The GSP9700 Vibration Control System includes Hunter's exclusive Road Force Measurement System to help detect potential tire uniformity causes of vibration that are not balance-related. This system utilizes a "road roller" which applies up to 1,400 pounds (635 kg) of force against the wheel and tire assembly to measure their combined uniformity. This simulated road force test helps verify if the assembly is "round" when rolling under load.
The GSP9700 Vibration Control System can also measure lateral and radial rim runout (out of roundness or side-to-side movement) to identify and separate wheel runout from tire runout. The system then calculates the contributions of the wheel and the tire to a potential vibration and presents the service specialist with easy-to-follow instructions on the appropriate corrective actions.
So air pressure can effect the contact patch which can be change the effective shape Of the tire under load, the runnout which can be changed by lower or higher air pressure will effect the balance as well.
Whether or not you can tell the difference on your vehicle or not depends on your specific vehicle as well as the percentage of tolerance that you balanced wheel and tire combination is within, which is pretty small in reality but can make a difference. Generally the more high performance car, combined with more feedback transmitted through the steering to driver, will let you know on a vehicle.
I have been able to tell on BMWs and even more on Porsche when tires are a few psi low than usually kept and have had tires have balance issues that could be corrected fully by adjusting the air pressure, and other time only partially by adjusting air pressure.
Hunter, seems to say in their two paragraphs up there that air pressure can effect runout and runnout can effect balance.
I wonder if you guys know more that the excepted experts at building tire balance machines.
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