The Carlyle Formula And Other Body Proportion Guidelines
Gerald E. Stark, Jr., BSME, CP, FAAOP
Much of what is known about body proportion comes anecdotally from artists and empirically from human factors engineers. The artist uses guidelines found to be aesthetically acceptable, while the engineer uses anthropometrics, the study of human dimensions, to create devices that interface with human use. Both have their value when creating devices that must function yet remain appealing with the human form such as prosthetics. The Greek sculptors and later artists of the renaissance studied human proportion, evident in Leonardo Di Vinci's "Vitruvian Man". Today, designers use body proportion tables and formulas based on the individual's height to address the population from the 5th to 95th percentile in any dimension. One of the most common formulas for arm prostheses is the Carlyle formula, which establishes that the humeral arm length, AC to lateral epicondyle, is .19 times the body height and the forearm length, lateral epicondyle to thumb tip, is .21 times the body height. Other texts differ slightly and place this measurement at .186 X BH for the humeral length and .254 X BH.4 A recent study by the author validates the Carlyle formula among 30 men with an average the humeral length equal to .18 X BH and lateral epicondyle to thumb tip at .23 X BH. 24 women were sampled and the measured ratios appeared to be slightly longer than the Carlyle guideline indicating that women may have longer limb lengths in relationship to their overall height. The humeral section was on average .22 X BH and forearm to thumb tip .26 X BH.
Most people are approximately 7 1/2 heads tall with the midpoint being approximately at the genitals.4 The height is approximately the same as the arm span from fingertip to fingertip in outstretched arms.3 The distance from the cubital fold to the wrist center is equal to the length of the foot.3 The relative sitting height of any individual is 52% of their height5 . Ischial height is .480 X BH, floor-to-knee center approximately .285 X BH, and floor-to-ankle center .039 X BH.2 More accurate dimensions used in human factors engineering look at body dimension ranges from the 5th to 95th percentile.
For weight distribution the Head is 6-8% body weight, Trunk is 40-46% body weight, legs 15-18% each (30 lbs for a 185 lb. man), feet 1.5-2% each, arms 5-6% for each (11 lbs for a 185lb man), and hands 1-2% for each1 . At the age of two the child is 50% the height of an adult and at age 4-5 the head is 80% the size of the adult1 . There is steady weight gain to the age of 6-7 when the child weighs 50% that of an adult1 .
The human animal has a protracted development time, approximately 20 years, which is the lifespan of other primates1 . In that time the body will grow 3 1/2 times in height, 7 times skin coverage, and body weight of 20 times1 . Body proportions change with development. The child is not an adult in miniature as is evident with their larger head and abdomen. An infant would have trouble touching their fingers over their head. A head of equal diameter in an adult would be approximately the size of a beach ball! This is why the human infant is born in a more premature state to allow the head's passage through the birth canal. Head growth occurs early; a child age 10 has a head 96% the size of an adult1 . A 1yr. child is 4 heads high, 4 yrs. child is 5 heads high, 9yrs is 6 heads high, 16 years 7 heads high, and ultimately the adult at 7 1/2 heads high1 . There is also a large variation of the growth of body parts. It has been shown that periods of growth last 4-6 months followed by bone thickening of 4-6 months1 . The body segments often alternate growth patterns. While the humeral section is thickening the radial section may be growing. This is why limb segments may look disproportionate in adolescents with larger feet and hands. The majority of growth in the arm is proximal humerus, distal radius, away from the elbow while a majority of growth in the leg is concentrated distal femur and proximal tibia, toward the knee1 .
Until age 6 limb growth is slow compared to body and head growth. Growth rates for boys and girls remain the same until age 9 and at age 1011 more height is gained through the growth of the limbs. Short young children grow more slowly over time.1 In adolescence taller children grow more slowly and shorter children more rapidly for a longer period of time.1 At age 10 1/2 to 11 yrs in girls, 12 1/2 to 13 in boys years there is a remarkable growth rate maintained for 2 years at the onset of puberty.1 Final height is reached at age 20 while the trunk may continue to grow until age 255. There is a general decline in height with women shrinking more than men to a proportional height of 7 heads.3 There is a 50% loss of strength from ages 30 to 70. Weight also decreases from age 50 in men and 60 in women5 .
Boys from birth are usually larger in stature until the onset of puberty with the difference between male and female height at 6-7%1 . The facial features of the male skull are more 90° and more angular. The male's shoulders broader with a shorter neck and parallel clavicles. Women's hips are the one dimension that is greater with a wider pelvic angle and rounded sacrum to accommodate the birth canal3 . Males have a 6:3 muscle to fat ratio and female 5:4 muscle to fat ratio contributing to their more rounded form3 .
The shortest people in the world are the Efe & Basua "pygmies" with an average height of 4' 9" for men and 4' 6" for women.5 The tallest people are the Dinka Nilotles from the southern Sudan with an average height of 6'0" for men and 5'6" for women.5 Two general rules apply to ethnic body proportion differences: Allen's rule follows that extremity length decreases as the region is closer to the poles and Bergman's rule is that body size variety increases closer to the poles.5
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1) Croney, J., Anthropometry for Designers. Revised Edition, Van Nostrand Reinhold, New York, New York, 1981.
2) Winter, D., Biomechanics and Motor Control of Human Movement, 2nd edition, Wiley- Interscience Publications, New York, New York.
3) Peck, S., Atlas of Human Anatomy for the Artist, Oxford University Press, Oxford, England, 1982.
4) Dreyfus, H. Anthropometric Data: Standing Adult Male & Female, 1966.
5) http://ergo.human.cornell.edu/DEA325notes/anthrodesign.html, Cornell University Erognomics Web, 8/23/02.
6) Northwestern University Upper Extremity Prosthetic Manual, Chicago, Illinois, 2002.