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A useful line of analysis is to consider the effect of scale changes for creatures which are similar in shape and only differ in scale. As the scale of an animal increases the body weight and volume increase with the cube of scale. The volume of blood flow required to feed that bulk also increases with the cube of scale. The cross sectional area of the arteries and the veins required to carry that blood flow only increases with the square of scale. There are other areavolume relationships which impose limitations on creatures. Some of those areavolume constraints, including the above one, are:
Thus to compensate for the body needs which increase with the cube of scale but the areas increase with only the square of scale the average blood flow velocity must increase linearly with scale. Blood flow velocity is driven by pressure differences. The pressure difference must be great enough to carrying the blood flow to the top of the creature and great enough to overcome the resistance in the arteries and veins to the flow. The pressure required to pump blood from the heart to the top of the creature is proportional to scale. The pressure difference required to overcome the resistance to flow through the arteries into the capillaries and back again through the veins is more difficult to characterize in terms of scale. The greater cross sectional area reduces the resistance but the long length increases resistance. The net result of these two scale influences seems to be that the pressure difference required to drive the blood through the bulk of the creature is inversely proportional to scale. The pressure difference imposed would be the maximum of the two required pressure differences.
Shown below are the typical blood pressures for creatures of different scales.
Blood Pressure versus Height and Weight for Various Creatures  

Creature  Blood Pressure (mm Hg)  Height of Head Above Heart (mm)  Weight (grams) 
Human  120  500  90000 
Cow  157  500  800000 
Duck  162  100  2000 
Cat  129  100  2000 
Guinea Pig  60  25  100 
Goat  98  400  30000 
Pig  128  200  150000 
Monkey  140  200  5000 
Dog  120  200  5000 
Turkey  193  300  15000 
Frog  24  25  50 
Giraffe  300  3000  900000 
Snake  55  25  100 
The linear regression of the logarithm of pressure on the logarithm of height yields the following result:
The linear regression of the logarithm of pressure on the logarithm of weight yields:
If blood pressure were proportional to scale then the coefficient for *log(Height) would be 1.0 and for *log(Weight) would be 0.333 since weight to proportional to the cube of scale. The regression coefficients are not close to the theoretical values but they are of the proper order of magnitude for accepting blood pressure as being proportional to scale.
The volume of the heart of a creature is proportional to the cube of scale. The volume of the blood to be moved is also proportional to the cube of scale. From the previous analysis the flow velocity is proportional to scale. Therefore the time required to evacuate the heart's volume is proportional to scale. This means that the heartbeat rate is inversely proportional to scale. The following table gives the heart rates for a number of creatures.
Heartbeat Rates of Animals  

Creature  Average Heart Rate (beats per minute) 
Weight (grams) 
Human  60  90000 
Cat  150  2000 
Small dog  100  2000 
Medium dog  90  5000 
Large dogs:  75  8000 
Hamster  450  60 
Chick  400  50 
Chicken  275  1500 
Monkey  192  5000 
Horse  44  1200000 
Cow  65  800000 
Pig  70  150000 
Rabbit  205  1000 
elephant  30  5000000 
giraffe  65  900000 
large whales  20  120000000 
A regression of the logarithm of heart rate on the logarithm of weight yields the following equation:
If heart rate were exactly inversely proportion to scale the coefficient for *log(weight) would be 0.333. This is because scale is proportional to the cube root of weight. The coefficient of 0.2 indicates that the heart rate is given an equation of the form
One salient hypothesis is that the animal heart is good for a fixed number of beats. This hypothesis can be tested by comparing the product of average heart rate and longevity for different animals. Because the heart rate is in beats per minute and longevity is in years the number of heart beats per lifetime is about 526 thousand times the value of the product. The data for a selection of animals are:
Lifetime Heartbeats and Animal Size  

Weight  Heart Rate  Longevity  Product  Lifetime Heartbeats  
Creature  (grams)  (/minute)  (years)  (billions)  
Human  90000  60  70  4200  2.21 
Cat  2000  150  15  2250  1.18 
Small dog  2000  100  10  1000  0.53 
Medium dog  5000  90  15  1350  0.71 
Large dogs  8000  75  17  1275  0.67 
Hamster  60  450  3  1350  0.71 
Chicken  1500  275  15  4125  2.17 
Monkey  5000  190  15  2850  1.50 
Horse  1200000  44  40  1760  0.93 
Cow  800000  65  22  1430  0.75 
Pig  150000  70  25  1750  0.92 
Rabbit  1000  205  9  1845  0.97 
elephant  5000000  30  70  2100  1.1 
giraffe  900000  65  20  1300  0.68 
large whale  120000000  20  80  1600  0.84 
Although the lack of dependence is clear visually the confirmation in terms of regression analysis is:
The tratio for the slope coefficient is an insignificant 0.15, confirming that there is no dependence of lifetime heartbeats on the scale of animal size.
If a heart is good for just a fixed number of beats, say one billion, then heart longevity is this fixed quota of beats divided by the heart rate. From the above equation for heart rate, lifespan (limited by heart function) would be proportional to scale raised to the 0.6 power.
The data for testing this deduction are:
Lifespan versus Weight for Various Creatures  

Creature  Weight (grams)  Life Span (years) 
Human  90000  70 
Cow  800000  22 
Duck  2000  10 
Cat  2000  15 
Guinea Pig  100  5 
Goat  30000  15 
Pig  150000  25 
Monkey  5000  25 
Dog  5000  15 
Turkey  15000  5 
Frog  50  3 
Giraffe  900000  25 
Snake  100  10 
For the data in the above table, admittedly very rough and sparse, the regression of the logarithm of the lifespan on the logarithm of weight gives
Thus the net effect of scale on animal longevity is positive. Taking into account that weight is proportional to the cube of the linear scale of an animal the above equation in terms of scale would be
This says that if an animal is built on a 10 percent larger scale it will have a 6 percent longer lifespan.
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