**Using a Scientific Calculator**

*The Power of the HP 50g*

Before I continue with the stair building thread, it occurred to me that it might be useful to include some thoughts on incorporating useful and powerful technologies into your construction projects. These won’t necessarily be in any particular order.

One such tool is the Programmable Scientific Calculator.

I bought my very first ‘beast’ in 1990. It was the HP 48SX when I was a Texas Aggie. Times have allowed for the evolution of technology to where we have the HP 50g today.

RPN (Reverse Polish Notation) is a valuable and powerful way to use the ‘stack’ features of the 50g to make very complex calculations in a very efficient and easy way. You can learn more about RPN, here.

**Using RPN for HP 50g Calculator in Construction**

To start with, I was helping someone out with how to calculate the radius needed to create an arch between an opening.

For this example we will use a 6’ (72”) opening, and the arch will start 16” down from the top plate height.

__Find the Radius for an Arch__

__Stack Line 2__: has the length in decimal inches (which is great for using in CAD when extreme accuracy is required)

__Stack Line 1__: has the same length but it was ran through a subroutine called FEET* which converts decimal inches into Feet-Inches-Sixteenths (FIS).

* The FEET routine in RPN is as follows:

The equation for other calculators is:

~ where **S**= the Span of the opening

~ where **R**= the Rise from the chord span to the top of the arch

**Radius** = (**S**^2 + 4**R**^2) ÷ (8**R**)

But that just makes it part of a circle. An ellipse/parabola is different entirely....unless you're framing for a math professor (like I did for a Rice U math prof once) you can eyeball half of it and flip it over to keep it symmetrical.

**Option 1:**

The first example is shown as having the top of the arch reaching the top plate height. So a 72" wide opening with a 16 inch rise from where the arch starts at the edge, up to the peak, would be a radius of 4'-0 ½” with no sub-framing.

This can be problematic unless sub-framing can be added above for the top edges of the plywood to be nailed to.

**Option 2:**

The second image shows 2x4 on-flat sub-framing, and the radius gets calculated using 14 ½” rather than 16”. So a 72" wide opening with a 14 ½ inch rise from where the arch starts at the edge, up to the peak, would be a radius of 4’-3 15/16” with 2x4 sub-framing.

Both ways end up with a 16” down from plate start point. The second way will result in an inch-and-a-half dropped part of the arch at its apex.

Have fun.

And, if you were thinking ELLIPSE for an arch, here’s the way that works.

The ellipse requires correctly locating the two focal points (foci) and then you can use them in conjunction with the edge of the arch to draw the shape using a non-stretching string.