Sunday, November 23, 2014

Low-Key Hillclimbs week 7: the gate

Low-Key Hillclimbs week 7, San Bruno Mountain East, was a great success.

This was the second climb this year for which we applied for, paid for, and received a permit for riding on roads which passed through parks. In this case Radio Road goes from Guadalupe Canyon Parkway (a 4-lane eyesore scarring San Bruno Mountain from the days when the goal was to completely cover the mountain with housing developments, a goal which has at least partially succeeded, but the road is still way overbuilt) up to the radio towers at the top of the mountain. The road is very lightly used, because not only is the park remarkably lightly used (diminished by too much of the mountains taken up by sprawled housing) but the parking is at the bottom of Radio Road. We were bypassing this parking area by going from westbound Guadalupe, through a fire access gate, directly to Radio on the northern side rather than take the route cars would follow, which is to cross Guadalupe, enter Radio on the southern side, then loop around and back under Guadalupe to return to the north side. The New Years race hosted by Pen Velo goes this way, accessing the main entrance from the northern side of Guadalupe, which it climbs from the east.

For our $400 permit ($5/rider for 80 riders) we asked for only one favor: that the fire gate be unlocked, so riders could pass through without dismounting, which is the normally fastest way up to the summit from the western side. I was promised this could be done, and while I was worried when the gate was still locked when I inspected it at 8:50 am (soon before sign-in started at 9:00), it was indeed unlocked for us just before our scheduled 10:00 start.

Since Guadalupe in places doesn't have much shoulder, I didn't want 80 riders heading up the hill together, so we sorted riders by speed (based on Low-Key points, USA Cycling results if I had no previous Low-Keys, Strava data if I could find that. For riders with points, I used an algorithm which split groups at places where the gap between the maximum points I had for riders was relatively large. This was to avoid the problem that riders extremely close in maximum points would be put into separate groups. The first rider in a slower group would still be significantly lower points than the slowest rider in the faster group. The exception to this was the tandems, who started in their own group between groups 3 and 4. I used a separate tandem group because tandems can be a big advantage to drafting solo riders on a route that has any flat sections due to the tandem's generally higher power-to-cross-section ratio.

So the first group set off, close to schedule, at 11:11 AM exactly, secure in the knowledge this would be a rare opportunity to ride to the top without any cyclocross moves, or without the added distance of looping around through the park entrance, the latter providing the additional delays of a sharp right turn and the chance of cars entering the park blocking the way.

But things went a bit wrong. We were for some reason shy on volunteers this week, an unusual state for Low-Key, and due to confusion over the number of groups, our sole volunteer at the turn-off thought the tandem group, which had started between groups "3" and "4", was the last group. It was not. We still had the sizable group 4 yet to come. Yet he shut the gate and rode up the hill.

A big part of the confusion may have been that there was a 4 minute gap between the tandems and group 4, but only a 3 minute gap between the other groups. The volunteer would have expected to see group 4 coming up the road but they were not. They were still a minute out of sight. This additional gap was likely because one of our two starters was riding with group 4, so had to, in addition to checking in riders, get on his own bike and get ready to start himself. This might have added just a fraction of a minute but he was starting groups on integral minutes so it bumped the gap from 3 to 4 minutes.

Stuff happens. With Low-Key every hill is a relatively new experience, so we don't necessarily get practice on every issue which can occur in any given week. The gate issue was new to us. We'd not worked out a protocol for how it was going to be handled. I'd generally assumed we'd deal with it after everyone had finished. But we should have worked this out in detail beforehand.

The lead few riders in group 4 saw the gate was closed and did the loop to the left. But most or even all of the riders following these riders took the faster route past the gate. However, crossing the gate, unless you're a skilled cyclocrosser, is a relatively slow process. You've got to stop, get off your bike, pick it up, hoist it over the small barriers to the side of the main gate, then remount your bike and re-accelerate. At least one rider I spoke to took an alternate approach of pushing her bike, diagonally and elevated, through the gaps main gate itself, then stepping through herself. I've done all of these things before (long way around, the side of the gate, through the gate) and the side of the gate option is the fastest. But most of these riders hadn't been here before and didn't necessarily know this.

Bike racing has many traditions, but fairness isn't one of them. There's many many examples every week in pro cycling. Weather changes during a time trial, causing later or earlier starters to face slower conditions, riders get held up by crashes in which they had no fault (generally this rewards riders at the front of the pack, but not always), groups are mis-directed by course marshals, perhaps following the route designated for support vehicles, or gates close at level-crossings for passing trains. All of these things happen: avoiding them is part of the luck with is part of the game. In this case, all I could do was to try to level the playing field as best I could, but I wasn't going to level it for everyone.

For example, consider the riders who looped around. They wouldn't have been tempted to do so had the gate been open, so the challenge of following the fastest route was one they faced that earlier groups had not. I had, however, carefully documented and mapped the route, describing that the gate might not be open and that riders should cross it. So while the riders taking the long-way faced an unfair navigation challenge relative to those who started in earlier groups, it was still a navigational challenge they could have been expected to meet.

Riders going through the gate, however, faced two challenges. One was simply getting through the gate. But the second was congestion. If you approached the gate in a group of four, you needed not only get past the gate yourself, but you needed to additionally wait for the three riders ahead of you to get through. The earlier groups with an open gate didn't face this problem.

But the gate came after a substantial amount of climbing and so any groups, especially in group 4 where riders tend to not have the pack-riding experience the mostly licensed racer population of group 1 have, tend to ride more their own pace on climbs than stick together in a tactical mass. Still, some did have the congestion issue. But congestion is a common issue when things go wrong in bike racing, and if I was going to apply the same compensation to all group 4 riders, as I felt I should since it was a mass-start event for them, I couldn't base it on those facing the most congestion. I had to base it on the conditions faced by those with relatively unimpeded access. To do otherwise would be unfair to group 3, for example.

So I had to establish how much time was lost by group 4 riders. One answer was provided by one of the riders: "I was helped by the stop". She felt she'd been in the read climbing Guadalupe, and the rest gained by crossing the gate gave her the strength needed to produce a stronger effort on Radio Road. Of course I didn't believe this actually benefitted her total time. But the point is important: it's what I have called the "elasticity of rest". When you're delayed by a time t, you get back some fraction of that time t from the effect of recovery on the rest of the effort. This was clearly evident, for example, at the trail race I ran at the same San Bruno park a month ago. Going into the water stop, the runner ahead of me blew through without drinking, while I slowed to a walk and drank a cup of carbohydrate solution. Despite the delay, I very quickly closed the gap that formed, refreshed by the few steps of walking.

This is an extreme example: a few steps of walking versus running is a very short rest, and the shorter the rest, the higher the elasticity or fraction of the lost work which is regained (elasticity is the fraction of work retained in a collision, for example of a ball bouncing off a floor, so I use it here to describe the fraction of lost work which is regained).

So I didn't want to overestimate the time lost in crossing the gate. At first, my reaction was 5 seconds is too short, that 10 seconds would be a good amount. A lot can happen in 10 seconds. If you take 10 seconds to run 100 meters, you lose a world-class track and field race. 3 seconds off the bike, 3 seconds across the gate, 3 seconds on the bike = 9 seconds.

But this neglects the loss of momentum. My next level of estimation was to play out the process of crossing the gate. You need to slow, get off the bike, cross the gate, get back on the bike, then accelerate. If I assign 3 seconds to each of these 5 steps, I get 15 seconds. That seemed more reasonable.

My first check of this was to see how the new adjusted times for the overall climb varied with group number. Here's a plot:

Note the times increase with each group, as expected, with group 1 the fastest, then group 2, then a big increase to group 3, then finally a smaller increase to group 4. From this plot there's no indication of any issue. If anything group 4 is doing better than expected based on the trend established by groups 1-3.

But I met some very sharp resistance, in particular from one rider, when I proposed 15 seconds. "A joke" is how he described it. So I knew I needed to do more: I needed to use a more quantitative approach.

So I defined a Strava segment for the gate crossing. This included the approach to the gate, the crossing of the gate, and the short stretch following the gate. I couldn't isolate the gate because Strava's segment matching is too loose. When I tried to place the end-points too close to the gate I got matches from rider data which didn't even cross it.

My first approach was to take two riders who had been assigned a finish time of within 2 seconds of 18 minutes, one in group 3 (Brian Ward), the other in group 4(Scott Byer). If my adjustment was correct, then these riders should have been of very similar speed. Indeed, Scott Byer, the group 4 rider, took 16 seconds longer on the segment than Brian Ward. To within my target precision of +/- 2.5 seconds, this was in agreement with my 15 second adjustment.

But this was just one isolated example. I then considered my own times on the segment. I'd ridden through the gate when it was open on my way to the summit immediately ahead of group 1 so I could record finishers. Previously I'd ridden the segment ten times, in each case crossing the gate. Some of these times were more rushed than others, on only a few efforts was a really making a maximal effort to get through as quickly as possible. My top three times were 13 seconds, 17 seconds, and 19 seconds slower than my time had been with the gate open. So this also was consistent with a 15-second adjustment.

But I wanted to go further, and look at aggregate statistics. So first I plotted time through the segment versus group number. Group 1 is the fastest, group 2 next, then group 3 and finally group 4 (ignore tandems here). I'd expect that for this segment, the same ordering would apply. So I wouldn't want to adjust group 4 times to match group 1 times, and I wouldn't even want to adjust group 4 times to match group 3 times. I want there to be a steady progression of times from groups 1 to 4: no disproportionate jump from group 3 to 4, but an increase in time nevertheless.

When I did this, I saw there was generally a 5 second increase in times of the fastest riders in each group, except for groups 3 to 4, where the jump (without any correction) was greater. No surprise there: the gate was shut for group 4. br>

This provided a quantitative approach to setting the adjustment. With 5-second precision, I was able to get a close to 5 second jump from groups 3 to group 4 with a 20 second, rather than a 15 second compensation. Here's the plot:


One thing you see here is that the spread in group 4 is larger than the spread in group 3. This is to some degree expected due to the nature of statistical distributions of riders and the fact group 4: group 4 is a "catch-all" group which includes riders of a broad range of fitness and goals. But the fact remains that congestion was a factor here.

I plotted versus group because initially I didn't have a way to plot versus rider time, but when I wrote the Perl code to do that, I got the following plot. Here I show time through the gate segment versus total time. If the compensation was perfect than I'd see no substantial difference in how riders from group 4 line up versus how riders in groups 1-3 line up. Of course, faster riders overall tend to be faster riders through the gate, as well.


As you can see from the plot, there's again more spread in group 4 times. But if anything, with the adjustment, the best group 4 riders now did better through the gate than the best riders from group 3, adjusting for total time. There's several riders who did a relatively long total time but had times through the gate, after the adjustment, competitive in group 3. The red dots in this plot were no group (tandem riders).

This doesn't address the question of recovery. If riders delayed at the gate were able to as a result climb a faster Radio Road, canceling some of the time lost at the gate, this analysis would miss that. One way to check for this would be to compare times on Radio Road to times on Guadalupe Canyon, omitting the gate crossing, for groups 3 and 4. If riders in group 4 benefitted from recovery at the gate then they would do better on Radio Road relative go Guadalupe than the riders in group 3. However, there's confounding factors, like the tendency of riders to try to follow a quick pace set by leaders, and the presence of faster leaders in group 3. So I'll leave it as is. If anything the addition of this sort of analysis would reduce the adjustment of group 4 times, and I'd prefer to give them the benefit of the doubt because the error was ours.

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