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Fireworks makers fill
the night sky with
myriad effects in
displays that are
popular all over the
world. Although the art
dates back to ancient
China, most of the
effects you'll see in a
typical display are
inventions of this
century. A typical
example is the
development of colored
flames. Before the 19th
century, only various
yellows and oranges
could be produced with
steel and charcoal.
Chlorates, an invention
of the late 18th century
and an industrial
product of the 19th
century, added basic
reds and greens to the
pyrotechnics'
repertoire. Good blues
and purples were not
developed until this
century, although it is
not unusual to find
unsafe display formulas
for blue stars in
earlier literature.
Most people
don't realize the
vast world of
physics that takes
place during every
fireworks show. The
science of
pyrotechnics
involves many
physics applications
that must be
considered to
produce entertaining
displays.
Pyrotechnicians must
take into account
the relationships
between vectors,
velocities,
projectiles and
their trajectories,
the explosion forces
behind burst
patterns, etc. These
are the topics
covered by this
page.
Basic principles of
pyrotechnic light
production
The
light emitters can be
grouped into two main
categories: solid state
emitters (black body
radiation) and gas phase
emitters (molecules and
atoms).
Black body radiation and
the grey body concept
A
black body is an ideal
emitter which is capable
of absorbing and
emitting all frequencies
of radiation uniformly.
The excitance (M)
of the black body, the
power emitted per unit
area, is defined as
where
s is the
Stefan-Boltzmann
constant and T is
the temperature. Thus,
we could obtain a
twofold increase in
radiation by merely
increasing the flame
temperature from, say
2000 K to 2400 K.
Furthermore, the
radiation also shifts
from infrared to visible
light as the temperature
increases. The
calculated emission
spectrum (the energy per
unit volume per unit
wavelength range) has
the following shape:
Fig. 1. Black-body
radiation.
In
the real world,
simplified models are
not of much help. Many
solids do emit light in
the same relative
proportions as a black
body, but not in the
same amounts. The
emissivity of a
solid substance is the
factor relating observed
and theoretical radiant
energy. The emissivities
of many refractory
metals and metal oxides
are higher in the short
wavelength end of the
visible spectrum - that
is, they look bluer than
expected when heated.
T, K OC Subjective color
750 480 faint red glow
850 580 dark red
1000 730 bright red, slightly orange
1200 930 bright orange
1400 1100 pale yellowish orange
1600 1300 yellowish white
> 1700 > 1400 white (yellowish if seen from a distance)
The atomic and molecular
emitters
As
you can easily see from
Table 1 (and very
probably know from
experience), it is not
possible to produce
anything but shades of
orange and yellow with
grey-body emitters. (In
principle, we could
generate blue light with
a hypothetical black or
grey body at 9000 K and
up, which is the
temperature of blue
stars, but such
temperatures are
unattainable for
pyrotechnicians.) For
other color, we need
specific emitters of
colored light.
Surprisingly few
emitters are used in
pyrotechnics, given the
vast range of atomic and
especially molecular
spectra available. In
fact, the production of
some color is still a
problem - next time you
see a fireworks display,
count all turquoises and
ocean greens you saw.
There are not many,
because there are no
commercially useful
emitters available in
the 490-520 nm region
(blue-green to emerald
green).
Color Emitters used Wavelength range
Yellow Sodium D-line atomic emission 589 nm
Orange CaCl, molecular bands several bands, 591-
599 nm, 603-608 nm
being the most intense
Red SrCl, molecular bands a: 617-623 nm
b: 627-635 nm
c: 640-646 nm
Red SrOH(?), molecular bands 600-613 nm
Green BaCl, molecular bands a: 511-515 nm
b: 524-528 nm
d: 530-533 nm
Blue CuCl, molecular bands 403-456 nm,
several intense
bands, less intense
bands between 460 nm
and 530 nm
The chromaticity diagram
and color perception
The human eye may not be
the best spectroscope
invented, but it is the
best instrument for
designing colored
fireworks. Although a
spectroscope can show
the presence or absence
of certain lines or
bands in the flame
spectrum, it cannot
decide whether the color
obtained looks pleasing
to the human observer.
Pure, monochromatic
color a'la lasers are
only a dream for
pyrotechnicians, but
well-designed impure
color do not lag much
behind.
The chromaticity diagram
shown below has been
designed with human
color vision system
(three base color) in
mind. It is not
necessary to specify the
intensities of all three
base color, because the
hue is not affected by
the brightness of the
light (the sum of all
intensities). We can
conveniently use the
fractional intensities
of two primary color,
and this gives us a
chart in two dimensions.
The sum of all three
intensities must equal
one, so the third
fraction can be easily
calculated.
In
order to avoid negative
primary color fractions,
the International
Commission on
Illumination published a
standard chromaticity
diagram in 1931 with
three unreal primary
color. The above diagram
and the color are based
on the commission's
recommendations.
The pure spectral color
can be found on the
curved line surrounding
the tongue-shaped region
of composite color. The
numbers along the curve
represent corresponding
wavelengths (in
nanometers).
Figure 2 shows the
chromaticity diagram
with a few emission
lines and bands of Table
2 drawn on the curve of
spectral color. The
color of the diagram are
only approximate.
Figure 2. Chromaticity
diagram with some
emission bands. Click on
the picture to see the
true-color version (44K
jpg).
All would be well if we
could just pick up the
light from the above
emitters. However, the
emitting molecules,
especially SrCl and
BaCl, are so reactive
that they cannot be
packed directly into a
firework. To generate
them, we need
pyrotechnic compositions
designed to generate the
above molecules, to
evaporate them into the
flame and to keep them
at as high temperature
as possible to achieve
maximum light output. To
get good color, there
must be substantial
amounts of emitters
present in the flame.
The emitters are not
alone: in order to
achieve the high
temperature, a fuel -
oxidizer system is also
needed, as well as some
additional ingredients.
The color of aerial
fireworks come
invariably from stars,
small pellets of
firework composition
which contain all the
necessary ingredients
for generating colored
light or other special
effects. They may be as
tiny as peas or as large
as strawberries. A
typical red star might
contain
Potassium perchlorate, 67% by weight
Strontium carbonate 13.5%
Pine root pitch (fuel) 13.5%
Rice starch (binder) 6%
Care must be exercised
in selecting the
ingredients. The
composition must be safe
and stable in storage.
In addition, it must
work as expected and
burn with a red color
once lit. For a deep red
we need only SrCl and
SrOH emission - and
nothing else. To
generate the emitting
molecules at a
sufficiently high
temperature, a
fuel-oxidizer system
(pine root pitch -
potassium perchlorate)
is used. Strontium
carbonate is used as the
Sr source, and chlorine
comes from potassium
perchlorate (KClO4
--> K+ +Cl- + 2
O2). An excess of fuel
is used to prevent the
formation of SrO, which
would solidify in the
flame and emit grey body
radiation. This will
result in a "washed-out"
color. Too much fuel
would be a disadvantage,
too, because the glowing
carbon particles quickly
overwhelm the red color.
Pure color also require
pure ingredients. Sodium
D-line atomic emission
is so strong and so
easily excited that even
minute amounts of sodium
impurities will quickly
ruin the color.
Potassium, with its weak
atomic lines, does not
interfere with most
color, and potassium
salts can usually be
used.
Organic fuels, such as
pine root pitch, various
gums and rosins and
synthetic resins, cannot
generate as high
temperatures as metallic
fuels. The
Pyro-technician is
tempted to use powdered
magnesium and aluminum
for his/her brilliant
stars, because they
provide an easy method
of raising the flame
temperature and
increasing the
brightness.
Unfortunately, the
molecular emitters are
quickly destroyed if the
flame is too hot. CuCl
is probably the most
fragile color emitter.
It can be used with
metallic fuels only with
difficulty.
Consequently, blue stars
are never very bright.
Another problem with
metals are their
oxidation products,
metal oxides, which are
powerful grey body
radiators due to their
refractory nature. Their
incandescent glow can
easily wash out all
color.
Over the years,
chemists, amateur pyro-technician
and professional fire
workers have solved most
of the problems of
colored flame
production. Excellent
formulations exist for
yellow, orange, red,
blue and green stars.
The problem I've been
working on is the
production of deep
forest green or ocean
green. As you can see in
Figure 3., there are no
bands in that region
(490 nm - 500 nm). A
composite color made of
BaCl and CuCl emissions
is an obvious choice,
but unfortunately BaCl
emission is seldom - if
ever - free from
interfering BaOH and BaO
emissions, which fall in
the yellow and
yellowish-green region
of the visible spectrum.
It seems that it is
easier to generate
greenish blue and
turquoise than the long
sought after bluish
green and forest green.
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The first two formulas you see are
primarily used to chart trajectories
like in the graph on the left that
shows the flight paths of 2" through
12" shells fired at 75 degrees.
These graphs are very useful tools
that allow pyrotechnicians to
visualize how high and how far their
shells will travel during a show.
This information can be used to aid
the process of choreographing the
show to music, and determining if
some shells will exceed the safe
zone for that particular site. The
Pythagorean Theorem is used to find
a certain initial velocity value if
the other two are known. This is
helpful in determining information
needed for the other formulas. The
Trigonometric Functions are also
used to find initial velocity
values, but are used to find
vertical heights, horizontal
distances, and firing angles as
well. Pyrotechnicians use these
mathematical methods along with
charts, graphs, and computer
programs derived from them to plan
their impressive displays.
