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Torque is what makes the wheels on the bike go round. Great research has been but into the sport in order to figure out how to increase the torque applied by the rider to the rear wheel, wile decreasing the torque required to make the wheel turn. Torque is produced the rider using a device called a crank.
The torque in the series of parts that drive the bicycle forward (called the drive train) is dependant on the size of the chain ring (the large gears mounted on the crank) being used, and the size of the rear cog being used. When the chain is on the smaller chain ring, the force through the chain must be greater because the chain ring is closer to the axis of rotation and must apply a larger force to equal the torque produced by the pedals.
Likewise, if a larger cog is used in back on the wheel, an larger torque is exerted on the wheel, and so produces a larger forward force at the tire. These higer-torque gears are good for climbing, where large forward forces are need at low speeds, but for flats and downhills, different gearing is needed, because the lower gearing does not provide much forward rotation (the rear wheel will not rotate as much for a single stroke of the pedal).
Detail of the drive train on a bicycle. The smaller the gear on the crank combined with a large gear on the wheel will produce large amounts of torque and large forward forces.
Work and Power
Although torque does have a lot to do with the bike and how it works, professionals and people in the know don't usually refer to torque the rider applies to the wheels. Usually, they'll talk about power. This makes much more sense, because cycling, in general, is a sport that requires you exert yourself for a relatively long amount of time, instead of just trying to exert the largest force you can (this isn't weight lifting).
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"Physics of Cycling." 123HelpMe.com. 28 Jan 2020
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Power is the amount of work done in a given amount of time. It doesn't take a rocket scientist to figure out that more power equals more speed. However, it has only been recently that measuring power output has become a common practice in training. Riders now train to maximize their power output. This is done a number of ways. There are special trainers that you can mount you bike into that will measure your power output:
The rear wheel is mounted into the trainer, and rolls on the roller. But the new and best way to measure power is using a power measuring crank. You aren't confined to a trainer, and can get some real riding done.
The newest craze in cycling has to do with making the power you produce go to making you go forward. The bicycle is one of the most efficient machines ever made (over 98% efficient for a nice bicycle in good condition), and can't be improved upon significantly. So, bike makers have turned to making the bike more efficient by making it slip through the air better. It may seem like a silly way to try and make a bike go faster, but it's not. This design idea is most visible in the type of race called the time trial. It is one man, by himself, racing against the clock. Aerodynamics come into special consideration here because there are not other riders around to break the wind (in packs, aerodynamics become less of an issue because within the pack, the air is almost moving with the riders, so the rider doesn't have to cut much wind).
There are a number of ways to reduce the drag produced by bike and it's rider. The most common way is with aero handlebars. These but the rider in a low tuck over the bike, reducing his profile to the wind. This is the most effective way of making you more aerodynamic (you can make yourself go as much as 2 miles per hour faster by some studies. That doesn't sound like a lot, but trust me, it is)
Using deep-rimmed wheels also cuts down on a lot of drag. The spokes of wheels tend to churn the air, making them less aerodynamic, using a deeper rim will shorten the spoke, along with making the rim itself more aerodynamic. A totally solid wheel is the most aero-wheel, that can be used, but they are heavy, can catch cross winds easily. For these reasons they are only popular in the time trials.
Finally, changing the shape of the bicycle frame can make it a little more aerodynamic. By making the tubes in airfoil shapes and tucking non-aero shaped parts out of the wind, a slightly faster bike can be made. This makes the bike a little faster, but not as much as the other methods.
People who are lucky enough to get paid to ride a bike will often use aero-helmets as well. These funny looking teardrop shaped lids do actually cut down on drag a good amount, but don't protect the head much and are pretty expensive, keeping them out of the hands of normal folk.
The most important points have already been covered though. What's next is to put all the covered points together to make sense of it all. The bicycle is an incredibly efficient machine. Nearly all the power put to the pedals goes to moving the bike and rider forward.
Unfortunately, there is no such thing as a perfect bicycle. For example, a very aerodynamic rider position will not allow the rider to produce as much power, and will also be very uncomfortable. Deep-rimmed wheels are aerodynamic, but they also have much more material at the outside edge, which means it requires more torque to get spinning, and so does not accelerate as fast. Very aerodynamic frames also tend to be much heavier.
Because of this, the people that are lucky enough to be paid to ride a bike use different bikes for different kinds of races. For races that involve lots of climbing at relatively low speeds, they will use a very light bike with very light wheels that accelerate well. For fast, flat races, riders will use a slightly heavier bike and wheels in exchange for better aerodynamics. And for time trials, where the rider is by himself and must cut the wind as best as possible, a time trial-specific bike will be used, which is the most aerodynamic bike you could use.