# Calculating the length needed between two bridged circles to produce a given angle / slope

Calculating the length needed between two bridged circles to produce a given angle / slope

I have two circles which I bridge together. How can I calculate the length / distance required between the two circles to have the angle / slope be 13 degrees

Example:

I create and bridge 2 circles.

1st circle radius 3


What formula would I need to use to calculate the length / distance required between the two circles to have the angle / slope be 13 degrees?

From the mnemonic 'SOHCAHTOA', you know tan (theta) = opposite/adjacent ...
so opposite = adjacent * tan(theta) =

so, starting with the top profile, ('opposite' height = 1) .. we know
h = 0.85 * tan (13 degrees)
.. but the (Pythonic) entry fields expect angles in radians.

Just a note: The 0.85 comes from (3.0-1.3) / 2 = 0.85

So to scale the 1 height (here in Y) to the right length, you could SY the top figure, followed by typing:
0.85 * tan(13/360 * tau)
into the 'Y' field of the scale operator's F9 'Adjust Last Operation' panel, which yields about 0.196.

• with a degree in math and 20 years of numerical programming, how have I never seen that mnemonic before? What are you using for your 3d-cad like annotations? Dec 31, 2021 at 16:20
• @MartyFouts Ancient English school curriculum, taught by demobbed WWII vets with a Victorian attitude.. :) Looking back from here, it would have been more useful to take the trig. equivalences approach? 2. The shipped 'Measureit' add-on, which can also give you readable vertex-numbers, etc. Dec 31, 2021 at 16:31
• @MartyFouts here's a video of it youtu.be/mnnc_EOSYlQ Dec 31, 2021 at 18:40
• @Marty Just brought up on /..?n[ui]x/gm/, so I like the way they think. And they're not constantly dumping stuff on my machine, ffs, or nagging me, trying to corner me in to their monopolized ecosystems. Dec 31, 2021 at 20:22
• @RickT Thanks for the edit :) Mar 6 at 8:38

I'm no good at trigonometry, so I'll just use this online calculator.
It also gives you the right formula if you wanna try by hand.

• Base is the difference between radius values (3 - 1.3 = 1.7)
• Angle is 13 degrees

So the Height required is 0.392 units.

• Slick! But the link is to the gif, not the calculator, and I can't seem to find the right one to pop in an edit for you :) Dec 31, 2021 at 11:44
• thanks for the heads up, works now :) Dec 31, 2021 at 11:46
• .. and it should be 0.85, not 1.7 .. you forgot to cut your cone in half :) .. (what a PITA I am ...) Dec 31, 2021 at 12:15
• Hey Robin, thanks for checking, I'm no math wiz :D. Though the numbers work out fine when i actually model it... [confused] Dec 31, 2021 at 15:14
• I might be up the creek myself / ... justification in my A. Dec 31, 2021 at 16:33