# Bicycling up hill, high gear or low gear

• Hetware
The force you can generate is mostly dependent on the weight of the rider because you can't push down with more force than you weigh.

#### Hetware

I know that the idealized problem using gears and force without considering biophysics will tell me there is basically no difference in energy between riding a bike up a hill in low or high gear. I have often wondered which actually uses more calories. Many people tend to go to a lower gear when going up hill. It feels easier. What I wonder is whether it really is easier in the long run. Of course, I am thinking within reasonable parameters so that there would be no physical injury due to putting excessive force on ones joints, etc.

Off hand opinion: The amount of energy used would be the same. However in low gear the rider applies less force on the pedals, but has to move his legs faster in comparison to high gear, assuming the speed up the hill is the same.

The energy expent by you is the same (m * g * change in elevation). And so is the work (force * distance). But if you climb the hill in 10 minutes in top gear, and in 20 minutes in low gear, the difference is the power (work/time). You must be 'stronger' to pedal the bike in high gear. If you climb the hill in the same time, then the power would be the same too.

That's all ignoring practical effects that may change your efficiency (standing on the pedals vs sitting, etc). Those things have to do with how hard your body works to make the pedals go around.

When climbing in high gear you would need to apply much more force to the pedals than when climbing in low gear (for climbing in the same time). This is because in high gear the distance your feet travel is much less than in low gear. To get work (or energy) = force x distance to be the same, the extra power is needed.

more torque[low gear ratio] will get you up the hill more easily compared to less torque[high gear ratio].

The work done is the same, but there's probably some optimal combination of speed and gearing, power x time, depending on the parameters of the rider, such as muscles, conditioning, ...

Remembering the relationship between energy and power and power and torque, if the energy is the same, a faster pedaling rpm will provide more power (over a pretty broad range of human pedalilng speeds) and get you up the hill faster.

This also means that the proper gear to be in (in this idealized scenario) is independent of your speed up the hill! The proper gear to be in is a function of your weight (which determines how hard you can press on the pedal and thus your maximum torque) and the incline of the hill only.

Last edited:
Well people like motors work best at their ideal speed, if you need too much force, I am sure, that you need more energy, but I guess you should ask in a biology forum for exact numbers. An easy way to check is, which way you sweat more, because that body heat is all burned calories.

Well people like motors work best at their ideal speed...
True - they are most efficient, meaning they produce the most energy output for the least energy input.
...if you need too much force, I am sure, that you need more energy, but I guess you should ask in a biology forum for exact numbers.
Notice that the sentence I wrote above doesn't mention force. Energy and force are not the same thing. And there is no such thing as "need too much force" in this problem because the the force generated is mostly dependent on the weight of the rider because you can't push down with more force than you weigh. In other words, the force is constant. But the energy is dependent on that force and the speed at which you are pedaling.

To compute Watts and Calories while riding up a hill, for every one revolution of a bicycle front tire, is this accurate?

Watts = ma*gr*pcl*s*sin(theta) + Rr

Calories = watts*0.2388459

m = Mass = 145kg
a = Pedal Speed = 22pi/9 rad/sec
gr = Gear Ratio = 44 : 18 (2.444 to 1) (This is gear ratio I use the most)
pcl = Pedal Crank Length = .175m
s = Front tire circumfrence = 2.2m
Rr = Rolling Resistance ?? (I plan to gather Rr by comparing computed and measured data)

"because you can't push down with more force than you weigh. "
Why so?

sganesh88 said:
"because you can't push down with more force than you weigh. "
Why so?
Because you'll just make yourself stand up!

russ_watters said:
Because you'll just make yourself stand up!

But you can pull up on the handle bars at the same time, increasing your downward force on the pedals.

It could be helpful to look at the boundary conditions.

At some high gear ratio standing on the pedals doesn't exert enough force to move the bike up the hill; you're speed will decrease until you stop.

At the other extreme, you peddle all day and don't move an inch; a 100% mechanical lose.

There is at least one optimum somewhere in between these two. Engineering experience should tell us to expect one extremal (best gearing) in a simple scenario such as this. With descrete gearing, two gear ratios could be equal candidates.

I worked as a bicycle courier for 6 years. I always went with the high gear on hills.

However:

- I most certainly did not get up the hill in the same amount of time. The whole point is to get to the top sooner.

- I do not start the climb in a high gear at the same ground speed as I would in a low gear. Again that's the whole point. I want the extra momentum to make it that much easier to get up the hill.

- Too much ground speed results in an increase in wind resistance, making the high gear climb harder than it would be otherwise.

I'm only talking about short climbs, of steep hills in the city. Cross country rides with long 10+ minute climbs are entirely different.

I rode a bike I built myself. It had a mountain bike frame, but road bike crank with a 53 tooth gear up front. I never once shifted down onto the smaller 38 tooth ring up front. That large ring up front combined with the largest ring on the micro cassette in the back gave tremendous torque. On flat ground I would have to aply downward pressure on the handlebars to keep the front wheel on the ground.

I only used that pairing when starting from a standstill, for perhaps 2 or 3 pedal strokes. I would climb 1 gear down from that in the back. Although I would start my climb perhaps 5 or 6 gears down, and shift as I climbed on a pace that would maintain a constant amount of required pedal force.

Last edited:
I am a biker and the total energy for a given time is about the same. If I am coming to a hill that I have ridden up before and I know I can shift down to gear 22 and pedal up fairly easy at 10 mph well I can also shift to gear 20 and pedal up at 12 mph. It takes more energy to pedal up in the higher gear but I am traveling faster so I am up and over the hill about 10% quicker. If I use x amount of energy for 10 seconds or y amount of energy for 12 seconds they both = Z

The only reason for gearing down low is the body is only capable of supplying a certain amount of blood and oxygen to the muscles if I use more energy than the muscles can produce then I get tired and can not ride up the hill without resting. I have to find a gear that uses energy at the same rate that my body can produce energy.

I can over load my muscles for a short period of time on small steep hills without much trouble.

It is like having a table saw with a 1/4 hp motor. If I push the lumber through the blade at the correct speed it never over loads the motor. If I push the lumber through the blade too fast it works for a few seconds then the motor over heats and the circuit braker trips and the motor stops running.

Last edited:
The optimum cadence (pedal RPM) for recreational bikers is about 50-60 RPM, according to many google hits on bicycle pedal RPM cadence. For professional bikers (competition) it is closer to 90-110 RPM. For physics power, it is torque (force on pedal x lever arm) x RPM ((60/2 pi) x radians/second). Caloric energy consumption rate is usually directly related to force (muscle fiber contraction), with little dependence on pedal RPM. So probably to get maxumum physics power, the gear ratio should be to get a comfortable pedal force at about 50-60 RPM.

Forget gears get a single speed. Then you won't have to ponder such problems.