Car Lengths

Exercise

You are driving on the highway at a speed of 60mph. An emergency occurs and you must slam the brakes. How many car lengths should you allow in front of you to ensure you will never hit a stationary object? How does that change if there is less friction in rain or snow?

 

Pre-requisites

There are pre-required concepts for this. To consider the facts on this matter, you must be familiar with the concepts of speed, acceleration, force, and friction. You must also know that 60mph is the same speed as 88 feet per second and that gravity on Earth is 32 feet per second per second. Assume the coefficient of friction on a normal day is 0.4 between car tires and asphalt while skidding.

 

Facts

When the emergency occurs, your brain needs to first recognize the event, make a decision, then send a signal via nerves in your body to your foot to activate the brake pedal. This process takes around 0.2 seconds. In that time, your car will move around 17.6 feet. Conveniently, this is around 1 “car length.”

Next, the brakes in your car need to activate. Assuming your anti-lock brake system is inactive, and you are in a typical passenger vehicle with a fluid brake system, it is safe to assume your brakes engage in another 0.2 seconds. Your car will go another 17.6 feet.

Last, the car tires will violently scrape against the ground (skid) to a stop. Assuming dry conditions and a coefficient of friction of around 0.4 for tires-and-road, the car will go a final 302.5 feet.

In total, your car may travel a total of 337.7 feet before coming to rest.

When it rains or snows, we may assume the coefficient of friction to be close to 0.2. In that case, your car will travel 1245.2 feet before coming to a complete stop.

Assuming a car is around 18 feet long, you may travel around 19 car lengths on a normal day by slamming your brakes. In rain or snow, that number increases to 69 car lengths.

 

Thoughts and Opinions

An unspecified amount of time ago, I was involved in a single-car accident with some of these same conditions. What was different was I did not stop, and I did strike the object.

Why do they say you need to travel “5 car lengths” behind a person on the highway if you need almost 20 car lengths to stop?

The wording of the question is very deliberate: these answers are true if you have a stationary object you are trying to avoid hitting.

When I was in my accident, I struck a large rock (about 3 feet tall, a few hundred pounds of demolished asphalt). It was road debris that fell out of the back of a truck. Because it was 5am and dark, it blended in with the road and I did not react at all, instead striking the stationary rock at a speed of at least 88 feet per second head-on. It tore a hole in the engine. I am blessed to be alive today to share these details.

Had I seen the rock, it would only take the length of around 1.3 football fields or 19 car lengths to make a decision to save my car and my life.

In normal circumstances there are not stationary objects on the road in front of you, there are moving objects. Assuming everybody follows the same rules of the road, then only the first two effects are relevant. For cars alone, you would only need 2 car lengths accounting for reaction time and the brake system time. Trucks on the road use air brake systems which take longer to engage. On average, 5 car lengths is a good rule for the everyday driver in mixed traffic.

 

Feel free to email me with your thoughts and opinions on this matter at andrew@ahogan.org.