While it is simple to place a Lincoln penny in the tread groove of a worn tire and use Abe's likeness as a guide, we don't think Honest Abe knows what's best for today's drivers.
The Lincoln penny tread depth test has been touted for years to be a suitable method of determining when it's time to get new tires. It's based on the premise you're driving on legal tread depths anytime the top of Lincoln's head is obscured by the tread and that a tire's ability to grip the road isn't greatly reduced in adverse conditions (rain, slush and snow) until the tread wears to about 2/32" of remaining depth. It then maintains you're ready for new tires at 2/32" and can see the penny above Lincoln's head.
A driver's ability to control their vehicle depends on the traction between their tires and the road. Tires don't require tread designs or even much tread depth to deliver traction on dry roads. A practical example of this is the racing slicks used on stock cars and open-wheel racers that provide traction at over 200 mph. However, tires do require tread designs to generate traction on wet, slushy and snow-covered roads. Liquids can't be compressed and require time and energy to move them out of the way as our tires drive through them. Those same racing slicks would lose traction at amazingly slow speeds anytime something prevented them from maintaining contact with the road.
So a tread design is necessary to direct water and slush from between the tire and the road, as well as provide edges that bite into snow. But that's only half the equation; because we've seen that tread depth also contributes to how well the design does its job.
The air our tires encounter at highway speeds can easily be compressed and moved out of the way with relative ease. However the same isn't true of liquids. When water collects on the road surface during rainstorms, the water depth, vehicle speed and vehicle weight, as well as the tires' tread designs and tread depths collectively determine when and if the tires will be forced to hydroplane and how quickly they can stop a vehicle.
A typical passenger car tire has about twenty square inches of total footprint surface and begins with about 1/3" of tread depth. While the majority of the footprint surface is made up of the rubber that grips the road, the remainder is the void of the grooves that make up the tread design.
If rain and wet roads are a concern, you should consider replacing your tires when they reach approximately 4/32" of remaining tread depth. Since water can't be compressed, you need enough tread depth to allow the rain to escape through the tire's grooves. If the water can't escape fast enough, your vehicle's tires will be forced to hydroplane (float) on top of the water, losing traction and increasing stopping distances.
Additionally, if snow-covered roads are a concern, you should consider replacing your tires when they reach approximately 6/32" of remaining tread depth to maintain good mobility. You need more tread depth in snow because your tires need to compress the snow in their grooves and release it as they roll. If there isn't sufficient tread depth, the "bites" of snow your tires can take on each revolution will be reduced to "nibbles," and your vehicle's traction and mobility will be sacrificed.

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