## Mean Maximal Gradient, Predictive Cadence and Gearing Analysis

Bike riders and coaches of all levels understand the importance of informing themselves about the demands of a forthcoming event or race. At it's most informal this process might be a quick glance at the route and profile, while at it's most rigorous a formal analysis of demands may include power analysis, pacing and equipment options, nutrition and hydration strategies. CPL's Event Models are ideal for this level of detail.

One of the factors frequently overlooked, or simply not considered in sufficient detail, is analysis of gradients and gearing. Sure, it's easy enough to look at a profile and see the length and average gradient of climbs, maximum gradient is often indicated too, but is this enough?

**Most Gradient Analysis Is Misleading**

A number of software products will readily show you a bucketed summary of "Total Distance at Gradient", either for a particular climb, or for an entire course. By "bucketed" we mean they will break the road down into small sections, calculate the gradient on each, then add up the total distance in sensible gradient "buckets" or bands. For example, 300 metres of road at 1.5% gradient goes in the 1-2% bucket, another 200 metres at 1.8% goes into the same bucket (the total distance in bucket total is now 500 metres), and so on.

The main limitation of this approach is that it fails to consider how close or how far apart these sections of gradient will be hitting the rider, or their order on the road. 1 kilometre of 10% gradient sounds pretty tough, but if it's really 100 metres of 10%, on 10 separate sectors, with several hundred metres of flat or event descent in between, then it becomes clear that this sort of analysis is at-best misleadiing and at-worst useless.

There is a paralell here with power and heart rate analysis. 10 minutes above FTP or above threshold heart rate tells us little about a ride unless we know how that time was distributed. Was it continuous?. Was it just a few seconds here and there, many times over? Gradient analysis has exactly the same considerations and what we really want is something equivalent to "Mean Maximal Gradient".

**Max Distance At Average Gradient**

A better way to do gradient analysis is in terms of "Max Distance At Average Gradient". Define some gradient buckets, as above, but this time scan the entire course looking for the maximum distance with an average gradient falling inside that bucket. By example, a 100k course from point A to point A is going to have 100km at a 0% average gradient. If the biggest climb is 10k at 5% then the max distance at 5% average is 10k and the max distance at -5% average may also be 10k. If that climb has a steeper section peppered with short pitches varying between 6 and 8% this analysis will reveal the max distance at averages of 5-6%, 6-7%, and 7-8%. Total distance in any of these buckets, by comparison, could be misleading or useless.

"Total Distance At Gradient" is an easy analysis to make, in fact it can be done manually, "by eye". "Max Distance at Average Gradient" is much tougher for humans, but relatively easy for a computer, which is well suited to scanning and calculating all continuous combinations of all sectors across an entire course.

CPL Pre-Event Models now include an analysis of Max Distance At Average Gradient in addition to Total Distance at Gradient.

**Predictive Cadence & Gearing Analysis**

The logical goal of gradient analysis is to make informed decisions about gear choice, given some range of acceptable cadence. But there are no good "rules of thumb" about the right minimum (climbing) or maximum (descending) gear for a certain course or certain gradients. Cadence is a product of road gradient and speed on the road. Speed on the road is a product of a rider's sustainable power output, weight, and to a lesser extent other components of resistance such as aerodynamic drag and rolling resistance. A 60 kilo pro who can hold 350 watts on a climb is not going to need the same minimum gear as an 85 kilo amateur with 200 watts.

In practise this means that the only way to make good decisions g is by relying on predictive event modelling. You want to know 1) what are the maximum and minimum average gradients encountered for at least some minimum critical difference. A 500 metre pitch works well for most riders. And 2) What cadence would a certain rider achieve on these pitches, through a range of different minimum and maximum gearing options. Only then can gearing decisions be considered optimium, adequate, or in some cases low enough to avoid catastrophe!

All CPL Pre-Event Models now include an analysis of minimum and maximum cadences achievable with a range of gear combinations including chainrings: 34, 39, 42, 50, 52, 53 and sprockets: 27, 25, 23, 13, 12, 11.