Mathematic model for breakaway advantage calculation



pauli

New Member
Jul 7, 2005
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OK, so if I'm a dumb newbie let me know...

I'm watching tonights stage and thinking that a breakaway on a wet day with a tail wind has a better chance of success than a breakaway on a dry day with a head wind. Obviously, the reason is that the advantage of the Peloton is that they waste less energy per rider in wind resistance. Has anyone ever come up with a mathematical model to calculate the specific advantage for various conditions?
I have no idea of the numbers so I'll just make up some that will probably be ridiculous - I really have no idea. : )

So lets say a single cyclist riding with no wind, on a flat, smooth road with no wind on a dry day at 50km spends 80% of their energy in wind resistance. A cyclist behind them will have 30% less resitance than the rider in front of them meaning they only have to expend 75% of the energy of the poor sucker breaking their wind.

How do the figures change if it starts raining? A guy in the Peloton has to spend energy on whacking into a heap of water as well as all the other things that cost energy when it was dry. The so wind resistance is now a lower percentage of total energy requirements.

Stick a mechanical cyclist in a wind tunnel and you'd be able to calculate the difference various conditions make.

This would mean that team managers could advise their teams on exactly how much more energy they'd have to expend if they are considering giving it a crack. They may be able to calculate something like:
Its very wet (+10% total energy required)
Its undulating (+15% total energy required)
The road is rough (+5% total energy required)
There is a 10knot headwind (+10% total energy required for Peleton guy; +30% total energy required for Breakaway guy. The difference of the two is = -20% total energy required)
... I could add a few other factors
= +5% total extra effort
--> add 5% to total differences between Peleton guy and Breakaway guy
Therefore if cycling at 50km/h, Peleton is expending 2% less effort than Breakaway guy. Since the Peleton is 30% better off before adding this difference, the calculation might show that a Peleton cyclist could ride at 58km/h whilst using the same energy as the Breakaway guy cycling at 42km/h.

Obviously, if the cyclist hears this he probably figures it is probably not a good idea (mostly because the headwind removes most of the advantages that the other factors give).

On the other hand, if it was a 10knot tailwind then the recalculated figures might be much more favourable because the wind-independant factors form a much higher ratio. So it might be more like the Peleton guy riding at 52km/h using the same energy as Breakaway guy riding at 48km/h.

Sorry for the long post.

Has anyone ever modelled this stuff properly?
 
pauli said:
OK, so if I'm a dumb newbie let me know...

I'm watching tonights stage and thinking that a breakaway on a wet day with a tail wind has a better chance of success than a breakaway on a dry day with a head wind. Obviously, the reason is that the advantage of the Peloton is that they waste less energy per rider in wind resistance. Has anyone ever come up with a mathematical model to calculate the specific advantage for various conditions?
I have no idea of the numbers so I'll just make up some that will probably be ridiculous - I really have no idea. : )

So lets say a single cyclist riding with no wind, on a flat, smooth road with no wind on a dry day at 50km spends 80% of their energy in wind resistance. A cyclist behind them will have 30% less resitance than the rider in front of them meaning they only have to expend 75% of the energy of the poor sucker breaking their wind.

How do the figures change if it starts raining? A guy in the Peloton has to spend energy on whacking into a heap of water as well as all the other things that cost energy when it was dry. The so wind resistance is now a lower percentage of total energy requirements.

Stick a mechanical cyclist in a wind tunnel and you'd be able to calculate the difference various conditions make.

This would mean that team managers could advise their teams on exactly how much more energy they'd have to expend if they are considering giving it a crack. They may be able to calculate something like:
Its very wet (+10% total energy required)
Its undulating (+15% total energy required)
The road is rough (+5% total energy required)
There is a 10knot headwind (+10% total energy required for Peleton guy; +30% total energy required for Breakaway guy. The difference of the two is = -20% total energy required)
... I could add a few other factors
= +5% total extra effort
--> add 5% to total differences between Peleton guy and Breakaway guy
Therefore if cycling at 50km/h, Peleton is expending 2% less effort than Breakaway guy. Since the Peleton is 30% better off before adding this difference, the calculation might show that a Peleton cyclist could ride at 58km/h whilst using the same energy as the Breakaway guy cycling at 42km/h.

Obviously, if the cyclist hears this he probably figures it is probably not a good idea (mostly because the headwind removes most of the advantages that the other factors give).

On the other hand, if it was a 10knot tailwind then the recalculated figures might be much more favourable because the wind-independant factors form a much higher ratio. So it might be more like the Peleton guy riding at 52km/h using the same energy as Breakaway guy riding at 48km/h.

Sorry for the long post.

Has anyone ever modelled this stuff properly?
www.analyticcycling.com
 
The advantage to a small pack when the roads are wet and there are lots of turns is that they can choose better lines around the corners - that sort of thing doesn't lend itself to modelling very well since it's largely dependent on the specific course and rider handling skills.

In today's stage two of the three in front made it through the crash but when the peloton came through the first 15 or so all went down. If the roads hadn't been wet it's likely the group of 3 would have been caught by the sprinters before the line and the pile-up would have been much smaller.