Find the angle of a slot on a cylinder

[EwanBryan]

Hi all,

Here's one to pick your brains, because it has been picking at mine for quite some time. I have been asking around but it seems to stump everyone who gives it an attempt. Nevertheless, I'm hoping the answer is simple to get to.

CONTEXT: I am an engineering student, and have been given a drawing not containing the necessary information for me, though I believe the information I need can be calculated. This will explain why the values provided are strange non-friendly numbers, as they are what are printed on the drawing.

PROBLEM:
I have a cylinder with an outer diameter of 0.519".
There is a slot on the outside of the cylinder that is 0.093" wide.
The slot wraps around the outer diameter of the cylinder at a 45 degree helix.
The slot continues wrapping around the cylinder for 0.23".
The 0.23" length is parallel to the center-line of the cylinder.

What is the angle at which the slot wraps around the diameter, marked x?

View attachment 36322

I hope that there is enough information, but I am completely lost with this. For any more information, feel free to ask.

Thanks!!

 

[EwanBryan]

An image that I missed out.

 

[Dr.Peterson]

PROBLEM:
I have a cylinder with an outer diameter of 0.519".
There is a slot on the outside of the cylinder that is 0.093" wide.
The slot wraps around the outer diameter of the cylinder at a 45 degree helix.
The slot continues wrapping around the cylinder for 0.23".
The 0.23" length is parallel to the center-line of the cylinder.

What is the angle at which the slot wraps around the diameter, marked x?

What is the meaning of "45 degree helix" in your context?

I would think it would mean that your angle x is 45 degrees. But then, it isn't entirely clear how you are defining x, either. The helix will not appear as a straight line in any one projection, but rather as a sinusoid.

 

[EwanBryan]

What is the meaning of "45 degree helix" in your context?

I would think it would mean that your angle x is 45 degrees. But then, it isn't entirely clear how you are defining x, either. The helix will not appear as a straight line in any one projection, but rather as a sinusoid.

Thanks for the reply Dr Peterson,

The 45 degree helix means that the slot wraps around the 0.519" diameter for 45 degrees. See the picture for a visual. Bear in mind that the slot wraps around for 45 degrees and finishes after 0.23".



Yes I agree, it is not clear how I am defining x, apologies for that. If the cylinder was dissected along its center-line and laid out as a 2D shape, what would be the angle marked x such that the hypotenuse runs through the center of the slot. See the picture below containing an image of the flattened slot feature compared to the slot wrapped around the 0.519" diameter. The 2D slot is highlighted in red.



The edges of the slot will not be straight but instead sinusoidal, like you said, but I believe, or at least hope, that would cause no issue when calculating x.

 

[Dr.Peterson]

If the cylinder was dissected along its center-line and laid out as a 2D shape, what would be the angle marked x such that the hypotenuse runs through the center of the slot.

The edges of the slot will not be straight but instead sinusoidal, like you said, but I believe, or at least hope, that would cause no issue when calculating x.

How does a straight line run through the center of a slot that is not straight???