Bicycle stability and centre of gravity (or mass)

In the current issue of CTC's 'Cycle' magazine there's an article by Chris Juden, the Technical Editor. Chris normally knows what he's talking about. The article compares two electrically assisted bikes. One has the battery higher than the other and he wrote: "The Trek has the battery high up, which makes the bike a little less stable." I'm not sure this is true.

The familiar balance a broom on one finger trick suggests a bike with a higher centre of gravity should be easier to balance. Tightrope walkers use the same principle with long balancing poles to keep them from falling off. Because their centre of mass swings through a longer arc, they are less likely to tip sideways. So I think an electric bicycle with a higher battery is actually more stable than one with a battery low down.

I haven't ridden any though, and Chris Juden has. I suppose it depends on what he means by 'stable'. I can see how a lower centre of gravity bicycle is easier to manoeuvre at slow speed or when pushing it along by the handlebars but if, for example, you want to balance a bike when stopped, it ought to be easier when standing up on the pedals to mimic a broomstick. Penny farthings are presumably stable (never ridden one of those either), and they are much taller than normal bicycles.

This appears to be confirmed on Wikipedia: Bicycle ... dynamics.

Center of mass location: A bike is an example of an inverted pendulum. Just as a broomstick is easier to balance than a pencil, a tall bike (with a high center of mass) can be easier to balance when ridden than a low one because its lean rate will be slower. However, a rider can have the opposite impression of a bike when it is stationary. A top-heavy bike can require more effort to keep upright, when stopped in traffic for example, than a bike which is just as tall but with a lower center of mass.

A cyclist moving in a straight line stays upright by steering the bicycle under its centre of gravity. The higher the centre of gravity, the wider the 'stability zone' beneath its sway and the easier it is to balance. So more stable I think, but only when moving forward at a certain speed.

If this is true, there must be a speed at which the stabilising effect of a higher centre of gravity kicks in – five miles per hour, perhaps (and a very high speed at which the gyroscopic effect of the wheels takes over). The stability argument is put forward for low rider racks on touring bikes and they are certainly beneficial when pushing and manoeuvring a loaded tourer at very low speed on foot. A set of panniers is much heavier than an electric bicycle battery and it may be that cycle tourists rarely reach a speed where raising the load would improve balance. I imagine low riders on the front relate in some way to easier steering.

According to Socrates, to make a right turn, you turn the handlebars left. I'll check this next time I cycle.

15 comments on “Bicycle stability and centre of gravity (or mass)”

  1. Alan wrote:

    I confess my head spins when I try to understand bike steering and balance. In practice, it varies between bikes: I steer my sit-up-and-beg folder by turning the bars in the direction I want to go. My diamond frame bikes go where I want them to with no command from me, of course. They just read my mind.

    On the subject of balance: at speed, there seems no difference to me whether the load is low or high. Science may say it's easier with a high centre of mass, but I don't notice any difference.

    At slow speeds, I do notice the difference, and a low CoM is easier. I figure that for a given mass and angle-of-lean, a low CoM has a lower moment so it's easier to control.

    I've never lost balance at high speed. Twice this year I've fallen off at zero speed. There's a lesson in there somewhere.

  2. Kern wrote:

    I have always found that weight distribution makes a noticeable difference when touring – heavier items always go to the bottom. When we started our Rockies tour we hadn't gone a kilometer before I had to repack the BoB trailer. Similarly the bike is always more stable when shoes are at the bottom of the panniers.

    Any stationary object will become unstable when its centre of gravity moves beyond the limits of its base. Therefore low is better for stationary objects.

    I don't know what physics are involved with balancing a bicycle in motion, but I can't see that raising the centre of gravity will improve stability.

  3. Patrick wrote:

    Socrates again:

    A short bicycle falls over more quickly than a tall one. So a kid's bike is actually more difficult to balance than an adult bike. Even if the bike is being balanced by some active mechanism, the frequency of oscillations around equilibrium will be slower for a tall bike. And slower is easier to control. So try moving your center of gravity up as high as possible. I know this sounds counterintuitive, but ...

    Bicycle physics is quite simple really: Mejinard et al (578Kb PDF).

    An explanation why a cyclist doesn't fall over: When a rider begins to fall to the left, the rider rights himself by steering into the fall (i.e. to the left). By steering into the fall, he begins to move along an approximate circular path (at least for a few milliseconds). Once on a circular path, the bike and rider experience a centrifugal force, acting in the outward direction from the circle. Thus inertia (centrifugal force and riding skill) is the agency providing stability in a fall.

    The same author: "Stability increases with increasing height of center of mass."

    It is very true though that a loaded touring bicycle is easier to handle when the pannier load is lower down (and when there are four panniers rather than two) and it seems to go against these arguments. Perhaps handling and stability are two separate things.

  4. Alan wrote:

    Yes, Meijaard Figure 3 demonstrates how stability varies with speed, which seems consistent with my personal experience. (I'm just looking at the pictures.) We might all agree that when riding a bike without touching the handlebars, balancing is easier at high speed than slow speed. We might call a low-speed characteristic "handling" and the corresponding high-speed characteristic "stability", but I'm not sure the literature uses those terms in those senses.

    But I've never read David Jones "Bicycling Science", so I confess my ignorance.

    My opinion remains that a bike that loves me (to use Mary's phrase) can read my mind.

  5. Mike wrote:

    Physics doesn't come into it when your front wheel drops into one of Cornwall's world-famous hub-deep potholes. Low-rider or high, fast or slow, even drunk or sober, if your front wheel stops dead you fall over!
    Similar results can be obtained by combining bike with ignorant van-driver, bike with apparently-blind pedestrian, and bike with !@*!*$*@ cow on road!
    Happy winter cycling, folks.

  6. Garry wrote:

    On, balance, I agree with you all!! 😀

  7. Patrick wrote:

    Alan wrote: I've never read David Jones "Bicycling Science"

    Me neither. I searched Google for David Jones "Bicycling Science" and found Bicycling Science By David Gordon Wilson, Jim Papadopoulos, Frank Rowland Whitt (MIT Press, 2004). The whole book seems to be available for reading online on Google Books. Page 268:

    Balancing a broomstick, or a bicycle, consists in making the small support motions necessary to counter each fall as soon as it starts, by accelerating the base horizontally in the direction in which it is leaning, enough so that the acceleration reaction (the tendency of the center of mass to get left behind) overcomes the tipping effect of unbalance. The base must be accelerated with proper timing to ensure that the rate of tipping vanishes just when the balance condition is reached. Taller broomsticks fall less quickly than shorter ones and so are easier to balance.

    Oh well. I'm not sure if balancing a broomstick and riding a bicycle are quite the same thing.

    Mike wrote: Happy winter cycling, folks.

    Thanks Mike. No cycling here today though. Minus seven this morning. If it was warmer I wouldn't be writing this nonsense, although I still don't believe a higher battery makes a bike less stable.

  8. Abigail wrote:

    Very informative chain – thank you. I'm one of few intrepid, some say insane, cyclists who rides throughout the snowy Canadian winter. This summer I went from a 55" to a 58" frame. My new setup is quite similar – I transferred my wheel set to the new frame, have a similar bar height and gear ratio (I ride fixed). The impact of a longer wheel base and higher centre of gravity really became apparent once the white stuff hit the ground. When cornering at low to moderate speed my wheels feel quite unweighted and I've had the bike slip out from under me on several occasions. I actually went to flat pedals in order to be able to get my foot down in a hurry. In effort to figure out if I'd just become a terrible rider, I reassembled my old smaller frame. Sure enough, lower centre of gravity, better stability. The wheels stay weighted throughout the at the same speed and angle and I stay upright.

    The same is true with cars. The wider the track and the lower the centre of gravity, the more stable the car and the less likely it is to roll over.

    Admittedly, if I rode around with a broomstick, I might be able to disperse my weight more evenly left to right, but as that would make steering whilst flipping off motorists a bit of a challenge, I think I'll just stick to my small frame for the season.

  9. Patrick wrote:

    Abigail wrote: I'll just stick to my small frame for the season.

    On a slippery surface this might be wise. My argument relies on the pivot point being where the tyre holds the road. A rough guess – the pivot point when cycling on ice is somewhere else. Centre of mass, perhaps.

  10. Alan wrote:

    I love the thought of you flying around Canada on a broomstick. Would you use drop bars or flats?

  11. Kern wrote:

    Abigail, my idea of Canadian winter broom usage is to sweep the front steps. I am in awe of your fortitude. Where from?

  12. Alex Rossie wrote:

    The higher the center of mass the less of an angle the object must be leaned before the center of mass lies outside the base and the object topples.

  13. jeannine rust wrote:

    Would the center of gravity be different on a bike for girl or a boy also I was thinking would it make your but feel better if there was a change in women or men bikes. on how they are made

  14. VC wrote:

    Most of the comments posted relate to falling off of a bike, dropping down sideways I assume, while moving forward. Except at very low speeds, doesn't seem to be much of a problem. I recently launched myself over the handlebars of my hybrid while travelling approximately 25 – 30 kph, by mistakenly touching the front brake. I'm wondering if I had been riding a road bike, with a lower CofG, if the accident would still have happened, assuming the same circumstances. I cycled on a road bike for years, decades even, and experimented with the front brake and wasn't able to get the bike to tip over frontwards, i.e. Over it's own front wheel. Any thoughts?

  15. Patrick wrote:

    I agree that a lower centre of gravity means less tendency to tip over frontwards, at least for a given wheelbase, because the leverage is less when the brake is applied. Taking this to its logical conclusion, if the centre of gravity was below the pivot point (which I assume is the centre of the front wheel) any tendency to tip forwards would be eliminated.

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