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weight ratio in primitive man as compared to that of contemporary man
V. Capecchi Institute of Anthmpology, Sicna Universi~,Sims, Italy
RI.
Rigato
The inverse proportionality between body size and strength/weight ratio, at the same somatic proportions, show that for the purpose of survival the small size of primitive man was an essential advantage.
Znstitutcof Physics, S&TMUniversity, Sicna, Itab Received 21 November 1979 and accepted 4 March 1980
1.Introduction Reference is made to the small sizes found in the paleoanthropological remains of Hadar in Ethiopia and of Laetolil in Tanzania (Johanson & White, 1979), and some fundamental properties, often neglected by anthropologists, are shown. The dynamic characteristics of today’s man and those of a hypothetical man of considerably smaller size are compared here, on the provisional assumption that there is parity between their anthropometrical proportions, average body density and maximum muscular unit strength (Smith, 1968). For this purpose, two men U and u’, with characteristics which satisfied the given hypothesis, and having body heights h and h’, respectively, with h > h’, are considered. If u’ is a primitive man leading a fatiguing life, a strong limbed, athletic contemporary man could be referred to by way of a comparison. Accordingly, in our first approximation, indicative values for h and h’ can be taken as h = 180cm,
h’ = 112.5 cm
so that a scale factor
may be established. 2. Relative Strength If the man U contracts a muscle of section S, the maximum force F, capable is F,= T,S
of which he is
where T,,, is the maximum unit strain. Since T,,, has been assumed to be independent of the size of the body, and therefore of the scale factor L, and as S is evidently proportional to LB, we obtain F, cc L= Journalof HumanEvolution(1980) 9,325-327 0047-2484/80/040325+03 $02.00/O
@ I980 Academic Press Inc. (London) Limited
326
V. CAPECCHI
AND
M. RIGATO
from which, generalizing, can be seen that muscular strength is proportional to the square of the scale factor. The relative strength fm, defined as strength/weight ratio, is now considered:
where m is the body mass and g the gravity acceleration. Since, in the given hypothesis, the average body density is invariable as regards the scale factor, the mass is found to be proportional to the volume, hence to L3. Therefore which is
fm-;
fm cx L-l
which is to say that the relative strength is inversely proportional to the scale factor. Thus, iff, is the relative strength of U’, we have
f,,, = L--If:
whence
fk = Lf,,, = 1*6f,,,.
Therefore, the relative strength of U’ exceeds that of U by 60 %. For instance, if U, having got hold of a tree branch, is capable of sustaining his weight with a flexed arm by exerting the maximum strength of his biceps, with the same effort U’ is able to sustain his own body plus a load equal to 60 % his weight (f: = l-6). With no load, therefore, U’ is capable of sustaining his own body with much less effort ; or, making the same effort, he is able to lift himself with an acceleration a=
Fi - m’g = Cfk -
m’
1)g = O-6 g m 5.9 m/s*
In conclusion, U’ can easily climb trees if he is using just his arms, but even with such boldness and rapidity that would be completely impossible for U. 3. Acceleration If U makes a sudden horizontal movement, the acceleration with which he can get aside is determined by the ratio between the horizontal component F, of the maximum force applicable to the jump and the mass of his body:
F
a = A! m
that is
a cc L-1
hence, the acceleration is inversely proportional to the scale factor. Which is to say that if a‘ is the acceleration of which U’ is capable, we have a = L-r a’
whence
a’=La=
1.6a.
Thus, should he have to jump aside in an emergency, such as if he had to avoid an aggressor or if he were to catch a moving object, U’ would be much better endowed than U, as he could count on an advantage in acceleration of 60 %.
THE
STRENGTH/WEIGHT
RATIO
IN PRIMITIVE
MAN
327
4. conclusions Within the limits that the given hypotheses and approximations adhere to, it can be concluded that because of his small size early man had a fundamental dynamic advantage. Indeed, although in actual fact he had inferior muscular strength, he was “intrinsically” stronger, as he was endowed with better relative strength, which enabled him to spring and climb much quicker than his larger counterpart. It should be pointed out that the above remarks stem exclusively from a comparison of size, hence they must be considered as resulting from general physical properties. One should also consider that, over and above his smaller size, primitive man had a more developed muscular system, as is clearly shown by the strong prints of the muscular insertions, much deeper and wider than in present day man. From the concurrence of such favourable conditions, therefore, it becomes apparent that the actual characteristics of early man entail much greater advantages than those determined in the foregoing notes, where calculations are based on the hypothesis of parity of anthropometrical proportions. In conclusion, it seems established that a small body size makes it easier to satisfy two basic needs: hunting for food and escaping environmental dangers. References Johanson, D. C. & White, T. D. (1979). A systematic assessment of early African hominids. 321-330. Smith, .J. M. (1968). Mathemnticul Ideas in Biology. Cambridge: University Press.
Science 203,
Riassunto
La proporzionalita inversa fra statura e rapport0 the l’uomo primitivo trovava nella sua piccola sopravvivenza.
forzalpeso, corporatura
a parita di proporzioni somatiche, mostra un vantaggio determinante ai fini della
RI.
Rigato
The inverse proportionality between body size and strength/weight ratio, at the same somatic proportions, show that for the purpose of survival the small size of primitive man was an essential advantage.
Znstitutcof Physics, S&TMUniversity, Sicna, Itab Received 21 November 1979 and accepted 4 March 1980
1.Introduction Reference is made to the small sizes found in the paleoanthropological remains of Hadar in Ethiopia and of Laetolil in Tanzania (Johanson & White, 1979), and some fundamental properties, often neglected by anthropologists, are shown. The dynamic characteristics of today’s man and those of a hypothetical man of considerably smaller size are compared here, on the provisional assumption that there is parity between their anthropometrical proportions, average body density and maximum muscular unit strength (Smith, 1968). For this purpose, two men U and u’, with characteristics which satisfied the given hypothesis, and having body heights h and h’, respectively, with h > h’, are considered. If u’ is a primitive man leading a fatiguing life, a strong limbed, athletic contemporary man could be referred to by way of a comparison. Accordingly, in our first approximation, indicative values for h and h’ can be taken as h = 180cm,
h’ = 112.5 cm
so that a scale factor
may be established. 2. Relative Strength If the man U contracts a muscle of section S, the maximum force F, capable is F,= T,S
of which he is
where T,,, is the maximum unit strain. Since T,,, has been assumed to be independent of the size of the body, and therefore of the scale factor L, and as S is evidently proportional to LB, we obtain F, cc L= Journalof HumanEvolution(1980) 9,325-327 0047-2484/80/040325+03 $02.00/O
@ I980 Academic Press Inc. (London) Limited
326
V. CAPECCHI
AND
M. RIGATO
from which, generalizing, can be seen that muscular strength is proportional to the square of the scale factor. The relative strength fm, defined as strength/weight ratio, is now considered:
where m is the body mass and g the gravity acceleration. Since, in the given hypothesis, the average body density is invariable as regards the scale factor, the mass is found to be proportional to the volume, hence to L3. Therefore which is
fm-;
fm cx L-l
which is to say that the relative strength is inversely proportional to the scale factor. Thus, iff, is the relative strength of U’, we have
f,,, = L--If:
whence
fk = Lf,,, = 1*6f,,,.
Therefore, the relative strength of U’ exceeds that of U by 60 %. For instance, if U, having got hold of a tree branch, is capable of sustaining his weight with a flexed arm by exerting the maximum strength of his biceps, with the same effort U’ is able to sustain his own body plus a load equal to 60 % his weight (f: = l-6). With no load, therefore, U’ is capable of sustaining his own body with much less effort ; or, making the same effort, he is able to lift himself with an acceleration a=
Fi - m’g = Cfk -
m’
1)g = O-6 g m 5.9 m/s*
In conclusion, U’ can easily climb trees if he is using just his arms, but even with such boldness and rapidity that would be completely impossible for U. 3. Acceleration If U makes a sudden horizontal movement, the acceleration with which he can get aside is determined by the ratio between the horizontal component F, of the maximum force applicable to the jump and the mass of his body:
F
a = A! m
that is
a cc L-1
hence, the acceleration is inversely proportional to the scale factor. Which is to say that if a‘ is the acceleration of which U’ is capable, we have a = L-r a’
whence
a’=La=
1.6a.
Thus, should he have to jump aside in an emergency, such as if he had to avoid an aggressor or if he were to catch a moving object, U’ would be much better endowed than U, as he could count on an advantage in acceleration of 60 %.
THE
STRENGTH/WEIGHT
RATIO
IN PRIMITIVE
MAN
327
4. conclusions Within the limits that the given hypotheses and approximations adhere to, it can be concluded that because of his small size early man had a fundamental dynamic advantage. Indeed, although in actual fact he had inferior muscular strength, he was “intrinsically” stronger, as he was endowed with better relative strength, which enabled him to spring and climb much quicker than his larger counterpart. It should be pointed out that the above remarks stem exclusively from a comparison of size, hence they must be considered as resulting from general physical properties. One should also consider that, over and above his smaller size, primitive man had a more developed muscular system, as is clearly shown by the strong prints of the muscular insertions, much deeper and wider than in present day man. From the concurrence of such favourable conditions, therefore, it becomes apparent that the actual characteristics of early man entail much greater advantages than those determined in the foregoing notes, where calculations are based on the hypothesis of parity of anthropometrical proportions. In conclusion, it seems established that a small body size makes it easier to satisfy two basic needs: hunting for food and escaping environmental dangers. References Johanson, D. C. & White, T. D. (1979). A systematic assessment of early African hominids. 321-330. Smith, .J. M. (1968). Mathemnticul Ideas in Biology. Cambridge: University Press.
Science 203,
Riassunto
La proporzionalita inversa fra statura e rapport0 the l’uomo primitivo trovava nella sua piccola sopravvivenza.
forzalpeso, corporatura
a parita di proporzioni somatiche, mostra un vantaggio determinante ai fini della