Bicycling And Gear Ratios

[cabinetman]

A friend and I were talking about bicycling. He and his wife live in Texas and are avid cyclists. He has a mountain bike with 18 speed, she has a ten speed (thin tire) bike.

He was saying the last time they rode together, they were riding up a hill (on pavement), and she noticed that his peddling action was faster than hers and asked him about it.

So, he explained that they both downshifted for the climb, but he couldn't say what gear he or she was in, but that she was in a slightly higher gear than he. I know the ratios are attributed to the size of the front and rear sprockets, and the tooth count. But, his question was that if there was a differential in the overall ratios of the two bikes at the time, was the work effort for both riders the same?
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[germdoc]

If you are going up a hill and pedalling faster, i.e., more revolutions, than your partner you are working less. I live in a very hilly area and have just about mastered most of the hills around here--shift up or down for maximum efficiency. One hill is a killer and requires 1st gear for the last 1/4 mile or so. I usually reverse the course so I go DOWN that hill instead of up it...

[docrowan]

Gears simply give more mechanical advantage. There is always a trade off for the advantage. The lower gear ratio requires less force (muscle power), but higher rpms to achieve the same speed. Since most people find it easier to pedal faster (for a short time) than to put forth the muscle power to climb a hill, it feels easier. Another example is rope and pulleys. If you add more pulleys, it requires much less effort to lift a load, but you have to pull the rope for a lot longer.

If both riders of the same size and weight are climbing the same hill at the same speed but with different gear ratios, both are performing the same amount of work and (probably) burning the same number of calories. But the one in the higher gear ratio will feel the burn quicker since the muscles are having to exert more force, albeit more slowly.

[natausch]

Trick question, she was based on the fact that she was riding a thinner tire bike. Single Trak/Mountain bikes are great for durability and trail riding, but on city streets they're an energy hog.

The wider the tire the more sufrace area, the more surface area the more traction, the more traction the more energy to move a wheel.

[germdoc]

If both riders of the same size and weight are climbing the same hill at the same speed but with different gear ratios, both are performing the same amount of work and (probably) burning the same number of calories. But the one in the higher gear ratio will feel the burn quicker since the muscles are having to exert more force, albeit more slowly.

Hmmm--I don't agree. The mechanical "work" is the same, according to W = F x displacement (distance), where force = mass x acceleration or mass x velocity over time .

However, the number of calories expended (physiological work) depends on intensity of the activity, which increases dramatically with increased resistance (pedalling in a higher gear). This is pretty obvious if you start out in a lower gear and have to shift down. Breaking out in a heavy sweat in our climate up here is a pretty good indicator of doing heavy work, and for me an indicator I should downshift.

[docrowan]

Hmmm--I don't agree. The mechanical "work" is the same, according to W = F x displacement (distance), where force = mass x acceleration or mass x velocity over time .

However, the number of calories expended (physiological work) depends on intensity of the activity, which increases dramatically with increased resistance (pedalling in a higher gear). This is pretty obvious if you start out in a lower gear and have to shift down. Breaking out in a heavy sweat in our climate up here is a pretty good indicator of doing heavy work, and for me an indicator I should downshift.

Very true, muscle power is much more complex than a simple physics formula. There will be a sweet spot for the average rider of the muscular force exerted versus the rpms.

[JR]

The short answer is that the amount of effort to move the bikes is expressed in "gear inches".

From Wikipedia: Gear inches is a system that assigns numerical measurements to bicycle gear ratios, to indicate how low or high a gear is.

The longer answer includes the weight of the bike and rider. Heavier weights require more effort to fight gravity up the hill. Also the resistance of the mountain bike tire compared to the road bike tire. As has been noted, the physiology of each rider makes a big difference in the kind of work they they are comfortable with.

Dr. Michele Ferrari has done quite a bit of work in this area. His VAM calculation was one of the most important training elements for elite cyclists. It should be noted that Ferrari has been controversial due to his assertion that EPO should be accepted for use by athletes, whereas it is widely reviled for use outside of is intended medical therapies.

JR

[LCHIEN]

assuming the bikes, resistance, rider weight etc are the same, just gear ratios

They are doing the same amount of work.

The difference is a smaller amount of force is applied through a greater distance.
with smaller gear ratios.

At some point you can't supply enough force to move the bike even if you stand on the pedal- you must shift to lower gears.

The human and gas engines, too, work best at certain RPMs. usually you try to cruise at comfortable RPMs. Gears will do it for you

[phi1l]

The rider with the fat tires will always be doing more work (other factors being equal). The primary reason is the mass in the tires & the angular inertia that must be over come to accelerate wheels. Angular momentum is what wakes the mountain bike more stable, but it also makes the mountain bike require more effort for each revolution to keep the bike moving.

[Alex Franke]

The real question here is this: If the bicyclists are on a freely-moving conveyor belt, will they still be able to take off? (Could not resist the callback.)

My feeling is that the person doing the most physiological work is the one who more feels like shifting down will make it easier to climb the hill at that speed.

[phi1l]

The real question here is this: If the bicyclists are on a freely-moving conveyor belt, will they still be able to take off? (Could not resist the callback.)

My feeling is that the person doing the most physiological work is the one who more feels like shifting down will make it easier to climb the hill at that speed.

This disregards fitness and training. When Lance Armstrong came back from cancer he had a much faster pace than before. This wasn't from fitness so much as from training. He trained to a higher peddle rate, is now more comfortable at the higher rates regardless of the effort required.