Converting wheel angle/degrees to mm

[Dylanamus]

Many aftermarket alignment kits show the adjustment range in degrees, so I thought I'd share the work I did on converting degrees to mm (seeing as most aligners report toe in mm, not degrees). Enjoy. :thumbsup:


Step 1. Calculate the Radius (in mm) of the wheel and tyre together.

Formula (2 * tire width * aspect ratio / 100) + (wheel diameter) = wheel + tyre diameter

Executing first equation:

Wheels are 15" and tyres are 195/50R, so (2 * 195 * .5) + (15 * 25.4) =
195 + 381 = 576

576/2 = RADIUS = 288

Step 2. Calculate the angle each side wheel + tire: multiply the sin of 1 degree by the radius of the rim + tyre, to give you the mm deviation from parallel with the centreline (CL)

Formula arcsin(radius) = radians per mm

Executing second equation:
sin(1) (degree) or sin(pi/180) (radian) = 0.017452

0.017452 X 288 = 5.026293mm

Conclusion For my wheel/tyre combo every 5.026293 mm equals one degree.


http://i50.photobucket.com/albums/f304/Dylanamus/fordeelan.jpg


I'll use the range promised by an ebay kit as an example (as below)

Adjustment range: -2.00 degrees to +5.00 degrees
Adjustment range:-10.05 mm to +25.13 mm

[omgzilla]

Nice work mate!

Could come in handy.

[CoZZm0]

Maths is great, but is it right? Using that it would mean with my recent wheel alignment with 185/60/14 tyres, i have got over 40mm toe in, per side. Report states ~6deg one side and ~7deg other side), on the rear of my car. Now that figure to me would seem to be not possible and would be *extremely* obvious. Also factory manual states the alignment tolerances in degrees, mm and inches and lists the following:

rear toe: -6' to 18 deg = -1 to 3mm = -0.04 to 0.12in

Now assuming that those numbers are all relative conversions of each other for whatever type of alignment equipment was being used that would put my alignment as reported for the rear to be within tolerances.

Does your formula relate specifically to the adjustment range of a product, rather than to a conversion based on specifications on a wheel alignment sheet?

Sorry if the question is stupid, but i'm just a little confused, maybe i'm interpreting the data wrongly or applying it wrongly?

[Dylanamus]

Maths is great, but is it right? Using that it would mean with my recent wheel alignment with 185/60/14 tyres, i have got over 40mm toe in, per side. Report states ~6deg one side and ~7deg other side), on the rear of my car. Now that figure to me would seem to be not possible and would be *extremely* obvious. Also factory manual states the alignment tolerances in degrees, mm and inches and lists the following:

rear toe: -6' to 18 deg = -1 to 3mm = -0.04 to 0.12in

Now assuming that those numbers are all relative conversions of each other for whatever type of alignment equipment was being used that would put my alignment as reported for the rear to be within tolerances.

Does your formula relate specifically to the adjustment range of a product, rather than to a conversion based on specifications on a wheel alignment sheet?

Sorry if the question is stupid, but i'm just a little confused, maybe i'm interpreting the data wrongly or applying it wrongly?

Degrees are always the same - 360 degrees in a full rotation. You might have applied the math incorrectly to your situation? It's important to understand the way the aligner measured your toe. That said, I found my rear wheels were 23mm toe out per side and that isn't EXTREMELY obvious to my eye, because the side skirts don't represent a perfect parallel to the centreline.

Either way 6 or 7 degrees is probably heaps too much toe for a street car (90 degrees would be sideways toe! - Think of it that way). Maybe ask your aligner how/usig what method they measured the toe and if they could provide that in mm?