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a spat ahead of the tire would be of benefit by reducing the amount of air that will pass over the rolling tire, thereby reducing the air resistance on the rotating tire.
The rear of the tire spats seem like they would restrict the air from leaving the rotating tire, causing unneeded drag.
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If you think about what a tire is doing, the point in contact with the ground is stationary (at least instantaneously), not spinning. The point on top of the tire is moving at twice the velocity of the vehicle.
Just in front of the point in contact with the ground, the air is being squooshed out, while just behind that point a vacuum is created that must be filled by air rushing around to the back of the tire. Both squooshing the air out in front of the contact patch, and a vacuum behind it, will consume engine power...
Maybe the whole point of the spat is not so much to keep air off the tire, but to create a partial vacuum to make it easier to squoosh the air out, and diverting air around to the back of the tire to make it easier for air to fill the vacuum created by that part of the tire leaving the ground.