Note: these estimations & calculations are taken by average and may be variations
*This estimation will be carried out by the difference between 2 individuals
1-subject (A): the short one 160 cm
2-subject (B): the tall one 190 cm
Note: both of them have the same muscle mass & weight ( 80 kg )
- the example will be in shoulder abduction "this calculation can be carried in most body movement".
1- the range of movement (ROM) :
-subject (A): the arm length = 0.42 x total body height
the arm length = 0.42 x 160 = 67.2 cm
( the circumference = 2πr) " the arm length = radius"
-since we moved 90° for shoulder abduction (1/4 of circumference ) (π = 3.14)
therefore ROM "X"= 1/4 x circumference
"X"= 1/4 x (2 x 3.14 x 67.2 ) = 105.6 cm
-subject (B): the arm length = 190 x 0.42 = 79.8 cm
-( the arm length = radius )
the ROM "X" = 1/4 x circumference (2πr)
"X^2" = 1/4 x ( 2 x 3.14 x 79.8 ) = 125.4 cm
Conclusion: subject (B) has greater ROM "X^2" with (18.75 %) than subject (A) which will make the movement more difficult for subject (B) than subject (A).
2- the fore needed for the 2 subjects to carry the same weight ( ex. 10 kg ) " torque (rotational force)"
-in shoulder abduction (dumbbell lateral raises), the fore needed from the muscle " medial deltoid " must be sufficient to carry both (the weight of the arm & the external weight ).
-subject (A) :
A- the rotational force of the weight of arm "Torque" : (τ =force x moment arm "MA")
-(MA^2): the distance from the shoulder joint to the center of gravity "COG" of the arm
-COG = 3/7 x arm length = 3/7 x 67.2 = 28.8 cm therefore (MA^2 = 0.288 m)
- the force: the weight of the total arm, the arm is (6%) of total body weight (80 kg) (gravity = 9.8 m/s²)
-the arm mass = 80 x 6% = 4.8 kg (weight = mass x gravity)
-the arm weight = 4.8 x 9.8 = 47.04 N
* The rotational force of arm = (force x MA^2)
torque 1 = 47.04 x 0.288 = 13.55 N.m
B- the rotational force of external weight "torque" : (torque = force x MA^1)
-MA^1 : the total arm length = 67.2 cm therefore (MA^1 = 0.672 m)
- the force: the weight of external weight (10 kg)
- weight = mass x gravity = 10 x 9.8 = 98 N
- the rotational force of external weight = weight x MA^1
torque 2 = 98 x 0.672 = 65.856 N.m
* The rotational force needed from muscle is ( torque 1 + torque 2 ) = 13.55 + 65.856 = 79.4 N.m
-subject (B) :
A-the rotational force of arm "torque" :
- the MA^2: distance from shoulder joint to (COG)
-COG = arm length x 3/7 = 79.8 x 3/7 = 34.2 cm (MA^2 = 0.342 m)
- the force: the weight of the arm
-the mass of arm = 80 x 6% = 4.8 kg
- the weight of arm = 4.8 x 9.8 = 47.04 N
-the rotational force of arm = (force x MA^2)
torque 1 =47.04 x 0.342 = 16.1 N.m
B- the rotational force of external weight "torque" :
-MA^1 : the total arm length = 79.8 cm (MA^1 = 0.789 m)
-the force: the weight of external weight (10 kg)
- weight = mass x gravity = 10 x 9.8 = 98 N
- the rotational force of external weight = weight x MA^1
torque 2 = 98 x 0.789 = 78.2 N.m
* The rotational force needed from muscle is ( torque 1 + torque 2 ) = 16.1 + 78.2 = 94.3 N.m
Conclusion: the force needed from muscle (Rotational force) to carry the same weight (10 kg) in subject (B) is greater with (18.75%) than in subject (A) which gives subject (B) a disadvantage as he needs to use more muscle force to carry the same weight as subject (A), it is in consideration that when subject is taller the internal (MA)"distance from the joint to insertion" increases which will make the output force slightly higher. but the effect of internal moment arm is not as much as the external moment arm. the external moment arm changed more than the internal (MA) which will make the net product increase in external (MA).
Overall: the short individuals have an advantage over the tall individuals in both ( ROM & force needed to carry weight ) as ROM for short individuals have less ROM which makes the movement easier and as we have shown that the short individuals the force needed from them to carry the same weight as for tall individuals is less, and this makes short individuals are better in weight lifting as (powerlifting) as they higher can lift as a percentage o their (body weight & muscle mass). but also tall individuals have an advantage as they have taller limps which can carry more muscle mass.
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