A Bicycle Clinometer

Hills! Every cyclist will develop a certain sensitivity – an accute awareness of the dynamics of road inclinations. We learn how to best pace our efforts when climbing the hills on the commute or training round – and we will certainly "sense it" when the incline becomes too steep for the bike's gearing, or when we have simply overestimated our physical resources.

But just how steep are those hills, in objective terms? Apart from the curiosity value, it would occasionally be useful to be able to know the real figures, so that we may develop a intuitive grasp of what it takes to climb a steep road of a certain grade.

When planning an itinerary for a cycle tour in some hilly region, for instance, it is natural to scrutinise available topographical maps for information about the terrain. Often we want to evaluate the relative steepness of alternative roads under consideration, and it may then be possible to gain a useful impression of the large-scale gradients by counting the transverse contour lines on a given stretch of road. Unfortunately, such exercises can rarely reveal the actual variation at a smaller scale.

Arithmetric expressions such as 1:10 (10%) or 1:5 ( 20%) doesn't mean very much anyway, unless we have something familiar to relate them to. What we want is a "conditioned sensitivity", and this could arguably only be won through personal experience of slopes which has surveyed grades of different magnitudes.

Many GPS enabled bike computers can save data for generating topographical profiles. However, elevation data derived from GPS observations (that is vertical sensing along the Z-axis) is in fact, and for various technical reasons, inherently quite imprecise and ”coarse-grained”, also when compared to the usual limited precision of consumer grade GPS horizontal positioning (sensing along the X/Y, or Lat/lLon axes).

A road's grade is basically calculated as the ratio between vertical distance gained (or lost) to distance travelled horizontally, and as we are mostly interested in grades where the latter dimension may be 10 or 20 times as great as the former, it is particularly unfortunate that it is the ratio's numerator unit, the altitude difference, which may have the worst precision. The consequence is that any small discrepancy in the altitude estimation input will be amplified, as it were, in the resultant angular calculation output.

To develop a realiable judgement of what constitutes a slope of a certain steepness then, one would ideally need some sort of angle meter which could be read in real-time. And – surprise, surprise! – it turns out that such an instrument can easily be made using a cheap (but very capable) integrated accelerometer/gyrometer sensor chip and an equally cheap microcontroller.