This is such a good question! Truck bed—or tonneau—covers help improve the aerodynamics of your truck by changing the way air flows over the cab and across the bed, which can help improve your gas mileage to some degree.
Without a cover, the bed of the truck—especially when the tailgate is up—acts more-or-less like a bucket, catching air as you drive and causing drag. It is this drag that then forces the engine to work that much harder, consuming more fuel. A good truck bed cover that seals properly allows air to pass over your truck without causing drag.
That being said, don’t expect a tonneau cover to drastically alter your gas mileage—the effect is really quite marginal and largely depends on the type of truck you drive, your driving habits, and the cover itself.
If you want to see a marked improvement in your gas mileage, a truck bed cover is a good place to start, but you should also make sure your truck is properly aligned, the air filter is clean, and the tires are at the correct pressure—all of these combined can significantly improve fuel economy.
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