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Ancient Life's Gravity and its Implications for the Expanding Earth.


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Galileo Galilei emphasised in the 17 th century how scale effects impose an upper limit on the size of life. It is now understood that scale effects are a limiting factor for the size of life. A study of scale effects reveals that the relative scale of life would vary in different gravities with the result that the relative scale of land life is inversely proportional to the strength of gravity. This implies that a reduced gravity would explain the increased scale of ancient life such as the largest dinosaurs. In this paper, various methods such as dynamic similarity, leg bone strength, ligament strength and blood pressure are used to estimate values of ancient gravity assuming a Reduced Gravity Earth. These results indicate that gravity was less on the ancient Earth and has slowly increased up to its present-day value. The estimates of the Earth's ancient reduced gravity indicated by ancient life are also compared with estimates of gravity for Constant Mass and Increasing Mass Expanding Earth models based on geological data. These comparisons show that the Reduced Gravity Earth model agrees more closely with an Increasing Mass Expanding Earth model.
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pag. 307
G. Scalera, E. Boschi and S. Cwojdzi´nski (eds.), 2012
THE EARTH EXPANSION EVIDENCE – A Challenge for Geology, Geophysics and Astronomy
Selected Contributions to the Interdisciplinary Workshop of the 37th International School of Geophysics
EMFCSC, Erice (4-9 October 2011)
Ancient Life’s Gravity and its Implications for
the Expanding Earth
Stephen Hurrell
11 Farmers Heath, Great Sutton, Ellesmere Port, Cheshire, CH66 2GX, United Kingdom –
Phone: +44 (0) 7753 587469 (
Abstract. Galileo Galilei emphasised in the 17th century how scale eects impose an upper
limit on the size of life. It is now understood that scale eects are a limiting factor for the
size of life. A study of scale eects reveals that the relative scale of life would vary in
dierent gravities with the result that the relative scale of land life is inversely proportional
to the strength of gravity. This implies that a reduced gravity would explain the increased
scale of ancient life such as the largest dinosaurs. In this paper, various methods such as
dynamic similarity, leg bone strength, ligament strength and blood pressure are used to
estimate values of ancient gravity assuming a Reduced Gravity Earth. These results indicate
that gravity was less on the ancient Earth and has slowly increased up to its present-day
value. The estimates of the Earth’s ancient reduced gravity indicated by ancient life are
also compared with estimates of gravity for Constant Mass and Increasing Mass Expanding
Earth models based on geological data. These comparisons show that the Reduced Gravity
Earth model agrees more closely with an Increasing Mass Expanding Earth model.
Key words. Ancient gravity – Reduced gravity Earth – Scale eects – Expanding Earth
1. Introduction
Galileo Galilei (1638) was probably the
first scientist to point out that larger an-
imals need relatively thicker bones than
smaller animals. He noted that the bones
of very large animals must be scaled out of
proportion in order to support the weight
of the animal. This is because when any
object increases in size its volume (l3) in-
creases quicker than its area (l2), and its
area increases quicker than its length (l).
For example, a simple box which was dou-
bled in length would be four times the area
and eight times the volume of the original
box. The leg stress in a large animal is pro-
portionally more than a geometrically sim-
ilar small animal because the weight of the
large animal has increased quicker than its
strength. This is commonly known as the
scale eect.
To overcome this shortfall in strength
with increased size, the legs of real large-
scale animals generally tend to be propor-
tionally thicker. Take for comparison the
thigh bones of a deer, a rhinoceros and an
elephant. As animals increase in scale the
relative thickness of their legs is greater.
The deer has the most slender legs, the
rhinoceros relatively thicker ones, while
the elephant’s legs are thicker still to sup-
port its massive bulk. The elephant is near
the upper size limit for land-based life.
The same basic principles can be seen
in land-based animals, plants and flying
birds. The largest insects have reached
the upper size limit for creatures without
bones. Mammals have reached the largest
size for animals with bones and a com-
plex four-chambered heart. Reptiles have
reached the largest size for animals with
bones and simple hearts. The largest plants
308 HURRELL: Ancient life’s gravity and expanding Earth
have reached the upper limit in size and the
largest birds have reached the upper lift-
ing capacity of their wings. For every form
of living creature there is an upper limit to
how large it can be.
The scale eect means that gravity
limits the scale of present-day land-based
life. This has been well understood for
many years by specialists in the field such
as Thompson (1917), Schmidt-Nielson
(1984) and others. The scale eect limit
presents a dicult problem for ancient gi-
gantic animals like dinosaurs. Over the
years, many dierent solutions to the prob-
lem of their large scale have been sug-
gested. Until at least the 1980s it was
widely thought that large sauropods lived
in water so the buoyancy eect permit-
ted them to grow large (Schmidt-Nielson
1984), but this idea is now considered in-
correct. Bakker (1986) was the main cham-
pion for the evidence that these large ani-
mals lived on land and his interpretation is
widely accepted today. Hokkanen (1985)
calculated a theoretical upper mass limit
for an animal in present gravity that lay
between 105to 106kg (10 to 100 met-
ric ton) but also found the athletic abil-
ity of the largest animal to be so low that
"a mass 106kg allows a running speed
of 6 km/h – a man could walk and over-
take". Conversely, many paleontologists
accept Bakker’s (1986) understanding that
sauropods were at least as athletic as mod-
ern elephants.
The concept that a reduced gravity in
the past may have increased the relative
scale of ancient life has been less well
researched but has been considered by
Kort (1949), Hurrell (1994, 2011), Mardfar
(2000, 2011), Erickson (2001), Scalera
(2002, 2004) and Strutinski (2011).
2. The relationship between relative
scale and gravity
The relationship between relative scale and
gravity can be examined using standard an-
imals as shown in Fig.1. Imagine there are
two animals of exactly the same shape, ex-
cept that the larger one is twice the lin-
ear scale of the smaller animal. Under the
same gravity, the stress in the larger ani-
mal’s legs would be double the stress in the
smaller animal’s legs. This variation can be
compensated for by adjusting the strength
of gravity: if gravity was one half as strong
for the larger animal, it would be four times
as heavy. Both the small and large animals
would have the same leg stress because
of the dierence in gravity. They would
be dynamically similar despite their dif-
ference in size because of the variation in
In the above example the relative scale
of life was increased because of the re-
duced force of gravity. This mathematical
relationship between the scale of life and
gravity can be defined as:
For a particular form of life the lin-
ear scale of land-based life is in-
versely proportional to the strength
of the gravitational field (Hurrell,
This can be represented in a formula as:
where Sris the relative scale of life, and
gris gravity relative to the Earth’s current
The eect of gravity on life’s scale is a
distinct mathematical relationship that af-
fects the basic building blocks of animals –
bones, ligaments, muscles and blood pres-
sure. A reduced gravity reduces the force
on any animal’s bones, ligaments and mus-
cles so they can all be thinner and weaker
for a particular scale of life. Blood pressure
is also reduced in a weaker gravity since
blood pressure is the hydrostatic weight of
blood (mass ×gravity).
This implies that the scale of ancient
life was shifted towards a larger size in a
reduced gravity. The most obvious result
of this scale shift is gigantic dinosaurs with
masses equal to several elephants but the
eects are also plain on smaller animals as
well. An elephant-sized dinosaur is notice-
ably more active and dynamic than any ele-
phant because the dinosaur evolved to live
in a reduced gravity.
HURRELL: Ancient life’s gravity and expanding Earth 309
Fig. 1. The force on geometrically similar animals in a dierent gravity illustrates the relationship between
life’s scale and gravity. An animal’s leg stress is due to the force of gravity. If gravity is halved then the
large animal can double its linear size while its leg stress will still be the same as the small animal’s leg
Formula (1) can be transposed to pro-
vide an estimate of ancient gravity based
on the relative scale of ancient life:
This paper calculates values for re-
duced gravity and weight on an assumed
Reduced Gravity Earth using ancient life
and introduces ‘shorthand descriptions’ to
denote this throughout the paper. For ex-
ample, gravity and weight 300 million
years ago may be defined as gravity300 or
g300 and weight300 or w300. Specific values
of reduced gravity are also given a ‘short-
hand description’ so that, for example, a
reduced gravity of 60% the present gravity
is given as 0.6g.
The values of calculated ancient grav-
ity also have a ‘confidence index’ allo-
cated which is a method of assigning a nu-
meric value to the confidence in the results.
Two methods are used to allocate a ‘confi-
dence index’. The first method is to define
a ‘reconstruction confidence index’ and
a ‘dynamic similarity confidence index’
and calculate a ‘total confidence index’ by
multiplying the two results together. The
310 HURRELL: Ancient life’s gravity and expanding Earth
Fig. 2. A modern rhinoceros and Triceratops both moving and acting in a dynamically similar manner.
‘reconstruction confidence index’ denotes
confidence in the original reconstruction of
the ancient animal. The ‘dynamic similar-
ity confidence index’ denotes confidence
that the animal moves and acts in a similar
manner to the animal used for comparison.
The second method used to define a ‘total
confidence index’ utilises the ratios of the
calculated values of Minimum gravity and
Maximum gravity when they are available.
The examples given throughout the paper
illustrate these methods more fully.
Various methods, such as dynamic sim-
ilarity, leg bone strength, ligament strength
and blood pressure are used to estimate
reasonably accurate values of ancient grav-
ity. Numerous comparisons could be used
to calculate ancient gravity but just a few
examples are given to illustrate the princi-
ples in more detail.
3. Dynamic similarity
Palaeontologists have noted that large di-
nosaurs appear to be dynamically similar
to smaller animals alive today (Alexander,
1983, 1989; Bakker, 1986).
In a reduced gravity this increase in the
relative scale of life is exactly what we
would expect. The relative scale of dynam-
ically similar ancient and modern life can
therefore be used to estimate the gravity at
the time of ancient life. In practice, the dy-
namic similarity of the largest life is the
most easy to compare since this life defines
the upper size limit for a particular form of
life in a defined gravity.
Triceratops –ATriceratops would ap-
pear to move like a bualo or a present-
day rhinoceros suggesting that Triceratops
would be able to move and gallop in a dy-
namically similar way to a rhinoceros as
shown in Fig.2. Triceratops lived about 68
to 65 million years ago and is about 1.67
times the size of a rhinoceros, so if both
animals are moving in a dynamically sim-
ilar way then the value of gravity about 66
million years ago can be calculated using
formula (2):
gravity66 =1/1.67 =0.6g
The Triceratops is a well-known ani-
mal so the ‘reconstruction confidence in-
dex’ is 0.9 out of a maximum 1. The
Triceratops is similar in general appear-
ance to a rhinoceros although Triceratops
also has a large tail so the ‘dynamic sim-
ilarity confidence index’ may be 0.6. The
‘total confidence index’ is therefore 0.9×
0.6=0.54. To sum up, about 66 million
years ago gravity was approximately 60%
of our present gravity with a confidence in-
dex of 0.54.
Ancient Dragonflies – Dragonflies
similar to modern forms were present in
the Carboniferous, dating from about 300
million years ago. These dragonflies were
usually large and occasionally gigantic
in size. The Muséum national d’Histoire
naturelle in Paris contains the only two
known examples of the famous giant drag-
onfly, Meganeura monyi. With a wingspan
of about 75 cm, it is still claimed by some
HURRELL: Ancient life’s gravity and expanding Earth 311
Fig. 3. A life-size reconstruction (72 cm wingspan) of Meganeuropsis permiana by Werner Kraus for the
University Museum of Clausthal-Zellerfeld. c
Werner Kraus 2003.
authorities to be the largest known insect
species to ever fly. This wingspan of 75 cm
is gigantic compared to that of 19 cm for
one of the largest modern species of drag-
onfly, the Giant Hawaiian Darner dragon-
fly, Anax strenuus.
Applying formula (2) to the ancient and
modern forms of dragonflies gives a value
for gravity 300 million years ago:
gravity300 =1/3.95 =0.25g
Gravity 300 million years ago was
25% of today’s gravity from a simple dy-
namic similarity comparison. There are
some fundamental assumptions used with
this comparison; both the ancient dragon-
fly fossils and the largest modern species
of dragonfly are assumed to have reached
the largest size possible for a dragonfly in
their respective gravities, and both the an-
cient and modern dragonfly are assumed to
be dynamically similar and have followed
similar lifestyles.
How accurate are these assumptions?
The ancient dragonfly which is commonly
accredited as being the largest has sev-
eral rivals which are very close to the fa-
mous giant dragonfly, Meganeura monyi.
Examples of these are Meganeuropsis
americana and Meganeuropsis permiana,
as shown in Fig.3, from the Lower Permian
fauna of Elmo. Given the fact that these
are both very close in size to Meganeura
monyi it would seem likely that this is
about as large as these ancient dragonflies
grew, even if there is some disagreement
about which was the largest.
A similar argument applies to the
largest present-day dragonfly. Although
the Giant Hawaiian Darner dragonfly is
the largest recorded size of dragonfly there
are other species approaching this size: the
Giant Petaltail dragonfly Petalura ingentis-
312 HURRELL: Ancient life’s gravity and expanding Earth
sima has a wingspan of approximately 16
cm, for example. It would seem that we can
safely assume that the sizes of the largest
ancient and modern dragonflies are su-
ciently accurate to calculate gravity 300
million years ago.
Is there any other way to check the
results? Since there are still dragonflies
around today there is an interesting method
of doing this. Experiments performed by
Marden (1987) loaded dragonflies with
weights to measure the maximum amount
that a range of dragonflies could lift.
The largest dragonfly that Marden exper-
imented with was Anax junius, which is
commonly known as the Green Darner
Dragonfly. The five individuals measured
had an average mass of 0.9752 grams and
an average maximum lifting force of 2.58
grams with an average wingspan of 10 cm.
Comparing these dragonflies to the ancient
dragonfly Meganeura monyi would give a
scaling factor of 75/10 =7.5. Using the
scale eect to calculate the weight and lift-
ing force of the ancient dragonfly assum-
ing it was dynamically similar to the mod-
ern dragonfly gives:
=411 g,
=145 g,
where Wsis the scaled weight, Wois the
original weight and sis the linear scal-
ing factor applied. Lsis the scaled lifting
force, Lois the original lifting force and
sis the scaling factor used. Obviously the
scaling factor will be the same to calcu-
late the scaled weight and the scaled lifting
This is clearly a dragonfly that couldn’t
fly in our present gravity since it weighs
411 grams but can only produce a lift-
ing force of 145 grams. We could reduce
the weight of the dragonfly by assuming
that gravity was 0.35gso that the lifting
force was exactly the same as the dragon-
fly’s weight. This gives a maximum possi-
ble force of gravity 300 million years ago
as 0.35g. Even this seems beyond reason-
able limits since it is dicult to imagine
a dragonfly that didn’t have any power re-
serves. It doesn’t seem a realistic proposal
especially if we consider that dragonflies
are predators that need to capture small
insects to survive and the female dragon-
fly must also mate in flight and then lay
its eggs in water – a sudden gust of wind
would drown our large dragonfly. It proba-
bly means that these calculations represent
an absolute size limit that could not be ex-
ceeded and was unlikely to be reached in
The ‘reconstruction confidence index’
must be good, perhaps as high as 0.9, since
the fossil dragonfly Meganeura monyi
looks like a larger version of a modern-day
dragonfly. The ‘dynamic similarity confi-
dence index’ must be high as well, perhaps
even 1, for similar reasons. Based on the
fossil Meganeura monyi, the ‘total confi-
dence index’ that gravity was 25% of the
present value 350 million years ago would
be 0.9.
4. Leg bone strength
Dinosaur reconstructions are based on fos-
sil bones fitted together to form complete
skeletons. It is these skeletons that in turn
tell us the size of the dinosaurs. Many
of the best known skeletons have been
made from bones that have been found to-
gether, apparently from one individual an-
imal, so palaeontologists are reasonably
certain that they are a realistic interpreta-
tion of that animal.
Obviously, skeletons alone cannot give
an animal’s weight directly. One method to
infer the weight of a living dinosaur is to
create life-like models of the reconstructed
animals although the accuracy of these re-
constructions relies on the skill of the mod-
Another method of estimating di-
nosaurs’ weight studied by Anderson et al
(1985) is to use leg bone dimensions di-
rectly to estimate the live weight of the an-
HURRELL: Ancient life’s gravity and expanding Earth 313
imal. Bone is not the inert material many
people believe; it is a living dynamic tis-
sue that is continually being modified and
replaced. Bone can become stronger after
exercise or can waste away through periods
of inactivity. Astronauts and cosmonauts
have particular problems in space because
their bones become weaker when they are
not subjecting them to the stress of grav-
ity. Animals’ bones, and in particular their
leg bones, grow thicker depending on how
much an animal weighs.
Anderson, a US zoologist, had a long
interest in the size of animals’ bones.
Anderson, together with a team, studied
the bones of a range of mammals to see if
there were any rules that would allow them
to estimate the mass of an animal from
just its leg bones. This would be very use-
ful for extinct animals such as dinosaurs.
The University of Florida where Anderson
worked had a large collection of mam-
mal skeletons complete with records of the
masses of these animals when they were
alive. That particular collection included
only a few really large mammals but an-
other member of the team, Hall-Martin,
who worked at the Kruger National Park
in South Africa, was able to measure the
bones of animals shot in the Park. The fi-
nal member of the team was Russell, a
Canadian dinosaur specialist.
The Anderson team chose to study the
major leg bones which are often well pre-
served in otherwise incomplete fossils. Leg
bones carry the weight of animals’ bodies
so would seem to be the obvious choice.
The bone lengths would be prone to errors
since some animals have long spindly legs
but other animals have short stubby legs.
A good indication of the mass of present-
day animals is the circumference of the up-
per leg bones – the humerus and the femur.
The humerus is the upper arm bone in us
but in the front legs in four-footed animals.
The femur is our upper leg bone – the thigh
bone – or in the back leg in four-footed
animals. The bones were measured where
they were the thinnest, and so the weakest,
usually about half way along the length of
the bones. These two circumferences were
then added together to give the total cir-
cumference of the humerus and femur. The
circumference of either the humerus or the
femur could have been used alone but this
might have lead to error since some ani-
mals place more weight on the front or the
rear legs. The use of the front and back legs
taken together tends to cancel out this er-
Table 1 and Fig.4 present raw data of
animal weight and bone dimensions kindly
supplied by Alexander (1995). The new
raw data is substantially similar to the orig-
inal Anderson team data and shows the
consistency of the concept. If you look at
the Fig.4 graph of weight-to-leg bone cir-
cumference for a range of four-footed ani-
mals you will notice that the graph is plot-
ted on a log scale so that a whole range of
dierent-sized animals from mice to ele-
phants can easily be shown on the one
graph. The points on the graph – which
are the plotted weights of various animals
– form a more or less straight band across
the graph. The Anderson team fitted a line
to the points they had based on statistical
analysis and estimated that the best line
that can be fitted to these points was de-
fined by the equation:
M=0.000084 ·c2.73,
where M=Body mass in kg and c=Total
of Humerus and Femur circumference in
mm. This equation can now be used to es-
timate the body mass of any animal from
just the humerus and femur bones. The ac-
curacy of the data can be checked and two
other lines have been added to the Fig.4
graph to show how a variation of ±30%
would aect the results. Virtually all the
plotted animals’ points lie within this er-
ror band with many much closer than this.
The formula is based on four-footed ani-
mals so it would seem reasonable to ap-
ply it to four-footed dinosaurs and the error
should certainly be within the normal error
As two-legged animals would need a
dierent formula, the Anderson team mod-
ified the four-footed equation so that only
314 HURRELL: Ancient life’s gravity and expanding Earth
Fig. 4. Graph of mammals’ leg dimensions plotted against weight as detailed in Table 1.
Table 1. Raw data of mammals’ leg dimensions for various weights.
HURRELL: Ancient life’s gravity and expanding Earth 315
the femur circumference is required. Their
equation for two-legged animals is:
M=0.00016 ·c2.73,
where M=Body mass in kg and c=
Femur circumference in mm.
One use of these equations would be
to calculate the weight of extinct animals
and the Anderson team applied their equa-
tions to a number of dinosaurs. One would
expect the results to have certainly been
within ±30% and in most cases a lot more
accurate than this. Most dinosaurs should
have been close to the best fit line. But
the results indicated dinosaurs were much
lighter than anyone had ever thought pos-
Since the bone results were first pub-
lished in 1985 the weights of dinosaurs
based on volume methods have been re-
duced to try to agree with these super-light
dinosaurs. However, this raised questions.
The weight for Diplodocus, for example,
was calculated at 5.8 tonnes from bone di-
mensions, which is similar to a modern-
day elephant. This doesn’t seem reason-
able if you compare an elephant skeleton
alongside a Diplodocus skeleton because
the Diplodocus skeleton is much larger.
As the two methods give very dif-
ferent results some palaeontologists have
advised abandoning the use of the for-
mula based on leg bones since they can-
not get dinosaurs light enough to agree
with the bone weight calculations. The dif-
ferences are so great for large bipeds that
Hutchinson et al (2007) concluded that: is almost certain that these scal-
ing equations greatly underestimate
dinosaur body masses ... Hence, we
recommend abandonment of their us-
age for large dinosaurs.
These results are fundamental to the
reduced gravity hypothesis. The Reduced
Gravity Earth theory predicts that leg bone
strength will be weaker in a reduced grav-
ity and this is exactly what we see in
practice. The body mass estimates based
on volume methods greatly exceed those
based on leg bone strength because they as-
sume gravity was the same in the past. This
variation between body mass estimates and
leg bone strength can therefore be used to
calculate ancient gravity when ancient life
was alive.
Tyrannosaurus rex – One meat-eating
type of dinosaur that shows a variation be-
tween the weight calculated from model
volumes and the expected weight from
bone calculations is Tyrannosaurus rex,
as shown in Table 2. Some of the es-
timated weights for Tyrannosaurus rex
are from dierent specimens so it would
be expected that these may be dierent
size animals which would have dier-
ent weights. The Tyrannosaurus rex ex-
amined by Henderson and Snively (2003)
is nicknamed ‘Sue’ and is the largest
Tyrannosaurus rex found to date. If only
one specimen (MOR 555) is considered its
weight based on the volume method only
varies between 5.4 to 6.6 metric tonnes
when studied by three dierent research
teams, Paul (1997), Farlow et al (1995) and
Hutchinson (2007). This same specimen
has also been used to calculate its weight
based on its bone dimensions by two re-
search teams, Anderson et al (1985) and
Campbell & Marcus (1993).
The bone dimension calculation indi-
cates the legs of Tyrannosaurus rex only
evolved to carry an animal that weighed
between 3.5 to 4.5 metric tonnes while the
volume method gives a mass between 5.4
to 6.6 tonnes. Using an average of these re-
sults to calculate gravity 65 million years
gravity65 =Calculated weight
Volume Mass =4.0
=0.66 g
The absolute maximum and minimum
values of gravity can be calculated from
the extremes of the weight estimates with
the absolute maximum and minimum be-
ing 0.83gand 0.53gabout 65 million years
ago. The confidence index can be calcu-
lated from the variation in the results. So
confidence index =Min gravity /Max
gravity =0.53/0.83 =0.63.
316 HURRELL: Ancient life’s gravity and expanding Earth
Table 2. Comparison of weight estimates in tonnes for Tyrannosaurus rex based on volume mass estimates
from models and leg stress estimates on bone.
5. Ligament strength of Diplodocus
Present-day horses and cattle have thick
ligaments called the ligamentum nuchae
running along the back of their necks to
support their heads.
The sauropod Diplodocus has neck
vertebra with V-shaped neutral spines as
shown in Fig.5 and Alexander (1989) sug-
gested that the V was filled by a lig-
ament that ran the whole length of the
neck and back into the trunk of the ani-
mal’s body. The ligament would have sup-
ported the head and neck while allowing
the dinosaur to raise and lower its head.
Alexander calculated that the mass of the
head and neck of Diplodocus would have
been about 1340 kg. The weight of the
neck and head acts 2.2 metres from the
joint and the ligament tension acts 0.42
metres from the pivot of the joint so by the
principle of levers the tension that would
be needed to balance the weight to the neck
and head would be 2.2×13400/0.42 =
70000 Newton.
The cross-sectional area of the liga-
ment was estimated to be 40000 sq mm and
from this it can be calculated that the stress
for a force of 70000 Newton would be 1.8
Newton per square mm. This is more than
the stress in the ligamentum nuchae of deer
with its head down and the ligament fully
stretched (which is about 0.6 Newton per
square mm). It would be enough or nearly
enough to break the ligament.
Stevens and Parrish (1999) suggested
that the problem of the weak neck liga-
ments could be overcome if a sauropod’s
neck was imagined as a sti, almost self-
supporting structure where the neck ver-
tebrae overlapped each other by around
50% to provide additional support. They
built a computer model of Diplodocus in
a neutral pose with its long neck at about
shoulder height dipping slightly towards
the ground. This depiction of a sti-necked
Diplodocus with its head held permanently
low removed the problem of a weak neck
ligament as well as the problem of high
blood pressure if the neck was held high.
These sti-necked reconstructions
were generally accepted since they seemed
to provide answers to real questions and
HURRELL: Ancient life’s gravity and expanding Earth 317
Fig. 5. V-shaped neck vertebra probably held the neck ligament used to keep Diplodocus’s neck erect and
this enables the ligament’s size to be estimated.
Diplodocus is now mostly depicted with
a sti, relatively useless long neck that
it couldn’t lift to reach the higher plants.
Many museums around the world and TV
series like Walking with Dinosaurs show
Diplodocus like this even though some
paleontologists disputed this view (Bakker
A more recent study by Taylor et
al (2009) presented additional arguments
against these sti-necked reconstructions
and concluded that:
Unless sauropods carried their
heads and necks dierently from ev-
ery living vertebrate, we have to as-
sume that the bases of their necks
were habitually curved upwards, ...
In some sauropods this would have
meant a graceful, swan-like S-curve
to the neck, and a look quite dierent
from the recreations we are used to
seeing today.
The problems encountered with
Diplodocus’s neck only occur because it is
assumed that gravity was the same in the
past. The Reduced Gravity Earth theory
predicts that the neck ligament would be
thinner in a reduced gravity and this is
exactly what we see in practice.
Due to a reduced gravity the actual
weight of Diplodocus’s neck 150 million
years ago would be:
weight150 =Mass ×gravity150.
The weight of the neck and head still
acts 2.2 metres from the joint and the lig-
ament tension acts 0.42 metres from the
pivot of the joint so by the principle of
levers the tension that would be needed to
balance the weight of the neck and head
would be:
Force =2.2×Mass ×gravity150/0.42.
Force =stress ×area,
318 HURRELL: Ancient life’s gravity and expanding Earth
so, rearranging to obtain gravity 150 mil-
lion years ago:
gravity150 =
=stress ×area ×0.42/2.2×Mass =
=0.6×40000 ×0.42/2.2×1340 =
This 3.4 m/s2calculated value of gravity
150 million years ago is much smaller than
the present-day value of 9.81 m/s2.How
accurate is this value of gravity? There are
a number of variables that might be dif-
ferent from the initial assumptions used;
the ligament could be larger if it expanded
outside the V-shaped neck bones, the force
of the neck’s weight would be lower if
Diplodocus held its neck more upright, and
additional muscles or ligaments might pro-
vide additional support. If the neck was
held at a 45 degree angle the downward
force of the neck would be reduced by
0.707. The ligament could easily be half
as large again if it extended outside the V-
shaped neck bones, increasing the area of
the ligament to 60,000 sq mm. So:
gravity150 =
=stress ×area ×0.42
2.2×Mass ×0.707 =
=0.6×40000 ×0.42
2.2×1340 ×0.707 =
=7.25 m/s2.
The results give a value for gravity
150 million years ago as somewhere be-
tween 34% to 72.5% of the present grav-
ity with the ‘best guess’ 53% of present
gravity. The confidence index can be cal-
culated from the variation in the results. If
the Minimum and Maximum gravity was
identical then our confidence index would
be 1. So confidence index =Min gravity /
Max gravity =0.34 /0.725 =0.47.
6. Blood pressure of Brachiosaurus
Because of its long neck the girae has
the maximum hydrostatic blood pressure
of any animal alive today. This high blood
pressure seems to be about the maximum
possible since the girae needs to use ex-
treme measures to maintain it. Because the
central blood pressure is high the heart’s
muscle has to be strong and a girae’s
heart can weigh up to 10 kg and mea-
sure about 60 cm long. The heart of an
adult girae is about 2% of its body weight
whereas in people it’s only about half a
percent. Giraes have arterial blood pres-
sures of 25 kPa at the bases of their necks
whilst standing. By extrapolation, the pres-
sure in the heart must exceed 30 kPa which
is about double the normal pressure in a
Brachiosaurus lived in the Late
Jurassic to Early Cretaceous, about 145
million years ago. It is generally recon-
structed with its neck sloping steeply up,
in a girae-like posture so the brain of
Brachiosaurus was about 7.9 metres above
its heart as shown in Fig.6. Calculations
assuming our present gravity reveal that
the total pressure dierence between the
brain and the heart would be 8590 kPa.
These problems of high blood pres-
sure would not exist on a Reduced Gravity
Earth because blood pressure is lower in a
reduced gravity. Blood pressure is propor-
tional to blood mass, gravity and height,
so it is possible to estimate ancient gravity
by comparing the blood pressure in ancient
life with the blood pressure in modern life.
The hydrostatic pressure dierence be-
tween the blood in the brain and the heart
can mostly be defined as the hydrostatic
head in metres. The hydrostatic pressure at
the base of the Brachiosaurus’s neck 145
million years ago can be calculated by:
Hydrostatic Pressure =
=blood density ×gravity145 ×height.
In a reduced gravity the hydrostatic
pressure would be reduced because
the weight of the column of blood
would be less and this would allow a
HURRELL: Ancient life’s gravity and expanding Earth 319
Fig. 6. The position of the head above the heart determines the blood pressure, or the hydrostatic head, at
the heart for a girae and Brachiosaurus.
Brachiosaurus’s neck to become much
longer than today’s girae. Blood is an
incompressible fluid whose density would
not vary in a dierent gravity so it seems
safe to assume that the density of dinosaur
blood was the same as girae blood. A
large girae about 5.5 metres tall would
hold its head 2.8 metres above its heart so
the hydrostatic head in its heart would be
2.8 metres.
The assumption that the blood pres-
sure above the heart of both the girae
and Brachiosaurus is the maximum that
the various tissues can withstand enables
a calculation of the value of gravity when
Brachiosaurus lived. We know:
Brachiosaurus Hyd.Pressure =
=gravity145 ×Brachios.Neck Height
Girae Hyd.Pressure =
=gravity ×Girae Neck Height
gravity145 =Gir.N.Height
Brach.N.Height gravity =
7.9×gravity =0.35 g.
Using the lowest neck height which
seems possible gives a hydrostatic head
of 3.9 metres. Using this hydrostatic head
would give:
gravity145 =Gir.N.Height
Brach.N.Heightgravity =
3.9×gravity =0.72 g.
My own ‘best guess’ about the posi-
tion of the neck for Brachiosaurus is that it
was somewhere between the two extremes.
This intermediate position gives a hydro-
static head of 5.9 metres, which in turn
would predict gravity to be:
gravity145 =Gir.N.Height
Brach.N.Heightgravity =
5.9×gravity =0.48 g.
So using the method of equating
the blood pressure in the long neck of
Brachiosaurus to a girae, gravitational
acceleration is calculated somewhere be-
tween 35% to 72% of our present grav-
ity 145 million years ago, with the ‘best
guess’ value working out at 48% of our
present gravity.
320 HURRELL: Ancient life’s gravity and expanding Earth
Table 3. Table of the variation of Earth’s gravity over hundreds of millions of years based on various
comparisons of ancient and modern life.
7. Ancient gravity results
The calculated values of ancient gravity
based on various animals using dynamic
similarity, leg bone strength, neck ligament
strength and blood pressure are reproduced
in Table 3 and Fig.7 in order to gain an
overview of the results.
Many forms of life can be used
to calculate ancient gravity using the
methods outlined in this paper. Table 3
includes calculated estimates for ancient
gravity based on the dynamic simi-
larity method for an ancient Scorpion, a
Dragonfly, Brachiosaurus, two Crocodiles,
and Baluchitherium, and also based
on leg bone strength for Plateosaurus,
Brachiosaurus and Tyrannosaurus.
The graph in Fig.7 shows the ‘best
guess’ value as circular dots of various
sizes in order to represent the gravity value
that has been calculated. It is notable that
the dots representing gravity show a gen-
eral trend of gravity gradually increasing
over hundreds of millions of years.
Many of the distinct methods of calcu-
lating gravity give very similar values. If
one animal which was subjected to a num-
ber of these calculation methods is taken
as an example, such as Brachiosaurus,we
can clearly see the similarity of the results.
Dynamic similarity gives 0.45g, leg bone
strength 0.56gand blood pressure 0.48g.
These ‘best guess’ values all give results
which are in broad agreement with each
other even though they use dierent meth-
ods to calculate ancient gravity.
Comparing dierent animals to one
another in the same time period also
gives broad agreement for the ‘best
guess’ value. Dissimilar animals that
were alive about 150 million years ago
such as Brachiosaurus,Allosaurus and
HURRELL: Ancient life’s gravity and expanding Earth 321
Fig. 7. Graph of the variation in Earth’s gravity over hundreds of millions of years based on the various
comparisons of ancient and modern life listed in Table 3.
Diplodocus also all give values for grav-
ity which are in broad agreement with each
other. Animals which were alive at other
times give dierent values for gravity.
One element that needs to be consid-
ered for the confidence index is the varia-
tion in size naturally seen in the living an-
imals of today. If the elephant is taken as
an example, there is a wide variation in the
size of elephants as a group. An African
male elephant tends to be the largest at
over 4 metres tall but the African female
elephant is usually slightly smaller and the
Asian female elephant smaller still at just
over 3 metres tall. We see a general varia-
tion from about 3 to 4 metres in height in
the largest animals alive today. If we as-
sume an average height of 3.6 metres for
the average African elephant then a rea-
sonable variation ±10% would give a size
range of about 3.2 to 3.9 metres for our
sample. The same, or an even greater, vari-
ation in size was probably true for the di-
nosaurs and other prehistoric life. It is pos-
sible to remove that variation in our liv-
ing model since we know what the aver-
age size is, but it is more dicult to re-
move this source of error in the extinct an-
imal since there is such a small sample of
fossils making it dicult to say if the liv-
ing animal was a large or small member of
the species. Because of this I believe that
even the best possible calculation of grav-
ity from ancient life would only be within
±15% of the true value at best and possibly
much worse than this.
In the graph the 0.8-1 confidence index
has been shown as the largest and black-
est of the dots. The size and blackness of
the dots reduce down as the confidence re-
duces until the 0-0.2 confidence index dots
are the smallest and faintest of all. Vertical
dotted lines are also shown coming out of
all the dots and these are a further attempt
to display this possible error on the graph.
The values used for the error bars have
therefore been set at: ±15% for 0.8-1 confi-
dence index, ±20% for 0.6-0.8 confidence
index, ±25% for 0.4-0.6 confidence index,
±30% for 0.2-0.4 and ±35% for 0-0.2.
The final element of the graph is a the-
oretical line to show how gravity may have
varied over time from 300 million years
ago up to the present day. It is interest-
ing to note that this gravity line lies well
within the error bars of the calculated val-
ues of gravity and even the estimates with
the lowest confidence index are still within
the error bars. In general, life indicates that
gravity was less on the ancient Earth and
has slowly increased up to its present-day
322 HURRELL: Ancient life’s gravity and expanding Earth
Fig. 8. A typical Expanding Earth reconstruction based on geological data.
HURRELL: Ancient life’s gravity and expanding Earth 323
Fig. 9. Earth’s changing gravity over time based on geological reconstructions of an Expanding Earth.
8. Implications for the expanding
The magnetic recordings on the ocean
floor have been mapped to give a detailed
account of the age of the Earth’s ocean
floor. By removing the ocean floor that
is known to be younger than a particu-
lar age, it is possible to reconstruct an-
cient Expanding Earth globes by rejoin-
ing the remaining ocean floors. A number
of reconstructions have been produced by
Hilgenberg (1933), Vogel (2003), Hurrell
(1994, 2011), Luchert (2003), Maxlow
(2005) and many others. Fig.8 shows a typ-
ical Expanding Earth reconstruction.
The estimates of ancient Earth’s re-
duced gravity, indicated by the larger rela-
tive scale of ancient life, can be compared
with estimates of gravity for Constant
Mass and Increasing Mass Expanding
Earth models. The force of the Earth’s
gravity is:
where M1and M2are the masses of the
two mutually attracting bodies, Ris the dis-
tance separating them and Gis Universal
Constant of Gravity and the calculated
force Fis eectively the force of gravity.
For a Constant Mass Expanding Earth
ancient gravity would be about four times
the present value which does not agree
with the results from ancient life. For an
Increasing Mass Expanding Earth gravity
would gradually increase over time as the
Earth grew in diameter and mass so this
agrees with the gravity results from ancient
This is a simplistic method of calculat-
ing the force of gravity since it assumes
that the density of the ancient Earth is
exactly the same as the present Earth. It
is much more probable that as the an-
cient Earth grew larger in size and mass it
would become denser as its core became
more compact due to the increasing surface
gravity (Hurrell 1994, 2003). This density
increase can be estimated by plotting the
known variation of gravity against the ra-
dius of other known celestial bodies, and
a graph of changing gravity on the ancient
Earth taking account of density variations
in the Earth’s core and mantle based on
other celestial bodies is shown in Fig.9.
The Reduced Gravity Earth model
agrees most closely with an Increasing
Mass Expanding Earth model rather than
a Constant Mass Expanding Earth model.
Estimates of ancient life’s gravity indicate
that Earth Expansion is due to mass in-
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Author’s Biographical Notes: Stephen Hurrell
lives near Liverpool in the UK where he has worked
in mechanical engineering design positions for
various companies. It was his role as a mechanical
design engineer at the UK’s Electricity Research
Centre that first oered him his insight into how
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This chapter covers some of the key case studies in neuroethology that have informed the understanding of how animals use vision to detect, identify and respond to predators and prey. It first outlines important principles of visual processing, including properties of light and the concepts of foveae, acuity and sensitivity. Then, the chapter looks at how meaningful features of an image are extracted as information passes through the visual pathway, in order to identify objects as predator or prey, using the toad as a model system. The next part of the chapter outlines the neurobiology of infrared vision in snakes. These ambush predators possess a highly specialised infrared visual system used to detect and target their warm-blooded prey. Finally, the chapter looks at specialisations of the visual system in aerial predators that enable them to capture prey while simultaneously coordinating flight, using dragonfly vision as an exquisite example.
Full-text available
WHEN Dinosaurs and the Expanding Earth was first published it proposed a startling idea to explain the long-standing puzzle of the dinosaurs' gigantic size. Stephen Hurrell presented scientific evidence that dinosaurs lived in a reduced gravity and this allowed them to grow to gigantic proportions. The Reduced Gravity Earth theory explains why all land-based life has shifted towards a larger scale on the ancient Earth. This includes gigantic dinosaurs, plants and insects. It is also a key piece of evidence that provides additional support for an Expanding Earth, something a few leading geologists have been suggesting for decades. Since its initial unveiling, the Reduced Gravity Earth theory has been widely discussed and debated. Individuals from laymen to professors are now arguing that gravity was lower on the ancient Earth. You can analyse the evidence for believing the controversial Reduced Gravity Earth theory and its implications for the Expanding Earth in this third edition of Dinosaurs and the Expanding Earth. PRAISE FOR PREVIOUS EDITIONS: 'something completely different ... an original work rather than a re-presentation of existing knowledge ... well presented.' GEOLOGY TODAY - Blackwell Science Ltd, 'Engineers (Hurrell) have shown that dinosaurs' bones could not have borne their weight ... much reduced surface gravity is essential for dinosaurs to have existed.' Professor S. Warren Carey, University of Tasmania, '... written in a plain straightforward style and its target is a wide public not interested in specialist treatises. Its clear and lively descriptions lead the reader straight to the core of the arguments. ... could well be the topics of joint scientific collaboration between engineers and paleontologists.' ANNALS OF GEOPHYSICS.
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Maximum lift production during takeoff in still air was determined for a wide variety of insects and a small sample of birds and bats, and was compared with variation in morphology, taxonomy and wingbeat type. Maximum lift per unit flight muscle mass was remarkably similar between taxonomic groups (54–63 N kg−1), except for animals using clap-and-fling wingbeats, where muscle mass-specific lift increased by about 25 % (72–86 N kg−1). Muscle mass-specific lift was independent of body mass, wing loading, disk loading and aspect ratio. Birds and bats yielded results indistinguishable from insects using conventional wingbeats. Interspecific differences in short-duration powered flight and takeoff ability are shown to be caused primarily by differences in flight muscle ratio, which ranges from 0.115 to 0.560 among species studied to date. These results contradict theoretical predictions that maximum mass-specific power output and lift production should decrease with increasing body mass and wing disk loading.
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Body size is a crucial life history parameter for an organism. Therefore, mass estimation for fossil species is important for many kinds of analyses. Several attempts have been made to yield equations applicable to dinosaurs. In this paper, we offer bi- and multivariate equations based on log transformed appendicular skeleton data from a sample of 16 theropods which were known from reasonably complete skeletal remains, and spanning a wide size range. Body masses of the included taxa had been found by displacement methods of scale models, based on measurements taken directly on the mounted skeletons. Seven of the bivariate regression analyses resulted in correlation coefficients equal to or above 0.975 and femoral length was the best available measurement (r=0.995; standard error of the estimate (%SEE)=19.26; percent prediction error (). Also, 32 multivariate analyses yielded equations with high correlation coefficients (r>0.990) and low standard errors.
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Flapping flight is a highly effective form of locomotion which has permitted the radiation of birds into a wide range of niches. In this chapter I explore how the mechanics of flapping flight have molded the flight adaptations of birds. The paper has three main threads. First, I describe recent theoretical and experimental studies on flapping flight aerodynamics and demonstrate how the mechanical requirements of locomotion are reflected in wingbeat kinematics, in vortex wake structure, and in the action of the pectoral musculature. Next, I consider how flight performance varies with size; scaling has become a central tool in the analysis of flight in birds and has proved a useful means of predicting how different mechanical, physiological, and ecological parameters change in importance with size, morphology, and behavior. However, scaling is frequently misinterpreted: it is size-dependence of the constraints on adaptation which lead to allometric consistency in avian flight morphology, and many of these constraints can be related directly to flight mechanics. Finally, I use a multivariate analysis of wing morphology to demonstrate how these constraints interact to different degrees in different birds and underlie correlations among flight morphology, ecology, and behavior. These threads are then brought together in a discussion of the conjectural relationships between fitness and the evolution of specializations in flight morphology.
A mathematical-computational method for determining the volume, mass, and center of mass of any bilaterally symmetric organism is presented. Cavities within the body of an organism such as lungs are easily accommodated by this method. Sagittal and frontal profiles, obtained from tracings of 'fleshed-out' skeletal reconstructions, are used to provide limits for defining transverse slices of the body. Any internal cavities are defined by their own sagittal and frontal profiles. The computations consist of mathematically slicing the body and any cavities into independent sets of transverse laminae and computing their masses, centroids, and moments with respect to the three coordinate axes. Further calculations produce the masses and the (x,y,z) coordinates for the centers of mass of the body, any cavities, and the body + cavities. Predicted body masses of large, extant mammals (elephant, giraffe, hippopotamus, and rhinoceros) are in close agreement with actual body masses. New, lower estimates for body masses of selected large dinosaurs, based on modern skeletal reconstructions, are also presented, along with numerical estimates of their centers of mass. This method is an improvement over earlier ones that relied on measuring displaced volumes of water or sand by scale models to estimate the masses, and suspending models by threads to estimate their centers of mass.