Tires

For any vehicle, it stands to reason that smaller diameter tires will result in higher engine RPM's at the same speed. It also seems to me that the odometer should read just as you report, less distance traveled for the smaller diameter tire. The odometer reading is based on counting tire revolutions. It is calibrated to determine distance based on the number of revolutions the tires turns. The tire with the smaller diameter has not traveled as far at the same number of revolutions as the larger diameter tire.

Both of these questions refer to changing tire sizes and the resulting affect on fuel economy. In both cases, we must assume that the "tall" tire and the "short" tire have a similar tread compound. In each case, switching to a tire with a smaller diameter can improve the fuel economy of a vehicle by 1) lowering the vehicle which will reduce the aerodynamic drag and 2)reducing the total weight of the tires and wheels on the vehicle. But, in order for the engine to turn over the same RPM's at any particular road speed, the final drive ratio must be adjusted for the smaller diameter tires. Failure to adjust the gearing will give you a false indication of savings (the odometer will say the vehicle has gone more miles that it really has gone) and the higher engine RPM (at the same speed) will actually burn more fuel than before.

Before changing tire sizes from the original on any vehicle, I strongly suggest checking with the vehicle dealer or manufacturer to see what is and is not recommended. A larger tire may rub something under the fender. Any change in tire diameter will effect gearing and odometer / speedometer readings. Know all the issues before making a change.

It's entirely possible the vibration is coming from the drive axle(s). It could be caused by balance or runout on one or more tires, wheels, hubs, etc. A big flatspot from brake lockup can cause this. The reason it happens only at certain speeds is at that speed the problem component is shaking at just the right frequency to match a natural resonance in the truck. The most common thing we see is high rear runout (from the combination of a tire and wheel) setting off the frame rails' natural tendency to bend in the middle, or "beam". This kind of shaking is supposed to be controlled by the truck's shocks and bushings. But on a high mileage truck, these items are probably pretty worn.

If it was my truck I'd go to a good tire shop and ask them to check rear tire runout ON THE TRUCK. Any up in the 0.100" range are suspicious. If they find one or more high ones, there are tricks they might be able to use besides simply throwing on new tires. They will also be able to check for high runout wheels, which are pretty common, especially steel wheels. If there are no high runout assemblies, they could go for balance. But that would tell me something is wrong with the truck. It would be very unusual to have to balance drive tires that have good runout.