Do-it-yourself snow tires

As we turn the corner into November, it’s getting to be the time of year when people in the northeast are preparing for winter. Covering swimming pools, pouring anti-freeze into pipes, and thinking about making an appointment to have snow tires put onto cars. Or, if you’re like me, you’re trying to think of a way to swap tires on your own in order to save a few bucks. For those of you who are not familiar with snow tires, they look just like regular tires, but can appear somewhat thicker. In trying to track down a new pair on my own, I was paying close attention to the diameter of a new set of wheels to ensure they were the same as my current pair. I began to think, why does this diameter matter so much? Surely it doesn’t have to be exact, tires wear down on their own over time, isn’t there room for error on the scale of a few centimeters? 

I learned that speedometers and odometers on cars such as mine make use of the rotational motion of the wheels to determine the overall speed of the car. A simplified diagram of an electronic speedometer is shown below:

Where a magnet in the wheel briefly comes in contact with an electronic sensor once every full revolution. This essentially measures the length of the period, or T; and from this the linear velocity can be determined. The computer on the car relates this measurement to the distance traveled because it is already preprogrammed with the radius of the wheels, and can extrapolate to define the velocity of a point on the outer wheel using a relationship similar to what we learned in class: v=(2πr)/T.

            If one were to install tires that were thinner or thicker than the original pair, the true radius of the wheels would be different than the car believes it is, and the calculated speed based on the measured T would be inaccurate. The same goes for the odometer, which uses the same function to keep track of total distance traveled. So, if I chose to replace my wheels with thicker ones, my cars odometer would underrepresent the total distance I travel, and my cars speedometer would display a speed slightly slower than what I am traveling. Thankfully, the computerized aspect of speedometers can be adjusted according to a change in the tire diameter, provided you have access to the proper equipment. 

            But, as a set of tires are used more and more, they wear down, and the overall radius of the wheel decreases slightly over time. So as a pair of tires is used, does the cars speedometer slowly accumulate error, overreporting the velocity, and the total distance traveled? The answer is yes. In fact, if you drive a car like mine with a 24-inch wheel diameter, losing even 2% of the radius, just ½ of an inch of worn rubber, can result in the same 2% change in the accuracy of the speedometer. This relationship can be seen using the equation v=(2πr)/T. If one were to decrease the radius value by 2%, while holding T constant, the magnitude of velocity would also decrease by 2%. The same is true for changing the period; a 2% decrease in T results in a 2% increase in the velocity. So, if one were to decrease r while the computer assumes that it is unchanged, the result would be a larger velocity value than the true value based on the constantly measured T. This means if the speedometer reads 60 mph while assuming r=12 inches, the car would actually be traveling more like 58.8 mph with true r=11.75 inches, based on the same measured value for T. 

Knowing this, the same effect is true if I were to purchase a set of snow tires with a larger radius than my current wheels. If I were to purchase 26-inch diameter wheels with snow tires, the change in actual radius would be on the magnitude of 8.3%. Using the relationship above I can estimate that if my speedometer were to show 60 mph, the car would actually be traveling 8.3% faster, or 65 mph. This inaccuracy could easily result in a speeding ticket.

            So, for those of you trying to track down a new set of tires, go the extra mile and visit a mechanic to have your speedometer adjusted if the diameter of your wheels changes. It might cost more up front, but it could help save you the steeper cost of a speeding ticket in the long run.

 

 

 

 

Sources:

- Attorneys, A. (2017, July 11). How Tread Wear and Tire Pressure Affects Speed. Retrieved October 24, 2020, from https://newyorkspeedingfines.com/tread-wear-tire-pressure-affects-speed/

- Woodford, C. (2020, January 06). How do speedometers work? Retrieved October 24, 2020, from https://www.explainthatstuff.com/how-speedometer-works.html