A Primer on Half-Step Gearing

Sometimes people use the term half-step to describe the sort of gears that a bicycle is equipped with. Since other people sometimes ask what this means, I shall attempt an explanation.

Well, way back in the dark ages, in the early days of three and four speed rear derailleur gears, it was found that a useful selection of gear ratios could best be obtained by maintaining a constant ratio between successive pairs of rear cogs. The same principle carried through pretty well to the new-fangled five-speed clusters, which attempted to defy all sane principles of enginerring practice.

Say, for the sake of argument, that it was found that it worked well to use cogs which gave about a 16% increase over their predecessor (ie ratio (of ratios) of 1.16)--this would give a reasonable range of five gears together with a tolerable gap between gears. Some crazed racing cyclists, however, decided that they could use more gears than even this.

Since workable clusters providing near constant ratios of successive pairs of cogs were well-known, the most practical way to provide more useable gears for a racing cyclist was to add another chainwheel of a size such that the increase of the ratio accomplished by the second chainwheel was as close to half the increase accomplished by moving from one rear cog to the next. In the case of the not-so hypothetical example above, one could use 52/48 giving an increase of 8%. After all, no racer could possibly want five more gears all lower than the lowest they already had, nor all higher than their highest. Instead, the extra chainwheel was sized as indicated, so that, in between the normal "steps" provided by the cluster, it would provide "half-steps".

Astute observers will notice that the above paragraph contains a technical error.

I have heard that, in the early days, since front derailleurs had not been invented, special plates were fitted to the cyclists' shoes to be used for moving the chain from one chainring to the other. I have never actually seen evidence of that, but I have seen bicycles fitted with rear derailleurs which required and permitted the rear wheel to actually be moved while riding as part of the shifting procedure. This eliminated the need for jockey wheels. (In fact, the rear derailleur was much like modern front derailleurs).

A much more verifiable fact, however, is that early front derailleurs were much better at shifting a chain across a chainrings differing by only a few teeth than up and down gaps of ten teeth or so, as modern racing bikes tend to be equipped with. Indeed, tight clusters must have existed in the days before front derailleurs, but by ignoring this fact we were able to provide a plausible and pleasing etymology of the term half-step.

To simplify the explanations given above, merely observe the following result only. Half-step gearing is a combination of chainwheels and sprocket cluster which gives you the following algorithms to find the gear ratios closest to the one you are currently using:

This is to say, the small chainring corresponds to all your odd numbered gear ratios (assuming you number your gears starting with 1), and the large chainring corresponds to all your even numbered gear ratios. The time to make use of a half-step, as we do on our tandem, is when cruising under good conditions; when you feel you can use a little bit different gear, you know where to find it. Coarse adjustments are made with the rear derailleur. Use a gearchart program to chart "52/48 across 14-17-20-24-28" for a canonical half-step setup, and look at the order of the ratios.

Of course, we should distinguish between real and bogus half-step gearing.

In the case of a modern racing corncob cluster paired with 52/48 chainrings, you would not get proper "half-step" gearing. Instead, you would end up with a situation where switching to the adjacent rear sprocket in the appropriate direction would be equivalent to switching chainrings. That is to say, all your "extra" gears would be wasted duplicates. Yes, this would probably not be useful on any bike under any sort of use, least of all a tandem, where you want to get as wide a range of gear ratios as possible.

Under the reverse condition, in which the rear cluster is spread out more than is appropriate, you end up with a situation in which the change of gear which can be accomplished by shifting the front derailleur is significantly less than half the effect of changing to the next sprocket. This is also useless, probably even more so, since your "twiddly" adjustment is in a limited range compared to the coarse adjustments your sprockets provide. Low quality bikes sometimes end up with such a "bogus" half-step system. Try charting "52/48 14-18-22-27-32" to see an example tending in this direction. Then compare with using the same cluster with 52/47 instead.

However, since any modern high-quality tandem probably has at least six sprockets in its rear cluster--probably even more--I would expect that a "non-racing cluster" will be carefully selected to work well as a half-step system, at least for the five smallest sprockets.

The idea behind adding a small chainring, or granny, to a half-step system is that you can suddenly drop into a low range when you anticipate a climb, and have coarser adjustments available at low ratios. I know of two reasons for using coarser adjustments at lower ratios; first is that you can tolerate a wider range of cadence when climbing because the change in resistive force is linearly related to speed as opposed to the situation of high-speed cruising which involves overcoming a resistive force of air resistance [this is second hand interpretation of the explanation], and secondly, you're not going to pick exactly the right gear anyway. With regards to the latter observation, remember that I ride 70's technology in an area with no long climbs.

Ideally, the top of your useable granny range should overlap somewhat the bottom of your useable half-step range. I find it is very important to know precisely where these overlaps occur.

To summarize, I would use a gear charting program (I do have C source for a simple one for those such as would know how to use it, but I don't really feel it is ready for "publication" in general) to plot the stock gears on your bike, to see if its apparent half-step setup is really bogus, before arbitrarily changing the middle chainring, since this is often fraught with other problems. I will likely make such a program available in ECMAScript (JavaScript) soon...

There really is no substitute for knowing your gears. Some people make little charts and tape them on the handlebars. According to the Nashbar catalogue, some of the latest bicycle computers with cadence will tell you your current gear ratio (these readings are only accurate when you are not freewheeling at all, of course, since it is derived by dividing your speed by your cadence and multiplying by a constant) Other people just have fantastic memories. But not me. Instead, I learn little tricks that allow me to remember my ratios on different bikes.

Now, if I could only spend as much time riding my bicycles as...