Galileo's Square Cube Law - Colorado Association of Science ...

Galileo’s Square Cube Law
&
Why Size Matters
National Science Teachers Association Conferences
Minneapolis - Nov. 30 th 2009 Phoenix - Dec. 5 th 2009
Colorado Science Conference
Denver - Nov. 19 th 2010

The New Science
• In 1638 Galileo published
Two New Sciences.
• Because the ratio between
area and volume changes
with size, size matters.
• Galileo’s Square-Cube Law
is one of the most
fundamental concepts in
all of science.

Science Gone Wrong
• Yet 3 & ½ centuries later
Galileo’s Square-Cube
Law is still being left out
of science education.
• Consequently most
everyone is still unsure if
size matters.

Does Size
Matter?
•It is a major failure of science
education that our society is
ignorant regarding this extremely
fundamental scientific question.

Misleading Experts
• Giant dinosaurs and pterosaurs appear to
conflict with Galileo’s Square-Cube Law
showing that size matters.
• Either 1) Galileo’s Square-Cube Law is
wrong or
• 2) the paleontologists claiming that there
is nothing odd about giant dinosaurs and
pterosaurs are wrong.

The evidence supporting Galileo’s
Square-Cube Law is overwhelming.
• Problem: The ‘experts’ are never
going to admit to being wrong.
• Science educators have an
obligation to be leaders in
determine what is good science.

What is Galileo’s
Square-Cube Law
• The area is the
square of the length
multiplier.
• The volume is the
cube of the length
multiplier.
• Changing the size
changes the ratio of
area to volume.
Height
Depth
Width

Scaling Example of Square-Cube Law
• If kite B is three times
taller than kite A.
• Then kite B has nine
times the surface area of
kite A; yet it weights 27
times more than kite A.
• Will kite B fly if its
weight to area ratio is
three times greater?
Kite A
Kite B

Larger flying objects require
disproportional greater power.
Applies to planes, helicopters, birds, and
other flying animals.

Consequences of
Scaling are not
Always Obvious.
• Simple objects may still work when they
are scaled up or down.
• Yet complicated objects such as flying
machines and biological objects will
usually fail if their size is outside their
normal narrow range.

Consequence of
being ignorant of
the Galileo’s
Square-Cube Law.

Galileo’s Square-Cube Law Applies
to All Science Disciplines
• Aerodynamics
• Biology
• Nanotechnology
• Astronomy
• Physics
• Chemistry

Smaller objects
have more
exposed area.
• Small grains,
powders, gives us
the coffee that we
want FAST!
• The small sticks
exposed more wood
at the surface for
burning.

Rate of Heat Transfer
• Food with large areas compared to their volume
cooked in only a few minutes.
• Food with a large volume compared to its surface
area require a few hours in the oven.

Larger Size Objects have:
• Greater difficulty achieving flight
• Greater stress so large objects are
more likely to break
• Slower chemical reactions.
• Lower heat transfer.

Galileo’s Square-Cube Law is fundamental
to understanding biology.

Diffusion Rates / Cell Division
• Cells need a high surface
area to volume ratio to
be efficient in passing
food and waste across
the cell membrane.
• Larger cells have a lower
surface area to volume
ratio.
• So cells divide rather
than grow larger.

Stress & Bad Health of Giants
• Stress on Robert
Wadlow’s legs is about
twice that of the girls.
• Likewise his difference in
blood pressure with
height is about twice that
of the girls.
• Giants and overweight
people tend to suffer
numerous health
problems.

Something has got to give!
• If you double the size of
an animal then
• 1) Weight is eight times
greater while
• 2) Supporting area is
only four times greater.
• Stress is twice as much
and so the legs are more
likely to break.

Larger Animals are More Likely to
Break Bones
• Small animals can fall great heights without harm.
• Conversely, horses often break their bones while simply
running a race.

• Elephant has the greatest absolute
strength yet the least amount of
relative strength.
• The smallest animals have the
greatest relative strength.
• Rhinoceros beetle can lift 850
times its own weight.
Strongest Animal:
Absolute Strength
and Relative
Strength.

Relative Power Effects How Birds Fly
• The humming bird has so much relative
power that it can hover and even the fly
backwards.
• The largest birds often need rising air
thermals to assist them with their flight.

When birds get too large they can
no longer fly

Relative Power
& Metabolism
• Heaviest flying bird = 25 pounds.
• Heaviest bat = 2.5 pounds.
• There are no modern day flying reptiles.
• Reason: birds have greater relative power
• 1) superior circulating respiratory system,
• 2) higher body temperature.

Smaller Mammals have
Greater Heat Lost
• Small mammals have to eat
constantly to replace their lost
thermal energy.
• A five ton elephant will eat
about 130 kg of food per day
• Five tons of mice will eat 720
kg of food per day.

Humans
change their
shape as they
grow
• As warm-blooded animals grow the surface to
volume ratio decreases.
• Effects the rate of heat transfer.
• Babies have more rounded features and
disproportionally large heads.

Larger Animals have:
• Lower relative muscle strength
• Greater stress on their bones so their
bones are more likely to break
• Less relative heat lost so larger animals
eat proportionally less food
• Lower heart rate.

The Biology Revolution
• The new biology requires a foundation in
mathematics and physics.
• Education reform: physics first.
• No real understanding until you write an
equation or make a hypothesis.
• Simply because something is alive does
not excluded it from the laws of physics.

Size & Heart Rate
• Smallest animals have
much higher heart rates.
• Mouse: 500 beats/min
• Human: 70 beats /min
• Elephant: 28 beats / min
• Heart rate to body mass:
R = (K m) -1/4 .

Biological Clock
• Cells are like engines: their metabolism rate is
directly related to the food and oxygen supply.
• Circulating system of smaller systems delivers
food and oxygen to cells at a higher rate.
• Lifespan is about a trillion heart beats.

Further Reading
• Scaling: the Physics of Lilliput - Morrison
• A Matter of Scale - Geoffrey West
• Scaling: Why Giants Don’t Exist - Fowler
• On being the Right Size - J. B. S. Haldane
• DinosaurTheory.com – David Esker

End of Presentation on
Galileo’s Square-Cube Law
Thank you
David Esker