OK, here's my Square Tire story: BTW, this happened several decades ago.
This is going to require some technical background.
When you look at the tread on a tire, you should notice that it repeats itself. You should also notice that the repeated elements aren’t all the same size. We call those elements “pitches” and the pattern the “pitch sequence”. It’s there to spread the noise and vibrations over a frequency range, rather than them all occurring at the same frequency. Spreading it over a range makes it harder to discern from the background noise/vibration.
I got a call from Ford that they needed some help understanding a problem they discovered. After a great deal of work, they had isolated the problem down to a vibration in their full size cargo vans, with diesel V8’s, with lockup transmissions, and 4.10 rear axles AND our tires at 42 mph when crowding the throttle (that means just pressing slightly on the accelerator pedal). Remove any one element and the problem wasn’t really there.
So we brought a team of vibration experts and FORD demonstrated the problem. Sitting on the floor of the van (No seats! It was a cargo van!), the unsupported side panels would vibrate like a kettle drum – and just as loud!! It would literally drive you insane with how loud it was.
They said they could do that with ANY set of our tires, but other makes/models didn’t do it at all. And of course, changing any of the other things also didn't produce the vibration.
To make a long story short, we were producing tires that had a high radial 4th harmonic because the pitch sequence sort of repeated itself every 90°. That 4th harmonic was combining with the 4 pulses per engine revolution (Worse on a diesel) and the lock up transmission, and the 4.10 gear ratio to produce a vibration that the side panels would naturally resonate at – and that occurred at 42 mph. Crowding the throttle made the engine pulses stronger without causing excessive vibrations in other frequencies, which disguised the problem.
Once we figured out about the 4th harmonic - and before we talked to Ford about it, our sales guy, who was one sharp cookie, realized we would lose business if we didn’t act quickly, so he had our engineers design molds with a pitch sequence that was more random, got the molds delivered in 60 days. and by the time we could sort this all out with Ford, we were delivering the new product. He also instituted a policy that if any consumer complained of such a vibration, we would overnight FedEx a set of tires from the new production to the consumer’s nearest dealer and exchange old for new free of charge.
Crisis averted!
To this day, I am amazed the sales guy anticipated the problems that the company was going to get into and figured out a way to fix them BEFORE they actually became problems! He eventually became a VP.
Now some of you may be aware that changing an OE part requires a re-qualification – and that takes time – AND – changing an OE part without informing the vehicle manufacturer is likely to get you disqualified from supplying ANY parts. EXCEPT that you are allowed to change certain things that aren’t covered by the qualification testing, and this pitch sequence thing was one of them. We gave several sets of tires to Ford for their testing and not only was the problem solved, but the new tires performed exactly like the old ones.