Engineering Anthropometry - Fundamentals and Assessment Tools for Occupational Ergonomics - page 199

and the standard deviation of m diff derives from

1 = 2

S diff ¼½ S x þ S y 2(r S x S y ) (9 : 16)

Examples
Example 1: What is the 95p shoulder-to-fingertip length? Assume the mean lower arm (LA) link length
(with the hand) to be 442.9 mm with a standard deviation of 23.4 mm. Also assume the mean upper arm
(UA) link length to be 335.8 mm and its standard deviation 17.4 mm.
The multiplication factor of k 64 (from Table 9.2) leads to the 95th percentile. But one cannot

calculate the sum of the two 95p lengths because this would disregard their covariance; instead, one
should calculate the sum of the mean values first, using Equation (9.13):

¼ 1 :

m ¼ m LA þ m UA ¼ 442 : 9 þ 335 : 8 ¼ 778 : 7mm :

Inserting the standard deviations for LA and UA into Equation (9.14), and using an assumed
coefficient of correlation of 0.4, one can obtain:

4} 1=2 mm

4 2 4 2 S ¼ {23 : þ 17 : þ 2 0 : 4 23 : 4 18 :

S ¼ 34 : 6mm

Now, one can calculate the 95p total arm length (AL), using Equation (9.1):

AL 95 ¼ 778 : 7mm þ 1 : 64 34 : 6mm ¼ 835 : 7mm :

Example 2: What is the average arm (acromion to wrist) length of an American pilot? it is known that for
a standing pilot, the 90th percentile acromial (shoulder) height is 1532.0 mm and the wrist height is
905.6 mm; for the 10th percentile, the values are 1379.5 and 808.6 mm, respectively. The correlation
between shoulder and wrist heights is estimated to be 0.3.
One must first calculate the mean acromion (A) and wrist (W) heights to be able to estimate the
standard deviations. For the 90th percentile this is, as per Equation (9.7):

m A90 ¼ (1532 : 0 þ 1379 : 5) mm = 2 ¼ 1455 : 75 mm :

Using Equation (9.1), with k ¼ 1 : 28 taken from Table 9.2, one obtains:

S A ¼ (1532 : 0 1455 : 75) mm = 1 : 28 ¼ 59 : 6mm :

The same result is obtained on using the 10th percentile.

S A ¼½ (1455 : 75 1379 : 50) mm = 1 : 28 ¼ 59 : 6mm :

Likewise,

m W90 ¼ (905 : 6 þ 808 : 6) mm = 2 ¼ 857 : 1mm :

S W ¼ (905 : 6 857 : 1) mm = 1 : 28 ¼ 37 : 9 mm:

½ or: S W ¼ (857 : 1 808 : 6) mm = 1 : 28 ¼ 37 : 9mm :