Resistance for different gear ratios

Why are some gear ratios more difficult to pedal than others on a bicycle. It feels as though I’m missing some very simple piece of reasoning!

• It takes a certain amount of energy to move a bike 100 feet. In a low gear (large rear sprocket) you turn the pedals around more times to get 100 feet, so there is less energy required per turn of the pedal. Commented May 27, 2020 at 22:01
• Does it help to consider a car gearbox/motor? The motor has a "preferred" or most-effective speed, and going faster or slower than that is sub-optimal. The gearbox lets the motor stay near its best speeds. Same goes for a bicycle.
– Criggie
Commented May 28, 2020 at 0:45
• Efficiency of some gear combinations is very slightly lower (like 1 or 2%). Especially for internal gear hubs. Commented May 28, 2020 at 5:59

To add to Nathan's correct answer, the concept at work here is mechanical advantage. Different gear ratios offer different mechanical advantages, and let you divide or multiply your torque to suit different conditions.

It's the same with a car: you pull away from a stop in 1st gear in a car, not 4th, because the engine doesn't have enough torque to manage it in 4th.

• Oh, it's well possible to start driving a car in 4th gear. It'll just kill the clutch in the long run... Commented May 28, 2020 at 6:58

Divide the chainring tooth count by the cog tooth count. Multiply what you get by the circumference of the back tire. That's how far one rotation of the cranks is moving the bike. So why would that take the same amount of effort with two different gear ratios?

The amount of energy and power required to move your bicycle a certain distance at a certain speed should always be the same.

Power is torque times rotational speed. Shifting gears allows you to choose between pedalling harder (i.e. more torque) or quicker (i.e. more rotations per minute).

There is a very small amount of losses in the transmission (like 3%) which can vary depending on the gears you use (like ±1% or 2%). For example “cross chaining” (using the large chainring in the front and large sprocket in the back or vice versa) can increase losses. With internal gear hubs it’s even more pronounced. But you’ll probably be unable to feel (or even measure) it.