136

Chihiro Inoue et al.

Research
paper

Heat balance of senko-hanabi and iron sparks
Chihiro Inoue＊†,Taiki Watanabe＊, and Yuzo Inokuchi＊＊

Kyushu University, 744 Motooka, Nishi­ku, Fukuoka­shi, Fukuoka, 819­0395 JAPAN
Phone: +81­92­802­3018†
Corresponding author: inoue.chihiro@aero.kyushu-u.ac.jp
Received: March 15, 2019 Accepted: June 24, 2019

Abstract
Sparks emitted from the sparklers or the ground iron rods are luminous owing to the phenomenon of heat radiation.
Hence, the colors of these sparks change depending on the temperature according to Planckʼs law. However, themechanism of determining the temperature has not been clearly explained in a quantitative sense. Therefore, in thepresent study, we investigate two types of sparks, senko-hanabi, a traditionally popular Japanese sparkler, and groundiron spark, a well-known metal spark, using the two-color temperature radiometry technique and a theoretical analysis onheat balance. The temperature measurement clarifies that the temperature of sparks in a senko-hanabi is lower than thatin the ground iron. The reason is revealed by the theoretical analysis that the heat production on a single spark of senkohanabi is 40 mW, which is lower than that of iron spark as 50 mW, and the fusion of potassium sulfate consumes 40% of
the heat produced on the sparks. We conclude that the fragile beauty of the senko-hanabi, attributed to the relatively low
temperature, is realized by two factors, less heat production and the fusion of potassium sulfate.

Keywords: firework, spark, senko-hanabi, iron, temperature measurement, heat balance
1. Introduction
There are several types of sparklers enjoyed all overthe world. Senko-hanabi (Figure 1) is one of the mostpopular sparklers in Japan since the Edo period (1603―1868). A senko-hanabi sparkler contains a “black powder”,
which is a mixture of charcoal, sulfur, and potassium
nitrate in relative weight proportions of 15%, 25%, and60%, respectively and does not comprise any metalpowers１）. This black powder is simply wrapped at one endof a twisted paper, being a 15 cm long thin paper string.
One holds the top end of the paper string and ignites thelower end, upon which a red-hot globule appears, andsparks are emitted. The sparks travel downstream andeventually burst and ramify to show the pine needle-likeshapes of fireworks.
In the past, Hoffmann３） and Denisse４） in Europe, andTerada５）in Japan were intensely interested in the physicaland chemical phenomena occurring in the senko-hanabi.
Nakaya and Sekiguchi６） initially identified that thesparkler retains the burning reaction using the ambientoxygen. Shimizu１），７） reported that potassium sulfide is an
important reactive product in the sparks. Maeda and hishigh school students８） conducted the chemical analyses
and discovered several potassium compounds in theFigure１ Senko-hanabi２）
The diameter of the twisted paper string is 2 mm. A globule
forms at the bottom of the paper string. Sparks are emitted
from this globule and reach up to several centimeters.

globule without potassium nitrate. This was because,potassium nitrate might quickly convert to othercompounds soon after the ignition, which is consistent
with Nakayaʼs findings６）. Ito９） estimated the crystal
structure of the globule. Itoh et al.10） conducted aspectroscopic study and confirmed the existence ofSci. Tech. Energetic Materials, Vol．
８０, No．
４,２０１９137(a) Senko-hanabi
The black powder is wrapped at the right side of the paper
string.

Figure２ Ground iron sparks
The grinder on the left side rotates clockwise at a
circumferential velocity of 30 m s­１. By pressing the metal rod
on the grinder, iron particles are ground, and sparks areemitted.

potassium ions inside the globule and the sparks. Recently,
we have succeeded in capturing the resolved images,
clearly identified that the sparkler undergoes a ratecontrolled process owing to thermal diffusion, andeventually formulated the ramification cascade of thesparks２），11）,12）.
Several other sparklers usually contain metal powders,such as aluminum and magnesium. The senko-hanabi andthe other sparklers, such as the ground iron sparks13）,14）,
shown in Figure 2, are luminous owing to the heatradiated from the spreading tiny particles. However, werecognize that the sparks in the senko-hanabi exhibit atypical fragile beauty, which is not observed in the othertypes of sparklers. This fact indicates that thetemperature and the heat balance characteristics might bedifferent for various types of sparks. In this study, wedemonstrate the findings with respect to the temperature
measurements to reveal the coloration mechanism anddiscuss the heat balance characteristics of two different
types of sparks in a quantitative sense.

2. Methods
We conduct the temperature measurements andtheoretical analysis of two types of sparks, the senkohanabi and ground iron-sparks. There is no oxidant
contained inside the particles of the sparks. The senkohanabi used in this study were produced by the TsutsuiTokimasa toy fireworks factory15） (Figure 3 (a)). In
addition, a pure iron rod and a carbon steel rod with thecarbon concentration of 1 wt.% (Figure 3 (b)) were groundto observe the iron sparks.

2.1 Temperature measurements
The color of the sparks emitted from both the senkohanabi and the ground irons is the result of heat radiationaccording to Planckʼs law. The two-color temperatureradiometry, an emissivity free measurement technique,
was employed for measuring the temperatures. The
instantaneous luminance ratio of red to green in everyimage pixel of the camera was converted to the respective

４２８(b) Iron rods
Top: SUY is pure iron. Bottom: SK105 is carbon steel with 1wt.% of carbon.
Figure３ Materials used to produce sparks.

temperature values using a previously calibrated equation.
As the lengths of the sparks in the senko-hanabi are in therange of l ~ 10­２ m, a high-speed video camera, Photron
SA-Z, was employed to perform the unsteady temperature
measurements. However, the lengths of the iron sparks
were much longer (l ~ 10­１ m), we used SONY α 7sII, ahigh spatial resolution camera to measure the spark
temperatures along the trajectory of the spark at every
unit pixel.

2.2 Physical properties
It is important to consider some of the physicalproperties of the sparks while performing a quantitative
calculation of their heat balance characteristics. A
chemical reaction of the black powder produces a globulein the senko-hanabi16）.
4 KNO３ + 7 C + S → 3 CO２ + 3 CO + 2 N２ + K２CO３ +K２S (1)The chemical reactions occurring inside the globule
produce gas and other compounds１），９）.
2 K２CO３ + (2x+1) S → 2 K２Sx + SO２ + 2 CO２
8 K２CO３ + (3x+1) S２ → 6 K２Sx + 2 K２SO４ + 8 CO２
4 K２SO４ + 7 C → 2 K２CO３ + 2 K２S２ + 5 CO２

(2)
(3)
(4)

Initially contained 0.1 g (100 mg) of the black powder
generates a lighter globule that weighs 30 mg by releasing
the massive gases. The globule consists of K２Sx, K２CO３,
K２SO４, and C, as measured by Maeda８）, in which thepotassium compounds are in the states of molten salts orsolid particles. Table 1 lists the main components of theglobule. An exothermic reaction of the sparks on thesurface of the globule continuously produces heat leading
to a higher temperature of over 1000 K.

138

Chihiro Inoue et al.

Table１ Main components of the senko-hanabi globule17)
Material
potassium sulfide
potassium carbonate
potassium sulfatecarbonMelting point[K]

Density[kg m−３]

Enthalpy of Fusion[kJ mol−１]

1113
1164
1342
3915*

1740
2428
2660
­

16.2
27.6
36.4
­

K２S
K２CO３
K２SO４
C

*decomposition (graphite as a reference)∆H = ­393 [kJ mol­１]

C + O２ = CO２(5)

As the sparks observed in the senko-hanabi are ejected
through a specific portion of the globule, we use the values
listed in Table 1 to analyze the heat balance.
The iron particles are not covered with the oxide film
immediately after they are ground. The oxidization
reactions are exothermic and occur on the surface, given
as follows:
Fe + 1/2 O２ = FeO
2Fe + 3/2 O２ = Fe２O３∆H = ­267 [kJ mol­１]∆H = ­822 [kJ mol­１]

(6)
(7)

Figure４ Visualized result (left) and temperature distribution(right).

The heat production of q ~ 500 kJ O２-mol­１ is ratecontrolled by the molecular diffusion of oxygen in theboundary layer surrounding the particle. The melting
point of pure iron is 1808 K, and that of carbon steel
containing 1 wt.% of carbon is 1623 K17）.

3. Results and discussions
3.1 Spark temperature
Figure 4 shows the visualization results of the senkohanabi and the corresponding instantaneous temperature
distribution with a space resolution of 20 µm pixel­１ The
temperature of the globule is determined according to themelting points of K２S and K２CO３ by the heat source ofcarbon oxidization２）. The results of the temperature
measurements of the sparks observed as light streaks orlight spots in Figure 4 are demonstrated.
Figure 5 presents the time-variant temperature valuesof the senko-hanabi sparks, in which each solid line
indicates the result of one specific particle. The lifetime ofthe spark τlife is defined as the time spent from its ejection
out of the globule until the burst, determined by thethermal diffusion time scale２）as follows:2τlife = (d /2)α(8)where the particle diameter of the spark is d ~ 10­４ m, andthe thermal diffusivity is α ~ 10­６ m２ s­１. The time t isnormalized by τlife as follows:t* = tτlife(9)Therefore, t* = 0 and t* = 1 indicate the moments of thespark spreading from the globule and bursting,respectively. The temperature of the sparks increases
continuously leading to a burst eventually at 1270 K―1330
K. The maximum temperature becomes close to theFigure５ Temperature profile of senko-hanabi sparks fromejection to burst. (40 droplets were measured,
reproduced from Ref. 2.)

melting point of K２SO４, indicating that the color of thesparks is strongly affected by the fusion of K２SO４. The
flying velocity of the sparks is measured as u ~ 100 m s­１ ２）.
Therefore, the distance from the globule to the bursting
point is approximately l ~ u· τlife ~ 10­２ m.
The flying spark temperature of the ground carbon
steel is shown in Figure 6. As the temperature close to thegrinder was sufficiently low and the brightness was too
weak to measure, the measurement position wasapproximately 100 mm downstream from the grinder. Inthe case of the pure iron spark, the temperature gradually
increases passing the melting point of pure iron, as shownin Figure 6 (a). This implies that the spark is in the solid
phase initially and turns into a liquid later owing to theheat from the oxidization reaction represented byEquations (6) and (7). The temperature declines after
reaching the maximum because of the heat dissipation

Sci. Tech. Energetic Materials, Vol．
８０, No．
４,２０１９139(a) Pure iron

４２８wt.％ of C M.P.

Figure７ Calculated temperature of the sparks with variant dvalues.

%/!%&*.
," ! -#%/#"#$'"" ,(+0 #$'"$!#"&$ '""+*)((b) Carbon steel containing 1 wt.% of CFigure６ Temperature of the iron sparks.
Top image shows a trajectory of the measured spark,
spreading from left to right.

that occurred, as the oxidization heat is no longer
produced after the particle surface is covered by ironoxide. In the case of carbon steel, the temperature
gradually increases and the spark melts to a liquid, as
shown in Figure 6 (b). When the spark “puffs” observed as
its expansion indicated by the arrows, the temperaturesynchronously increases. Since the puffing is caused by
the existence of carbon17）, the temperature profile isdifferent from that of the pure iron spark. However, thecoincidence between the maximum temperatures of thepure iron and carbon steel sparks as Ts ~ 2000 K indicatesthat the oxidizations of iron are the most dominant heatsource.

3.2 Heat balance
We calculate the heat balance of the sparks byconsidering the spark as a spherical particle with a typical
diameter of d = 10­１ mm. As the Nusselt number of thesmall particle is equal to 2, the boundary layer
surrounding the particle is defined as δ ~ d /2. For
ambient air, the thermal conductivity is defined as λ = 26mW m­１ K, molecular diffusion coefficient is D = 1.8 10­５m２ s­１, oxygen concentration is C = 8.9 mol m­３, and thetemperature is Tair = 288 K. The enthalpy of fusion ofK２SO４ is L = 36.4 kJ mol­１. The overall heat balance under
the steady state in unit time is formulated considering theterm of heat production on the left-hand side and therespective terms of heat dissipation in the ambient air byheat transfer, radiation, and fusion on the right-hand side.

(10)

where σ is the Stephan-Boltzmann constant, defined as σ =5.7 10­８ W m­２ K４, the emissivity is assumed to be unity,
mmelt is the mass of the melting material, and M is themolar mass. For senko-hanabi sparks, approximately 20wt.% of the particle (ρ ~ 2000 kg m­３, refer to Table 1)
comprises K２SO48）, all of which are assumed to melt during
τlife. The heat balance of the senko-hanabi sparks is
deduced as follows:""%/!%&*.&'"%/#" $ '%!# (11)$'"!-$"$'#%"$&!
$$For ground iron sparks, the fusion term can be neglected
at the steady state (around the maximum temperature),
because the fusion is complete. The energy balance is thenprovided as follows:"'"%/#%/!%&*.&$'"!-$"$'#%"$&(12)

We solve Equations (11) and (12) to obtain thetemperature Ts at a specified d . The calculated results areshown in Figure 7. We find that the temperature of theiron spark is higher than that of the senko-hanabi spark,
and the temperature of the smaller particles tends to behigh. It is observed that at d = 10­１ mm, Ts = 2100 K in theiron spark, and Ts = 1390 K in the senko-hanabi, which areconsistent with the respective measurement values shownin Figure 5 and Figure 6. This confirms the validity of theheat balance analysis conducted. The agreement between
the experimental and the analytical results also indicatesthat the frictional heat produced by the grinder
demonstrates minimal effect on the iron sparktemperature.
Figure 8 shows the absolute amount of heat at eachterm of Equation (10). As d increases, the sparks increasein size, resulting in larger surface area and volume, andChihiro Inoue et al.

H140

Figure９ Ratio of heat consumption at d = 10­１ mm.
Total amount of heat consumption is equivalent to that of heatproduction, 40 mW in the senko-hanabi spark, and 50 mW in theiron spark, respectively.
(a) Senko-hanabi

respect to the iron sparks, the heat transfer attributes to60% and the radiation consumes 40% of the total heatamount because of the higher temperatures (Ts = 2100 K).
We conclude that the fragile beauty of the senko-hanabi,attributed to the relatively low temperature, is realized by
two factors, less heat production and the fusion of K２SO４.

H

4. Conclusions(b) Iron spark
Figure８ Heat balance characteristics of the sparks.

therefore, the amount of heat tends to increase, as well.
We observe the following difference between the twotypes of sparks: the fusion of K２SO４ is significant only inthe senko-hanabi sparks, and the radiation is more
dominant in the iron sparks. The amount of heatproduction is lower in the senko-hanabi sparks than in theiron sparks, because the heat production rate owing to theoxidization reactions defined in Equations (5) ― (7) arelower in the senko-hanabi. The heat consumption ratio at d=10­１ mm is shown in Figure 9. The heat production of thesenko-hanabi is 40 mW and that of the iron spark is 50 mW.
The heat transfer to the ambient air and the fusion ofK２SO４ are the most dominant factors, accounting for over
40% of the total heat consumption in the senko-hanabi,
whereas the radiation only accounts for 10% of the heatconsumption due to the relatively low temperature. With

We measured the temperature of the sparks in thesenko-hanabi and the ground iron using the two-color
radiometry technique to reveal the heat balance in aquantitative sense. By comparing the experimental andtheoretical results of these two types of sparks, wesucceeded in identifying the differences in theirtemperature and the heat balance characteristics, whichwere the essence of the coloration mechanism. The
temperature of the senko-hanabi sparks was observed to
be lower than that of the iron sparks, because the heatproduction by carbon oxidization was lower than that due
to the iron oxidization reactions, and the fusion ofpotassium sulfate in the senko-hanabi consumed 40% of
the produced heat. These two factors contributed to thefragile beauty of the senko-hanabi sparklers observed
since the Edo-period.
In this study, we investigated the well-known groundiron sparks to discuss the effect of the isolated metal
powders. However, further analysis is necessary to clarify
the coloration mechanism of the hand-holding type ofsparklers that comprise a mixture of several metal
powders and a strong oxidant.

Acknowledgement
This study was partially supported by KAKENHI (17H00844 and 19K21934).

References
1) T. Shimizu, “Hanabi no Hanashi”, Kawade-Syobo (1976). (inJapanese).
2) C. Inoue, Y. Izato, A. Miyake, and E. Villermaux, Phys. Rev.
Lett., 118, 074502 (2017).

Sci. Tech. Energetic Materials, Vol．
８０, No．
４,２０１９3) A.W. Williamson, Chemical News, Dec. 24 (1864).
4) A. Denisse, Feux DʼArtifice, Chap. 9 (1882).
5) T. Terada, “Terada Torahiko zuihitsu-syu”, Iwanami-Bunko(1964). (in Japanese, originally written around 1927).
6) U. Nakaya and Y. Sekiguchi, Bulletin of the Institute ofPhysical and Chemical Research, 6, 1083­1103 (1927). (inJapanese).
7) T. Shimiz, J. Industrial Explosives Society (Sci. Tech.
Energetic Materials), 18, 359­369 (1957). (in Japanese).
8) A. Maeda, et al., “Senko-Hanabi no kenkyu”, Shinjuku HighSchool (1962). (in Japanese).
9) H. Ito, Chemistry and Education, 39, 682­685 (1991). (inJapanese).
10) K. Itoh, D. Ding, and T. Yoshida, J. Pyrotechnics, 25, 14­27(2007).

141

11) C. Inoue, M. Koshi, H. Terashima, T. Himeno, and T.
Watanabe, Sci. Tech. Energetic Materials, 74, 106­111(2013).
12) C. Inoue, M. Koshi, T. Himeno, and T. Watanabe, Sci. Tech.
Energetic Materials, 77, 51­58 (2016).
13) J.C. Manson, Traité du fer et de lʼacier (1804).
14) R.W. Buzzard, Bureau of Standards Research Paper, 11, 527­540 (1933).
15) Tsutsui Tokimasa Toy Fireworks, http://tsutsuitokimasa.
jp/16) M.S. Russell, “The Chemistry of Fireworks”, Royal Societyof Chemistry (2009).
17) D. L. Perry, “Handbook of Inorganic Compounds”, CRC(2011).

４２８