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Q. Does Economos’ 1981 paper, The Largest Land Mammal, prove that gravity was the same 23 to 34 million years ago?

A. This old paper by Angelos Economos is sometimes quoted as positive proof that gravity was the same when the largest land mammal existed. [1]  A typical use of Economos’ paper to confirm the belief that there has been no variation in ancient gravity is given in Biology of the sauropod dinosaurs: the evolution of gigantism when the authors state “we have to assume that there were no secular variations in Earth’s gravity in the Phanerozoic geologic past (Economos, 1981)” and science writers, such as Brian Switek on National Geographic, have used this to claim, "paleontologist [have] debunked the proposal that Jurassic gravity was weaker." [2]  In practice, a more rigorous examination of Economos' paper indicates that it does not prove gravity is unchanged, so it would be unwise to offer it as firm proof that the Earth’s ancient gravity was the same as now.

In his 1981 paper Economos first presents the evidence that all life is limited in size based on hyper-gravity experiments on a mouse, rat, chicken and dog and then extrapolates the maximum upper size possible for a mammal based on this data. He concludes that the maximum upper size limit for a mammal is 20,000 kg, which he notes is about the same weight estimated for the largest known mammal Baluchitherium (also known as Indricotherium or Paraceratherium) so assumes that gravity was the same 23 to 34 million years ago.

Economos advocates that gravity imposes a metabolic cost on all life that is higher for larger animals due to their larger mass. This increasingly higher metabolic cost is due to the scale effect although it is not explained in these terms within his paper. Using experiments on small animals subjected to higher gravity in a centrifuge the gravitational tolerance of a mouse was 7g (7 times normal gravity), a rat was 5g and a dog and chicken 3g. He then proposes that as the gravitational tolerance “decreases with increasing body mass, an upper limit for body size would be reached, that “largest” mammal having a gravitational tolerance equal to terrestrial gravity”. In this he has presumed that gravity was the same in the past. This assumption is then verified by plotting three of these hyper-gravity results on a graph using a double-logarithmic plot and extrapolating the largest mass that any mammal could achieve as 20,000 kg. A graph is shown below using the original data given by Economos.
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In the discussion section within his paper Economos notes that the,


“… estimated maximum size of a land mammal is tentative but its agreement with the estimated size of the largest known mammal can hardly be coincidental. Though gravitational tolerance of only a few species has been determined, the extrapolation … seems to be warranted.


… for the presented upper body mass: this model fits available data from a number of species.”


Although these statements give the impression that gravity was the same in the past there are a number of observations that challenge this view. The paper mentions two other species, other than the mouse, rat and dog species data that is used on the graph to define an upper body mass limit. Neither of these two extra species data agrees with the three species data used to predict the upper mass limit for a mammal.


In the main body of the paper the gravitational tolerance of a chicken and dog are both given as 3g but only the data for the dog is used within the graph to estimate the upper mass limit for mammals. There is a very extensive difference in the mass of a dog (which seemed to be about 7 kg judging from the graph) and a chicken which typically weighs about 3 kg maximum. No explanation for the favoured use of the dog data instead of the chicken data is presented in the paper even though this would have a dramatic effect on the estimated upper body mass.


Also, Economos notes that an approximate gravitational tolerance for a man based on this data would be about 1.7g and this value also doesn’t fit the graph. If the chicken and man's gravitational tolerance data (as given) was included in the graph it would lower the predicted maximum mammal weight.


In addition the value of 1.7g for a man’s gravitational tolerance value doesn’t withstand closer scrutiny. What does Economos mean when he says that a man has a gravitational tolerance of 1.7g? Since he is suggesting that the upper gravitation tolerance for 1g is 20,000 kg it implies that a man could withstand 1.7g for the whole of his life with no ill effects. He describes gravitational tolerance as meaning that “small mammals could adapt and survive for extended periods in stronger [gravitational] fields than large mammals”.


How likely is it that a man could survive for an extended period in 1.7g and can this assumption be checked in any way? We know that the human frame can withstand much higher levels of gravity. Fighter pilots can be subjected to several g in rapid turns but this is only for short periods and causes pooling of the blood leading to rapid unconsciousness in a relatively short time. Also a pilot needs to wear a “g suit” even though he is sitting down and he is never expected to stand up and move around in this increased gravity. A long period gravitational tolerance must be much lower than this short term value.


There is another method of predicting the gravitational tolerance of a man that is much more accurate than Economos’ assumption. We know that a larger man feels the effects of gravity more than a smaller man because of the scale effect. If one man was twice the scale of another then the stress on his body due to gravity would be twice the effect the smaller man feels - this is effectively 2g. It is therefore a relatively simple matter to estimate that a giant feeling the effect similar to 1.7g would be the height of an average man times 1.7. An average European or American male is 1.78 m (5 ft 10 in). So the effective height for a man feeling gravity at 1.7 times an average man would be:


= 1.78  x 1.7 = 3.026 m (10 ft 1 in)


Now we have this figure we can simply check if any human giants have attained this value and how they coped with the increased gravitational stress.[3]


The tallest giant ever verified was Robert Wadlow who was 2.72 m (8 ft 11.1 in) tall when he died at age 22. Even this size began to take its toll, he required leg braces to walk and had little feeling in his legs and feet. His gravitational tolerance would only be 1.52g and yet he had severe health problems even at this reduced value. Sultan Kösen is a Turkish Farmer who was born in 1982. He currently stands at 2.51 m (8 ft 3 in) tall but must use crutches in order to walk.


It seems clear that the gravitational stress limit of 1.7g for a human - as suggested by Economos - was much too large. Giants have problems due to their large size and most extremely tall people tend to experience serious disabling medical conditions. Can we estimate a more reasonable gravitational tolerance for a man?


An effective gravitational tolerance from 1.4 to 1.5 would be experienced by all giants from 2.492 to 2.67 m tall. John Rogan was the second tallest verified human at 2.67 m (8 ft 9 in) but he lost the ability to stand or walk.  Gabriel Monjane was 2.65 m (8 ft 8.3 in) tall and suffered leg problems during his lifetime, especially late into his life, and became crippled after falling and breaking his hip.


An effective gravitational tolerance from 1.3 to 1.4 would be experienced by all giants from 2.314 to 2.492 m tall: Donald A. Koehler stood 2.49 m (8 ft 2 in) tall and was generally recognized as the tallest man in the world from at least 1969 until his death in 1981 from a reported heart condition. Julius Koch was 2.459 m (8 ft 0.8 in) tall and had his legs amputated after they developed gangrene. Alexander Sizonenko was a 2.39 m (7 ft 10 in) tall Soviet basketball player. He was said to have increasingly impaired mobility in later life. He died in 2012 at the age of 52.


An effective gravitational tolerance from 1.2 to 1.3 would be experienced by all giants from 2.136 to 2.314 m tall. The largest man in Britain for nearly 4 decades was Christopher Greener peaking at 2.292 m (7 feet 6.25 inches) in height. [4] In the late 1960s and early 1970s, Greener was an international basketball player for the Great Britain team, and was often seen at the Crystal Palace National Sports Centre. He often worked as an actor in various roles focusing on his great height and regularly appeared in various television programs. Yao Ming is retired Chinese professional basketball player who was the tallest active player at 2.29 m (7 ft 6 in) when he played in the NBA during his final season. In 2010 Yao developed a stress fracture in his left ankle and he eventually announced his retirement from basketball due to these injuries in 2011.


Although it is clear that a gravitational tolerance of 1.7 is too high by a large factor the allocation of a more realistic value is subjective. Giants suffer serious debilitating health problems due their large size and these problems become progressively worse at larger size. How inactive can we allow our giants to become? Giants above a gravitational tolerance of 1.5 often need some sort of aid in walking, above 1.4 there is still some mobility problems, and even though giants above 1.3 are reasonable active they appear to be more prone to injury due they large size. I would therefore recommend an effective gravitational tolerance limit of 1.3 as a more realistic value for a man who “could adapt and survive for extended periods” assuming a reasonably active lifestyle.


Including these more realistic gravitational tolerance estimates, as shown in the graph below, predicts that an African elephant is about as large as any animal is likely to get in our present gravity using the same method as Economos used for estimating the upper mass limit for a mammal. We can also see there is considerably more variation in the data than Economos allowed. The real values of gravitational tolerance are so imprecise that the species are only within ± 30 % of the predicted values.

In summary it can be seen that Economos’ 1981 paper, The Largest Land Mammal, uses a restricted set of species data that reinforce assumptions about ancient gravity and this is sometimes presented a firm proof that the Earth’s gravity was the same as the present value 23 to 34 million years ago. If additional data and more realistic values of gravitational tolerance are incorporated in the prediction it indicates that an African elephant is about as large as tolerable in our present gravity. I would recommend that further research is needed in this interesting area of study.



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Further Reading


  1. Economos 1981. The Largest Land Mammal (pdf) here
  2. Sander et al 2010. Biology of the sauropod dinosaurs: the evolution of gigantism (pdf) here
  3. List of tallest people  here
  4. Christopher Greener here  



Updated 3May13