Wow... been filming today, didn't think this thread would be so popular.
There seems to be a lot of misunderstanding here regarding the formula I posted:
-El Mariachi made the erroneous claim that a 20'' arm is only 25% bigger than a 16'' arm
-Kiwiol erroneously claimed that I was citing surface area
-Ursus/Goudy erroneously cited Frankhauser's calves as an exception to my formula
...I'll address each of these misunderstandings individually.
El Mariachi: a 20'' arm is 25% bigger than a 16'' arm
This is actually wrong, but only when you understand what the circumference actually represents. If you think a circumferences increase linearlyly with a mass/volume (it doesn't), then you might assume that you can simply divide 20 by 16 to get 1.25 and think a 20'' circumference is 25% bigger than a 16'' arm.
But it's not.
Imagine two soup cans, big catering-size monster soup cans. Both cans are the same height (ten inches tall), but one can is 20'' around (circumference) while the other is only 16'' around.
How much bigger is the 20'' circumference can than the 16'' circumference can.
Well, let's compare the formulae:
Volume of 20'' around 10'' tall can = pi(Circumference/2pi)2 x height = pi(20''/2pi)2 x 10'' = (202/2pi)x10
Volume of 16'' around 10'' tall can = pi(Circumference/2pi)2 x height = pi(16''/2pi)2 x 10'' = (162/2pi)x10
When you divide (for a ratio), the height and 2pi factors cancel... (Volume of big can)/(Volume of small can) = 202/162
And... 202/162 = 400/256 = 1.56 ....the 20'' can is 56% bigger than the 16'' can.
So, very obviously, if a ten inch tall can that's 20'' around is 56% bigger, 56% heavier than a similar ten inch tall can that's only 16'' around.... then a guy with a 20'' arm has 56% more muscle in his arm than a guy with a 16'' arm, if both men have the same length humerus (upper arm bone).
So we could expect a proportionate bodybuilder to gain approx 56% extra bodyweight in going from a 16'' arm to a 20'' arm... for the average height bodybuilder, this means a 20'' arm requires approximately 250 lbs of lean muscle.
Kiwiol: I'm citing surface area
No. If you still don't understand the diffence between an increase in a square dependent measurement like girth and an increase in a linearly dependent measurement like length, then I've got a little thought experimet for you:
Imagine two matchboxes... a big matchbox and a little matchbox.
Big Matchbox is a bully; he taunts Little Matchbox: "Hey wimpy Little Matchbox, I'm twice your weight. That means I'm twice as big as you: I'm twice as wide... twice as tall... and twice as thick!"
But Little Matchbox knew a little mathematics, so he just laughed:
"Bullshit Big Matchbox, you are a liar! You might be twice my weight... but you arn't twice as wide; nor are you twice as tall or twice as thick as me. Everyone knows that a bundle of matchboxes twice as wide, twice as tall and twice as thick as a single box of matches would be TWO matchboxes wide; TWO matchboxes tall and TWO matchboxes deep."
"Two by two by two... that's a bundle of EIGHT matchboxes." ...shrieked Big Matchbox, realising his mistake.
Little Matchbox laughed: "You are not eight times heavier than me... you are just twice my weight, therefore considering our identical proportions you are only 26% taller than me; 26% wider than me and only 26% thicker than me. Because the cube root of two (twice) is 1.25992. To be twice my height; twice my weight and twice my thickness you'd need to be EIGHT times my weight... because weight and volume are cube dependent, not linear."
See the difference?
Arm size is NOT linear... it's not like a string getting longer without getting any thicker... arm size is NOT cube-dependent... as arm size increases an arm gets thicker and taller, but it doesn't get any longer...
Arm size is square-dependent... so differences in arm size are a ratio of the SQUARES of he circumferences... because we are talking about an increase in cross-sectional area.
Remember, ratios for linear measurements like lengths... ratios of squares for measurments like areas... ratios of cubes for measurements like volumes.
Ursus/Goudy: Frankhauser's calves as an exception to my formula
Actually no. There may be a maximum possible arm size for a certain bodyweight... but that doesn't mean there is a corresponding minimum arm size.
Taking someone like Eric Frankhauser (spelling?) for example, it might seem the discrepancy between his somewhat sub-par arms and exceptional calves disprove my formula... but that is not the case.
Actually, the formula I posted holds for calves too... once you appreciate that there is about a two inch difference between the MAXIMUM calf measurement at a particular bodyweight and the MAXIMUM arm measurement at that same bodyweight.
So:
15'' arm would go with 150 lbs ...but allow for a 17'' maximum calf measurement... and so on:
16'' arm would go with 171 lbs ...but allow for a 17'' maximum calf measurement
17'' arm would go with 193 lbs ...but allow for a 18'' maximum calf measurement
18'' arm would go with 216 lbs ...but allow for a 19'' maximum calf measurement
19'' arm would go with 241 lbs ...but allow for a 20'' maximum calf measurement
20'' arm would go with 267 lbs ...but allow for a 21'' maximum calf measurement
21'' arm would go with 294 lbs ...but allow for a 22'' maximum calf measurement
22'' arm would go with 323 lbs ...but allow for a 23'' maximum calf measurement
23'' arm would go with 353 lbs ...but allow for a 24'' maximum calf measurement
24'' arm would go with 384 lbs ...but allow for a 25'' maximum calf measurement
...guys like Frankhauser (usually of Northern European descent with lots of Brehin genes) are NOT off the scale; their massive calves are within two inches of the maximum arm measurement allowable at their particular lean bodyweight.
Frankhauser, I'm assuming, is about 230 lbs in those recent photos... so according to my simple scale his MAXIMUM arm measurement is about 18.5'' to 19'' (which he doesn't meet) and his MAXIMUM calf measurement is approximately 21'' (which he might actually be approaching).
The scale still works for calves too... just that with calves, almost no one is near the maximum possible measurement for teir bodyweight (due to racial factors)
Remember, my scale gives the bodyweight required to achieve a certain arm measurement (and by adding two inches gives the bodyweight required to achieve a certain calf measurment)... that doesn't mean everyone at those bodyweights will match those measurements: it means NO ONE significantly exceeds those measurements without the concordant bodyweight.
Sorry for the long post, hope that explains the misunderstandings.
The Luke
