(2005-08-20) Rationalized Beaufort Wind Scale
In "force n" weather, the wind speed is proportional to n3/2
The widely-used Beaufort scale was devised in 1806,
by Sir Francis Beaufort (1774-1857), rear admiral, hydrographer to the Royal Navy.
It was adopted by the British Admiralty in 1838,
and has been in international use since 1874.
Originally, the Beaufort Wind Scale did not refer to specific wind speeds,
but to the effect of the wind on a full-rigged ship, and the amount
of sail which should be carried.
Since "force 12" meant a wind that 'no canvas can withstand',
the original scale did not extend beyond that point.
Each Beaufort number still corresponds to a variety of common observations
which can be made at sea or inland.
For example, in a "force 0" condition:
'Smoke rises vertically. Sea is like a mirror.'
Since 1946, the Beaufort scale has been defined in terms of the speed of the wind,
measured by an anemometer placed 10 meters above the ground.
"Force n" means a wind speed around V.n3/2,
where V is a speed of about 1.871 mph
(we're told that the 1946 scale was officially based on a speed of 0.836 m/s, or about
1.87008 mph, which is slightly too low to be consistent with modern tables).
Any speed V, in mph, between 62Ö26/169 and
146Ö46/529 yields agreement with
the rounded "mph" scale below
(and also with the "km/h" scale, which is
somewhat less restrictive).
Most tables erroneously
give 18 mph instead of 17 mph as the
upper limit for a moderate breeze; this is inconsistent
with the rest of the table, for any value of V.
(Consistent) Beaufort Scale
Denomination of the wind
Wind speed (V nÖn)
0 to 0.6
0 to 1
0.7 to 3
2 to 5
4 to 7
6 to 11
8 to 12
12 to 19
13 to 17
20 to 28
18 to 24
29 to 38
25 to 31
39 to 49
Near gale, moderate gale
32 to 38
50 to 61
Gale, fresh gale
Coup de vent
39 to 46
62 to 74
Fort coup de vent
47 to 54
75 to 88
Storm, whole gale
55 to 63
89 to 102
64 to 72
103 to 117
To find the Beaufort number corresponding to a
given speed, one divides that speed by V, and finds the whole number closest
to the cubic root of the square of that ratio.
As a result of this modern definition,
the Beaufort scale can be extended beyond the traditional limit
of "force 12" for extremely violent winds.
We have not traced the existence of a "standard" value of V; we shall simply
note that a value V = 0.8365 m/s (or any value between 0.83626 m/s and
0.8368 m/s) will agree with the above tables in mph or km/h, but
that (inexplicably) tables published in knots imply a value of V falling
in the incompatible range of 0.8401 m/s to 0.8433 m/s (once the inconsistent value of 16
knots published for the upper limit of a moderate breeze is lowered to 15 knots).
Wheather reports for sailors commonly use the Beaufort scale or quote wind speeds
the media may prefer different units for wind speeds in different parts of the
World: m/s (Sweden, Denmark), km/h (France, Germany, Canada), mph (United States).
(2005-08-20) Saffir-Simpson Hurricane Scale (SSHS)
The customary scales for hurricanes (Beaufort force 12 and "above").
In August 1969, Hurricane "Camille" hit the Mississipi-Alabama coast
with what would be "force 23" winds in an extended Beaufort scale:
200 mph to 213 mph.
However, the Beaufort scale is rarely extended
(if ever) beyond force 12.
Instead, the strength of hurricanes is described with the following scale,
which was originally devised in 1969 by
a consulting structural engineer, and Dr.
Robert H. Simpson (b. 1912)
director of the National Hurricane Center (NHC) from 1967 to 1974.
The NHC considers anything below category 1
to be either a tropical depression (D) or a
tropical storm (S).
Categories 1 and 2 are Hurricanes (H) above the Beaufort
force 12 threshold.
Categories 3, 4 and 5 are major hurricanes (M).
There's no need for a category 6.
The above pressures
and surge heights (estimated by Bob Simpson)
were originally part of the SSHS definition.
However, in 2009, the NHC moved to base the definition of the SSHS
purely on wind speeds (expressed in knots, kt).
The new scale is unambiguously called
Saffir-Simpson Hurricane Wind Scale (SSHWS).
It became effective on 2010-05-15 and was revised on 2012-05-15.
In the Atlantic, the record-breaking hurricane season of 2005 included three
category-5 hurricanes, named Katrina, Rita and Wilma (in chronological order).
At this writing (Oct. 2005) Wilma is the most intense hurricane ever
observed in the Atlantic basin, featuring the lowest sea-level atmospheric pressure
ever recorded in the Western Hemisphere outside of
tornadoes (882 hPa).
In the Northwest Pacific Ocean, only 9 typhoons
have surpassed the intensity of Wilma.
(The terms typhoon and hurricane describe the
same phenomenon, but are used in different parts of the Globe.)
The costliest hurricane ever was hurricane Katrina
(August 23 to 31, 2005) which caused an estimated $200 billion in damages and at
least 1281 fatalities (official count at this writing).
After hitting land as a mere category-1 hurricane north of Miami on August 25,
the eye of Katrina made landfall again in Louisiana
at 6:10am (CDT) on Monday, August 29, 2005.
as a category-4 hurricane...
By 11 am, the storm surge had breached the levee
system protecting New Orleans from Lake Pontchartrain.
Most of the city was subsequently flooded.
The names of Hurricanes comes from a preapproved yearly list
of 21 names with initials A through W (skipping Q and U) which is reused
every 6 years, except that names of violent hurricanes are
The 2005 season had so many major storms that the last ones
had to be named after letters from the Greek alphabet
(Alpha, Beta, Gamma, Delta, Epsilon, Zeta).
Atlantic Hurricane Names
Hermine Ivan Jeanne
Philippe Rita Stan
Alpha Beta Gamma Delta Epsilon Zeta
Arlene Bret Cindy Don Emily Franklin Gert Harvey Irene Jose Katia Lee Maria Nate Ophelia Philippe
Rina Sean Tammy Vince Whitney
Atlantic Hurricane Names
Arlene Bret Cindy Don Emily Franklin Gert Harvey
Irma Jose Katia Lee Maria Nate Ophelia Philippe
Rina Sean Tammy Vince Whitney
The list of retired names is typically decided in March of the following year.
At this writing (2012-10-28, 11am EDT) there are great fears that Hurricane Sandy
will make the list, as it threatens New-York City and other areas to the North
of the region commonly affected by Atlantic hurricanes.
It made landfall in New-Jersey on Monday night (2012-10-29) after falling just below hurricane strength.
The following names have been retired, before the 2014 season:
Stan (2005) and
(2005-08-20) Fujita scale for tornadoes
Local twisters are primarily measured against a 6-rung scale (F0 to F5).
Within tornadoes, the wind can reach speeds
in excess of 280 mph (450 km/h).
If the Beaufort scale was applicable, this would mean force 28 or 29.
Instead, all tornadoes are ranked using the following scale, from weakest to strongest,
which was devised in 1971 by
Ted Fujita (1920-1998) at the University of Chicago.
The Original Fujita Tornado Scale (1971-2007)
Wind speed (km/h)
Twisted antennas, broken branches
60 to 110
Uprooted trees, vehicles turned over
120 to 170
Lifted roofs, small projectiles
180 to 250
Walls tipped over, large projectiles
260 to 330
Houses destroyed, some trees lifted
340 to 410
Large structures lifted, incredible damages
420 to 510
Since February 1, 2007, a revised scale has been used which is known
as the Enhanced Fujita scale (EF).
The Enhanced Fujita Tornado Scale
Minor damage. Some roof damage, shallow trees knocked over, etc.
65 to 85 mph
Moderate damage. Roofs stripped, mobile homes turned over, windows broken.
86 to 110 mph
Considerable damage. Cars lifted off the ground, roofs torn off houses, large trees uprooted.
111 to 135 mph
Reports of well-constructed houses totaled, trains and big rigs overturned, heavy cars thrown off ground.
136 to 165 mph
Houses and whole frame houses completely leveled, cars thrown and small missiles generated.
166 to 200 mph
Houses and frames swept away, steel enforced concrete structures badly damaged.
Cars thrown like toys.
(2006-12-02) Measuring in Decibels (dB)
A general-purpose logarithmic scale for physical power.
In a given medium, a signal carries a certain power
(or a power flux) proportional to the square of an associated
"amplitude" (which may be variously defined).
The "amplitude" of an oscillating linear system is preferably defined as the
of an intensive quantity
(like voltage). The
square of that amplitude divided by
the RMS of the
corresponding power is called "impedance".
If we divide by a power flux instead, what we obtain
is known as a "characteristic impedance"
(see below the example of
sound, where the amplitude is a pressure).
Conversely, since the characteristic impedance of
the vacuum is traditionally expressed in ohms
(it's 376.73...W) the "amplitude"
of the electromagnetic field
should be expressed in V/m, which identifies the electric field (E).
The relative magnitude of two signals may be expressed equivalently
as a logarithmic function of the ratios of their powers (P) or as the same logarithmic function
of the squares of their amplitudes (A).
If decibels (dB) are used, the relative
magnitude of the signal (compared to some other signal of reference)
is defined by either of the following expressions,
which involve decimallogarithms.
Relative magnitude (or level) in dB =
10 log( P/P0 ) = 20 log( A/A0 )
When the amplitude doubles,
the power becomes 4 times as high and
the level is raised by roughly 6 dB.
If the amplitude is multiplied by 10, the power is 100 times higher
and the level is raised exactly 20 dB.
From relative ratios to absolute measurements :
Decibels are most useful to express ratios of related signals (for example the
signals at the input and the output of an electronic amplifier).
However, specifying a conventional "reference" signal readily establishes
an "absolute" decibel scale.
Each choice of a particular reference establishes a different "absolute" scale.
The most popular such scale
(especially among electrical engineers) is the
for which the zero level (0 dBm)
is a signal whose total (harmonic) power is one
milliwatt (1 mW).
L = 10 log ( P / 1 mW ) dBm
Measuring Sound in Decibels (dB)
Sound Intensity Level (SIL) and
Sound Pressure Level (SPL)
As sound propagates, it carries a certain power per unit area of a small surface
perpendicular to the direction of propagation.
This physical quantity, called sound intensity,
is measured in watt per square meter
When expressed in decibels, that acoustic power
(per unit of receiving area) is called sound intensity level.
The reference level (0 dB) is, by convention,
a sound whose intensity is
The level (L)
of a sound whose intensity is
I (expressed in W/m2 )
L = [ 10 log ( I ) + 120 ] dB (SIL)
According to the general scheme outlined above,
the amplitude of a soundwave is most commonly defined as its
acoustic pressure p
(which is equal to the
the RMS of the rapid local variations in air pressure).
A sound intensity of 10-12 W/m2
corresponds to an acoustic pressure po which depends
on temperature and pressure.
The above is rigorously equivalent to:
L = [ 20 log ( p / po )
] dB (SIL)
However, in daily practice, a different sound reference is often used
which is defined by an acoustic pressure of exactly
20 mPa, regardless of ambient conditions
This gives rise to a slightly
different scale, called "sound pressure level"
and identified by the acronym SPL (which is, unfortunately, often omitted).
20 log ( p / 20 mPa )
[ 20 log ( p ) + 94 ]
The SPL approximation is commonly used
by practitioners who are satisfied with the mere measurement of acoustic pressure.
The SPL scale is usually assumed to coincide numerically
with the (correct) SIL scale
for dry air at room temperature under normal pressure...
Let's check that:
For dry air under normal pressure, this would correspond to a toasty temperature
of about 40°C. Conversely, at room temperature
(20°C) Z would be around 413.2 Pa.s/m
which yields po = 20.33 mPa.
L = [ 20 log ( p ) + 93.84 ] dB (SIL)
(air, 1 atm, 20°C)
So, the two formulas would match perfectly around 40°C
and would be less than 0.2 dB off at room temperature.
The loudest possible sound is 191 dB.
This popular piece of trivia is to be taken
with a grain
of salt, since some of the natural assumptions
normally describing sound make little or no physical sense when the
saturation limit is approached. Never mind,
here goes nothing...
If a sound is a perfect sinewave, the acoustic pressure which appears in the
SPL formula is about 70%
(i.e., 1/Ö2) of the maximum
deviation from ambient pressure.
Disallowing negative pressures, the latter quantity
cannot exceed the ambient pressure (which we assume to be the normal
atmospheric pressure of 101325 Pa).
So, the acoustic pressure (RMS)
cannot exceed 71647.6 Pa.
The saturation level for a sinewave
would thus be about 191 dB.
Formally, a square wave
could be 3 dB louder (194 dB).
However, neither answer is satisfactory, because most assumptions about sound
collapse well below such pathological levels.
In particular, large pressure disturbances are dissipative (they heat up the air
itself) and cannot be described as waves in a linear
system (power flux need not be proportional to the
square of acoustic pressure).
(2006-12-11) Apparent and absolute star magnitudes
(134 BC, 1854)
The absolute magnitude of a star is its apparent magnitude 10 pc away.
On June 22, 134 BC
(proleptic Julian calendar).
a new star (nova) appeared in Scorpius which was as bright as Venus
and could be spotted in the daytime. It remained visible to the
naked eye until July 21.
To the best of my knowledge, the
corresponding nova remnant hasn't been identified. Could it be
According to Pliny,
this rare event is what prompted
Hipparchus of Nicaea (c.190-126 BC)
to compile a new catalog of all visible stars
(you can't spot new things without an inventory of old ones).
had previously listed only 675 relatively bright stars.
The catalog that Hipparchus produced in 129 BC
listed 1080 stars that he classified into six magnitudes,
from brightest (first magnitude) to faintest (sixth magnitude).
To record the position of stars on the celestial sphere,
Hipparchus invented the system of spherical coordinates
(latitude and longitude) that would later be used
to locate points on the
surface of the Earth.
The magnitude system of Hipparchus was popularized by
Almagest and became standard.
it turns out that a star of the first magnitude in that system is about
100 times as bright as a star of the sixth magnitude.
Thus, in 1854, the British astronomer
proposed to refine the Ptolemaic rating system by turning it into a
strict logarithmic scale, where a difference of 5 magnitudes would separate
two stars whose brightnesses are in a ratio of 100 to 1.
So specified, the modern system of stellar magnitudes
extends to faint objects (beyond magnitude 6) and very bright ones
stars, the planets,
the Moon, the Sun) which are assigned a magnitude
below 1, or even a negative one...
The Sun has a magnitude of -26.7.
At a magnitude of -1.6,
Sirius is the brightest object outside the solar system.
The faintest stars detected so far by the largest telescopes have a magnitude of 23 or so...
Up until the 1950s, the magnitude system was "calibrated" on
(a-Lyrae) which was defined to be of magnitude zero
over any part of the spectrum.
With modern, more practical, standards (outlined below) Vega's
visual magnitude is now listed to be 0.03.
As brightness decreases by a factor of 100 1/5,
magnitude increases by one unit.
This factor is known as Pogson's ratio, in honor of
100 0.2 = 10 0.4 = 2.51188643150958...
This simply means that one
star magnitude is exactly equal to 4 decibels
However, star magnitudes are very rarely (if ever) expressed in decibels.
Historically, the relation is reversed: The idea for expressing
powers in decibels came from the stellar magnitude system !
There are 20 stars of the first magnitude (magnitude less than 1.5) 60 stars of the
second magnitude (magnitude between 1.5 and 2.5) about 180 stars of the third
magnitude (between 2.5 and 3.5) etc.
This tripling pattern holds for relatively bright stars but tends to be less
explosive thereafter (it looks more like a mere doubling for stars
around magnitude 20).
Most physicists would probably prefer to base star magnitudes
on their bolometric output powers
(in which all electromagnetic frequencies carry equal
weight). This is rarely done, if ever, except for the Sun itself.
Ideally, the visual magnitude of a star should be based on the
power it emits in the visible spectrum,
using the same standard photopic response of the human retina
on which the definition of the lumen
is based (although the dark-adapted scotopic response might
be more relevant to direct telescopic observations by humans).
In practice, however, various standard filters are used instead which allow an
of a star's magnitude in different portions of the electromagnetic spectrum.
In the main, the emission spectrum of a star is close to that of a
blackbody and calibrated comparisons of the different flavors
of magnitude are used to determine a star's surface temperature (T).
Regardless of what spectrum-specific "flavor" of star magnitude is used,
the absolute magnitude of a star is defined as
what its apparent magnitude would be if it was observed at a distance
of 10 pc (10 parsecs is about
To determine the absolute magnitude of a star, its distance must first be estimated
(using parallax or other methods) so that the apparent magnitude can be
adjusted, knowing that the observed power flux varies as the inverse
square of the distance.
Conversely, the absolute magnitude of some stars may be known from
other considerations (e.g., the absolute magnitude of a Cepheid
variable star is a function of the period of its oscillation in brightness).
Some distances can thus be derived from apparent magnitudes,
without the need for delicate parallax measurements
(which aren't possible for intergalactical distances).
(2015-07-18) The pH Scale (1909, 1924)
A logarithmic scale for acidity, devised by Søren
Sørensen (1868-1939) in 1909.
Before it was given a quantified meaning, the notion of acidity was recorded through
the color changes it induces in a large lineup of
indicator substances, still commonly used today
(including litmus, which dates back to 1300 or so).
The pH of a solution
(at first, Sørensen wrote p[H+] ) is the opposite of the decimal
logarithm of the activity of the hydrogen ions (H+) in it:
pH = - log10 [ H+ ]
Since 1924, in all related contexts,
a lower-case initial "p" has indicated the opposite of the
common logarithm of whatever quantity is associated with the rest of the symbol.
For example, pKA = -log KA
More precisely, we should talk about the activity of the
(H3O+) since every bare hydrogen ion in water will instantly combine with
at least one
water molecule. For non-acidic solutions or dilute acids,
this complication can be ignored, because the number of water molecules so combined is
an insignificant portion of the total number of water molecules.
Strictly speaking, the activity of a solute is a
thermodynamical quantity which need not be strictly proportional to
For dilute solution, however, this is an excellent approximation which is universally
adopted. In particular, the
constants given in all modern chemical references are for "activities"
equated to the concentrations expressed in moles per liter (mol/L).
There's only one exception to this convention, but it's an important one:
When water is used as the solvent, the concentration of undissociated water molecules
remains constant, except for extremely concentrated solutions
(for which the whole model breaks down). With ludicrous precision:
Because it's very nearly constant and largely irrelevant, that concentration
is incorporated into the well-known ionic product for water (at 24.9°C):
H2O « H + + OH -
KW = [ H+ ] [ OH - ]
= 10 -14
For pure water, electrical neutrality implies that
[ H+ ] = [ OH - ]
so that both concentrations are equal to 10 -7.
Thus, the pH of pure water is 7.
This decreases with temperature; at 50°C, the pH of pure water is only 6.6.
The pH of pure water depends on temperature.
KW / (mol/L)2
Human blood is a buffered liquid of pH 7.4. It's normally tightly regulated,
chemically and organically, to a healthy pH range between 7.35 and 7.45.
Most pH values ordinarily encountered are between pH 0
(e.g., hydrochloric acid, HCl, at a concentration of 1 mol/L)
and pH 14 (e.g., sodium hydroxide, NaOH, at 1 mol/L).
Most meters won't go beyond those limits, but there's nothing sacred about them:
Solutions twice as concentrated as the two we just quoted can still be
considered dilute, but their pH values are respectively -0.3 and 14.3.
In water, chemical reactions are often critically dependent on acidity.
For example, an acidic stop bath
is normally used when processing photographic films
to put an abrupt end to the action of the developer
(which can only operate in an alkaline solution).
That's more efficient and more precise than an amateurish plain water stop-bath which
would merely slow down the action of the developer by diluting it greatly.
In concentrated solutions, water no longer plays the rôle of an overwhelming
solvent. Even if we keep believing that activities are proportional to concentrations
(per unit of volume) we must acknowledge that there's no longer a direct
proportionality between the volume of the solution and the number of water molecules in it.
We must also get rid of the aforementioned simplified equation for the dissociation of water and
restore a proper
for it (which reduces to the previous one in the dilute case):
2 H2O «
H3O + + OH -
KU = h [ OH - ]
/ [ H2O ] 2
= 10 -17.486
Working out the pH of a complicated aqueous solution:
Computing pH = -log h from the initial concentrations of all the
reactants is a basic engineering skill that all undergraduates are expected to master.
Surprisingly enough, the tradition is to teach them a murky method which is only effective
in conjunction with simplifying assumptions made
a priori which are supposed to test the intuition of the student
(that's summarized by the infamous
The only merit of that method is to quickly give good approximative answers...
in academic tests designed for it!
It's important to realize, by contrast, that a simpler method yields directly
the algebraic equation satisfied by the concentration h of hydrogen ions
(whose logarithm is the opposite of the pH).
Here's that two-step method:
The lack of a net electric charge then yields the equation satisfied by h.
Note that only the concentrations of charged ions are needed to carry out
the second step. So, we may as well think of the first step as the algebraic
elimination of the concentrations of neutral species.
Let's apply this to the example of a weak monoacid with a dissociation constant
KA = 10 -4.76
(this value is for acetic acid)
at concentration c:
AH « H + + A-
h [ A- ] / [ AH ]
[ A- ] + [ AH ]
By eliminating [ AH ] we obtain [ A- ] = c / (1+h/KA ).
Likewise, for the dissociation of water itself, we have:
H2O « H + + OH -
KW = h [ OH - ] = 10 -14
Let's plug the ensuing value [ OH- ] = KW / h into the neutrality equation:
[ OH- ] + [ A- ] = [ H + ]
KW / h + c / (1+h/KA ) = h
This is a cubic equation in h which would turn into
a quadratic one if we knew a priori that
KW / h is negligible
(which is the normal assumption presented with the RICE recipe for acidic solutions).
This would entail:
c = h (1 + h/KA )
h2 + KA h - KA c = 0
As usual, for the sake of numerical robustness,
I recommend shunning the traditional quadratic formula when solving any quadratic equation
which may have small solutions (in this day and age when direct and inverse
trigonometric or hyperbolic functions are as readily available as the lowly square-root function).
Instead, let's consider the quadratic equation in h
whose roots are x exp(-y) and -x exp(y):
(x exp(-y) - x exp(y)) h
- x 2 = 0
pH of acetic acid (CH3COOH) at various molar concentrations.
For historical reasons, vinegar and acetic acid are often
rated by volume,
in a way similar to alcoholic spirits.
A molar solution (60.052 g/L) is 5.6881% by volume,
or "56.881 grains" (same thing, by definition).
Citric Acid :
(CH2 COOH)2 COH COOH
The above can be readily generalized to more complicated cases,
without the need for a priori simplifications.
Let's illustrate this with
citric acic, second only to acetic acid in the heart
of old-school photographers,
who routinely measure its molar concentration (c) by
weighing its monohydrate
(C6H8O7 , H2O)
at 210.14 g/mol.
Here, H3A will stand for the undissociated molecule
of citric acid and the citrate anions,
partially hydrogenated or not, are:
Their respective concentrations verify the following equations:
h [H2A- ]
= K1 = 10 -3.13
h [HA2- ]
/ [H2A- ]
= K2 = 10 -4.76
h [A3- ]
/ [HA2- ]
= K3 = 10 -6.39
= [H3A] K1 / h
= [H3A] K1K2 / h2
= [H3A] K1K2K3 / h3
c = [H3A] ( 1
+ K1 / h
+ K1K2 / h2
+ K1K2K3 / h3 )
which gives [H3A] and, thus, the concentrations of
all citric species.
Electrical neutrality then provides the desired relation between h and c :
That function gives directly the concentration of a solution of
Conversely, an algebraic equation must be solved to predict the pH
obtained from a given concentration, as in the following table:
pH of citric acid
(CH2 COOH)2 COH COOH
at various molar concentrations.
In the above discussion of citric acid,
the emerging expressions suggest introducing a cubic polynomial
and using its derivative as follows:
(2015-09-15, drafted in 2001) Scoville Scale for Pungency / Piquancy
Hotness of peppers (French: poivrons).
Burning sensation in the mouth.
the language of the Aztecs, 6 adjectives describe the hotness
of chili peppers in order of increasing pungency:
cocopetzpatic, cocopetztic, copetzquauitl, and cocopalatic.
sailed West in search for a more direct route to Asian spices, what he
found instead were the spices of the New World, the pungent capiscums, or
chili peppers, whose piquancy was so important to the Aztecs.
Pungency (also called piquancy, spicyness, burn, hotness, heat,
warmth, bite, sting or kick)
is a component of food flavor which happens to be technically
different from taste and smell, as it relies on chemoreception by the free
(undifferentiated) nerve endings of the
mostly in the tongue but also in the rest of the mouth, in the nose and in the eyes.
That makes very pungent compounds effective in self-defense
pepper sprays which can incapacitate an aggressor.
The pungency of chili peppers is primarily due to a potent alkaloid called
[ trans-8-methyl-N-vanillyl-6-nonenamide ] identified in 1816 by
Bucholz (1770-1818). More than a dozen related
capsaicinoids have been found in nature:
The three major capsaicinoids :
Dihydrocapsaicin may occur in
concentrations similar to those of capsaicin itself.
Both have about the same pungency
(if the potency per mole was the same, dihydrocapsaicin's slightly higher
molar mass would make it only 0.66% less pungent). In most cases, 90% of
the pungency of chili peppers is attributable to these two alkaloids.
When the third major capsaicinoid
is included as well, about 98% of the pungency is usually accounted for.
Minor capsaicinoids :
All the other capsaicinoids are considered minor.
About half-a-dozen minor capsaicinoids occur in chile peppers.
The most important are homodihydrocapsaicin and homocapsaicin.
Others (including norcapsaicin and nornorcapsaicin)
do not occur naturally in significant concentrations.
At high concentrations, capsaicinoids are extremely painful and may be harmful.
In the tongue, cells with vanilloid receptors may be damaged or destroyed by
high levels of capsaicin. Contrary to popular belief, however, capsaicin
does not cause ulcers or any other direct damage to the stomach
lining or to the rest of the digestive tract.
The Scoville Pungency Scale :
The original quantitative pungency scale was devised in 1912 and is
named after its inventor, the American pharmacologist
Wilbur L. Scoville
(1865-1942) who was then employed by the Parke Davis Pharmaceutical Company.
Dr. Wilbur Scoville was born the year Abraham Lincoln was assassinated
(his middle name was "Lincoln") and had already achieved some notoriety in
1897 with the publication of a pharmacy textbook entitled "The art of
compounding: A text book for students and a reference book for pharmacists
at the prescription counter"
(P. Blakiston, Son & Co., Philadelphia). In an
expanded version by Glenn L. Jenkins (1898-) and others, that text was
re-edited 60 years later, under the title "Scoville's The art of compounding".
Scoville had found that the chemical methods avaible at the time were
unable to detect the presence of capsaicin at the very low concentrations
which made the human tongue react: Even minute amounts of capsaicin will
trigger the tongue's pain receptors (free trigeminal nerve endings).
Ignoring the mockery of some of his colleagues, Scoville thus decided
that the needs of the spice trade would be best served by a physiological pungency
scale directly based on human sensory perception (a so-called
organoleptic scale) which he described in 1912:
Organoleptic Test is carried out from
one grain (64.79891 mg) of
pepper macerated overnight in 100 mL of ethanol
(the solubility of capsaicin in water would be too low for this extraction step).
Once filtered, that solution is rated by a panel of trained testers/tasters.
A rating of N Scoville heat units (SHU)
means that most panel members feel the solution to be somewhat
pungent when one volume is diluted in N volumes of sweetened water
(the substance will typically still be
detectable at a dilution about twice as high).
Scoville ratings apply to other pungent chemicals besides capsaicinoids.
For example, zingerone
(the pungent ingredient of cooked ginger) is 1000 times less pungent than capsaicin.
There are no capsaicinoids in ordinary black pepper,
which derives most of its pungency from
piperine (and its more pungent
Piperine was first isolated in 1819 by
Hans Christian Ørsted and
has been found to be 70 to 80 times less pungent
than capsaicin. Common black, white and green peppers are all obtained from
the various stages of maturity of the
(unrelated to the fleshy "chili
peppers") which is the fruit of an evergreen vine called the Peppercorn Vine
(Piper Nigrum), native to the Malabar Coast of southwestern India, and to
the island of Sri Lanka.
In ground pepper, chavicine turns into piperine, which explains
a decrease in pungency.
Alkaloids: Piperitine, Piperoleine A & B, Piperanine, Piperine,
Pungency may be either measured directly by such organoleptic tests, or
it may be deduced from the known concentrations of all pungent ingedients
and their previously established respective pungencies (using a table like
the one provided below). A common approximation, which is roughly valid for
the relative concentrations of capsaicinoids observed in typical chili
peppers, is to obtain the number of Scoville Heat Units (SHU) by multiplying
by 15 the total concentration of capsaicinoids expressed in ppm. For
example, habaneros (rated at 300000 SHU)
contain 20000 ppm (or 2%) of capsaicinoids.
This rule of thumb begat a new unit endorsed by the
American Spice Trade Association
An ASTA unit is essentially defined to be 15 SHU, so
that you obtain the approximate pungency of any compound by forgoing the
multiplication by 15 in the above rule. Also, ASTA rating procedures
achieve better consistency in organoleptic tests by comparing different
compounds over a whole range of perceptions, not just at the threshold of
detection, as with the original Scoville test: Chemicals are given ratings
in an A:B ratio if they are judged to give equally pungent solutions at
respective dilutions that are in a B:A ratio.
To obtain more consistent pungency measurements,
Paul W. Bosland (professor of horticulture at
State University and co-founder of the
Institute) has pioneered the use of
high-performance liquid chromatography (HPLC) to
obtain the concentrations of the main capsaicinoids (and/or other pungent
By definition, the pungency of a given mixture is obtained by adding the
known pungencies of all its chemical components
weighed by their respective concentrations (by weight).
That method has been endorsed by
the American Spice Trade Association for the "ASTA units"
described above, but the Scoville scale remains much more popular for publication
(the ASTA unit is thus now considered to be equal to 15 SHU, de jure).
The pungency of hundreds of varieties of chile pepper has been rated this way.
Ratings do depend on different crops of the same variety and may even vary from pod to pod.
According to the "Guiness Book of World Records",
the record in 2001 (first draft of this article)
was a 1994 measurement of 577000 SHU for a "Red Savina" habanero pod.
This variety is a natural mutant strain discovered in 1989 by Frank Garcia (GNS
Spices Inc., of Walnut, CA) who spotted a single red pod in the
middle of his field of orange habaneros.
Since then, the record for chili peppers has been broken several times:
Now, could anyone
tell me what SHU ratings are described as
coco, cocopatic, cocopetzpatic, cocopetztic, copetzquauitl, or cocopalatic?
Some dangerous neurotoxins have been found to be
many times more pungent than capsaicin itself. They can inflict
and chemical burns.
They could even kill a human being, in gram quantities:
is about 1000 more pungent than pure capsaicin (16 000 000 000 SHU).
has been rated around 5 300 000 000 SHU.
Other Types of Pungency :
Some spicy foods are normally not assigned any Scoville rating at all...
(2005-11-26) The Richter Scale of Earthquake Magnitudes (1935)
The seismic energy radiated is the basis of a rationalized Richter scale.
The original Richter Scale was devised in 1935 at the California Institute of Technology
by Beno Gutenberg and Dr. Charles F. Richter. More modern versions of that scale have been
devised which are adequate to measure the largest earthquakes while being roughly compatible
with the traditional 1935 definition for small earthquakes.
The 1935 Richter Scale of Richter and Gutenberg
(now called local magnitude) was defined as
a logarithmic scale;
strictly based on readings from a particular type of instrument then used at CalTech
Magnitude 0 was arbitrarily assigned to an earthquake that would cause a
maximum combined horizontal displacement of 1 micron (1 micrometer)
on such an instrument at 100 km from the epicenter.
(This reference level is so low that negative magnitudes are very rarely quoted.)
If that amplitude increases by a factor of 10, the
local magnitude increases by one unit.
The problem with this viewpoint is that the amplitude originally considered by Richter
is not a simple function of the energy released, except for the smallest earthquakes.
There are nonlinearities and the duration of the earthquake is also an important factor,
especially for very large quakes which may last several minutes...
Mercalli Intensity Scale: The effects measured at a particular location.
Wood-Anderson seismographs at Caltech.
Charles F. Richter & Beno Gutenberg: log E = 11.8 + 1.5 R
Seismic Moment, Hiro Kanamori: M is about 20000 E.