°, 0.835437 Nm
alpha Baluncore JBA difference
90.0 1.#NAN00000 1.181486720 % 1.$E+00
85.0 1.#NAN00000 1.176990806 % 1.$E+00
80.0 1.#NAN00000 1.163537282 % 1.$E+00
75.0 1.#NAN00000 1.141228536 % 1.$E+00
70.0 1.#NAN00000 1.110234352 % 1.$E+00
65.0 1.#NAN00000 1.070790615 % 1.$E+00
60.0 1.#NAN00000 1.023197514 % 1.$E+00
55.0 0.967817262 0.967817262 0.0E+00
50.0 0.905071337 0.905071337 0.0E+00
45.0 0.835437272 0.835437272 3.3E-16
40.0 0.759445025 0.759445025 2.2E-16
35.0 0.677672942 0.677672942 0.0E+00
30.0 0.590743360 0.590743360 1.1E-16
25.0 0.499317864 0.499317864 5.6E-17
20.0 0.404092257 0.404092257 -5.6E-17
15.0 0.305791265 0.305791265 3.3E-16
10.0 0.205163016 0.205163016 4.4E-16
5.0 0.102973353 0.102973353 -1.2E-16
 0.0 0.000000000 0.000000000 2.1E-16
[code]

 

[JBA]

Note: I have done multiple edits of this post so see the below post for my latest input.

 

[JBA]

@Baluncore

Thankfully, my issue is now fully resolved and we still have full correlation.

My late night investigation just revealed that: Atan(L1/(D2*PI) = 33.995°, so using D2*PI() is the correct interpretation for my analysis.
Sometimes the hardest part of getting an answer to an issue is figuring out what question to ask.

 

[Baluncore]

Sometimes the hardest part of getting an answer to an issue is figuring out what question to ask.

When we know the right question, we also know the answer, and so do not need to ask it.

“The only interesting answers are those which destroy the question”. —Susan Sontag.