On Bicycles, and.... what else is there?

I previously posted a route profile for the Chanteloup climb near Paris, France. This is a climb with an amazingly rich cycling history, going back to Velocio who used it to demonstrate the superiority of multi-gear bikes to the fixed-gear bikes which dominated professional racing in the early 20th century. Later it became the sight for the "Poly de Chanteloup" event, which was contested by randonneurs and professional racers. The randonneur event unfortunately seems to have died, but the professional race continued as the Trophée des Grimpeurs , a traditional last race of the season until sponsorship was lost in 2010 and it also expired. Jan Heine, in his highly recommended book "René Herse" , has the following quote about the gearing of the winning tandem in the 1949 randonneur contest. I posted this last time but I repeat it here because I find it remarkable: A single chainring was sufficient for the 14% of the climb of Chanteloup, which had to be climbed e...

In my last post on the subject of barometric altimetry, it was discussed that a moving altimeter may report a lower altitude than a stationary one, due to the dynamic pressure of the air piling up in front of the moving cyclist. The amount of this altitude increase is determined by a coefficient between zero and one relating the effective wind speed to the cyclist speed. Before that, I described how I'd combine a barometric altitude signal with a GPS signal to get the best of both: the short-term responsiveness and reliability of the barometric altimeter with the general accuracy of the GPS (at least when there's a signal). I'd applied this to randomly generated data , which were derived using a simple pacing model with the bike power-speed equations. The effect of dynamic pressure on measured altitude is simply derived from Bernoulli's equation : Δz = ‒½ ( k dp v )² / g, where Δz is the error in altitude, v is the speed relative to the wind, k dp is the coeffici...

I never could wrap my head around this stuff. Bernoulli's_principle basically says that when an incompressible fluid is moving more rapidly, the pressure drops. Air is obviously included in the list of incompressible fluids, leading to all the activity at SFO not so far south of where I live. In some physics class in my distant pass, the professor justified this by launching into a set of differential equations . You stare at the equations, one after another, and sure enough it's hard to dispute any one of the steps, but that doesn't mean the result actually makes any sense . Differential equations, after all, are just a model. There's no physics in differential equations. The physics is in particles bouncing around: scattering elastically and inelastically, transferring momentum, transferring energy. Scattering, if anything, is the heart of physics. So I envision gas molecules bouncing around, energy scattering between various degrees of freedom, minding their...

Okay, back to altimetry. After painstakingly constructing simulated altitude data consisting of the following: true altitude GPS altitude signal: tends to fluctuate and drop out for periods, never deviates too far from the true altitude, at least in my model barometric altitude: smoother than the GPS and never drops out, but has a slowly varying offset from the true altitude So the approach I take is to first identify points at which the GPS signal is good. At those points, I calculate a difference between the GPS and barometic altitudes. I then locally average these distances using my favorite smoothing function, cosine squared: The key is to pick the time constant. Too short a time constant, and you don't suppress the GPS fluctuations. Too long a time constant and the barometric error may change sufficiently that the correction is no longer accurate. So I picked: τ = 100 seconds. When the GPS signal drops out, I don't do the averaging to calculate the correction amplitud...

I'll now describe the model I used for the various altitude signals. This is probably a bit more elaborate than it needed to be, I admit. But I like realism. First, the altitude versus time, as this was the most complicated. I started with Fourier coefficients generated using normal random magnitudes each chosen with an rms value proportional to a Lorentzian factor 1 / [1 + (s / λ)²], where λ is a reference distance of 10 km, describing the approximate length of a typical climb. This distribution is nice because it keeps enough of the high-frequency component for things to be interesting, but while allowing the low-frequency components to generate nice continuous climbs. The phase for each component was then randomized from 0 to 360 degrees. But this doesn't represent a realistic profile, since the random Fourier components yield peaks and valleys of the same shape. So I transformed the altitude using the following: z → (50 meters) ln [ 1 + exp(z / 50 meters) ], which you...

A discussion on the GoldenEmbed mailing list got me thinking. GoldenEmbed is an open source hardware project to produce an ANT+ compatible cycling head unit: one which can record power from a variety of ANT+ compatible power meters such as Quarq Cinqo , SRM , and MetriGear Vector . It's built out of some nice modules available from SparkFun , basically a modern version of what Radio Shack used to be: a source for electronic hobbyists. The project was inspired by the Quarq Qollector prototype shown at Interbike, and Tim Clark of MetriGear's similar ANT+ sniffer used in Vector development. The MetriGear data logger which in part inspired GoldenEmbed So some of the GoldenEmbed guys mentioned you could go beyond ANT+ sniffing and incorporate GPS and barometric altimetry: SparkFun sells all of the required hardware. Cool! This enables the development of the functionality Garmin provides. So the question is: what's the best way to manage both GPS-based altimetry and baro...