Deer Physics and Winter Weather

As winter kicks into full gear, rural communities like Hamilton will see an increasing number of deer active on roadways. Hunting season tends to result in deer moving around frequently, which can be especially bad when combined with increased hours of darkness in the winter, where deer are harder to see while driving. Last year in New York, according to AAA, there were an estimated 60,000-70,000 accidents involving deer, and some NY repair shops report three times as many deer-related repairs in their shops in winter months compared to other seasons. Considering the relationship of cars and deer--an obstacle on the road--has many connections to physics!

Braking and Friction:

When you see a deer on the road, your ultimate goal is to stop your car before reaching the deer. Thanks to modern advancements, most cars have anti-lock braking systems, which are significantly more effective than traditional breaking at quickly stopping your car. With anti-lock brakes, the car rapidly and repeatedly “presses” the brake, rather than just pressing and holding the brake. Anti-lock brakes work well because they allow your car to maintain static friction to stop. With normal braking, the car would stop via kinetic friction, as the wheels are locked and the car is sliding (rather than rolling). The static coefficient of friction is greater than the kinetic coefficient of friction, which explains why anti-lock braking can be so much more effective than traditional braking.

Friction and Weather:

Now let’s consider how the weather could play into our interaction with the deer. Under normal conditions, we can estimate the static coefficient of friction to be 0.70 for our car’s tires on dry asphalt. However, this same car may have a static coefficient of friction of just 0.40 in rainy conditions (and even lower in snow and ice)! When braking, the force of friction between the car tires and the asphalt is what stops the car. The force of friction is equal to the coefficient of friction, μ, times the normal force. The normal force for a car traveling in the x-direction on a flat surface should be equal to the force of gravity (mg). Therefore, normal force is not impacted by the dryness or wetness of the road. Considering our different static coefficients of friction:

Dry: F(fr)=0.70*F(N)

Wet: F(fr)=0.40*F(N)

Above, F(N) is the same magnitude in both cases. Thus, wet roads have a reduced force of friction, and therefore have an increased stopping distance. That means it's especially important to be vigilant for deer in the distance when driving on wet roads!

Speed and Collisions:

In the unfortunate case that you are unable to stop before the deer, let’s consider the resulting collision. If we treat the deer as a “wall” (in this case, it won’t move), we can examine the effect on the car at different speeds. Let’s consider a 1300kg car that stops over 0.05s when colliding with the deer.

If traveling at 25m/s (about 55mph):

Momentum (p) → p=m*v → p=1300*25 → p=32,500kg*m/s

Force (F) → F=m*a, where a=delta v/delta t

a=(25-0)/(0.05-0) → a=500 m/s^2

F=1300*500 → F=650,000N

If traveling at 15m/s (about 35mph):

Momentum (p) → p=m*v → p=1300*15 → p=19,500kg*m/s

Force (F) → F=m*a, where a=delta v/delta t

a=(15-0)/(0.05-0) → a=300 m/s^2

F=1300*300 → F=390,000N

Recalling Newton’s Third Law, for every action there is an equal and opposite reaction, the force exerted by the car on the deer will equal the force exerted by the deer on the car. Look at those two forces above….. A difference of just 10m/s has a difference of 260,000N!!!! This is good to remember when driving during times of heavy deer traffic, as driving slow can significantly reduce the damage done to your car in the event of a crash. Just because most of the speeds near Hamilton are 55mph doesn’t mean you have to drive that fast!

This post inspired by the news video: https://cbs6albany.com/news/local/earlier-darkness-can-mean-an-increase-in-car-vs-deer-collisions

Coefficient reference: http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/frictire.html