Without stepping on any toes, my initial reaction is that the taller lifter has done more work, but is not necessarily stronger.
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The element you are missing is the time it takes them to lift the bar at that 1RM. If both 1RMs are equal in cadence, then yes, the taller man is moving the same weight in the same time over a *greater* distance, and is thus producing more force, more work, and more power. So if you define "strength" as "ability to produce force in a given context", then the taller man is stronger in this case.
I've attached a picture of the situation. The first graph is the position of the bar for some hypothetical lift for two lifters, one taller than the other, lifting the same weight. Note that the lifters use the same relative bar path and take the same time, but one has to move the weight further due to his height. The rest of the graphs are physical output measures. As you can see, the taller man produces more of everything. He has to in this situation. My vote: the taller man is stronger.
Now let's change things and assume that the 1RM takes longer to perform for the taller man. The second picture is the result. Look what happens: the taller man still does more work, but he now produces less force and less power. Why? Because he's moving the bar more slowly.
So who is stronger here? After all, in the end the taller lifter has still potentiated the bar with more energy than the shorter lifter; that is, when they drop the weight the taller man's bar will hit the ground with more force. But the smaller guy got his work done faster, and at any time before the end of his lift he had the bar higher in the air. My vote is for the smaller guy in this case.
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Without stepping on any toes, my initial reaction is that the taller lifter has done more work, but is not necessarily stronger.
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I'll say strength is the application of force to something or someone, but in this case, to something outside of the gym and specifically a barbell. So let's say I was a wrestler and I have to go against one of the guys in the original example, I think I'd pick the shorter guy, based on my rationale above. This assumes that I know their skill levels, athleticism, etc are exactly equal as well.
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The same weight moved over a greater distance would be more work performed. Assuming rep speed is the same the lifter with the longer limbs would make more horsepower.
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I would argue that although the taller lifter is doing more work, he/she is not stronger. But I'm a short guy who loves to argue, so I may well be biased.
TMPHBITEU
Argument is useful, especially when it allows us to think these things through productively.
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Work = Force x DistanceOriginally Posted by Ian Kovtunovich
Power = Work / Time
If they both complete the lift in the same time then yes the tall guy is more powerful. The tall guy is doing more work (because he is moving it further) in the same amount of time.
From what I gather, powerlifters might be the strongest but Olympic lifters are more powerful. Olympic lifters move smaller weights (compared to powerlifter deadlift, for example) but they move these weights very quickly. So although the Olympic lifter is doing less work than the powerlifter, that work is being done by the Olympic lifter in a way shorter amount of time. I think I read that the second phase on a clean is the most powerful movement in all of sports.
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this naturally leads to the interesting discussion about which body types are best for which sports. From what I've observed, in powerlifting and olympic weightlifting even the guys in the largest weight classes are not going to be more than 6'0 or 6'1, and the lower weight classes are dominated by average or short height guys. Throwing sports don't have many people that are much under 6'2 or so, with many being much taller. Strongman is of course dominated by giants because if I'm 5'9 and some guy from Norway is 6'9, he's going to have a much easier time loading an atlas stone than I will. I've mentioned this before, but it seems relevant to the discussion
anthropometry in everything
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Work = Force x Distance is only valid when the force is *constant* over the distance. So if the force vs. distance curve deviates at all from horizontal line, you gotta go to the more complicated formulas given here:
http://hyperphysics.phy-astr.gsu.edu/hbase/wcon.html
But yeah, a complete analysis of the system would have to consider all the torques on all the levers and account for the added weight of the lifter's body (the taller man probably weights more). Even an analysis using just the center of mass of the system is a bit complicated, because the COM of a human shifts as his body moves, as opposed to a nicely structured barbell.
Also, whether levers help or hurt depends on the situation. Consider two "proportional" men both doing a deadlift. The bar starts in a *fixed* position, so the bar is relatively lower on the taller guy's body, thus his starting position will be more compromised. This is opposed to the squat, where the bar starts in relatively the same place (on the back) for both men.
In then end, though, you must accept the standards of your sport. If weightlifting doesn't break ties by height, then you'd better just lift MORE than the shorter guy. Still, I think the relative merit of using height to break ties, rather than 100 grams of bodyweight, should be discussed more.
Rip's sub
Just test them both on a knee extension machine and we'll know for sure.
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