bdocs rambling

Brachistochrone

I was struck by this GiF recently, at:

http://imgur.com/5t32VJU

This little video shows three possible paths – the straight line (the shortest), a path that descends quickly and then becomes flat as it gets to the destination, and one in between, looking more elliptical* in shape.

Ever wondered what downhill profile of road will get you most quickly to the bottom of the hill freewheeling from a given point T (the top) to a given point P (the pub)? Now you know – it’s a cycloid, appropriately enough. Now I just need to think about the best shape of road from the pub to the top for the fastest ascent for a given a) wattage, and b) for a given pedal pressure…

…The classical problem is well-known as the difficult to solve Brachistochrone problem. See http://www.math.utk.edu/…/m231f08/m231f08brachistochrone.pdf for a solution – minimising a quantity over a famiły of functions, or http://www.osaka-ue.ac.jp/ze…/nishiyama/math2010/cycloid.pdf which is perhaps a little more accessible and talks a little more about the cycloid (the resolution of the problem).

Even more arcanely (I was going to say more interestingly, but I’m realistic about reading endurance!) the cycloid, as the second article says, is isochronous. It means that even if you start freewheeling from a rest position R half way down the hill, it still takes the same time to get to the pub. Why? Briefly, because starting higher up, at the intermediate point R you are moving, whereas starting from R you are at rest. Weird, huh? It’s the same for any point R, no matter how close to the pub.

*the elliptical path is nearly as fast as the cycloid – but not quite!!

Having used the Tacx non-smart i-Genius turbo trainer for a while, I have also been using my Tacx smart Flow trainer a lot recently.

The Tacx Flow is great value, the lowest price Tacx trainer that is fully smart, i.e. ANT FE-C and Bluetooth bidirectional. Thus the trainer software (Tacx films or 3rd party like Zwift, on laptop or handheld device where applicable) will control the Flow brake, and the Flow sends all speed, power and cadence data to the training software.

You can also control a smart trainer like the Tacx Flow with the Garmin x20 series, i.e. such as the 520 or 820 that have the right data protocols.

At this low end of the Tacx range, you are limited to 6% uphill simulation and 750W power, but I don’t find this too much of an issue. Because it doesn’t have a motor to help simulate downhill freewheeling (like the I-Genius I also have) you work harder downhill to make up for it being easier at 7% uphill and above because the resistance is limited to simulating 6% max.

The Tacx Vortex does 7% and 950W but not worth quite a bit extra price in my opinion. I have published quite a bit on all this on Facebook to my cycling Club I have also described how Zwift offers the option of increasing what they call “difficulty” from the default standard 50% to something higher. This increases resistance on hills, lowering cadence and speed and leaving power the same.

Tacx have something called “virtual speed” which decreases reported speed uphill and increases it downhill to compensate for the maximum simulated uphill and downhills on trainers like the Flow and Vortex.

The much more expensive Tacx Neo, Genius and Bushido don’t need that.

DCRainmaker always offers good information, especially his “all you wanted to know…” page which is at www.dcrainmaker.com/2016/07/everything-you-ever-wanted-to-know-about-ant-fe-c-and-bike-trainers.html
32 minutes ago

Having seen this excellent blog post on Facebook about the Westerham Cyclery,

and linked to it from there – https://summit2ride.com/2016/10/05/the-cafe-ride-westerham-cyclery/ I thought I should add my own pictures and very positive comments, having been hosted into hosted by their very friendly staff! I went there to meet up with a cycling Glasgow Green Cycle Club friend, Susie Goodwin, and then to ride one of the climbs back over the North Downs.

The highlight of my visit, I have to own up to, was the (two pieces of!) bread pudding, but they have all sorts of cakes and drinks, plus a well stocked bike shop, a very safe place in the courtyard to park (and lock if desired) the bike, and tables and seats in that courtyard for

a quiet al fresco rest.

I am based near Glasgow in Scotland, but now, added to the Spitfire café in Biggin Hill, Westerham Cyclery will be at the top of list for my next ride south of London when visiting family. The café garden is a great place to meet people and relax.

From a riding point of view, there are quite a few climbs back over the North Downs, including Chalkpit Lane which I rode on another visit. My first return was via the signposted route from Westerham to Croydon, which is a more gentle climb that anyone can manage, so go ahead and make a visit!

After a little fall from my bike (ouch!) I have some time to do some reading! See

This is the easier side of the Tak, but there are some very steep little ramps, limited to 10-11%, which is a critical 2% or so less than the north side, where the steeper parts are also longer. On this side, however, there is plenty of less steep road where a rest can be taken, back in the saddle. I have been up a few times on my geared bike, and also single speed but only on 46/18, 69″ gear. i think that is a sensible maximum for me! There is a ford about half way (surprisingly there is a loch, not at the bottom but also half way up) and at the top the views from the car park viewpoint are all the way over to Grangemouth, the Forth Bridge and the new crossing. Very much worth the climb!!