I have a long 15% grade on my standard ride. I always stand up for the entire hill ('cause I'm that macho. jk).

By standing, I mean that I just put my weight on the high pedal, and let my weight push it down, rinse and repeat. It's essentially like a stair-stepper machine. I'm not saying that's the most efficient way, but that is what I do.

I can do this in the lower gear or the next-to-the-lowest gear ("second"). It does not work in the third gear.

So here's my question. It doesn't seem to be any harder for me in second gear than in first.. That is, I'm just doing my stair-stepping. Yet, I go faster that when in the second gear.

Same effort. Go faster.

So shouldn't that violate some law of conservation of energy, causing the universe to explode?

Your pushing a bigger gear-inch, you're moving the wheels farther per crank revolution.

That's my guess, or my story and I'm sticking to it, feel free to pick me apart.

Bill

I bet if you were sitting and pedaling you would be able to tell the difference. With each stroke you are just lifting your body weight. When it gets hard enough that your body weight wont push the pedal then
you can tell the difference easily before that the difference is there just to small to feel it.

Once you introduce the physiologic element of your body with muscle fatigue, circulatory system, and respiratory system it's no longer a simple physics problem. Physics says for a given speed and drag force the rider needs to input a fixed amount of power independent of the gear chosen. But clearly some gears make it easier than others to produce that power. Choose too low a gear and you waste energy just spinning your legs madly, conversely, too high a gear and you can't produce enough force to keep the pedals spinning. Somewhere in between is the happy medium which gives the highest efficiency. In your case that seems to be second gear. First is too low and therefore inefficient while third is too high.

+1 on above comments. You mentioned "same effort, go faster". If you have a heart rate monitor, check it sitting and standing. I'll bet your HR is higher when you stand.
Just a thought.

The power OUTPUT of your body has to be the same for the same work in the same time... but what you're missing is your body's efficiency - the ratio of how much total power your body produces to get the power output that you need to deliver. So it's usually faster to stand and climb, but you're really not as efficient standing, so you're wasting more power in waste heat and other factors.

You're also not efficient in too big of a gear for physiology reasons so not as much power gets to the pedals even though it seems like you're really working hard.

Check the HRM. It's likely that your HR is higher in the higher gear.

however, it is possible to stand when climbing and rest at the same time, if one reduces the cadence sufficiently. It gives the quads a break and, as you say, uses body weight to advantage. Not as efficient as staying seated in the long term, though.

How long is this 15% section? What gear are you using? I know sometimes standing in a too low gear will slow me because
when the pedal bottoms out (or something like that) it's an effort to keep the spin going.

I also find when I am on a 15% grade on my road bike I can't have a "too low" gear.

In the lowest gear, if you have wide range gearing, you may have to put significantly more effort into keeping the bike stable.

This can add to the energy required, reduce the efficiency of pedalling, and increase the perception of effort

The amount of work required to get up a steep hill is the same regardless of what gear you're using. Higher gears require more power and will result in higher speed but the hill will be over sooner.

If you're just using bodyweight and not pulling up on the bars your power is relatively low. It's not going to make a big difference to how you feel going up at 300 vs 270W. Even if you're putting out more power it's not going to make a big difference until you get close to exhausting your anaerobic stores by the top of the hill.

You may be at your preferred stair-climbing cadence in your 2nd gear and not able to comfortably increase cadence in your lowest gear.