Special Report: Walkable Streets

Vehicle Speed and Stopping Distance

Vision Zero calls for a commitment to 30 km/h speed limits on most city streets in part because a vehicle's stopping distance increases dramatically with its speed.

By Ryan McGreal
Published August 29, 2016

Back in April, I unpacked some of the physics behind the Vision Zero commitment to 30 km/h speed limits. More recently, Michelle Martin followed up with a thoughtful look at the cognitive psychology factors, particularly the reduction in peripheral vision at higher speeds.

But there's another component to vehicle speed that should push us toward embracing lower vehicle speeds: the stopping distance of a moving car. Obviously, a big part of making roads safer is preventing crashes and collisions, and a shorter stopping distance means it is more likely a driver can brake to avoid colliding with another driver, a cyclist, a pedestrian, or something else.

The general way to calculate braking distance is through the formula:

distance = v^2/2μg

where v is the initial velocity, μ is the coefficient of friction (between 0 and 1) and g is the gravity of the earth.

But stopping distance also includes the time the driver spends thinking before beginning to apply the brakes. A highly skilled, alert driver can start to brake in a little over half a second, but the average driver will take at least a second and some drivers, including elderly drivers with slower reaction times, can take 1.5 seconds, two seconds or longer to react.

For dry asphalt, the coefficient of friction is usually around 0.7, though it is higher with anti-lock brakes. And of course, the earth's gravity is 9.8 metres per second per second.

So if we conservatively assume a one-second thinking time and a 0.8 friction coefficient for dry asphalt, we can calculate the total vehicle stopping distance at various speeds.

Vehicle Stopping Distance by Speed, Dry Asphalt
Speed (km/h) Distance (m)
Thinking Braking Total
10 2.78 0.49 3.27
20 5.56 1.97 7.52
30 8.33 4.43 12.76
40 11.11 7.87 18.98
50 13.89 12.30 26.19
60 16.67 17.72 34.38
70 19.44 24.11 43.56
80 22.22 31.49 53.72
90 25.00 39.86 64.86
100 27.78 49.21 76.99

In the stacked bar chart below, the blue bar is thinking distance and the red bar is stopping distance.

Chart: Vehicle Stopping Distance by Speed, Dry Asphalt
Chart: Vehicle Stopping Distance by Speed, Dry Asphalt

Between 30 and 40 km/h, the stopping distance increases by 50 percent!

If the asphalt is wet or icy, the coefficient of friction is significantly reduced. Let's look at the same vehicle speeds but with a friction coefficient of 0.4:

Vehicle Stopping Distance by Speed, Wet Asphalt
Speed (km/h) Distance (m)
Thinking Braking Total
10 2.78 0.98 3.76
20 5.56 3.94 9.49
30 8.33 8.86 17.19
40 11.11 15.75 26.86
50 13.89 24.60 38.49
60 16.67 35.43 52.10
70 19.44 48.23 67.67
80 22.22 62.99 85.21
90 25.00 79.72 104.72
100 27.78 98.42 126.20

Again, in the stacked bar chart below, the blue bar is thinking distance and the red bar is stopping distance.

Chart: Vehicle Stopping Distance by Speed, Wet Asphalt
Chart: Vehicle Stopping Distance by Speed, Wet Asphalt

At a higher vehicle speed, not only does a vehicle have more kinetic energy, but it also takes a much longer distance to come to a stop, reducing the chance that the driver will be able to avoid a collision in the first place.

Combined with the fact that peripheral vision decreases, as speed goes up, the evidence is overwhelmingly clear: if we want streets that are safe for all the people using them, including people walking and people biking, we need to reduce vehicle speeds.

This is why the global Vision Zero movement is calling for a 30 km/h speed limit. At higher speeds, it is simply not possible to make our streets safe and inclusive.

Calculate Stopping Distance

If you want to play around with the stopping distance formula, the following form will calculate thinking, braking and total stopping distance based on the values in the input boxes above it.

Speed (km/h)
Thinking Time (s)
Friction Coefficient (0-1)
Thinking Distance (m)8.33
Braking Distance (m)4.43
Total Distance (m)12.76

Ryan McGreal, the editor of Raise the Hammer, lives in Hamilton with his family and works as a programmer, writer and consultant. Ryan volunteers with Hamilton Light Rail, a citizen group dedicated to bringing light rail transit to Hamilton. Ryan writes a city affairs column in Hamilton Magazine, and several of his articles have been published in the Hamilton Spectator. He also maintains a personal website and has been known to post passing thoughts on Twitter @RyanMcGreal. Recently, he took the plunge and finally joined Facebook.

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[ - ]

By KevinLove (registered) | Posted August 29, 2016 at 13:37:42

Although 30 km/hr is a big step forward, lower speed limits are not enough.

What is necessary is to separate and protect vulnerable people from dangerous machinery. Every factory in Hamilton does this, because the Ministry of Labour really does practice Vision Zero.

What this means in practice ranges from car-free zones to physical guards of steel and concrete to unravelling the transportation routes of people vs. car drivers.

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By Ryan (registered) - website | Posted August 29, 2016 at 14:09:29

It's interesting to play around with the stopping distance calculator by adjusting the thinking time. For example, if we leave the friction coefficient at 0.8 and set the speed at 50 km/h, here's how the thinking distance changes based on how quickly the driver reacts:

-----------------------------------
Thinking Time and Reaction Distance
-----------------------------------
Time (s)  Distance (m)
          At 30 km/h     At 50 km/h
-----------------------------------
    0.6         5.00           8.33
    0.8         6.67          11.11
    1.0         8.33          13.89
    1.2        10.00          16.67
    1.4        11.67          19.44
    1.6        13.33          22.22
    1.8        15.00          25.00
    2.0        16.67          27.78
-----------------------------------

For slow-reacting drivers, the difference in thinking distance between a car going 30 km/h and a car going 50 km/h is huge: an extra 10 metres (33 feet) at a 1.8 second reaction time and an extra 11 metres (36 feet) at a 2.0 second reaction time!

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By Michelle Martin (registered) - website | Posted August 29, 2016 at 19:10:48 in reply to Comment 119897

And of course we know that reaction time is affected by obvious factors, like alcohol/drug use or using cell phones, GPS's, radio dials... And we know that fatigue will slow reaction time, along with distraction from worries, or to-do lists.

The really fascinating (and scary) thing about reaction time is that so many factors can affect it. Environmental, or external factors can slow reaction time; for example, did you know that simply driving on a winding road slows our reaction time, as we have had to devote a larger share of our attention to steering than we would on a straight road (hello, suburban crescents and drives). This article makes for a fascinating read: http://www.visualexpert.com/Resources/re...

Comment edited by Michelle Martin on 2016-08-29 19:11:13

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By mdrejhon (registered) - website | Posted August 30, 2016 at 12:54:28

I have a comment: Patience level of drivers

  • There are drivers find it fun and calm to drive slowly through the cacophony of downtown core, just merrily inching slowly forward and enjoying the sun, glancing at the scenery, incidentally noticing new businesses.

  • And there are drivers find it highly stressful, the sensory overload, rushing for an appointment, being used to a quicker drive in the past, and getting annoyed at the longer drive, accelerate quickly to the next car and stop quickly, etc.

There's a continuum in between.... One big side effect of converting an arterial (50kph) into a local road (30kph) is the status quo and change feels difficult. For the scenario of a theoretical King 30kph local car lanes next to LRT (slower speed compensating for the moving cars being more frequent adjacent to revitalized King sidewalks) it will likely piss off a lot of impatient drivers who haven't yet chosen to be patient or taking alternate routes -- it can take a long adjustment period (people taking other routes, e.g. widened RHVP, adjusted Barton, etc).

Hopefully the construction detour period is well-designed to let people become used to alternate routes.

Driving my car through a clogged revitalized business corridor is generally preferable (for me and a huge many others) than driving a stop-n-go rush-hour 401, but this may not be the case for every single individual, in what situations they get stressed during driving.

Comment edited by mdrejhon on 2016-08-30 12:59:07

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By peterrush1 (registered) | Posted June 13, 2017 at 22:35:22

so you can look at the distance formula https://www.studypug.com/algebra-help/li... or you can look at the cost of society of a slow commute/transportation. It's difficult to quantify the cost of a human life, but we can quantify the cost of longer commute.

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