I’ll Never Use Geometry After High School — I was wrong

Colin Bitterfield
4 min readJan 8, 2024

I am working on adding “Starlink” to my RV and needed to make a bushing for the pole mount to connect it to a chainlink fence pole. $20 v $150 mast. I have a number of 3d printers including resin based ones.

So the problem starts with both a metric to sae conversion along with how to do practical geometry.

The “Starlink” version of a pipe adapter can be found on their website.

The chainlink rail can be found at Lowes or Home Depot

chainlink rail
SAE (btw. not accurate, they got metric and smaller)
Bottom View of the Adapter.

“designed to attach to any pole with a max diameter of 2.5" (64 mm)”

Notice that were are already playing with conversions. (Use 64mm) for the 1 3/8" convert and round down. Turns into 34.925 mm (I used 34.9). The issue is the inner dimension of the adapter is 74 mm not 64mm and you need to take the wall thickness into account.

Notice that we need to create a top (with larger areas) and a bottom with smaller areas and then connect them with a CADD loft. Also if you notice we will need to drill some holes for screws and that they will be on 120 degree centers.

I came up with this the first time but quickly realized an error.

Mistake

It takes some very interesting math to make this work out.

Finished math with error

The centerline for each of the three spokes is 0, 120, 240 degrees and 32mm (radius).

We need to fine the number of degrees

The problem is we need the centerline for construction but we need the degrees or radians for 1/2 the distance on each side.

The problem is we need to find the number of degrees to start and end the tab wedge using the construction line as reference. We need the total number of degrees for the tab (8.2mm) at 37.2 mm from the centerline.

Find the central angle given the arc length and radius

Given the following values

Arc Length (S) = Radius (r) * Theta (⍉)

8 mm = 37.2 mm * ⍉

8 / 37.2 mm = (37.2mm * ⍉) / 37.2 mm

0.21505376344086 (radians) = ⍉

radians to degrees:

Radians to Degrees

A central angle calculator to check the work is located here.

Central Angle Calculator

Now let’s plug this back into our CADD program.

Note the tab should be 8mm (and we get 7.98 mm)

In the CADD program, all of the parameters are defined as variables so we can make adjustments to the variables and the sketch will update accordingly. This shows one of three of the tabs. (dash lines are for construction and are not part of the 3d part)

CADD replicates the tab area for 3 around the circle so you don’t need to draw the other lines.

So now we have the bottom circle.

The important part here is that you can use variables in CADD and adjust but you have to know the formulas. This program is smart enough that I could have put the formula in for all of it and had it calculate radians and us that in the sketch.

This is what the final part will look like (Test section 2mm)

3d part for test jig

When the design is done, I will complete the part and slice the bottom and top sections for a 4mm jig to test the print prior to final 3d print to avoid wasting materials.

This bushing is printed with ABS like resin that is hardened with UV light. For long term survivability outdoors it will need to be painted with UV resistant paint.

The top central angle:

Top Central Angle
Math
Top Jig

The final product looks like this

Final Product

In conclusion high school math is still useful 40 years later. It is also very relevant to 3D printing.

I created an equation so that I could just change arc length and the entire 3d object would update automatically. This helps with the final finish. Also I needed to reduce the size of the inner dimension by a 1/2 mm.

--

--

Colin Bitterfield

NIST certified Security Professional | 10+ years experience in infrastructure security and compliance | Experienced in creating security programs.