Acoustic Guitar Bridge Pin Taper Angle Calculation.

[Mothman]

Hello

I've just registered with the site and created the username Mothman because my maths (moths) is full of holes !

I googled for a method to calculate the taper of an acoustic guitars bridge pin.

I came across the attached Bridge Pin Taper calculation and now seek help to understand it.
I'm not even sure if the methods correct, although the result would imply that it may be as 3 degrees is a good possibility
from other guitar information I've read. Anyway, now I'm curious about the calculation.

My Current Understanding
I've numbered the calculation steps 1 to 11.
The triangle represents half of the bridge pin.
The triangle is made up of two similar triangles so the angles are similar.
I remember the formulae SOH, CAH, TOA

What I don't understand
How did he get X = 1.163 ? No mater how I expand the brackets or substitute for c, I don't get 1.163 !
Is there a better way to calculate the taper of a bridge pin from the information given ?
Any help with steps 6 to 11 would be much appreciated.

Thanks in advance.

Click Image To Enlarge:

 

[Deleted member 4993]

Hello

I've just registered with the site and created the username Mothman because my maths is full of holes !

I googled for a method to calculate the taper of an acoustic guitars bridge pin.

I came across the attached Bridge Pin Taper calculation and now seek help to understand it.
I'm not even sure if the methods correct, although the result would imply that it may be as 3 degrees is a good possibility
from other guitar information I've read. Anyway, now I'm curious about the calculation.

My Current Understanding
I've numbered the calculation steps 1 to 11.
The triangle represents half of the bridge pin.
The triangle is made up of two similar triangles so the angles are similar.
I remember the formulae SOH, CAH, TOA

What I don't understand
How did he get X = 1.163 ? No mater how I expand the brackets or substitute for c, I don't get 1.163 !
Is there a better way to calculate the taper of a bridge pin from the information given ?
Any help with steps 6 to 11 would be much appreciated.

Thanks in advance.

Click Image To Enlarge:

View attachment 2636

From similar triangles:

(B+x)/x = a/c

B/x = 0.108/0.062 - 1 = 0.046/0.062

x = 0.863 *0.062/0.046 = 1.163174

 

[Mothman]

Thank You

Subhotosh Khan

Thanks for the reply and explanation.
I see now where I went wrong.
I made a stupid mistake !



Click Image To Enlarge:

 

[Mothman]

Hello Again

Thanks for the help.