Any math geeks out and about? RED PILL ME

[Frodo]

I ran across an interesting math problem that I would like a geeky answer to if possible

See the image

I did not want to punch holes, I wanted to use my chisels instead, SO

I lined my chisel up on the center of the first hole and made holes.  I stopped at the end on the center hole

In my mind, There is no difference, OH WAS I WRONG

this was the bill on a baseball cap,  the edge of the bill was 1/2'' passed the spot it was supposed to be

the bill had grown by 1/2''

RED PILL ME,  how did this happen? 

 

[SaintJoy18]

Ok Frodo... Here goes my mathematical reckoning... Been a while since I had to think in terms... I make no guarantees about this but it's good to exercise the grey matter

Using the chisel pushes the leather apart, whereas using the punch removes the leather between.

Therefore, by pushing the leather you are adding distance/length. Multiplying the number of stitches by the variable of the length you obtain the total of the length. Subsequently this can be written as the variable equals the distance divided by the number of stitches.

7x = 0.5 (7 being the number of holes punched on the bill, x being the variable, 0.5 being the overall distance/expansion of the length of the bill)

X= 0.5/7 (same function as above solving for X)

X = 0.07142857 (length of each individual stitch hole in inches)

0.07142857 = 1.8143 mm

By using the punch and removing the leather you would have the following:

7(1.5mm) = X

X=10.5mm

10.5mm = 0.4134 inches, here's where things change.

Knowing that the chisel has pushed the leather creating additional length you can use the difference between that length, and the material removed to find the overall increase in the length "added by removing" material (there will naturally be some outside expansion as the punch is pushed through to remove the center).

0.5 - 0.4134 = 0.0866 inches (slightly more than 1/12th of an inch has been added to the overall length, an inconsequential amount)

Use Tony's recommendation of the 1.5 mm punch next time

(WHEW! math brain still works....)

Edited October 14, 2020 by SaintJoy18
clarification

[Frodo]

28 minutes ago, SaintJoy18 said:

Ok Frodo... Here goes my mathematical reckoning... Been a while since I had to think in terms... I make no guarantees about this but it's good to exercise the grey matter

Using the chisel pushes the leather apart, whereas using the punch removes the leather between.

Therefore, by pushing the leather you are adding distance/length. Multiplying the number of stitches by the variable of the length you obtain the total of the length. Subsequently this can be written as the variable equals the distance divided by the number of stitches.

7x = 0.5 (7 being the number of holes punched on the bill, x being the variable, 0.5 being the overall distance/expansion of the length of the bill)

X= 0.5/7 (same function as above solving for X)

X = 0.07142857 (length of each individual stitch hole in inches)

0.07142857 = 1.8143 mm

By using the punch and removing the leather you would have the following:

7(1.5mm) = X

X=10.5mm

10.5mm = 0.4134 inches, here's where things change.

Knowing that the chisel has pushed the leather creating additional length you can use the difference between that length, and the material removed to find the overall increase in the length "added by removing" material (there will naturally be some outside expansion as the punch is pushed through to remove the center).

0.5 - 0.4134 = 0.0866 inches (slightly more than 1/12th of an inch has been added to the overall length, an inconsequential amount)

Use Tony's recommendation of the 1.5 mm punch next time

(WHEW! math brain still works....)

my head just blew up,  The emt was called,  I hold you directly responsible for my Copays  

LOL   Thank you...Tony already scolded me.  

 

bungle in the jungle

Edited October 14, 2020 by Frodo

[Retswerb]

2 hours ago, SaintJoy18 said:

Using the chisel pushes the leather apart, whereas using the punch removes the leather between.

Therefore, by pushing the leather you are adding distance/length.

Waaaaait a minute though. If this were true, think of the effect it would have using a chisel to punch holes along one side of a belt or strap. If the chisels are increasing the length of the leather along that run you would end up with a really noticeable bend along the strap.

I think the spaces in between the chisel holes absorb the ‘excess’ leather pushed aside by the chisels. Especially with chisel tines as thin as shown in the first pic, I think the answer is somewhere else.

[MedusaOblongata]

I think Retswerb has a point. If you use a stitching chisel with 7 (or whatever) points, the two on the far ends should prevent the leather from stretching in between them. This would be easy enough to test, though. Take your strip of leather, measure it precisely, punch holes, then measure it again. On the other hand, if each tine has a sharp point but not sharp edges, then it could be stretching or pushing the leather apart by the length of each hole, kind of like what you'd get if you drove a nail into the leather.

 

One thing I've done to try to stop leather from changing shape and size on me while I'm working with it is I stretch the leather as far as I can with my hands in each direction before I cut it, thinking that might prevent it from stretching afterwards. I'm only partially successful with this, though, because sometimes the leather will stretch, shrink, or both, and two pieces I cut to the same size by laying one on top of the other for the cut will end up different sizes and shapes, making my work take much longer than it would if I knew what I was doing.