Need Math Help

[trackman]

Need to know how many square inches there is in a arch that is 28” long an 33” at tallest point. Thanks 

[dgman]

I was told there would Be no math here!

[teachnlearn]

There are math formulas for calculating a elliptical which would be half a elliptical or Archimedes parabola. Each formula would work. There is a explanation pdf on.

Calter2006_Article_GatewayToMathematicsEquationsO.pdf

I won't try to explain the math here since its probably easier to look at the pdf and plug in the numbers.

RJF

[new2woodwrk]

This may help:

https://www.omnicalculator.com/math/arc-length

https://www.mycarpentry.com/arch-calculator.html

https://homeguides.sfgate.com/square-inches-arched-window-50139.html

Edited September 2, 2020 by new2woodwrk

[Dan]

Is the arch half of a sphere? Can you give us a tough drawing? 

[trackman]

1 hour ago, Dan said:

Is the arch half of a sphere? Can you give us a tough drawing? 

My wife is going to replace the windows in a church. Not that they need improvement lol. The top arch is 28” along the base, at the 14” halfway point from base to top of arch is 33”. 

[dgman]

If it were me, I’d measure the arch as a rectangle. It would be easy to calculate square inches to that, then round down a few inches.

[trackman]

36 minutes ago, dgman said:

If it were me, I’d measure the arch as a rectangle. It would be easy to calculate square inches to that, then round down a few inches.

At $1.21 per square inch we need it to be more accurate. 

[amazingkevin]

#,s are not my fortay!!!

[jollyred]

The area of the  arch is half of a circle, which you can get from the formula A= 1/2 x Pi x radius squared.  14 inches would be the radius which gives an area of 308 square inches.

The area of the rectangular part would be A = W x H.  This area is 14" x 33" squared = 462 square inches.  (the height shown in the picture seems a lot more than the width of 28", so I am using the height of 33" here.  If that is wrong, substitute the correct value)

The total area is then 308 + 462 = 770 square inches, which at 1.21 per sq inch gives $932. 

Tom

[teachnlearn]

I did some crafted soldered glass work and never knew of a supplier that shipped colored glass in anything other then square or rectangular shape which was cut down. So measuring the each pane as a rectangle seems appropriate to ordering the glass and cutting it to size. Same project as any woodworking project. There is going to be so much cut off waste to make the shape. 'There were some specific jeweled, or shaped glass, but it was a decorative insert.' RJF

[Dan]

If all you are doing is the half circle at the top of the window use the area of a circle and divide in half. Area =  (3.1416 x radius xradius) / 2. If the window is 28 inches wide the area is (14 x 14 x 3.1416) / 2 = approximately 308 square inches. Someone should check my work before you go with that number. 

[trackman]

7 hours ago, teachnlearn said:

I did some crafted soldered glass work and never knew of a supplier that shipped colored glass in anything other then square or rectangular shape which was cut down. So measuring the each pane as a rectangle seems appropriate to ordering the glass and cutting it to size. Same project as any woodworking project. There is going to be so much cut off waste to make the shape. 'There were some specific jeweled, or shaped glass, but it was a decorative insert.' RJF

When the wife is asked to give estimate on the total job (design, build, install) she figures a price per square inch. This is a good way to cover material an labor.