# Hyperbike performance skepticism

Gizmodo points to this site advertising the hyperbike, a new kind of human powered vehicle:

The designer makes a number of claims, including that:

• It's safer than conventional bikes because it has three points of contact and so is more stable.
• It's more efficient because of the large wheels, high gearing and because of whole body involvement rather than legs.

I'm quite prepared to believe that it's safer, not because it's more stable—bicycles are actually extremely stable at speed once you know how to balance them—but because the user is in a protective cage. It wouldn't be that hard to build a recumbent bike with similar properties if you wanted to.

I'm a lot more skeptical of the performance claims. I wonder if anybody has actually ridden this than that fast. Here's what the site says:

The Hyperbike will be the fastest & safest human powered vehicle on the road.

The circumference of an eight foot diameter wheel is roughly twenty-five feet and cadence, or the rate at which a person pedals, is most comfortable at a rate of 13 beats every 15 seconds. Gearing that allows an operator to rotate the wheels four times each pedal cycle, or at a 1:4 ratio while at the comfortable cadence rate will produce a speed upwards of 50mph.

Using the whole upper body, an operator, unobstructed by a seat and able to "throw" weight into each pedal thrust bouncing each stroke, like hill climbing on a conventional bike, will move the Hyperbike fast and effectively on all grades.

This is simply confused. The limiting factors in bicycle top speed have nothing whatsoever to do with the gearing of the bike. This is easy to see by doing some simple math.

Your average reasonable road bike has something like a 53/42 chainring combination on the front. That means that it's got 53 teeth on the big ring. It probably has an 11 or 12 tooth smallest cog on the back. For convenience, let's say it has a 52/13 for a 4:1 maximum gear ratio. The wheel itself is approximately 700mm in diameter, or 2.2 meters in circumference. So, every pedal revolution at the highest gear ratio moves you forward about 9 meters. A typical amateur cycling cadence is 80-100 rpm, which maps to 720-900 meters/minute or 27-34 mph. By the simple expedient of putting a readily available 11 tooth cog on the back and 55-tooth chainring on the front you can get to 41 mph at 100 rpm.

But these limits are purely theoretical because what's really important is power. Plugging these speeds into Analytic Cycling we can compute the power required to go at these speeds, which is 300, 561, and 947 watts respectively. For reference, few untrained cyclists can maintain 300 watts for more than a minute or two. Even elite cyclists have trouble maintaining 500+ watts for any length of time. To put this in miles per hour terms, maintaining 25 mph for an hour is doable by amateurs but quite hard. The hour record stands at around 31 miles.

At this point it should be obvious that the gearing isn't the limiting factor in the performance of a bicycle. But a bicycle only works the lower body whereas the hypercycle lets you recruit your upper body muscles as well, so maybe that helps. First, this isn't as big an advantage as you think. The upper body muscles are comparatively weaker than the lower body muscles, which is why racing wheelchairs are somewhat slower than standard bicycles despite having superior aerodynamics. So, all other things being equal, you might get 30-50% more power with the hyperbike but you'd be unlikely to get twice as much. Because the power/speed curve is cubic this might get you a speed improvement of 20%, but nowhere near doubling the speed.

But of course, all other things aren't equal because the vast majority of the energetic cost of riding a bicycle is wind resistance. The completely upright position of the hyperbike is vastly aerodynamically inferior to the partly upright position of a typical road bike (let alone a recumbent bike, which is why land speed records are always set on fully faired recumbent bikes). I would imagine that this increases the surface area by 50-100%, which would more than compensate for the somewhat increased power of recruiting the upper body muscles.

Just as a final check, if you plug 50 mph into Analytic Cycling's model, you come away with a required power output of 1695 watts, even with normal bicycle aerodynamics. If you can put out 1695 watts for more than a few seconds I'm pretty sure there are some people on the Olympic team who would like to talk to you.

UPDATE: The power/speed relationship is cubic, not quadratic. The air resistance/speed relationship is quadratic, but then you multiply by speed again.

The UCI hour record is 49.7km (slightly less than 31 miles) in an hour, but this requires the competitors to use 1972-era bike and a restricted cycling position. The hour record on a wedgie (slightly less restrictions on position and aerodynamic technology, but still no fairing) is 56.4km. The record for purely human power with no restrictions on position or aerodynamics is 86.5km. The IHPVA competitors typically develop a bit more than 300W and are less efficient by around 10% inside the fairing because of temperature problems.

You can't get any more power using your arms as well as your legs because your legs can use all your heart and lung capacity when working flat-out.

### October 2012

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