ALT-6 Gas Mileage and Tires
Tires can affect gas mileage in a number of ways. The most obvious would be an under inflated tire. This condition increases drag and friction requiring more effort to keep the wheel rolling and that requires the engine to work harder reducing mileage. This also creates heat as the side walls are flexing more often then they are designed to and heat leads to failure. Notice on an under inflated tire how they squat on the bottom, but at the same time they are normal on the top. Imagine this amount of flex taking place throughout the tire as it rotates. This builds up heat to a dangerous level very quickly.
The manual for your car will give what the manufacturer considered the best overall air pressure for the tire. Taking into consideration the weight of the car, handling characteristics with factory installed wheels and tires in place. The tire itself will have another air pressure listed on it showing the maximum safe pressure for that particular tire.
The pressure indicated on the tire will be the higher of the two, so naturally you would think the higher the air pressure the less drag, and you'll get better mileage. This may be true, but be careful, the car manufacture has done extensive testing to come up with their numbers. They look at the overall comfort and safety of the car and its occupants rather then the fail safe maximum pressure the tire can tolerate. I recommend following the car manufacturer's recommended pressure.
Increasing the size, circumference may also increase your mileage. But again this throws everything out of wack. Your speedometer and odometer will not read accurate. And again it may create unsafe handling characteristics as well. A much safer way would be to change the ring and pinion in the differential to a set with less reduction. You will still need to alter the speedometer drive to match, but except for some change in the power curve the handling characteristics should remain the same.
Tread pattern can affect mileage as well, for open highway long distance driving a less aggressive tread will give better mileage and less tire noise as well. Taking a mud and snow grip style tire to highway speeds will increase the friction as well as the noise level. Your mileage will drop and the life expectancy of the tire will decrease as well. Buy your tires to match the majority of your driving and follow the car manufactures recommendations and you will be able to drive with confidence knowing you are doing all you can to remain safe.