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I am planning to develop a bicycle on my own for a competition. But the main requirement of it is that it must be able to develop a maximum speed. If I am able to cast the sprockets with gear ratio say 10:1 or something like 100:1, will there be any practical hindrance to it?

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Well, absent a special geared hub to get 100x you'd have to use an idler shaft and two chains, but if that's what you want then have at it. Some weirdly high ratios have been used when setting speed records, running behind a vehicle to break the wind. –  Daniel R Hicks Dec 17 '13 at 11:56
    
Penny-farthing and exceptionally long legs? –  James Bradbury Dec 17 '13 at 14:05
    
If you used a smaller pitch chain than bicycles normally do you could do this with a normal-ish bicycle, but to make it work properly you'd be better off taking the drive out to the side. That way you could use stock bicycle chain with 12:1200 cogs and a 1m diameter chainring. Of course, to pdeal that would mean a wheel the size of that 12T cog... –  Mσᶎ Dec 17 '13 at 20:37

4 Answers 4

The main hindrance will be actually getting going from a standstill. This kind of thing has been done quite a bit and is called motor-pacing and involves riding a very highly geared (usually fixed-gear) bike behind a fast car with some kind of fairing to reduce wind resistance on the bike. Speeds of well over 100mph have been reached.

This kind of bike is totally unsuitable for riding anywhere but a specially controlled long straight under the right conditions.

Check out this video for an idea of what's involved.

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The first such record was set about 100 years ago riding behind a train. Carpenters had fitted the track between the rails with wood planks to ride on, and the cyclist rode behind a special passenger car that had an extended platform with wind breaks on each side. I vaguely recall that the record achieved was 60 mph. –  Daniel R Hicks Dec 17 '13 at 12:41
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1899, at 63+ mph, by Charles "Mile-a-minute" Murphy. The current absolute speed record is held by Fred Rompelberg at 167 mph. He used a double reduction gear (70/13 connected to a 60/15 for a total gear ratio of 21.5) and his wheels were 18 inches in diameter. –  R. Chung Dec 17 '13 at 14:20
    
@R.Chung 18" is pretty small. Presumably this was some sort of recumbent? –  Daniel R Hicks Dec 17 '13 at 16:13
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The new version of this is downhill mountain bike racing. Pick a very steep slope, groom the snow flat and see whether you die before you break the record. Same idea, just using the motor to get you up the mountain rather than pull you along. The record for that is 222 km/h (138 mph). It's still "looks like a bicycle" record setting, worse than the multitudinous UCI handicap class speed records. –  Mσᶎ Dec 17 '13 at 23:38

The other answers given here are correct in that there are physical limitations to the size of a single chainring; however, you can get around that limitation by building a "double reduction" gearing system where you sequentially link, say, a 4-to-1 gear ratio with another 4-to-1 gear ratio to get a final ratio of 16-to-1. As noted above, Fred Rompelberg set a speed record at 269 km/h by using a double reduction gear: a 70/13 connected to a 60/15 for a final total gear ratio of 21.5. His wheels were 18 inches in diameter and his tires were about an inch thick, so each rotation of his feet around the crank moved the bike about 35 meters. 269 km/h is 75 meters/second, so his cadence at top speed was just under 130 rpm. Below, you will see that this will turn out to be important.

And now we come to the real limiting issue. Under usual conditions, your maximum speed is limited by the power you can produce, not your gear ratio. The power needed to cycle on flat smooth ground with no head or tailwind has two components: a component needed to overcome aerodynamic drag and a component needed to overcome rolling and mechanical drag. Aerodynamic drag force varies with the square of airspeed, so the power needed to overcome aerodynamic drag force varies roughly with the cube of speed. On the other hand, rolling and mechanical drag force is nearly constant, so the power needed to overcome it varies roughly linearly with speed. In the Rompelberg speed attempt, and in other similarly "paced" attempts, he rode behind a specially-designed motor vehicle designed to minimize aerodynamic drag. However, the rolling drag remains. The power needed to overcome rolling drag is approximately Crr * total mass (in kg) * speed (in m/s) * the gravitation constant (9.8 m/sec^2) where Crr is the "coefficient of rolling resistance" and can be thought of as including bearing and other transmission losses. On firm ground with modern tires and a modern chain-drive system, Crr is often in the range of .005. Thus, moving a total mass of 100 kg at 75 meters/sec would require around 370 watts of power, on flat firm ground in the absence of aerodynamic drag. If the pacing vehicle were unable to eliminate all aerodynamic drag, the power demand would be higher.

Now we turn to human production of needed power. Power is the product of force and velocity, and we can either produce a given amount of power with a combination of high pedal force and low leg speed, or high leg speed and low pedal force. As you might expect, pedal force and leg speed are inversely related: the higher the pedal force, the lower our leg speed and the higher our leg speed the lower the pedal force we can produce, so there is a trade-off between the two. In general, it has been observed that for most humans, power is maximized at a point where leg speed and pedal force are roughly half of their maximums (that is, if we know a rider's maximum leg speed and maximum leg force, power is maximized in the neighborhood of half of the maximums). For many trained cyclists, maximum cadence is in the range of 200 to 250 rpm, and we can generally observe that they produce maximum power in the neighborhood of 120 rpm. And that is consistent with our observation that Rompelberg's speed record was set at just under 130 rpm.

So although you could construct a bicycle with 100-to-1 gearing (via a double or triple reduction system), you probably would not be able to produce the required power at the "sweet spot" in cadence in order to attain your speed goal.

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There are a couple of obvious problems:

  • You'll never ever be able to pedal 100:1 with normal wheel sizes, even with a fully-faired bicycle
  • Smallest cogs are eleven teeth iirc, so you'd have to have a 1100-teeth chainring, which is approximately twenty times the size of a 55-teeth chainring, so you'll have clearance problems
  • getting the 1100-teeth chainring to be stiff enough to not wobble under load
  • getting going from a standstill
  • You'll probably not be able to have front shifting.

But other that that, no.

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To get 100x he'd have to have a 1100 tooth chainring. –  Daniel R Hicks Dec 17 '13 at 11:57
    
Oh. Right. Updating... –  arne Dec 17 '13 at 12:35
    
You can get around some of those problems by having a 10:1 gearing to the midpoint between the pedals and the axle, then another 10:1 from there to the axle. –  Kris Peters Dec 17 '13 at 14:49
    
Still 10:1 is actually quite hard to achieve on a bike. For an 11 tooth cog, you'd need a 110 tooth chainring, which doesn't exist, and if it did, would probably hit the ground assuming a conventional bottom bracket height, or not have enough rigidity to operate properly. –  Kibbee Dec 17 '13 at 17:54
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104 tooth cogs have been done before as custom jobs though, such as Donhou's "land speed bike" (donhoubicycles.com/land-speed-bike). –  Batman Dec 17 '13 at 18:35

The main problem is that the gear ratios of a transmission multiply or divide torque. A 100:1 transmission means that the torque you are generating is being divided by 100. If the resulting torque is less than what is needed to move the bike, then you won't be able to turn the pedals.

If you are on a smooth, level road, with well inflated tires, and no headwind, then the torque required to begin moving is close to zero, and so having your torque cut by 100 might not be an impediment against beginning to move. However, as soon as you start moving, impedance builds due to air drag and rolling resistance. As soon as this impedance adds up to your torque / 100, you cannot go any faster.

High gears allow our muscles to work slowly, similar to doing a slow bench press. You probably know from weight lifting that your maximum force is developed during a slow lift. If you can press a 200 pound bar off your chest quickly, that means you can handle quite a bit more weight. Using a high gear is somewhat like doing a slow lift; you're developing a greater force. High gears also allow us to reduce wasteful motion of the legs, improving our efficiency. However, the gear must not be so high that the output torque is less than the force that is required to maintain the desired speed (a force opposite and equal to the total drag).

The increase in gear ratio allows you to develop more torque against the pedal crank, but at the same time, the output torque diminishes. The output torque must not diminish to the point that you cannot maintain speed. So there is a trade-off happening which means there is some optimal point. This point depends on you, of course: your body geometry, strength and weight, and on the conditions: slope, wind, surface, bicycle (tires, etc). Also, the intended riding distance! You might be able to sprint a mile in a high gear that would be inappropriate for you to use for a 100 mile road trip.

You probably know from experience that a gear that feels ideal on level ground may be overpowered as soon as you encounter an incline: you make an extra effort, yet the bike slows down. This is because the output torque is too low to push the bicycle up the hill. Switching to a lower gear allows you to then maintain a speed that would be impossible in the high gear.

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