Exercise weights usually are based on some standard unit (in the USA, pounds) and then come in integer multiples of that unit- 1, 2, 3, etc., and eventually by about 10 or so start skipping in higher multiples, i.e., 15, 20, 25, etc.

What got me thinking about this was the long and difficult search for hand weights between 1 and 2 pounds. I eventually found 1.5 pounds and 0.75 kg (about 1.65 lbs).

What I was wondering is if there would be any demand for weight sets that increase in weight by a fixed proportion. For the simplest example, take the square root of 2 which is approximately 1.41. IOW, each weight would be the square root of 2 heavier than the previous one of the series, so every weight would be slightly more than 41% heavier than the previous one, every second weight would be twice as heavy, and so forth.

If that’s too big an interval, use the cube root of 2 ≈ 126%

Since I’ve never seen or heard of anything like this, I suppose it must not be as nifty an idea as it seemed to me at first. Maybe the usual way is simpler. But I’d like to hear the Dopers chime in.

There is room to put more than 1, let’s say up to 4 or so, weights on each end of the dumbbell/barbell. Doesn’t that change the composition of the “optimal” set? The type of training may also have something to do with what weights are required.

I think the OP is talking about standard dumbbell sets. At my gym, they start at 7.5 lbs, then go in 2.5 lb increments to 25, then 5 lb increments to 100.
Changing the increment to something exponential might result in fewer weights, but that isn’t really a benefit, since there are generally many people trying to use a finite set of weights at the same time. If the 30’s aren’t available, I can make do with the 25s or 35s, but if the next increment was 42, that would be a big step. I don’t know of any research that has documented the “optimal” step increment, and the system as it stands has been used without too many complaints for many decades.

Yeah, it occurred to me that at the higher end of a weight range any geometric progression is going to start producing jumps that on an absolute scale are too much. Just as a side question, how much do they recommend increasing your weights as you get stronger?

The “rule of thumb” is if you can do 3 sets at 8-10 reps, you get to increase your weight by around 10% the next time. At least that was Darden’s guide in High Intensity Bodybuilding back when. Who knows what kids these days are doing. (FWIW, I tend to pyramid-up, 5 sets of 6 reps, something like 140/160/180/200/220 on the incline Hammer strength machine. Once I can do 6 reps at the max weight, I’ll increase the starting point by 10% or so.)

The more advanced you get, the smaller the increases possible. As you progress and get closer and closer to your genetically pre-determined limit, the smaller and smaller the increases get as a percentage.

Your first year of lifting, maybe you can increase your max by 50-80%. If you could keep that up for five years, you would be world champion. But you can’t. So it is more a matter of five pounds here and ten there.

Part of it might be that in Olympic lifting (and, I believe, powerlifting) you cannot increase your attempt weights by less than half a kilo. Nobody breaks a record by ten grams. Most gyms IME have two and a half pound weights, rather fewer have one and a quarter pound plates.

Not that it matters all that much. Doing reps with 227 1/2 is not that much less fatiguing than reps with 230, so you are going to need a deload cycle at nearly the same time as you would either way. And those kinds of very small fluctuations tend to be lost in the background of strength level fluctuations anyway (having a stressful week at work is going to affect your 5RM more than 5 pounds worth, IOW).

When I started lifting, my 10RM in the bench went from 40 to 120 in a year. Going from 120 to 185 took three years. Going from 185 to 205 took seven years.

I have no athletic ability, but boy, am I stubborn.