Yesterday I finally managed to achieve one of the things on my 'to do' list that's been sitting there for about a year – attend a 'Have a Go' session at the velodrome in Cambridge. For those that don't know it, it's New Zealand's new (which means about two years old) world-class velodrome and now 'home' to New Zealand cycling. It's an impressive building – probably more so from the inside than the outside.
Walking into the central area the first thing that greets you is a terrifying view of the banking on the corners. We were told it's 43.5 degrees. It's the kind of slope you'd find on a steep slide in a playground. And we're meant to cycle on it.
But our instructor built us up gradually to this. First off, was just getting used to the bikes – large, with a high (fixed) gear, and back-pedal braking. The last of these means no free-wheeling – they need pedalling all the time. There's a nice flat area at the bottom which allowed us to do a couple of laps of the track and get used to starting and stopping, both of which are quite technical affairs. Next, we were up on the blue strip on the inside of the track. That's banked, but not as much as the main track. Once we had this sorted, we were allowed up onto the main track on the straights only, which are less steep. Then the really scary bit. The main track all the way round.
Although scary the first time, it's really not – or at least shouldn't be – for a physicist. The key is simply to be going fast enough. With a bike that highly geared, on a smooth track, with no wind to worry about, that's not difficult. The physics isn't too tricky to do either. Cornering requires a net centripetal force (one towards the centre of the circle) to act – one that's proportional to the square of your speed. The banking ensures that this is more-or-less provided by the normal force acting from the track onto the bicycle. In fact, at the pathetic speeds we were doing (maybe up to 30 km/h? my forty-something year old legs didn't seem to work the way they once did…) the banking was providing more than enough centripetal force. This means there's friction acting as well, in this case an upwards force keeping us on the banking. Our bikes were certainly far from perpendicular with the track when we were going round – we were leaning outwards with relative to the track, but a spectator would have seen us leaning inwards relative to the flat.
Go fast enough (and some quick calculations suggest this is easily in reach of a proper cyclist) and there'll be no friction required at all – and the bike should make a neat 90-degree angle with the track. From the spectator's point of view, the cyclist will be leaning over at 43.5 degrees. Faster still, and the banking won't be enough to provide that centripetal force, and friction will then be required – this time acting down the track. The cyclist will need to lean inwards relative to the track.
Just as there's a minimum speed required in order to get around the banking (according both the instructor and my own physics calculations about 25 km/h – and she made sure we were up to it before letting us off the blue strip), there'll also be a maximum speed possible to take the corner safely, even with that extreme banking. My quick estimate of this is around 120 km/h, which I think is beyond what a track cyclist will be able to get to. [Extra note: these calculations make an assumption of a coefficient of static friction of around 0.8. But given that some sprinters can actually maintain a stationary postion on the banking (so they don't have to lead in the 'sprint') there's clearly more to it than that – possibly the coefficient of static friction is particularly high!]
So, overall, not so scary after all. I'm looking forward to having another go.