So first things first!
What determines muscle strength?
Muscle fibre type (there are three types) aside, the most important mechanical determinant of muscle strength is the cross sectional area of the muscle.
Muscle length - for reasons i don't exactly know and didn't find on the internet - does play far less of a role in strength, if at all.
About relative strength, ants and elephants
Now you're correct that a 100 pound guy lifting 200 pound is lifting the same amount relative to his weight as a 200-pound guy lifting 400 pounds.
However, even if these guys have the exact same proportions, it is more difficult for the 200 pound guy to lift 400 pounds than it is for the 100-pound guy to lift 200 pounds.
Now you'll probably think: "wait a minute - both guys are of equal proportions, percentage of muscle and have to lift the exact same percentage of their own weight, how is it supposed to be more difficult for the biggger guy?" and you're asking the right question!
Remember that in the earlier paragraph i've mentioned that muscle strength depends on the cross sectional area of the muscle(s)?
A cross sectional area is a 2-dimensional measurement - let's keep this in mind for now.
So one of the factors important in our discussion about strength, is a 2-dimensional measurement, but what's the other one?
Well, the other factor is of course the weight of our athletes, be it the weight of their body or the weight they move.
The weight of something depends on its volume and volume is - you guessed it - a 3-dimensional measurement.
So far so good, but let's have a look at the relationship of these two measurements with each other.
Let's say we have two cubes of different sizes but (obviously) equal proportions, both cubes are made of a material which weighs 1.000 kg/m³:
- Cube a) is 1m/1m/1m and thus has a bottom area of 1m².
- Cube b) is 2m/2m/2m and thus has a bottom area of 4m².
Cube a) has a volume of 1m³ and thus weighs 1.000 kg - these 1.000 kg are distributed over an area of 1m², making for a weight-loading of 1.000 kg/m².
Cube b) has a volume of 8m³ (because 2m x 2m x 2m = 8m³ duh) and thus weighs 8.000 kg - these 8.000 kg are distributed over an area of 4m², making for a weight-loading of 2.000 kg/m².
So despite the fact that our cubes are made of the same material and have the exact same proportions, the bigger cube has to withstand twice as much (!) weight-loading, because it's 8 times as heavy as the lighter cube, but has a bottom area (this goes for the surface area too!) which is only four times as big.
Now let's go back to the weights being lifted.
Let's say we've got a robot which weighs 100 pounds and can also lift 100 pounds and now we want a robot which's able to lift 200 pounds, but - for the sake of the argument - the proportions of the robot have to stay the same.
Since we know muscle strength is determined by the cross sectional area of the muscle, we must build second robot in a size, where its muscles have a cross sectional area twice as big as the smaller robot - because we want him to lift twice as much weight.
Now since we have to keep the proportions, what happens when building the bigger robot is that while his muscle cross sectional (2-d measurment) area increases by the power of 2, it's volume (3-d measurement) and thus also its weight increases by the power of 3.
So while the bigger robot is twice as strong as the smaller one, its three times as heavy.
Despite being equal in proportions, the smaller robot is able to lift 100% of its own weight, whereas the bigger robot can only lift 2/3 (66.66...%) of its own weight.
What i've just described to you, is the square-cube law and it's the reason ants can lift many thousand times their body weight, whereas Elephants are very weak in relation to their weight.
All this is just due to smaller animals (and humans) having to carry less weight in relation to their muscle cross sectional area than their bigger peers.
This is also the reason that:
...smaller fighters are faster and have more cardio than bigger ones.
...smaller weightlifters are (more easily) stronger in relation to their weight.
TL;DR:
When scaling a body up, weight increases way faster (³) than muscle strength (²).
Range of motion and limb length
Let's say a guy with average proportions, who's 6'0" tall, squats 400 pounds as a one rep max.
When this guy does his squat, the squat obviously has a certain range of motion.
Now let's imagine that over night, the guys legs have gotten 4" longer and thus our guy is suddenly 6'4".
All of a sudden, the guy - once recovered from his workout - tries to squat 400 pounds again, but all of a sudden, he fails.
Whats has happened?
Well, mechanically speaking, the guy - when he was 6 foot tall - had just enough strength to move the weight (let's say) 20 inches - that was his full range of motion for his one rep max of 400 pounds.
Since his leg length has increased though, his range of motion too has increased and since
work = force × distance, it follows that if you increase distance, you also have to increase force.
In this example, the guy all of a sudden trying to lift the same amount over a greater distance (since the ROM has increased) requires him to do more "work" but since his maximum output is already reached when squatting 400 pounds for 20" (400 lbs × 20" = 8000 "units of work" maximum), he's obviously not able to squat 400 pounds for let's say 24", because 400 lbs × 24" = would require 9600 "units of work", which exceeds his maximum strength.
The easiest example where you'll be able to experience it in real life when lifting, is doing lateral raises, but one time with the arms stretched out completely, and once with the arms slightly more bent.
The image below - although very simplified - does help visualizing and imagining the difference limb length makes in the range of motion and thus the amount of work required to move the same amount of weight:
View attachment 813112
That was a ton of text i guess. I hope this helps though, cheers bud!
