# Why is the front pedal gear larger than the rear wheel gears?

1. Apr 27, 2013

### hihiip201

As titled:

When moving at a constant velocity, say drag force is the only resistive force, don't we want to amplify the force output? why would we want to use a larger gear for the paddle than the rear wheel's?

I understand that we will need to paddle faster with a larger gear output, but why is this more convenient? Is it due to human physiology?

I have been wondering about why is that riding a bike through at some velocity is easier than running at the same velocity, even if I ride the bike standing (so the energy spent on standing is about the same).

thank you

2. Apr 27, 2013

### Danger

I assume that you mean a "pedal". A pedal is something that you use to turn the crank of a bicycle, or operate the foot controls of a car, or a couple of other things. A "paddle" is something that is used to propel a boat or shift gears on a horrendously expensive automobile.
Given that you mean the bicycle variety, the reason for the bigger sprocket in front is that it increases your speed of travel. When it comes to the issues that you mentioned, that's when multi-speed sprocket sets come into play. You shift gears the same as in a car as the need arises.

3. Apr 27, 2013

### hihiip201

I see, but why can't I travel at the same speed at ease by running? hence pushing on the ground with a smaller force? (where as on the bicycle, im actually supplying a larger force but for a smaller distance).

4. Apr 27, 2013

### Danger

Keep in mind that I'm an uneducated amateur, but my thinking is that the inertia of the frame combined with the angular momentum of the wheels is at work. If you've ridden a single-speed bike, which is the only kind that existed when I was a kid, you know that it takes a pretty hefty bit of "oomph" to get it going, and it gets easier as your speed increases. I always found it more efficient at high speed. When running, it gets harder as you go faster because your muscles don't have the mechanical advantage of gearing, you have impact issues with your feet on the ground, the jarring effect of your feet on the ground affects your breathing (most people won't notice that, but as someone with terminal COPD I can assure you that it exists), even the airflow into your snout can be different because of the relative postures of riding or running.
The foregoing are simply my opinions, though. If someone with relevant credentials contradicts me, believe them instead.

Last edited: Apr 27, 2013
5. Apr 27, 2013

### jeffrey c mc.

The force, or energy is being applied to the pedals from whence to the front sprocket. Where it is redirected as rotational energy. Look into the mechanical forces as applied to sprockets and gears and pulley's. As to the question about running and riding a bike, the bike stands at an UN-varying height, the runner does not. The bike being rolled on wheels offers less friction, if the analogy can be seen in that regard. The bike also uses gears and allows for only the force pushing down on the pedals, while a runner has to push their weight up against gravity every stride, while also working against inertia, viz, propelling the runner forward.

6. Apr 27, 2013

### Spinnor

Ignoring friction, which is low for a good bike, and ignoring air resistance, which is low for slow speeds, and riding on a level road, the biker once up to speed does no work. You can't say the same for the runner.

7. Apr 27, 2013

### hihiip201

when you say "harder" because it doesn't have the mechanical advantage:

the reason why i started this thread is because I found out, the force you have to apply on the pedal is actually higher than the force that you propels yourself and the bike forward.

and as i record,when lifting we try to use mechanical advantage to lift heavier weights, but why is riding a bike the opposite?

8. Apr 27, 2013

### hihiip201

In the case that we are propelling forward, isn't friction actually desirable (as the matter of fact needed) to counter the drag force in order to maintain a constant speed?

9. Apr 28, 2013

### Danger

I think that you have sort of dived into the middle of the pool before learning to swim. The crank length of the pedal-sprocket connection is an example of leverage at work. When you stand on that pedal, your body mass and gravity are doing most of the work of pushing it down, sort of as if you were doing what I believe are called "squats" in a gym, not the same muscles that are required to push yourself forward at the same time as you are pushing downward in the case of running. (I said "most" instead of "all" because some people actively pull up on the handlebars to increase their apparent mass, which requires arm muscle energy expenditure.)
Friction is necessary for movement, but less is more. As long as you have enough of a contact patch to achieve traction, you don't want more. More means extra rolling resistance, which works against you. That's why bicycles have such skinny tires. (The fatter ones on off-road units are to accommodate knobs for traction in non-solid materials like mud.)
The chain aspect of the gearing is either fixed (as was mine), or changeable by a couple of different shift mechanisms. That works the same way that it does in a car. You use a really steep ratio for acceleration (1st gear) and a really shallow one for top-end speed. Intermediate ratios are used to transition between those two extremes.

Last edited: Apr 28, 2013
10. Apr 28, 2013

### CWatters

The short answer is yes it's due to human physiology.

Last edited by a moderator: May 6, 2017
11. Apr 28, 2013

### rcgldr

It's assumed that a rider can generate enough torque to handle the effective gearing related to a larger front sprocket than rear sprocket on a level road. The gear ratio multiplies the speed and divides the torque. On some bicycles, mostly the "off road" type, there may be a "granny" gear, which is a front sprocket that is smaller than the largest rear sprocket, which divides the speed, but multiplies the torque, allowing a rider to pedal up a steep hill, although at a very slow speed.

The effective gear ratio is sometimes multpilied by the tire diameter to give the equivalent tire size if there was no gearing.

wiki articles:

http://en.wikipedia.org/wiki/Bicycle_gearing

http://en.wikipedia.org/wiki/Gear_inches

12. Apr 28, 2013

### jeffrey c mc.

Hello again;
Think about the force vector moment(s) of a runner. It is changing, the body is falling as the stride forward is being made, then the forward leg overcomes this moment, and then propels the body in a forward motion. So, the inertia moment vector is changing with each stride. To overcome this changing force vector, more energy is used, then that of a bicycle. Inertia and momentum, these two are the principles in question in regards to your musings, I believe.

13. Apr 28, 2013

### hihiip201

I think I will have to disagree that gravity doing most of the work, well at least it's just an idle process.

when we are "falling" on the padal, sure that is due to gravitational force and the decrease of our center of mass in the vertical direction. But we are converting that gravitational potential energy into kinetic energy for horizontal movement, before every "gravitational" stroke downward, we must first push our COM back up again and that still requires energy from our body, I don't think we are getting a free meal here.

Last edited: Apr 28, 2013
14. Apr 28, 2013

### hihiip201

force vector moments means the net force vector on the runner? or the momentum of the runner?

15. Apr 28, 2013

### hihiip201

me and my friend discussed this over dinner.

and we think that, it could be because if our velocity is relatively constant, the extra energy is due to we having to exert successive impulses (high force) between some small time increment instead of a constant - finite force. and our body tends to draw more energy when exerting a force of large quantity.

Last edited by a moderator: May 6, 2017
16. Apr 28, 2013

### Danger

Can you quote the exact sentence in which I said that we are?
It's about efficiency, not perpetual motion.
Put it this way: If you have to go 100 km—and let's make it interesting by adding a 50kg backpack—would you rather walk or ride a bike?

17. Apr 28, 2013

### jeffrey c mc.

If something is moving it has momentum. For every action their is an equal and opposite reaction. Inertia is a quality, it's a product of mass and velocity that equals momentum. The law of inertia states that an object in motion will stay in motion until acted on by an outside force. So, in the the stride forward the vector force moment is down and to the front of the runner; when the foot is planted, the leg lifts the body, energy is applied to the knee and hip; this changes the force vector; essentially pushing the hip forward; which moves the torso forward. So the forward leg is acting with a force vector which is behind the hip joint and moving forward. It's this change in force vectors that results in a net increase in the energy needs of the runner. The bike is at an un-vary(ing) height, it uses levers and sprockets, it has axles, and wheels, it's a mechanical system, by which all these mechanical aids result in less energy needs. The human movement is a complex system though, it's not as glib as I describe it.
http://www.physicsclassroom.com/Class/vectors/u3l1a.cfm
http://www.physicsclassroom.com/Class/newtlaws/u2l1b.cfm
http://www.physicsclassroom.com/Class/newtlaws/u2l1c.cfm
http://www.physicsclassroom.com/Class/momentum/u4l1a.cfm

Jeffrey

18. Apr 29, 2013

### Lsos

Your force output only needs to be as large as the drag force...which at slow speeds is very low. Why would you need to AMPLIFY your already large leg force to an even larger wheel force when you're only trying to fight a puny drag force? It would be the equivalent of using a large crowbar to open a bedroom door. Or a large breaker bar to turn on your faucet to brush your teeth. Yeah it would make the job easier, I suppose...but it would take an unnecessarily long time.

+

=

If you wanted to increase the force by using a smaller sprocket in the front, you would have to pedal much faster. You could easily end up pedaling madly and still be at walking pace, because you simply can't pedal any faster. Yet, you still have a huge surplus of strength which is going to waste. You can pedal much harder because of the mechanical advantage...but the small sprocket doesn't allow you to exploit this.

So we increase the sprocket size. This makes is harder to pedal, but you don't need to pedal as fast. And the bike moves faster. Eventually you reach a point where the sprocket is too large. You might be able to pedal faster, but you just don't have enough strength to do it.

Last edited: Apr 29, 2013
19. Apr 29, 2013

### CWatters

Because when running your whole body is going up and down. In theory the energy used to raise your body is returned to you and stored in your legs (which act as springs) however your body isn't very good at that. The result is that the energy required for running is much more dependant on your weight than it is when cycling. I believe they reckon you need to cycle three miles to burn off the same energy as a one mile jog/run. If the power required is that much less for cycling then it's not unreasonable to assume you can go faster on a bike for the same power output.

Gearing is all about matching the speed of the bike to the speed of the pedals (the cadence) so that you are asked to deliver that power at an rpm you body is most comfortable with. This gearing will be different for different types of bike. For example the old "penny farthing" bicycle...

http://www.britannica.com/EBchecked/media/4516/James-Starleys-penny-farthing-bicycle-1883 [Broken]

..had no gearing in the modern sense. Instead they used a large wheel to perform this matching.

Last edited by a moderator: May 6, 2017
20. Apr 29, 2013

### A.T.

You can, if you don't have to support your weight, using your muscles: