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From the time of the invention of the chain driven bicycle, the possibility has existed to use non-round chainwheels to vary the mechanical advantage (gear ratio) according to the position of the cranks at any given instant. There have been two basically different and contradictory approaches to this:
Around the turn of the century, shortly after the development of the chain driven bicycle, someone came up with the bright idea of elliptical chainwheels. The idea was that the large radius of the chainwheel would drive the chain when the cranks are horizontal and the small radius would pull the chain when the cranks are vertical.
The theory was that while the cranks are horizontal you can pedal more efficiently, and thus can push a higher gear. When the cranks are vertical, you get a lower gear due to the smaller effective radius of the chainwheel. The lower gear is easier to push, and you get through the dead spot sooner. This looks great on paper, but doesn't work out so well in practice.
The major problem is that this design tends to hurt people's knees. The high gear when the cranks are horizontal encourages the rider to push too hard, and we all know that pushing too high a gear is a common cause of knee problems. In addition, the low gear when the cranks are vertical means that the knees are moving extra fast when they are changing direction from going up to down and vice versa. This "whiplash" effect caused most users to abandon elliptical chainwheels. Ever since the chain driven bicycle was invented, elliptical chainwheels have been re-invented and re-abandoned for the same reason every ten or fifteen years.
Biopace is a patented non-round chainwheel design made and licensed by Shimano. To a casual glance they resemble elliptical chainwheels, but on closer examination they turn out to be the exact opposite of the classical elliptical design. The product of extensive research and computer-aided design, Biopace chainwheels have the small radius engaged when the cranks are horizontal, the large when they are vertical. This is because the Biopace design is based on a dynamic analysis of the motion and momentum of moving cranks and legs, unlike the static, geometric analysis that produced classical ellipticals.
The theory is that during the power stroke, when the cranks are more or less horizontal, you are using the power of your legs to accelerate your feet, which get going quite fast in the lower gear provided for that part of the stroke. The momentum of your feet then carries the pedals through the "dead spot" when the cranks are near vertical. Since the rider doesn't push as hard during the power phase of the stroke, and motion is slower when the leg is changing direction, the Biopace design is gentler on the knees than even round chainwheels.
Biopace chainwheels are particularly suitable for touring cyclists and time trialists, or any application that involves a steady, fairly constant cadence. They allow healthy, efficient pedaling at slower cadences than is possible with round chainwheels. They are especially suitable for triathletes and mountain bikers. The triathlete benefits because the motion is a little bit closer to that of running, making the transition easier.
The mountain biker particularly benefits, because the Biopace design somewhat smooths out the delivery of power to the rear wheel. In climbing on loose surfaces, the limiting factor is often traction. The rear wheel tends to break loose during the maximum power phase of the pedal stroke, wasting most of the cyclist's energy. The Biopace chainwheel works like a storage device, storing power during the main power phase of the stroke as the feet accelerate, then delivering the stored power to the rear wheel during the "dead center" phase when the cranks are near vertical. The same average amount of power is delivered to the rear wheel, but in a smoother, less pulsating flow. All the energy is used to propel the bike forward, without the high-power peaks spinning the rear tire or causing the bike to "wheelie."
Among other bikes, I run Biopace on several of my fixed-gear machines, where high cadences are quite common in descending hills. In practice I have found no less ability to spin fast with Biopace chainrings, and, if anything, they permit me to spin faster without bouncing in the saddle.
Here's why: While your feet go around in circles, your legs basically go up and down in a reciprocating motion. With Biopace chainrigs, your leg speed is faster in the middle of the stroke (when the cranks are horizontal) but slower at the top and bottom of the stroke (when the cranks are vertical.)
The slower motion at top and bottom means that as your leg changes direction from upward to downward, or downward to upward motion, it will do so at a slightly slower, more gentle speed. The increased leg speed near the middle of the stroke is the result of a more gradual accelleration/decelleration with the leg moving in the same direction. Bouncing in the saddle generally results from difficulty with changes in leg direction, not speed in the middle of the stroke. Thus, as Biopace makes it easier on your knees, it also can help you spin faster without bouncing!
It is possible to mix Biopace and round chainwheels on the same crankset, but I would not recommend it. When chainwheels are mixed, it is usually a small Biopace with a large round ring. The idea is to take advantage of the Biopace's superior climbing performance at low RPM's, and have the big round ring for descending and spinning fast.
The problem is that Biopace rings are more comfortable at low RPM's, and round rings at high RPM's. When you shift from a small Biopace ring to larger round ring, you go from a fast cadence on the Biopace to a slower cadence on the round ring--just the opposite of what is wanted. I have tried this arrangement on both a road bike and a mountain bike, and found it extremely irritating.
The opposite arrangement (large Biopace/small round) makes even less sense. If you like the large Biopace, you will like a small one too. The only reason I can think of for setting up a bike this way is if you need a lower low gear than you can get with Biopace. For instance, the smallest Biopace for the 74 mm bolt circle is a 26, but you can get a 24 tooth round ring in that size. For the 110 mm bolt circle the limit is 36 teeth Biopace vs. 33 teeth round; for the 130 mm bolt circle, 42 teeth Biopace, 38 teeth round.
There is a slight variation in tension resulting from the varying angle between the two straight runs of chain as the axis of the chainring rotates, but this has not generally been of a sufficient magnitude to cause any problem in practice for me.
Biopace chainwheels were made by Shimano and were also made under license by some other manufacturers. The shape of genuine Biopace chainwheels is not a simple ellipse, but a more complicated shape which Shimano describes as a"point-symmetric egg curve." Other crankset makers have made similar designs, generally of simpler shape (pure elliptical) but oriented in a similar manner to Biopace chainwheels. Examples are SR's "Ovaltech" and Sugino's "Cycloid."
Non-round chainwheels remain controversial, especially among racers who think that everyone should ride racing bikes, but, in my opinion, they are of real value for the vast majority of non-racing cyclists. Unfortunately, this useful option has become all-but-extinct.
For a normal upright bicycle, this index tab should be hidden behind the right crank.
For recumbents, the chainring should be rotated forward by 1 bolt position.
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