Newton’s Laws

26 January 2014

Why do people on bicycles get so agitated about close passes, when they’re happy passing other vehicles closely? Isaac Newton has the answer.

Sameness is not equality

A few days ago, someone posted this on Twitter:

Now, if you read the thread, you’ll note that I was keen to jump on the objectionable idea that someone would wilfully endanger me because they’d seen someone else filtering through stationary traffic.

But this post isn’t about that. It’s to do with the deeply problematic principle of treating road users as the same rather than equal, a principle reinforced by the reply that Greater Manchester Police gave:

Fortunately, whilst the idea that I shouldn’t be made to pay for someone else’s actions (let alone their perfectly legal actions) is too complex for some people to grasp, the difference between sameness and equality largely boils down to some very basic physics.

And that can be explained with nice simple pictures.

So let’s go.

The device

I’m going to introduce a device that I’m sure you’ve seen before: Newton’s cradle.


Newton’s cradle is primarily intended to illustrate conservation of momentum and energy, but if you’ve ever used one you’ll be well aware that the more steel balls you lift the more energy there is in the system – the more of a bang you get when they crash together – and also that the higher you lift them the more energy there is.

So. Here’s your common or garden Newton’s cradle in schematic form.



Before we start, we need to make a slight change to the standard Newton’s cradle. My bicycle and I together have a mass of pretty much exactly 100kg, whilst – say – a Ford Mondeo plus one occupant have a mass of around 1500kg. The ratio of mass is 1:15.

So in order to get the ratio of masses correct, we’ll need a 16-ball cradle: one ball for the person on a bicycle, 15 for the person in a car.



When a bicycle, or a car, or a steel ball moves, it has kinetic energy. I’m going to consider two scenarios: a person on a bicycle at 10mph (a speed which would be typical when filtering through stationary traffic) and a person in a car driving at 30mph (a typical speed when passing someone on a bike).

In order to represent the energy of our person on a bicycle, we’ll raise the relevant ball by a height h.


Good. We now have some unit of energy that is proportional to someone on a bicycle at 10mph. If you’ve used a Newton’s cradle before, you’ll know that the above will result in: a pretty gentle “clack” as the balls meet. Naturally, with one ball falling from quite a low height, the 15 other balls will barely move. (Imagine that they’re all stuck together, like a car is.)

Next, we need to look at the energy that a car has at 30mph. We’ve accounted for the mass already with the number of balls; all that’s left is to account for speed.

Now, although the energy in the balls of Newton’s cradle rise linearly with height, the energy of a body of mass rises with the square of its speed. At 30mph, three times 10mph, any given mass has nine times the kinetic energy it has at 10mph. So we need to lift the balls to nine times the height of our previous example, 9h.


Again, if you’ve used a Newton’s cradle, you probably get the idea—BANG! (Though, of course, you’ll perhaps only really have a good idea if you’ve welded three cradles together.)

Imagine what it’s like if the car’s doing 60mph. We’d need to suspend the balls on wires four times as long in order to achieve the height of 36h that would represent the equivalent energy.

And, of course, whilst some of those 15 balls on the right make up the incredibly protective outer shell of the car, none of the single ball on the left represents protection of the person on the bicycle. In a way, you’re slamming 15 standard steel balls into an egg.

The big bang

This basic physics is why people riding bicycles at 10mph inches away from cars present no greater risk than scratched paint, whilst those who drive cars at 30mph inches away from people on bicycles risk killing others.

It is why a legal system and a policing view that is based on sameness is wrong, and why we need to understand equality and build a legal and policing system that counteracts the inequity of the physics.

And it is why people who do things like this should, quite simply, not be on the road.


  1. Charles Craddock 27 January 2014 1:06am #

    Thank you for this article which is very clear. Although I support that explanation in its clarity and intensity, I would like to express my dismay at your conclusions.

    It seems indisputable based on your explanation that it is necessary to separate road traffic spatially and/or temporally on the basis of their mass and speed.

    Once you have written this article, how cannot you not assert that large differences in speed and mass of different road users in the same space must be eliminated as much as possible?

    Legislation and policing are futile at best without segregation.

    If I contribute the fact that road traffic is inherently unsafe, legislation and policing alone might even have a damaging effect overall by encouraging more people into close proximity with cars & trucks under the circumstances that you have so clearly portrayed. It would certainly not encourage those too afraid to cycle now to start doing so.

    While road safety is about more than infrastructure, the role of legislation and policing as you describe can only work as part of a wider approach to accident prevention.

    • Bez 27 January 2014 8:10am #

      Oh, I’m absolutely not arguing that law is a fully adequate substitute for protected infrastructure. Hopefully a skim of a number of other articles on here should make that clear. Legislation – certainly all but the most radical – will not significantly increase uptake, either, as you say; but I disagree that it would act as some kind of honey trap that would see more people killed.

      I certainly disagree that “legislation and policing are futile”. There are a lot of people who use the roads already who would benefit from greater protection.

      Remember, even after 40 years of serious investment and commitment, not all roads in the Netherlands have protected cycling infrastructure. You can change a lot of laws in 40 years.

      So, yes to protected infrastructure, but why not also safer roads?

      • Charles Craddock 27 January 2014 10:51am #

        As roads are inherently unsafe, it cannot be reasonable to depict the problems of vehicles of differing mass and speed, as done so elegantly here, without proposing to minimise this conflict as far as possible.

        Therefore to extrapolate the conclusions of the article to legislation and policing without proposing separation of vehicles represents an oversight.

        I support legislation and policing as indispensable components of accident prevention.

      • Charles Craddock 27 January 2014 11:42am #

        My reply should have read:

        As roads are inherently unsafe, it cannot be reasonable to depict the problems of vehicles of differing mass and speed being in close proximity, as done so elegantly here, without proposing to minimise this conflict as far as possible.

        Therefore to extrapolate the conclusions of the article to legislation and policing without proposing separation of vehicles represents an oversight.

        I support legislation and policing as indispensable components of accident prevention.

  2. Richard Burton 27 January 2014 8:54am #

    Thank you for such a clear explanation of why there is such a difference between vehicles and people. Unlike your previous correspondent, I don’t see this as mandating segregation, but it does demonstrate where the problem lies: fast, heavy vehicles. Acknowledging that problem is the first step, but most people blame the pedestrians and cyclists for just being there.

    • Charles Craddock 27 January 2014 12:34pm #

      Thank you for your comment.

      I propose that this article unequivocally leads to the conclusion that differences in speed and mass of road users in the same space must be eliminated as much as possible.

      I concede your point that this does not mandate segregation in every instance, it could involve forcing road users to travel at lower speeds by road design. However, where speed differences cannot be eliminated types of traffic must be separated.

  3. Farnie (@farnie) 27 January 2014 11:04am #

    Also worthwhile pointing out that a car/lorry/coach travelling at speed, creates a large section of low pressure air effectively pushing anything of smaller size/mass further into the road and possibly into the path of vehicles behind.

    • Bez 27 January 2014 11:11am #

      Yes, indeed, someone on a bike can be destabilised by a pressure wave and then sucked back towards the traffic. Having spent half my degree studying fluid dynamics I probably ought to go into that aspect of it at some point :)

  4. Sarah S 27 January 2014 11:31am #

    Very well put, Clear, precise, concise. An animated version would make a great TV or cinema advertisement.

    • Tim 18 June 2015 10:40am #
  5. Paul M 27 January 2014 3:54pm #

    While the youtube clip of the courier aptly illustrates the physics of your argument, care should be taken over making moral conclusions from it.

    Should the driver be taken off the road? His behaviour is indeed deeply disturbing but I would argue that it derives not from lack of effective education of drivers or sanctions against their bad behaviour, but from other factors which drive them towards it. For example, while more than half of all states in the USA impose the death penalty on murderers, the murder rate in the USA is much higher than it is in the UK so evidently its deterrent effect is imperfect – imprisoning or banning bad or lethal drivers isn’t going to stop bad or lethal driving.

    The thing which drives Mr Sprint to behave the way he does is probably mainly his terms of employment. This has becomes one of the great unspoken scandals of UK employment practices, but professional drivers of all types are now employed on terms which is likely to make them dangerous to other road users, whether on foot, bicycle or indeed in another motor vehicle.

    Starting with couriers, there has been an explosion in their numbers in recent years, as a result of internet shopping. Courier delivery used to be an expensive proposition mainly used by businesses who needed assurance that important documents etc would reach their addressee same day. To some extent that is still the case. Retail couriers however are a different story. Internet retailers strive ot keep prices down to compete with high street retail, and that means keeping a lid on delivery costs. The result is not just complaints about driver behaviour of course, the internet retailers’ customers complain loudly and frequently about the quality of service they get as deliverees – Yodel seems to be the most notorious example but there are plenty of others in that particular hall of shame.

    Apparently guys who work for companies like City Sprint and Yodel get as little as £1 per delivery. Underneath that arse behind the wheel, there might just be some poor schmuck trying to scrape a living in an unforgiving world. With such huge pressure it can be expected, though not condoned, that they will drive aggressively and put other road users in danger.

    And it is not just couriers. Addison Lee cab drivers are also paid per trip, but additionally they have to pay a daily “rent” for their vehicles so they have to get a certain number of trips in before they see any net income whatsoever. I understand that similar circumstances prevail for construction trucks – in many cases they own their own vehicle but in a way that makes matters worse, as they can’t just say shove it, have your vehicle back I’ll get another job.

    Dangerous practices on the roads and indeed in many other places such as building sites are driven by economic pressures, mainly imposed by corporations on individuals. When the shit hits the fan, the individual is the one who gets it in the neck. His employer is rarely in the dock with him, but he should be. Until we fix this, no amount of non-segregation tinkering is going to improve things very much.

  6. Ricardo 27 January 2014 11:40pm #

    There’s another big difference between me squeezing between slow moving or stopped cars, and having them almost scrubbing my shoulders. On the former situation, I’m aware of other vehicles, and can control the distance and speed. On the latter, I might be surprised by a car overtaking me at close range, and unable to maintain safe distance.
    By the way, although the fellow rider on the video has plenty of reasons to be mad, that kind of approach will never have any positive result. Here in Lisbon, when I get the chance, I try to speak to that kind of driver in a polite and calm way. Aggressiveness from my end will only result in an escalate of anger and, eventually, might end up with physical violence.
    Thanks for the great article!

  7. Biddy Walton 19 February 2014 8:24pm #

    Thank you for the post. My mind had been running along similar lines looking for shareable illustrations of the disproportionate effects of collisions to share at . I do not have video editing software to capture the right bit and have not found the still image so compelling but this video gives a good visualization – see the watermelon at 1.09.

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