Special Report: Walkable Streets

Why Vision Zero Calls for a 30 km/h Speed Limit

The short answer is: because physics. For the longer answer, we need to review some classical mechanics you may remember from high school.

By Ryan McGreal
Published April 18, 2016

One of the core principles of the Vision Zero approach to traffic safety is that on streets where people on foot cross paths with people in automobiles, it is imperative that the automobiles maintain a speed low enough to prevent death or serious injury in the case of a collision. This is generally taken to mean maintaining vehicle speeds at or below 30 km/h.

Some readers may wonder why this particular speed is so often recommended - and adopted - by cities committing to Vision Zero. The short answer is: because physics.

For the longer answer, we need to review some classical mechanics that you might remember from high school.

Kinetic Energy

The kinetic energy of a moving object is the energy the object possesses as a result of being in motion. Obviously, an object sitting at rest does not have any kinetic energy, but once it starts moving, it has kinetic energy - and when it is moving faster, its kinetic energy goes up.

But there is something very important about the relationship between an object's speed and its kinetic energy. It is not a linear relationship, in which a certain increase in speed produces an equivalent increase in energy. Instead, it is a quadratic relationship: if you double an object's speed, its kinetic energy doesn't double, it roughly quadruples. Likewise, if you quadruple its speed, its kinetic energy increases roughly 16-fold.

The formula to calculate kinetic energy is as follows:

Kinetic energy (Joules) = 1/2 X mass (kg) X velocity (m/s) squared

Let's apply the formula with a real vehicle at various speeds. My car is a 2012 Honda Civic sedan, which has a curb weight of 1,198 kg (2,641 lb). The following table calculates its kinetic energy at various speeds between 10 km/h and 100 km/h.

Kinetic Energy by Speed, 2012 Honda Civic Sedan
Curb Weight Speed Kinetic Energy (J)
(lbs) (kg) (km/h) (m/s)
2,641 1,198 10 2.8 4,622
2,641 1,198 20 5.6 18,487
2,641 1,198 30 8.3 41,595
2,641 1,198 40 11.1 73,947
2,641 1,198 50 13.9 115,542
2,641 1,198 60 16.7 166,380
2,641 1,198 70 19.4 226,462
2,641 1,198 80 22.2 295,787
2,641 1,198 90 25.0 374,355
2,641 1,198 100 27.8 462,167

Here's how that looks when you plot the kinetic energy (Y axis) against vehicle speed (X axis):

Chart: Kinetic energy by speed, Honda Civic
Chart: Kinetic energy by speed, Honda Civic

As you can see, the kinetic energy increases in a curve, not a straight line. That is what is meant by calling kinetic energy a quadratic formula rather than a linear formula.

Another important thing to note is that heavier vehicles increase kinetic energy even more dramatically. The following table calculates kinetic energy at the same speeds for a Toyota Camry, a popular mid-sized sedan.

Kinetic Energy by Speed, Toyota Camry
Curb Weight Speed Kinetic Energy (J)
(lbs) (kg) (km/h) (m/s)
3,240 1,470 10 2.8 5,670
3,240 1,470 20 5.6 22,680
3,240 1,470 30 8.3 51,029
3,240 1,470 40 11.1 90,718
3,240 1,470 50 13.9 141,748
3,240 1,470 60 16.7 204,116
3,240 1,470 70 19.4 277,825
3,240 1,470 80 22.2 362,874
3,240 1,470 90 25.0 459,262
3,240 1,470 100 27.8 566,990

And the following table does the same calculations for a Chevrolet Silverado, a popular full-size pickup truck.

Kinetic Energy by Speed, Chevrolet Silverado
Curb Weight Speed Kinetic Energy (J)
(lbs) (kg) (km/h) (m/s)
4,567 2,072 10 2.8 7,992
4,567 2,072 20 5.6 31,968
4,567 2,072 30 8.3 71,929
4,567 2,072 40 11.1 127,874
4,567 2,072 50 13.9 199,803
4,567 2,072 60 16.7 287,716
4,567 2,072 70 19.4 391,613
4,567 2,072 80 22.2 511,495
4,567 2,072 90 25.0 647,361
4,567 2,072 100 27.8 799,211

As you can see, the sheer physics involved makes the risk outcome for pedestrians pretty inevitable. At vehicle speeds below 30 km/h, the risk of fatality for a pedestrian struck by a vehicle is very close to zero. As speeds increase, fatality risk increases quadratically according to the rising kinetic energy of the faster-moving vehicle.

I should note here that the vehicle's mass also contributes significantly to its kinetic energy. The following chart shows the kinetic energy at various speeds for all three profiled vehicles, with the addition of the curve for a person on a bicycle for comparison:

Chart: Vehicle Speed and Kinetic Energy
Chart: Vehicle Speed and Kinetic Energy

That Silverado has 1.7 times the mass of the Civic. At any given speed, it also has 1.7 times the kinetic energy.

Vehicle Speed and Pedestrian Fatality Risk

The following chart from World Resources Institute shows how that risk of fatality changes as speed goes up.

Chart: Pedestrian death risk by vehicle speed
Chart: Pedestrian death risk by vehicle speed

This is clearly and abundantly documented in road safety research. The classic source is a 1997 UK Department of Transportation Study titled Killing Speed and Saving Lives, which found that pedestrian fatality risk rose from just 5 percent when the vehicle was going at 32 km/h (20 mph) to 45 percent when the vehicle was going at 48 km/h (30 mph) and a staggering 85 percent when the vehicle was going 64 km/h (40 mph).

Likewise, a 1999 research review by the United States Department of Transportation National Highway Traffic Safety Administration surveys a wide sweep of traffic studies and concludes:

Reductions in vehicle speeds can have a very significant influence on pedestrian crashes and injuries. Pedestrians suffer much more serious injuries when struck by high-speed vehicles than when struck by vehicles going more slowly. Also, many pedestrian crashes would be prevented entirely had the vehicles been traveling more slowly, since driver and pedestrian would have had more time to perceive the risk and react.

Incidentally, the report also notes that speed limit reduction is more successful when accompanied by physical changes to the street to induce traffic calming:

The accumulated weight of evidence from studies of traffic calming is that pedestrian injuries and total, or motor vehicle, crashes and injuries are closely related. Traffic calming which reduces motor vehicle crashes and injuries also reduces pedestrian injuries and severities.

So it is particularly distressing that the City of Hamilton has nominally committed to Vision Zero but refuses to commit to the 30 km/h speed limit that classical mechanics tells us we need to maintain to make our streets truly safe.

Instead, we are compromising with a more modest reduction to 40 km/h - and only in selected locations - on the shaky assumption that it will be more politically palatable to people who are inclined to favour their convenience over other people's safety.

40 km/h speed limit signs ready to be deployed (Image Credit: City of Hamilton)
40 km/h speed limit signs ready to be deployed (Image Credit: City of Hamilton)

The basic problem with this half-measure is that there is no arguing with the laws of physics.

Calculate Kinetic Energy

If you want to play around with the Kinetic Energy formula, the following form will calculate kinetic energy based on the values in the input boxes above it.

Weight (lb)
Weight (kg)
Speed (km/h)
Speed (m/s)
Kinetic Energy:41595 J

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.

26 Comments

View Comments: Nested | Flat

Read Comments

[ - ]

By jason (registered) | Posted April 18, 2016 at 20:50:48

there is zero reason why every residential side street in Hamilton shouldn't be 30km. And 40 is fine for most minor arterial roads like Wilson, Locke, Dundurn, Kenilworth etc..... The city's addiction to speed needs to end.

Permalink | Context

By jim (anonymous) | Posted April 19, 2016 at 04:56:30 in reply to Comment 117732

Comments with a score below -5 are hidden by default.

You can change or disable this comment score threshold by registering an RTH user account.

Permalink | Context

By orangemike (registered) | Posted April 19, 2016 at 17:49:21 in reply to Comment 117736

there is no broad public opposition to this. there is whining and sobbing from car culture cul de saccers like jim graham and socre and the other members of the brain trust that is "the hamiltonian" comment section.

Permalink | Context

By a reach too far (anonymous) | Posted April 19, 2016 at 18:19:31 in reply to Comment 117765

the car culture is a broad representation of Hamilton. Until that is accepted it cant be fixed

Permalink | Context

By orangemike (registered) | Posted April 20, 2016 at 18:11:30 in reply to Comment 117766

"Until that is accepted it cant be fixed" many dont and wont accept it and are fixing it as we speak. thank you to them.

Permalink | Context

By a reach too far (anonymous) | Posted April 20, 2016 at 19:09:21 in reply to Comment 117793

No they really aren't

Permalink | Context

By Translation (anonymous) | Posted April 19, 2016 at 07:33:44 in reply to Comment 117736

"the somewhat thorny issue of broad public opposition to such nonsense" = Entitled Hamilton Drivers that have had their every whim catered to for 60 years.

Permalink | Context

By NIMBY (anonymous) | Posted April 18, 2016 at 21:41:05 in reply to Comment 117732

Comments with a score below -5 are hidden by default.

You can change or disable this comment score threshold by registering an RTH user account.

Permalink | Context

By jason (registered) | Posted April 19, 2016 at 06:59:54 in reply to Comment 117733

Oh I think 30k city-wide would be fantastic. But this isn't what we call a progressive town. 40 on those larger streets would be a vast improvement over the 50-60 that is common. But if anyone needs signatures to go 30 on such streets, I'll sign.

Permalink | Context

By NIMBY (anonymous) | Posted April 19, 2016 at 11:49:42 in reply to Comment 117737

Comments with a score below -5 are hidden by default.

You can change or disable this comment score threshold by registering an RTH user account.

Permalink | Context

By Ryan (registered) - website | Posted April 19, 2016 at 12:11:24 in reply to Comment 117752

Don't be that guy.

Permalink | Context

[ - ]

By KevinLove (registered) | Posted April 18, 2016 at 21:48:12

It is very informative to put in the table the values for my bicycle, a Pashley Roadster Sovereign. The result for a 20 kg bicycle at 20 km/hr makes it quite clear why cyclists have already achieved Vision Zero.

The Dutch "Sustainable Safety" model does not rely upon speed limits, but upon engineering to provide safety. It is useful to see Mark Wagonbuur's recent video essay on Utrecht, a city about the same size as Hamilton. Please be sure to watch the video at the end. Not once are car speed limits mentioned. But look at the infrastructure!

Every piece of that infrastructure can be easily built in Hamilton. Utrecht did it. We can too!

Permalink | Context

By Ryan (registered) - website | Posted April 19, 2016 at 15:54:01 in reply to Comment 117734

Don't forget body weight. In my case, my weight plus the weight of my bike (a late model Norco Bushpilot) is around 215 lbs. Here's a table for all the speeds I can realistically achieve (including going downhill):

Curb Weight  Speed          Kinetic    
(lbs)  (kg)  (km/h)  (m/s)   Energy     
-----------------------------------
 215    98     10     2.8      376
 215    98     20     5.6    1,505
 215    98     30     8.3    3,386
 215    98     40    11.1    6,020
 215    98     50    13.9    9,406
-----------------------------------

I've got the same overall kinetic energy going 50 km/h on my bike as I have going 14.3 km/h in my car.

By the way, if you want some unpleasant reading, do a google search on "kinematics of trauma".

Permalink | Context

[ - ]

By Willem (anonymous) | Posted April 19, 2016 at 00:19:47

This is sound, but you might want to make the explicit connection between kinetic energy and damage/injury/chance of death.

Permalink | Context

By Ryan (registered) - website | Posted April 19, 2016 at 15:54:50 in reply to Comment 117735

Maybe it's worth writing a follow-up that goes into more detail on Newton's laws of motion and what it means that the energy of the moving vehicle needs to go somewhere when the vehicle abruptly stops.

Permalink | Context

[ - ]

By Surbanite (anonymous) | Posted April 19, 2016 at 07:32:56

I'm with Willem on this. Is there any data on what kinetic energy the body can withstand? Or does that question even make sense? Presumably, this would be quite different depending on the age of the pedestrian but along the lines of the design theory of Ages 8 to 80, perhaps there is data for those 2 age groups which would help with the thorny issue of the broad public perception, 30 km/h is nonsense ?

Permalink | Context

By LASTYEAR (anonymous) | Posted April 19, 2016 at 15:46:04 in reply to Comment 117738

At least three of the pedestrians killed last year were hit a speeds of less than 30kph.

Permalink | Context

By KevinLove (registered) | Posted April 19, 2016 at 19:21:15 in reply to Comment 117757

If you are being run over by a vehicle that weighs over 4,500 lbs, you are going to get crushed. Vehicle speed is irrelevant.

That is why it is important to have 100% segregation of cars and bikes.

Permalink | Context

By ryanssockpuppet (anonymous) | Posted April 20, 2016 at 08:02:12 in reply to Comment 117768

Comments with a score below -5 are hidden by default.

You can change or disable this comment score threshold by registering an RTH user account.

Permalink | Context

By the lunatics are in the comments (anonymous) | Posted April 20, 2016 at 08:08:31 in reply to Comment 117780

no one is forcing you to come here and read (or post). if you truly thought none of this mattered you would ignore it. but I guess you realize that the truths and realities discussed here are barelling towards you and threatening your cushy self-centred life... sorry old man, the guard is changing.

Permalink | Context

By ryanssockpuppet (anonymous) | Posted April 21, 2016 at 07:55:41 in reply to Comment 117782

Comments with a score below -5 are hidden by default.

You can change or disable this comment score threshold by registering an RTH user account.

Permalink | Context

By Selma (anonymous) | Posted April 19, 2016 at 20:27:29 in reply to Comment 117768

Comments with a score below -5 are hidden by default.

You can change or disable this comment score threshold by registering an RTH user account.

Permalink | Context

[ - ]

By Map (anonymous) | Posted April 19, 2016 at 09:05:20

Is there a map available showing streets by speed limit in Hamilton?
I looked on the City website but couldn't find anything (a common occurrence).
I wish I could hack Google maps better.

Permalink | Context

By Ryan (registered) - website | Posted April 19, 2016 at 09:14:44 in reply to Comment 117741

That's exactly the sort of thing a robust open public data policy should be able to provide. Unfortunately, Hamilton is extremely lacklustre on open data, and the smidges of data it does provide tend to be in clunky, inaccessible formats like PDF.

Permalink | Context

[ - ]

By Anonymous Adam (anonymous) | Posted April 19, 2016 at 16:00:19

I am pretty sure that getting hit by a car at 20km is around 90% chance of fatality. 30km 95% 40km 96% and so on...., I know I made this up, but it shouldn't take a genius to figure out getting hit by a car is near fatal nearly all the time, so trying to prove a point to lower speed limits only matters if you remove the cars from the road or segregate them from anything else that could use the road.
Its like a DOT helmet, yeah it can withstand such and such an impact, but you will probably be close to death if you get hit that hard, a higher rating helmet only gives you that extra percent of survival...if you get hit, you are in trouble regardless

Permalink | Context

By Ryan (registered) - website | Posted April 20, 2016 at 10:06:38 in reply to Comment 117760

Most of the fact claim guesses you make in your comment are wrong.

I am pretty sure that getting hit by a car at 20km is around 90% chance of fatality 30km 95% 40km 96% and so on....

It's actually 5% at 30 km/h, 45% at 48 km/h and 85% at 64 km/h, as the studies linked in the article show.

it shouldn't take a genius to figure out getting hit by a car is near fatal nearly all the time

No, it isn't. The vehicle speed is a huge determinant in the severity of the collision.

trying to prove a point to lower speed limits

It's not about trying to prove a point, it's about trying to minimize the risk of fatality and serious injury.

if you remove the cars from the road

In a few cases, it makes sense to make a street pedestrian-only, but that is not practical for most streets at the present time.

or segregate them from anything else that could use the road.

Physical separation makes sense in some contexts; for example, bike lanes are safer and attract more riders when they are physically protected from automobile traffic.

In other contexts where it is not practical to physically separate vehicles, the best solution is to ensure that vehicle speeds are low enough to a) minimize the risk of collisions (since slower-moving vehicles can stop more abruptly) and b) minimize the risk of injury if a collision does happen.

Permalink | Context

View Comments: Nested | Flat

Post a Comment

You must be logged in to comment.

Events Calendar

Recent Articles

Article Archives

Blog Archives

Site Tools

Feeds