3/24/2017 1:53 PM

**Edited Date/Time:** 3/24/2017 2:13 PM

If you take p1p's model of a ***perfectly horizontal offset plane** (this is important for the calculations I did), you can calculate pretty much whatever you want with some basic algebra, geometry, and trig. Take the below picture (original courtesy of calfeedesign). All calculations rounded...

The knowns/constants are in black. I chose a 74° HT per the OP's original problem. I arbitrarily chose a 12" fork *leg* length. I chose a 25mm offset per one of the requested offsets from the OP's original problem.

If we know HT angle, we can plumb-line down from the bottom of the HT (or from anywhere, frankly as we're just looking at the base steering axis/HT angle) to get us a helpful right triangle. All angles of a triangle add up to 180°, so 180° - 74° - 90° = 16°

Since we already have the HT angle (74°) and the length of one side (fork leg length of 12"), we can use the sin trig function and a little algebra to get us length of the side that we plumb lined (the vertical line). sin (74°) = x/12" = 11.54"

Now that we have two sides of a right triangle, we'll use the Pythagorean Theorem to get the length of our last side for this part. √(12^2 - 11.54^2) = 3.29".

Great! We have all measurements and angles for inner/smaller triangle. Functionally, this would be like a 0 offset flatland fork, but we're talking offset forks, so let's move on to the 25mm offset...

From the smaller triangle we have a short side measurement of 3.29". 25mm == .98", so 3.29" + .98" = 4.27".

We already have the plumb line length of 11.54", so using the Pythagorean Theorem again, we can calculate the hypotenuse length of the "new" triangle. √(4.27^2 + 11.54^2) = 12.3".

Now we have all side lengths of the outer triangle (which represents the geometry for our 25mm offset). But we have only one angle, the right angle. Normal trig functions won't help here, so we have to move to the inverse trig functions. I used sin above, so I'll use the inverse sin now. sin-1 (11.54/12.3) = 69.75°.

Now that we have two angles of the 25mm offset triangle, we can calculate the final angle. 180° - 69.75° - 90° = 20.25°

And there you have it. Again, there are rounding errors, but you get the idea.

P.S: The short answer for a 32mm offset is an angle of 68.5° (replacing the 69.75° from before), so not much difference mathematically but definitely noticeable by the rider.

ETA: *If you take "classical" bicycle design, offset is actually the length *perpendicular* to the steering axis/HT angle. When you consider that, the functional HT angle will absolutely change with a different offset, which I think is what Steve was referring to. Not sure I care enough to figure that out right now, haha.