Theory Of Egg Boiling
Despite its apparent
simplicity, most cooks are daunted by the
prospect of producing a perfectly boiled egg.
This anxiety means that few, in the modern day,
even make the attempt to do so.
It has been known since
medieval times that two seemingly identical eggs,
cooked in the same manner, could have very
different consistencies when opened.
In earlier centuries, these
variations had been attributed to the
intervention of mischievous or malevolent spirits,
and appropriate prayers were offered before and
during the boiling process. Samuel Pepys noted in
his diary of 1665, however, that such requests
for divine assistance often appeared to have
little effect on the culinary outcome!
It was not until the
twentieth century that scientific progress
finally led to recognition of the real causes of
the problem: The inconsistency in egg cooking
related to there being far more variables
impacting on the process than had been previously
The physics, chemistry and
mathematics which ultimately led to a solution to
the problem of perfect egg boiling are
unquestionably complicated, and this has,
unfortunately, led to most egg boilings now being
attempted only within academic and research
The purpose of this article
is to summarise for a lay readership the
theoretical issues involved, and provide a step
by step guide to the practical process required
to successfully boil an egg.
It is the earnest hope of
all the academics who have contributed to the
article that it will encourage many more cooks to
develop the confidence to try it for themselves.
The variables that
impact on the boiling of an egg:
1 - The egg, itself:
There are two inherent
properties of an egg that impact on its behaviour
when boiled: One is its size and the other is its
Quantifying these two
properties has posed significant challenges to
the finest scientific and mathematical minds.
The first major
breakthrough occurred in 1968 when Professor
Sandy Yoke of Oxford University was awarded the
Nobel Prize for Mathematics for her resolution of
what is known as the "Shape Profile Problem".
Isaac Newton in his Principia
Mathematica had already deduced that all
eggs are egg shaped. He had also concluded that
for an egg of a specific volume, there are an
infinite number of maximum diameters, maximum
lengths and shell curvatures that can contain
that same volume. These differences in geometry
cause the passage of heat to differ through eggs
of identical volume. This obviously affects their
Professor Yoke proved that
the impact of egg geometry on cooking properties
could be fully described by just two variables:
the volume of the egg, usually denoted by the
lower case letter, v, and its "shape profile
coefficient", usually denoted by the lower
case letter, s.
The second breakthrough
came in 1976 when a postgraduate chemistry
student at Cambridge University, John White,
realised that the density of an egg related to
Chemical changes gradually
occur within the substance of an egg from the day
it is laid. These ultimately result it being
described as "bad". These changes also
affect the boiling properties of the egg. John
White not only calculated the relationship
between freshness and density, but also between
density and those boiling properties. He
mathematically described this latter relationship
with a coefficient he named the "culinary
density" of the egg. This is usually denoted
by the lower case letter, c.
The boiling properties that
are directly related to inherent properties of an
egg were, therefore, found to be fully described
by its volume (v), its shape profile coefficient
(s) and its culinary density (c).
Practical application of
the above theory, however, had to await the
development of an instrument that could
accurately measure v, s and c. This came in the
form of the magnetic image resonance or MRI
scanner. After scanning an egg, these machines
are able to directly provide values for these
Most household, of course,
do not own an MRI scanner. Fortunately, one can
be found in most hospitals, and the staff who
operate such machines are often only too pleased
to allow eggs to be scanned between the use of
their machines for patients.
When attending the hospital
to have your eggs scanned, take a whole box of
eggs. They can all be scanned while you
are there, hence avoiding the need to return on
every occasion that you are planning to boil an
Don't forget to mark the v,
s and c values on each egg in permanent marker as
soon as it is scanned to avoid any later
uncertainty as to which egg was which!
2 - Temperatures:
There are three
temperatures, or sets of temperatures, that are relevant
to the boiling of an egg. These are the
temperature of the egg itself prior to boiling (t);
the temperatures of the environments in which the
egg is kept when not being boiled (e values), and
the temperature of the water in which it is
In the context of this
article we are examining only the Special Theory
of Egg Boiling. In the Special Theory, certain
assumptions are made to simplify the theory and
practice of producing a correctly boiled egg.
The key simplifications
relate to environmental temperatures or e values.
The Special Theory assumes
- the room in which the egg is
boiled is kept at a constant temperature prior to,
and subsequent to, the boiling of the egg.
- the egg has remained in that
environment for at least two hours prior to
- the egg is consumed either in
that room or one kept at the same temperature,
and that the egg does not experience any
temperature changes in moving from the cooking to
the eating room.
- the egg will be consumed as
soon as its temperature has fallen to 45 degrees
The above simplifying
assumptions are helpful because:
- the time taken for correct
cooking depends on the temperature of the egg
immediately prior to boiling. The mathematics is
simplified if the egg is at the same temperature
as that of its pre-boiling environment.
- an egg continues to cook, due
to residual heat, when removed from the boiling
water, and the extent of that additional cooking
relates to its rate of cooling. This, in turn,
relates to the environmental temperature,
together with the time and temperature at which
the egg is finally consumed.
The General Theory of Egg
Boiling takes account of changes in environmental
temperatures at any stage of the process. It
therefore includes multiple values of e (e1,
e2, e3 to en)
together with durations within those environments
(de1, de2, de3
to den). It also includes elements of
differential calculus to take account of
temperature gradients between successive
The General Theory also
contains terms to account for a temperature of an
egg prior to boiling that differs from the pre-boiling
The General Theory is,
therefore, a powerful tool which allows a
perfectly boiled egg to be consumed under any set
of relevant variables. The massive increase in
computational complication, however, makes it
extremely cumbersome. Indeed, some would go as
far as to say that it is impractical for everyday,
Many people beileve that
the boiling temperature of water is always 100
degrees celsius. This is not always the case,
however, as the boiling temperature of water will
be influenced by any impurities in the water
together with factors that affect atmospheric
pressure. The latter factors include height above
sea level, the local acceleration due to gravity
(variable across the Earth's surface because the
planet is not a perfect sphere), and atmospheric
Fortunately the problem of
impurities can be solved by boiling the egg in
distilled water. All the other factors affect the
one figure of barometric pressure (b) and this
can be easily measured with a barometer at the
location that the egg is boiled. There is no term
for the boiling temperature of the water in the
boiling time equation, below, as this is
calculated from the barometric pressure.
Clearly, using the Special
Theory, e and t are equal and can both be
measured by simply taking the temperature of the
room in which the egg is to be cooked.
It is possible to buy a
thermometer and barometer combined in one
attractive, wall mounted display case. Why not
get one for your kitchen?
3 - Personal
There is no one definition
of a perfectly boiled egg because different
people have different preferences in relation to
hardness or softness.
The Special and General
Theories of Egg Boiling are designed to produce
consistency in relation to a defined preference.
They do so by use of the hardness coefficient, h.
This is a number between 0
and 1. A zero value for h would result in an
uncooked egg. A value of 1 would result in an egg
cooked to the maximum level of hardness that it
is possible for the constituents of an egg to
variables used in the Special Theory of Egg
||Time for egg to
remaing in boing water
worked example, below
||Volume of egg
coefficient of egg
squared per square centimetre
||grams per cubic
||Temperature of egg
prior to boiling
environment in which egg is kept when not
pressure at which egg is boiled
||grams per square
coefficient of egg
time equation from the Special Theory of Egg
T = h2vsc / b(20 + t + e)
Worked example using the
typical values in the above table:
T = (0.6 X 3.14 X 3.14 X 5
X 520 X 103 X 1.03) / (1033(20 + 20 +
T = 15842405.28 / 61980 =
255.61 seconds or 4 minutes and 16 seconds
The step by step
process for boiling an egg in accordance with the
Special Theory of Egg Boiling:
The above theory and the
resulting equation allow the exact boiling time
required for any egg to be calculated. The
cooking process must be standardised, however, to
eliminate random variations.
This standardised process
is as follows:
a - Have
the egg scanned with an MRI scanner, as described
above, to ascertain the values of v, s and c.
b - Write the v, s and c values
on the egg in permanent marker as soon as it is
scanned to avoid any later uncertainty as to
which egg was which!
c - Ensure that the room in
which the egg is to be cooked is maintained at a
d - Leave the egg in the room in
which it is to be cooked for at least two hours
prior to cooking in order that it attains the
same temperature as that room.
e - Just prior to cooking, note
the values of t and b.
f - Bring a pan of distilled
water to the boil.
g - Use the boiling time
equation to calculate the required egg boiling
h - Immerse the egg in the
boiling water for exactly the period, T.
i - After removal from the
boiling water, place the egg in an eggcup,
ensuring that the environmental temperature
surrounding the egg remains constant and at the
j - Monitor the temperature of
the egg with a thermometer until it reaches 45
degrees celsius and then consume at once.
The academics who have
contributed to this article hope that the above
explanations and guidance have demonstrated that
boiling an egg is a task well within the
capabilities of anyone with a basic knowledge of
We hope that it will
encourage readers to obtain the limited amount of
specialist equipment required and to try to boil
eggs of their own. After all, what tastes better
and what is healthier than a properly boiled egg?
Good luck and good dining!