Minimum speed on a board track.

I'm wondering if a heavier rider needs to ride at a higher speed to stay on the boards on a 42 degree banked velodrome than a lighter rider.

It often seems that way (watching how slow junior riders can go around the banking without sliding off compared to adults) but...

a)I’m not clever enough to know how the physics works. It seems to me like a heavier rider would be pushing the tyres into the track more and therefore have more grip than a lighter rider. Perhaps this is the case up until a point and then the extra weight overcomes the grip?

And b) I suspect a lot of why junior riders can go slower is due to them having less fear and so being less tense and having a smoother pedalling style. Tensing up, white knuckling the bars and jerky pedalling are definitely detrimental to keeping the rubber side down and the collarbone in one piece.

Whatever the case, I can’t recommend strongly enough against trying to find the limit of grip.

It will end with you falling off, you almost certainly will leave some lycra behind and probably some skin too, you will probably damage the track and you may take out other riders too.

How heavy is heavy because some of those track boys are huge?

Also not everyone slides down the track on the longest lap.

Thanks M_V and Dogs for your input. I'm a cycle coach and run track training sessions and have two heavier riders (100 kg) who claim they need to be going faster than 28-30 KPH to stay on the boards whereas the vast majority of us are quite secure at 28. M_V is right about smooth pedalling keeping you from slipping. With smooth pedalling I can circulate at about 24 kph However the force of gravity pulls harder on heavier objects and I therefore suspect that a higher speed may be required to increase the centripetal force that prevents gravity from pulling the rider down when the weight is increased.

There's formulae about this in the Level 2 Track coaching resources from BC.

I can't remember if it factors in rider weight though, possibly not.

Tyre choice & pressure, track temperature and track surface age might also play a factor.

I fully support M_V in saying:

I can’t recommend strongly enough against trying to find the limit of grip.

Everyone is there to have a good time, so safety is paramount.

I treat the minimum safe speed like a cliff edge, e.g. I wouldn't walk so close to the edge that the slightest misstep means I'd fall in the sea.

track temperature and track surface age might also play a factor.

Definitely. I could ride so slow and upright around meadowbank that I had to lean the bike over a bit when my inside pedal was at the bottom of the stroke to avoid it hitting the track.

If you ever come across that formulae from the Level 2 Track coaching resources from BC I'd be really interested. Thanks for your input.

I am not too heavy but heavy enough and from my so far amateur experience at LV is that as soon as my tyres start losing their grip I feel that I have to put much more power to stay in my line up the banking otherwise it skids sideways and feels terrifying! A tiny millimetre of that side movement and I can feel it right away (you can see the difference of how much easier it feels when your tyres are good and brand new).
Also regarding forces you have to think the triangulation/basic trigonometry of those in a 3D fashion (vertical gravity dictated by counter force from board resistance + lateral force pulling you down to the left. And all that of course affected by your forward acceleration (third dimension). The more the gravity, the more the board resistant AND the force that wants to take you down the banking.

All explained pretty nicely here:
http://alex-cycle.blogspot.com/2015/01/?m=1

To find how your actual weight translates in all this formula, you’ll have to analyse it in relation with the g force.

I quote the last paragraph that gives a nice example:
“ Things get much more interesting for the world's best track sprinters, who experience around 2g in the turns during their flying 200 metre time trial. If you have a 95kg track sprinter flying around at 75km/h, the bike, wheels and tyres are supporting the equivalent down force of over 200kg.
This is why track sprint bikes and wheels have to be made extra strong, and also partly why track sprinters run extra high pressure in their specialist tubular tyres.”

The weathered afzelia surface on Meadowbank gave significantly more traction at lower speed than an indoor Siberian pine surface velodrome, however when you did slide off you certainly did not slide as far as you would for any comparable speed on an indoor track .... and the splinters were harder to remove in one piece :-(

My first experience on an indoor track was sliding down the banking and tearing my brand new team kit on my hip.
Now I know not to ride Michelins.

http://alex-cycle.blogspot.com/2015/01/?­m=1

Thats a great blog for the mathematically curious track racer !

This is quite an interesting discussion, thanks for posting, also that Alex Simmons' blog 👍. As my local velodrome has a very steep banking at 47°, I'm very interested in the theories that this question arises, even though I'm a noob in physics. So I'm sorry to say there is little I can contribute in this. The most I can say, is that almost everyone I have seen sliding down the banking (quite a few actually), had inferior tyres and didn't keep enough pressure on the pedals. No significance in rider weight being very heavy or light. Keeping enough pressure somehow creates traction and therefor grip, at least in my experience (again, no idea how the physics are explained).

Slightly concerning that he quotes kilograms as the units for both mass and weight 🤔

Why? Physics are typically in metric.

Weight should be in Newtons.

Why?

Because anyone attempting to explain the behaviour of a bike on a banked track needs to be clear on the difference between mass (which is measured in Kilograms) and weight (which is measured in Newtons). The author of the article seems to be a bit confused about this difference (paragraph 7 of the article).

He says: '...an object with a mass of 80kg will also weigh 80kg'

He means: 'an object with a mass of 80kg will also weigh 784.8 Newtons' (on Earth obvs where weight is equal to mass * g)

Physics are typically in metric.

I'm really sorry I don't understand what this means.

A long time has passed, but here you go if still of interest.

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There doesn't appear to be any force pushing the rider to make a wider turn, this obviously happens on the flat and can also happen on less steeply banked tracks.

Would R(v) be the force at play?

I'd have to re-read the accompanying text next to the figures and even then I'm not sure I could answer you.

Objects in equilibrium (ie no net forces) continue to go in the direction and speed they were already heading. Forces are only needed to change direction.

If the bike/rider was going round the bend but started to drift out/up the track wouldn’t that be a change in direction?

Direction is always a straight line, so to go round a corner you need to be applying a continuous force resisting going in a straight line. If you start drifting wide it means the net size of that force has reduced.

On the bend at speed, the rider is not in equilibrium - they are accelerating towards the centre of the turn radius. The centripetal force is R(h) in the diagram, the horizontal component of R.

@M_V

There doesn't appear to be any force pushing the rider to make a wider turn

You could draw a force diagram with respect to the rider's own frame of reference while cornering, and then there would be an apparent centrifugal force. It's cancelled by R(h) if they stay on their line; if it's greater than R(h) they are drifting out/up.