112 pcd, c/o Google

For five holes, measure the centre distance between two adjacent holes and divide that number by 1.175.

Martin.

three randomly positioned points on a circle.

Yes, but simultaneous equations might be needed if one does not know the subtended angles? Only need two points if the subtended angle is known.

You can buy a little gadget to measure wheel bolt/stud PCD or as others have said measure distance between two holes and then put that into one of the online PCD calculators.

You need to know what you are doing though as I had a client who bought a set of custom made wheels with an enlarged offset for his Bristol and he got the PCD wrong so had to scrap the wheels. I did bore one out to check the correct PCD to my measurements not his.

Edited By JasonB on 28/11/2016 07:59:45

Measure with calipers:

PCD = (diameter of centre hole) + (diameter of one wheel nut hole) + 2*(distance between centre and wheel nut hole.)

The same will work for the vent holes though they will be harder to measure.

Yes, yes, yes. Even Euclid would have used simultaneous equations, if the three points were truly random. Need two equations to solve with two unknowns. Not actually difficult, as a mathemetician, but just necessary.

'All' Euclid did was to give the unknowns arbitrary values and develop a formula from x, y, z, etc algabreically and prove it geometrically. The proof meaning that it worked for any measured values you might choose. He was a great mathemetician of his day, but whether he actually worked them all out himself, as the first to ever do that, is questionable. Some were doubtless simple (or complex) proofs of other's already practical knowledge. He actually documented all the proofs as a record at that time. He did get one or more wrong, mind?

This problem is made simple by knowing the number of points around the PCD. The answer can be documented to as many decimal places as you wish, but Euclid didn't work in decimals, did he? Halves, quarters eighths, etc would have been his units for values less than units still? But Euclid's Theorems did not require units to be proofs. Inserting values into theorems is still required to solve the problem, to arrive at a definitive answer for any set of data points – to however many significant figures you care to work to.

Quickly looking at the three random hole problem suggests to me three "easy" ways of solving the problem: Draw it out, use trigonometry and final co-ordinate geometry. They all use the 'perpendicular bisector'. I personally would use the co-ordinate geometry route if only out of elegance.

JA

Edited By JA on 28/11/2016 11:51:12

Muzzer

That is interesting, but I have never seen a wheel/tyre balancing machine that did anything other than use a tapered centering plug to pick up with that central bore.

Friend of a friend needs to be extremely careful in how he has spacers made and fitted if he doesn't want sheared wheel bolts/studs and then the wheel parting company at speed.

The wheel should be located on a spigot that forms part of the hub, as it will be as originally fitted on the car by the manufacturer. If you are making spacers, the spacer needs to be bored with a female spigot housing on its inside face that has a tight fit to the hub spigot. In turn the spacer also needs to have a hub centric spigot machined on its outer face to locate snugly in the wheel centre.

Both female and male spigots on the spacer need to be exactly co-centric with each other, or it can set up a centrifugal imbalance which can be impossible to balance out, and be dangerous as it puts a lot of loading force on wheel bearings and ball joints.

ALL of the wheel bolt /stud clamping effort is designed to be only for that, in other words neither the studs/bolts or their cone shaped mating surfaces are designed to take any lateral shear force, the hub to wheel spigot should take care of that.

If you know all this already, my apologies.