Years ago I wrote a set of dome functions for an iOS calculator application — MACalc. I was tempted to write a custom iOS app, but calculating the surface area of a dome is only the first step. We usually want to multiply that number by a different number to estimate the price of a dome shell or how many cubic yards of shotcrete we’ll need. Integrating dome functions with a calculator was more useful.
When Apple released iOS 11, they stopped supporting older 32-bit applications like MACalc. It hadn’t been updated since the iPhone 5 was released. We’ve grown to depend on that calculator. We use it all the time. Now it’s gone. We needed something new.
We found is PCalc Pro. It runs on the iPhone and iPad. Plus there is a Mac version. It’s also programmable. Of course, that’s the trick. You must have PCalc Pro since PCalc Lite doesn’t support programmable functions.
It’s $9.99 on the App Store. It’s a comprehensive calculator that runs in algebraic or RPN modes, supports hundreds of functions and is worthwhile on it’s own.
Installing PCalc dome functions is easy. Open this page in the web browser on the device running PCalc. Click either the Algebraic or RPN version of the dome functions depending on what mode you prefer using PCalc. For me it’s RPN.
These functions are for spherical domes and half oblate ellipsoids. For 90 percent of our needs these are enough. Plus they are the easiest to use since it only requires a diameter and height. It mirrors the same functionality of the standard Dome Calculator on our website.
For prolate ellipsoids or partial oblate ellipsoids you will still need to use our web based Advanced Calculator.
Set up PCalc by clicking the “(i)” button then turning on “Multiple Memories”.
Short instructions are to save the diameter in memory 1 and height in memory 2, click “f(x)” and select the Dome worksheet. It shows a variety of calculated results. Click on any result to push to the calculator for more work.
Let’s try a couple examples.
The first Monolithic Dome was 105-feet diameter by 35-feet tall. It’s a 3 to 1 ratio low-profile sphere. Type in “105” then click “m in” followed the number “1” on the number pad. That saves the diameter in memory 1. Type “35” then click “m in” followed by the number “2” on the number pad. That saves the height into memory 2. Now click “f(x)” and select “Dome” or “Dome RPN” depending on the mode you are in. The worksheet should show:
- Dome Diameter — 105
- Dome Height — 35
- Floor Area — 8,659.01
- Floor Circumference — 329.87
- Floor Radius — 52.5
Oblate Radius of Top — 78.75 Oblate Ratio — 1.5 Oblate Surface Area — 13,628.24 Oblate Volume — 202,043.68
- Sphere Radius of Curvature — 56.875
- Sphere Surface Area — 12,507.47
- Sphere Surface Distance — 66.89
- Sphere Volume — 173,982.06
Note that Dome calculates both oblate and spherical calculations together. We did this rather than create two worksheets for convenience. Just ignore the results for oblate functions for now (because nobody wants to build 105 by 35 foot half oblate ellipsoid).
The Diameter and Height are there as confirmation you are working with the diameter and height you intended to use, plus you can click either one to push them to the calculator if you need them later. The floor calculations are universal for oblate and spherical domes. The surface distance is measured from the dome apex following the curve to the ground.
Units are the same as input. Since we used feet, the answers are in feet, square feet, and cubic feet (as appropriate). For example, the dome is 173,982 cubic feet in volume and 12,507 square feet for surface area.
The Oberon is typically 32-feet diameter by 13-feet tall. It’s always a half oblate ellipsoid. Type “32” then click “m in” followed by number “1” on the number pad. That saves the diameter into memory 1. Type “13” then click “m in” followed by number “2” on the number pad. That saves the height into memory 2. Now click “f(x)”, select “Dome” or “Dome RPN” to see the results:
- Dome Diameter — 32
- Dome Height — 13
- Floor Area — 804.25
- Floor Circumference — 100.53
- Floor Radius — 16
- Oblate Radius of Top — 19.69
- Oblate Ratio — 1.23
- Oblate Surface Area — 1,411.66
- Oblate Volume — 6,970.15
Sphere Radius of Curvature — 16.35 Sphere Surface Area — 1,335.18 Sphere Surface Distance — 22.31 Sphere Volume — 6,377.96
Again we ignore the spherical answers and focus on the oblate results. We see that a 32-foot diameter Oberon is 804 square feet of living space. The surface area is only 6,970 square feet.
The iPad and Mac versions work the same way.
Customizable and Supported
PCalc is fully customizable from the look-and-feel to exactly what each button does. You can assign specific functions from the Dome worksheet to single buttons. The iPhone version changes if you hold it horizontally, showing more buttons. You can have quick access to dome areas, for example, if you set individual buttons to return Floor Area, Oblate Surface Area, and Sphere Surface Area.
PCalc is regularly updated so we expect to use it for years to come.