Originally Posted by gyozadude

When we ride a bike, we must do Continuous Work to overcome resistive forces, such as friction, rolling resistance (i.e. resistance to the deformation of the tires against the road), and wind resistance. Continuous Work is measured as energy output per unit time, which we should all know is Power. On a bicycle, our legs must continuously spin the crank arms and this powers the bike and propels it forward. Another key concept that people need to understand is that of Torque = Force x radial length. In any type of conversion for circulating power into locomotion (e.g. pedaling a bike), we always must deal with Torque, and this gives rise to the concept of gear ratios, as we'll read below.

First basic thing to impart is: How fast we go on a bike is determined by the power output of the rider spinning the pedals relative to the resistance forces (friction, wind, gravity, etc.) At any moment in time, the bike/rider's forward speed responds to power output to match the speed of the bike to the power output. So if the rider pedals harder, the bike speeds forward until friction/wind resistance, gravity are in equilibrium. The reverse, if the ride eases off pedaling and coasts, the bike slows down until resistive forces (wind) is low enough to match the reduced power output.

Second basic concept to impart: The maximum (aerobically sustainable) power humans can deliver by spinning pedals occurs in a narrow range of 60 - 90 RPM. Many other factors are required to allow a rider to produce optimum power, such as frame size, seat height/leg extension, crank arm length, stem height, stem extension, hip position over the pedals, foot position, physical fitness, etc. But for any properly sized bicycle, and at any level of physical fitness, we will observe that a rider can aerobically sustain pedaling only within this narrow range of RPM. Much has to do with bio-mechanics, and things you'll read about include muscle twitch speed, aerobic recovery time, lactic acid build-up, etc. But in general, too slow a cadence and the muscles cramp up, and too fast of a cadence one wastes energy controlling the form of his spin and impart less to force at the pedals. Individuals do vary in power and fitness. But for any individual, the maximum sustainable power they can achieve without going into oxygen debt is achieved in the narrow range usually between 60 - 90 RPM.

This brings us to the 3rd basic concept: Multiple bicycle gears widen the range of conditions a rider can continue to pedal efficiently by enabling the rider to continue to spin at 60 - 90 rpm. The gears achieve this by allowing the rider to change the gear ratio, and thus change the torque that his pedaling ultimately exerts on the rear wheel. Take the example of a rider on flat road w/ tail wind riding a 52/13 (4:1) ratio on a 700x25c road bike at 80 RPM. This equates to roughly 2 meter circumference x 80 RPM x 4:1 ratio x 60 minutes/hr = 38400 meters/hr = 24 mph. The rider makes a turn, loses the tail wind, and now the road has a 1% slight uphill. The force of gravity and the loss of tail wind means the rider must fight quite a bit more resistive forces. He gears down to the small ring in the front and mid cog in the rear 40/17 (2.353 ratio). His torque on the rear wheel increases to 1.7 times his previous ratio due to gear reduction (ratio of 4 relative to ration of 2.353). This puts 70% more torque to the rear wheel, which helps overcome the new gravitational potential the rider faces going uphill without wind assist. But this increase in torque comes at a cost of speed. Before, we were spinning the rear wheel at 4:1 ratio relative to the RPMs at the crank. Now we spin at just 2.353 revolutions of the rear wheel per turn of the crank. This means if our rider sustains 80 RPM, his forward speed drops to just 14.12 mph. Considering that this is still as fast as someone running in the Olympics for a long distance marathon, it's far better than having to get off the bike to push. If we only had one gear, 52:13 ratio, the extra uphill grade would push us to have to increase force at the pedal about 70%. We couldn't sustain that power output so we'd have to slow down, and then we'd be spinning probably less than 50 RPM, and that would probably require us to stand up and honk on the pedals, further lowering RPMs, and now we've dropped out of our optimal power output range. We'd be doing only 9 - 11 MPH and unable to sit down to sustain the force required to turn the pedals. After 2 minutes, the rider cramps his legs and gets off the bike to rest and sit and wish he had wider gear ratio.

So to recap: 1. Bikes work by using gears to transfer pedaling power into locomotion. 2. Humans exert power at the pedals most optimally spinning at 60 - 90 RPM. 3. Gears allow us to sustain that spinning in the optimal RPM range by changing gear ratios to drive the rear wheel and thus change torque in exchange for speed.

Does that explain things?