For those of you pulling out the maths/physics, you're only considering the vertical displacement. Most of you are forgetting about the arc (rotation) in the sagittal plane and any arm pull (mostly thinking of the snatch and clean here).
I learned a long time ago not to bring maths to a kettlebell fight
This is a good point.
Personally, I don't have much interest in actually or accurately calculating the forces involved in KB ballistics.
The points I've tried to make are definitely based on simplified approximations.
One of those points is that, all else being roughly equal, a 4-8kg increase in bell size is going to have a much bigger effect on power generation per rep than a slightly higher velocity/shorter rep time (within the range that a person can actually increase speed in a KB ballistic lift). Of course, by qualifying with "all else being equal" I'm waving away a lot of factors with the assumption that they aren't going to vary much (the height of the snatch lockout for example) or that any variation won't be significant.
The only way to truly measure the power output of a swing or a snatch is to have a timestamped forceplate under the lifter with a timestamp video.
A lot of information can be derived from the accelerometer (and if I did have a forceplate and camera, I 'd definitely have an accelerometer on there for data gathering too).
These together would allow us to see how much drive is coming from the hips alone (with no additional force from the pull) or, mostly in the snatch, how much you were pulling up with the arm...
...Your arm is a rope, don't confuse flight time with the time it takes for you to generate your force into the floor.
One of my assumptions is that flight time doesn't vary much. You can move the bell a little faster with a lighter weight, but not by a lot and therefore the effect of bell weight is much more than the effect of bell velocity. So the quote above raises the issue that maybe flight time isn't a good enough proxy for the actual application of force at the hips. Does that force application time vary with different weights to a significant enough degree to outweigh the effect of a higher mass? I don't know the actual answer, but I'm a little doubtful, just because the times involved are so short. We're talking a fraction of a second vs. a slightly bigger fraction of a second.
But now I'm getting lost in the mathematical weeds again, and my concern is more with practical training applications. The article posted by
@watchnerd made the point that heavier bells are not always better and the reasons I agree with that are mostly not related to power. Sure, there's the extreme case of swinging bells you can barely get above knee height. But often it's more a matter of sticking with a bell you comfortably own and can be aggressive with, or moving up to a bell that's more of a challenge. With 8kg jumps between bells, there's often a big gap there, although with 4 or even 2kg jumps it's less of an issue. And of course there are lots of transition/break in strategies for increasing bell size, and lots of programming around multiple bell sizes in the same session or program.
When I'm choosing what bell to use, I mostly don't care whether it's the optimal size for power. I am more likely to consider whether a heavier bell will:
--Distort my technique to an unsafe or unpleasant degree.
--Fit my current training goals and whether I have planned around incorporating it.
--Make it impossible to complete my planned session, sustain a consistent output throughout the session, or complete it at my desired RPE.
--Be sustainable within the context of my overall training. Am I physically prepared to absorb the greater stress of the heavier bell, or will it leave me feeling beat up?
--Be fun or otherwise satisfying to use.
--Teach me something useful.