Rear wheels are at the receipt of power from the engine in the form of Torque being generated. And larger sizes will ensure comeover of torque requirement in heavy duty applications. Traction force will be higher as compare to smaller wheels at receipt of power.
The back wheel is used for traction and because of bad terrain the wheel must be bigger to ensure good grip. The front wheel is only used for steering and at low speeds need not to be bigger.
You however get 4 wheel drive tractors with big wheels in front as well.
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Another reason for the smaller wheels is to have it running down hill all the time.
Only joking.
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Aid to the farmer using the tractor. It improved his site line in seeing the rows as a big wheel would be an obstruction.
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Allis Chalmers used fairly large front wheels and I believe Massey-Harris had one where the wheels were equal. But, for the most part, there wasn't much load on the front and farmers need to be able to cultivate row crops. So, if you run small narrow front wheels (or a single tricycle wheel), you got some distribution of the compaction, i.e., fat tire w/load, thin tires w/o load, fat tire with load. Some manfacturers opened up the front wheels to the same width as the back and that worked great when you took them out on the highway at 40 mph, but it was harder to steer when you were trying to get into corners without taking out fencerows in the process.
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Front tire smaller? Sight line is good answer, farmers like to cultivate from any direction and old ways are caried on too; farmer used less energy to turn the smaller wheels without power assist steering.
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