Surrey Cycle Racing League Courses

Cyclists in southeast England are indebted to Glyn Durrant, who with his team of supporters and local club members, runs the Surrey Cycle Racing League. These very popular races are held throughout the year on a number of courses around the region. This article takes a look at the characteristics of the courses raced in the Surrey League.

Thanks to Russell Short, Surrey League course are available as routes on Strava. You can download this file and open it in your browser to see a map that displays thirty-one circuits. The markers indicate the finish line and the name of the course, if you hover over it. The different colours help identify where loops pass over the same roads.

The courses have a range of characteristics, each one suiting some riders better than others. Although they are all road races, shorter circuits like the 4.6km lap around Kitsmead Lane are repeated many times, giving more of a criterion feel, in contrast with longer routes like the 24.1km Lingfield loop that offer less opportunity to memorise the finishing straight.

The amount of climbing is a key feature. For example, the Newchapel course is almost pan flat, whereas Beachy Head has an elevation gain of 228m over a length of 11.7km. Since you end up at the same point on each loop, we can assume that you are climbing for about half of the distance, giving an average climb (and descent) of 3.9%.

The organisers tend to position the chequered flag at the top of a rise, but the final effort required on Milland Hill is far greater than, say, Seale, which is slightly downhill for the indicated finish line. The rider leading the last Milland Hill climb will tend to be someone who can generate a high level of power at the end of the race. In order to identify steep finishes, the gradient of the final kilometre is calculated using the finish line as it appears in the Strava route. This is not 100% reliable, because the actual finish line can be different on the day.

Some courses are more technical than others, involving twists, turns and sharp corners. These favour riders with good bike-handling skills. One way to assess this is to calculate the “fractal dimension” of the route. This method is a bit experimental, so it would be interesting to receive comments from riders on whether they agree with the ranking. The metric gives something close to one for smooth, straight courses, but higher numbers for twisty circuits. None of the routes is very technical, but Sharpethorne and South Nutfield score more highly, due to their having some very sharp turns.

Putting all this together leads to some interesting results. Consider the amount of climbing versus the length of each circuit. Beachy Head is a medium length route that is well suited to climbers, though heavier riders have a chance to catch up on the fast descent. Sharpethorne, Staplefield and Lingfield are long and hilly, whereas you have less time to recover from the climbs at Ladies Mile, Staple Lane and Seale, because they are much shorter. Meanwhile Milland Hill and Bletchingly form part of a medium-length hilly group, contrasting with the Laughton, Coolham, Kirdford group of flatter courses. The very flat Newchapel course should suit the heavier diesel-powered TTers.

Dist_climb

Taking account of the technical nature of the courses, Newchapel, Sharpethorne and Beachy Head form a triangle of extremes. The flat non-technical Newchapel course can be ridden at a very high average speed. Sharpethorne requires both climbing ability and good bike handling skills. Beachy Head is hilly but not too technical. Most of the other routes are intermediates.

Tech_climb

The hilliest course does not necessarily have the steepest finish. That honour is reserved for the brutal climb that concludes Milland Hill, though the Bletchingly finish is also tough. Note once again that this depends on where the finish line is positioned on the day – I’m sure the finish of Beachy Head was at the summit, last time I did it!

Climb_final

The Surrey League offers a range of courses that provide opportunities for different types of riders. None of them is super-technical. Unfortunately we don’t have any mountains so strong puncheurs tend to do well. Remember that it is well worth reminding yourself what type of course you are riding, before you start the race. A spreadsheet summary of the data is available here: SurreyLeagueRoutes

The fractal nature of GPS routes

The mathematician, Benoît Mandelbrot, once asked “How long is the coast of Britain?“. Paradoxically, the answer depends on the length of your measuring stick. Using a shorter ruler results in a longer total distance, because you take account of more minor details of the shape of the coastline. Extrapolating this idea, reducing the measurement scale down to take account of every grain of sand, the total length of the coast increases without limit.

This has an unexpected connection with the data recorded on a GPS unit. Cycle computers typically record position every second. When riding at 36km/h, a record is stored every 10 metres, but at a speed of 18k/h, a recording is made every 5 metres. So riding as a lower speed equates to measuring distances with a shorter ruler. When distance is calculated by triangulating between GPS locations, your riding speed affects the result, particularly when you are going around a sharp corner.

Consider two cyclists riding round a sharp 90-degree bend with a radius of 13m. The arc has a length of 20m, so the GPS has time to make four recordings for the a rider doing 18km/h, but only two recordings for the rider doing 36km/h. The diagram below shows that the faster rider will have a record of position at each red dot, while the slower rider also has a reading for each green dot.  Although the red and green distances match on the straight section, when it comes to the corner the total length of the red line segments is less than the total of the green segments. You can see this jagged effect if you zoom into a corner on the Strava map of your course. Both triangulated distances are shorter than the actual arc ridden.

Cornering.pngIt is relatively straightforward to show that the triangulation method will underestimate both distance and speed by a factor of 2r/s*sin(s/2r), where r is the radius of the corner in metres and s is speed in m/s. So the estimated length of the 20m arc for the fast rider is 19.4m ridden at a speed of 35.1km/h (2.5% underestimate), while the corresponding figures for the slower rider would be 19.8m at 17.9km/h (0.6% underestimate).

We might ask whether these underestimates are significant, given the error in locating real-time positions using GPS. Over the length of a ride, we should expect GPS errors to average out to approximately zero in all directions. However, triangulation underestimates distance on every corner, so these negative errors accumulate over the ride. Note that when the bike is stationary, any noise in the GPS position adds to the total distance calculated by triangulation. But guess what? This can only happen when you are not moving fast. The case remains that slower riders will show a longer total distance than faster riders.

The simple triangulation method described above does not take account of changes of elevation. This has a relatively small effect, except on the steepest gradients, thus a 10% climb increases in distance by only 0.5%.  In fact, the only reliable way to measure distance that accounts for corners and changes in altitude is to use a correctly-calibrated wheel-based device. Garmin’s GSC-10 speed and cadence monitor tracks the passage of magnets on the wheel and cranks, transmitting to the head unit via ANT+. This gives an accurate measure of ground speed, as long as the correct wheel size is used (and, of course, that changes with the type of tyre, air pressure, rider weight etc.).

According to Strava Support, Garmin uses a hierarchy for determining distance. If you have a PowerTap hub, its distance calculation takes precedence. Next, if you have a GSC-10, its figure is used. Otherwise the GPS positions are used for triangulation. This means that, if you don’t have a PowerTap or a GSC-10 speed/cadence meter, your distance (and speed) measurements will be subject to the distortions described above.

But does this really matter? Well it depends on how “wiggly” a route you are riding. This can be estimated using Richardson’s method. The idea is that you measure the route using different sized rulers and see how much the total distance changes. The rate of change determines the fractal dimension, which we can take as the “wiggliness” of the route.

One way of approximating this method from your GPS data is, firstly, to add up all the distances between consecutive GPS positions,  triangulating latitude and longitude. Then do the same using every other position. Then every fourth position, doubling the gap each time. If you happened to be riding at a constant 36km/h, this equates to measuring distance using a 10m ruler, then a 20m ruler, then a 40m ruler etc..

Using this approach, the fractal dimension of a simple loop around the Surrey countryside is about 1.01, which is not much higher than a straight line of dimension 1. So, with just a few corners, the GPS triangulation error will be low. The Sella Ronda has a fractal dimension of 1.11, reflecting the fact that alpine roads have to follow the naturally fractal-like mountain landscape. Totally contrived routes can be higher, such as this one, with a fractal dimension of 1.34, making GPS triangulation likely to be pretty inaccurate – if you zoom in, lots of corners are cut.

In conclusion, if you ride fast around a wiggly course, your Garmin will experience non-relativistic length contraction. Having GPS does not make your wheel-based speed/cadence monitor redundant.

If you are interested in the code used for this blog, you can find it here.