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How To Measure The Mass And Balance Point Of A Human Limb?


davekm

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Preferably the forearm. I can't spend big money on x-rays, nor can I chop my arm off.  I've asked this elsewhere - LINK

I know the volume of my forearm, using the Archimedes method, for 10 equal segments of my forearm.

I've also looked at x-rays to work out roughly tissue distribution. Only issue, in terms of precision, is there is quite a big difference in density between bone, fat and muscle. On average, bone is 1.7500 g/cm and muscle is 1.0599 g/cm3.

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Preferably the forearm. I can't spend big money on x-rays, nor can I chop my arm off.  I've asked this elsewhere - LINK

 

I know the volume of my forearm, using the Archimedes method, for 10 equal segments of my forearm.

 

I've also looked at x-rays to work out roughly tissue distribution. Only issue, in terms of precision, is there is quite a big difference in density between bone, fat and muscle. On average, bone is 1.7500 g/cm and muscle is 1.0599 g/cm3.

 

I could easily answer this for you if I had more information.  Does the "forearm" include the hand, fingers, etc.?

 

Well, never mind....on second thought I still couldn't answer it, I'm afraid.  Your best bet is to cut off your forearm, I figure.  Then you can find the balance point by trial and error as you try to balance it on the index finger of your other hand, see?  Your arm would still have some important uses.  Mice could use it as a teeter-totter, for example.

Edited by Moronium
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Thanks. It is a toughie. It would be just the forearm, no hand or upper arm. Chopping my arm off would give a easy answer, but I'll pass. :D

 

Well, your choice, Dave, but I can't help but note that you aint no devoted scientist.  A true scientist is always willing to make immense sacrifices if that's what it takes to determine the truth about important issues, ya know?

Edited by Moronium
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Thanks. It is a toughie. It would be just the forearm, no hand or upper arm. Chopping my arm off would give a easy answer, but I'll pass. :D

At university my girlfriend and I once estimated the weight (mass) of of each of her breasts by getting her to stand on scales while I supported each in turn to a point at which it felt weightless to her and noting the drop in indicated weight on the scale. 

 

Probably not amazingly accurate but you could do the same thing for your arm, letting it relax completely while someone just supports its weight.   

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Preferably the forearm. I can't spend big money on x-rays, nor can I chop my arm off.  I've asked this elsewhere - LINK

 

I know the volume of my forearm, using the Archimedes method, for 10 equal segments of my forearm.

 

I've also looked at x-rays to work out roughly tissue distribution. Only issue, in terms of precision, is there is quite a big difference in density between bone, fat and muscle. On average, bone is 1.7500 g/cm and muscle is 1.0599 g/cm3.

 

 

I asked one of our master divers about this. These professionals must be able to determine what proportional trim weights to wear for very specific dive purposes. I figured that he might know something about proportional mass of different body parts. Turns out he did know and referred me to an extremely interesting book entitled:

 

Human Body Dynamics: Classical Mechanics and Human Movement

 

The entire book is available as a pdf file:

 

I think it has the answer to any question you might have about the human body dynamics.

 

On Page 302 there is a table:

 

TABLE A.2.3. Relative weight and length of body segments for adult men and women

 

Body segment  Weight

Whole body 100

Forearm  1.9

Hand  0.6

If you weigh 90 kg ( as I do) your forearm should be about 1.7 kg, and hand about 0.5 kg, but I am not going to chop mine off to check! You may do so if you like.

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At university my girlfriend and I once estimated the weight (mass) of of each of her breasts by getting her to stand on scales while I supported each in turn to a point at which it felt weightless to her and noting the drop in indicated weight on the scale. 

 

Probably not amazingly accurate but you could do the same thing for your arm, letting it relax completely while someone just supports its weight.   

 

I bet something else was getting weightless too.

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I bet something else was getting weightless too.

Well it came about due to the English expression for commenting on a woman with a large bust "You don't get many of them to the pound", as when buying apples by the pound at the greengrocer. So we thought, what do they actually weigh. It is more than a pound of course. 

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At university my girlfriend and I once estimated the weight (mass) of of each of her breasts by getting her to stand on scales while I supported each in turn to a point at which it felt weightless to her and noting the drop in indicated weight on the scale. 

 

Probably not amazingly accurate but you could do the same thing for your arm, letting it relax completely while someone just supports its weight.   

Sorry, one data point from a single source is insufficient. 

 

Please send your Uni gf to my place, and I will repeat the experiment and we can correlate our data.

 

I may even waive my customary fee if you send pics.

Edited by DaveC426913
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Preferably the forearm. I can't spend big money on x-rays, nor can I chop my arm off.  I've asked this elsewhere - LINK

 

I know the volume of my forearm, using the Archimedes method, for 10 equal segments of my forearm.

 

I've also looked at x-rays to work out roughly tissue distribution. Only issue, in terms of precision, is there is quite a big difference in density between bone, fat and muscle. On average, bone is 1.7500 g/cm and muscle is 1.0599 g/cm3.

 

Seriously though, how accurate does it need to be?

 

You have the volume of ten segments (and incidentally, already setting a pretty low limit on accuracy probably. Also: where do fingers end and forearm begin? Where does elbow end?).

 

It's bone, ligament and muscle throughout its length, so can assume that density is similarly uniform.

 

Just assume your ten segment prototype is an accurate enough model.

 

 

The balance point will simply be the halfway point where the masses on either side are equal.

 

 

You'll end up with a single segment that contains the balance point, but you won't know where along that segment the point is.

 

Use this truncated cone calculator to refine the segment until you have offset the imbalance in the masses of the other 9 segments.

https://keisan.casio.com/exec/system/1223372110

 

 

Example:

Let's say your calculation of flesh density is 1.1 that of water. All your masses will be +10% of volume.

 

s1: 108cc = 120g

s2: 150cc = 150g

s3: 108cc = 120g

s4: 91cc = 100g

s5: 82cc = 90g

s6: 73cc = 80g

s7: 64cc = 70g

s8: 55cc = 60 g

s9: 45cc = 50g

s10: 45cc = 50g

 
Total: 890g.
 
The balance point is in segment s4, with 390g on one end and 400g on the other.
So, within s4, the balance point is very near the centre, with only 10g difference.
 
Substitute your own numbers.
Edited by DaveC426913
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