Interesting to me...but probably boring here

StanFoster

Active Member
Joined
Nov 16, 2003
Messages
17,139
Location
Paxton, Il
Aircraft
Helicycle N360SF
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I find angles interesting...so I am posting this in case someone else likes to read this stuff. Not much flying topics anyway...so I posted another off topic thread.

One of the stairways in my shop has curved stringers that iron shoes have to be ground to fit to. You would think that one angle would do it....but it doesnt. Any angle on a curved stairway gets shallower as you go to move to the outside ....and likewise gets steeper as you move to the inside.

The iron shoes are centered on this curb stringer...and the inside face of the shoe is right on a 36 inch radius circle. The shoe is 1 5/16 inches wide, or 1.3125 inches, and that makes the outside radius 37.3125 inches. If you figure the bevel angle to grind this shoe at the inside radius of 36 inches...the other side will not fit nicely as the curb has a slightly shallower angle on that side.

How much angle difference...and how big of a gap would there be if I just simply ground it at one angle? Thats what I wanted to know so I sat down with my calculator...and figured that the angle of the shoe at the 36 inch radius was 47.168 degrees...Excuse the exactness...but I like to figure fine...then round off later. The angle on the outher side of the shoe just 1.3125 inches away is 46.144 degrees. That is a 1.024 degree change that has to be ground to make these shoes fit nicely.

That doesnt sound like much...but a degree is quite a bit. So my next question was how much of a gap would there be if I ground both sides one of the angles and just slapped it down on the curb?? If you just take any $10 trig function calculator...you can find this valuable information in just a few strokes. Remember sine, cosine, tangent laws? I just used the tangent law which in any right triangle...the tangent of the angle equals the length of the opposite side divided by the adjacent side.

So lets take the first angle of 47.168 degrees...The tangent of this angle is 1.07869. Simply multiply this times the width of the shoe which is 1.3125 inches..and you arrive at 1.416 inches. That is how high the bevel of the cut is across the shoe on the inside.

The outside of the shoe is at 46.144 degrees. The tangent of this is 1.04075. Again,,,multiply this times the width of the shoe...1.3125 inches and you arrive at 1.366 inches. That is the height of the bevel on this side.

The difference between these two is right at 0.050 inches. This is slightly less than 1/16 of an inch...and would be a very unacceptable gap in my opinion. A 64th of an inch can even look huge with the right light.

I set up a jig set to the inside angle and first cut these to one angle. Then I took each shoe to my disc sander...and did the finesse grinding on the other side to adjust for that 1.024 degree difference. What I end up with is a shoe that fits the helical surface of the curb.

I know this isnt a common fascination with most people...but I love figuring the math thats goes into each of the many steps in a curved stairway.

I know this is elementary to Chuck Beatty, and I can only imagine the computations that goes through that mind of his.


Stan
 

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Mike- Thanks for the comment...and I am not being modest here at all, but I am no ways the best at what I do. Believe me....I have seen stairways that leave me feeling about 2 feet tall...but with a new catalyst burning in me to try and improve my own work.

I am happy to say I have seen a steady progression in my work over the years....and when it levels off....thats when I have reached my peak. But I have a long ways to go to catch up to some stairmasters I know.

Stan
 
I am not being modest here at all, but I am no ways the best at what I do. Believe me....I have seen stairways that leave me feeling about 2 feet tall...

Huh?

Why is it that people that are really good at something make statements like this?

Stan,

Your work is awesome. I can’t hardly cut a board straight much less figure all those angles you are talking about. I got lost there! :confused: I built a few big farm shop doors and they turned out ok. I could not figure out how to get the angles just right for the cross braces so those braces didn’t fit just right. LOL:D
 
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