109

CHAPTER 5

TNT EQUIVALENCE OF FIREWORKS

5.1 INTRODUCTION

5.1.1 Explosives and Fireworks

Explosives are reactive substances that can release high amount of

energy when initiated (Meyer 1987). Explosive materials may be categorized

by the speed at which they expand (Bahl et al 1981, Chou et al 1991, Khan

and Abbasi 1999). Materials that detonate are said to be "high explosives"

and materials that deflagrate are said to be "low explosives". Explosives may

also be categorized by their sensitivity. Sensitive materials that can be

initiated by a relatively small amount of heat or pressure are primary

explosives and materials that are relatively insensitive are secondary or

tertiary explosives.

Detonation is an explosive phenomenon whereby a shock wave

coupled to a flame front propagates through the reaction mixture at supersonic

speeds relative to ambient gases. Blast waves resulting from the detonation of

strong explosives like TNT exhibit close to ideal wave behaviour (Cook et al

(1989 and 2001) Lees 1996, Balzer et al 2002). The pressure profile over time

of an ideal blast wave can be characterized by its rise time, the peak

overpressure, duration of positive phase and total duration (Sochet 2010).

In deflagrations the decomposition of the explosive material is

propagated by a flame front which moves slowly through the explosive

110

material. The volume of a gas-air mixture is generally high and the energy

release rate is relatively slow. The blasts are characterized by more regular

blast waves that propagate at a subsonic speed. Explosives depend on

properties such as sensitivity, velocity and stability. Chemical explosives may

consist of either a chemically pure compound or a mixture of an oxidizer and

fuel.

Due to the effects of the shock wave during detonation, the oxidizer

and fuel interact to trigger chemical reactions. Some of the well-known

explosives are TNT, nitro-glycerine, RDX, PETN, HMX and nitrocellulose.

Fireworks are used for mainly fireworks display purposes and consist of

various chemical compounds. The heat released by explosion is often used to

calculate the TNT equivalency according to principle of energy similarity

(Rui et al 2002)

Figure 5.1 Distribution of energy in an explosion (Rui et al 2002)

The total energy generated by an explosive reaction can be

electromagnetic energy or mechanical energy. These energies in turn can be

Total energy

generated by

explosive reaction

Electromagnetic energy

High frequency electromagnetic energy

Visible light electromagnetic energy

Infrared energy

Low frequency electromagnetic energy

Mechanical energy

Overpressure of shock wave

Earthquake wave and crater formation

Shattering of cartridge and fling of its fragments

111

subdivided as shown in Figure 5.1. The compositions of firework mixtures

consist of a fuel, an oxidizer that oxidizes the fuel necessary for combustion,

colour producing chemicals and a binder which holds the compounds

together. In all explosive accidents involving fireworks mixture, the damage

or consequences appear similar to that of a high energetic compound such as

TNT. Since fireworks share similar characteristics of class A explosives like

TNT, and may reach the explosive potential of an explosive chemical, It is a

cause for concern due to associated hazards. An attempt has been made to

employ the ARC thermal characterisation of fireworks mixtures to calculate

its TNT equivalence of explosion. These chemicals often need to be handled

in a very safe manner.

In case of fireworks mixtures the oxidizer and fuel under right

conditions may explode if ignited. Further, all the fireworks compositions are

finely divided powder mixtures. Finely divided metals present a hazard to

violent explosion when ignited, and are susceptible to ignition by static

electricity more easily due to their conductive character. Hence firework

mixtures need to be handled very carefully. A slight deviation from the

strictly followed procedures for safe handling can turn the mixture into an

explosive chemical.

The expected form of an ideal shock wave from an unconfined high

explosive is shown in Figure 5.2.(Held 1983, Formby and Wharton 1996,

Sochet 2010) It is characterised by an abrupt pressure increase at the shock

front, followed by a quasi-exponential decay back to ambient pressure. A

negative phase follows, in which the pressure is less than ambient, and

oscillations between positive and negative overpressure continue as the

disturbance quickly dies away. Correspondingly, a typical design blast load is

represented by a triangular loading with side on pressure, Pso, and duration,

112

characterized by the Figure 5.3 (Ngo et al 2007). The area under the pressure-

time curve is the impulse of the blast wave.

Figure 5.2 Pressure distributions in a medium during passage of a blast wave

Figure 5.3 Typical design of blast load plot

Ambient P

Time, (min)

Pso

- PsoPositive Phase

Duration

Negative Phase

Duration

Duration

Time, (min)

Impulse

t0

Pso

113

Figure 5.4 Characteristic curve of an explosion: obtained from

overpressure and impulse profile (Alanso et al 2006).

In the case of an explosion it is possible to obtain the over-

pressure–impulse–distance relationship, called here the ‘characteristic curve’.

Highest isobars

Explosion’s origin

Over pressure

Characteristic curve

Distance

Distance Z1 Z2

ZZ

Z

Z

I

II

I

P

P

PP

114

Figure 5.4 (Alanso et al 2006) shows graphically the meaning of the so-called

characteristic curve, traced from the shock wave’s over-pressure–distance and

impulse–distance pro les. Distance to explosion’s centre (Z1, Z2....., Zn) can

also be included, to display all the information in the same diagram (Alanso

et al 2006).

5.1.2 An Overview of Explosion Models and its Applicability to

Fireworks Mixtures

An explosion is a rapid increase in volume and release of energy in

an extreme manner, usually with the generation of high temperatures and the

release of gases. Also, an explosion (meaning a “sudden outburst”) is an

exothermal process (i.e., liberation of energy) that gives rise to a sudden

increase of pressure when occurring at constant volume. It is accompanied

by noise and a sudden release of a blast wave. Thermal explosion theory is

based on the fact that progressive heating raises the heat release of the

reaction until it exceeds the rate of heat loss from the area. At a given

composition of the mixture and pressure, explosion will occur at a specific

ignition temperature that can be determined from the calculations of heat loss

and heat gain. Depending on the shock wave produced, explosions can occur

as detonation or deflagration, with or without a confinement in the

surroundings (Sochet 2010). Corresponding to the magnitude of an explosion,

the two most important and dangerous factors are over pressure, and scaled

distance of damage.

The above discussed parameters are necessary to predict the effects

of thermal explosion and estimate the extent of these hazards. To assess the

significance of damage, models are necessary to calculate dangerous

magnitude as a function of distance from the explosion centre. Most data on

explosion and their effects, and many of the methods of estimating these

effects, relate to explosives.

115

Although there are many explosion models available, TNT

equivalence model is widely accepted and in use. In recent years Multi

Energy Model, TNO and Baker -Strehlow-Tang (BS/BST) model also being

in use by many researchers (Beccantini et al 2007, Melani et al., 2009, Sochet

2010).

5.1.3 TNT Equivalence

The blast wave effects of explosions are estimated using TNT

equivalence techniques (Formby and Wharton 1996, Lees 1996). It is cited as

a standard equivalence model for calculating the effects of various explosives

and compares the effects to that of TNT. Parameters such as peak

overpressure, impulse, scaled distance and equivalent weight factor. (Held

1983, Frenando et al 2006, Lees 1996, Cooper 1994, Simoens and Michel

2011) are employed to calculate the TNT equivalence.

5.2 MATERIALS AND METHODS

5.2.1 TNT Equivalence Model

The term “TNT Equivalence” is used throughout the explosives and

related industries to compare the output of a given explosive to that of TNT

(Frenando et al 2006, Lees 1996; Cooper 1994). This is done for prediction of

blast waves, structural response, and used as a basis for handling and storage

of explosives as well as design of explosive facilities. This method assumes

that the gas mixture is involved in the explosion and that the explosion

propagates in an idealized manner. It is an ideal thermal explosion model

which considers explosion as a single entity; the explosive nature is measured

in terms of TNT equivalence;

TNT Equivalence =Mass of TNT, (g)

Mass of explosive, (g)(5.1)

116

TNT equivalence gives the impact of an explosive material to that of the

effect of TNT. TNT equivalence depends on the nature of the explosive,

distance, heat of detonation and the equivalent weight factor (Held 1983). The

various parameters involved in TNT model are peak overpressure, impulse

and the scaled distance. The equivalent mass of TNT is found by (Sochet

2010), Equation (4.2)

W =ME

E TNT(5.2)

where, W is the TNT Equivalence, is the empirical explosion efficiency, M

is the mass of explosive charge (g), EC is the heat of combustion of explosion

material (J g-1), ETNT is the heat of combustion of TNT (4765 J g-1)

5.2.2 Scaled Range

Scaling of the blast wave properties is a common practice used to

generalize blast data from high explosives. Scaling or model laws are used to

predict the properties of blast waves from large scale explosions based on

tests at a much smaller scale. The scaling law states that self – similar blast

waves are produced at the same scaled distance when two explosives of

similar geometry and of the same explosive material, but of different size, are

detonated in the same atmosphere.

The scaled range is measured as,

Z =R

W / (5.3)

Where, Z is the scaled range (m), R is the distance (m), W is the TNT

Equivalence Weight (g)

117

5.2.3 Overpressure

The pressure resulting from the blast wave of an explosion is

known as the overpressure. It is referred to as “positive” overpressure when it

exceeds atmospheric pressure and “negative” during the passage of the wave

when resulting pressure or less than atmospheric pressure. As regards the

magnitude of an explosion, one of the dangerous factor is overpressure, which

is chiefly responsible for damage to humans, structures and environmental

elements.

The overpressure is measured as (Rui et al 2002),

P = 1.02(W) /

R+ 3.99

(W) /

R+ 12.6

(W)R

(5.4)

Where, R is the distance (m), W is the TNT Equivalence Weight (g), the

above equation has been widely used by researchers in the past (Frenando

et al 2006, 2008, Lees 1996, Held 1983, Rui et al 2002)

5.2.4 Multi Energy Model

In this model, combustion develops in a highly turbulent mixture in

obstructed or partially confined areas (Beccantini 2007, Sochet 2010, Melani

et al 2009). Unlike TNT model, it considers explosion not as a single entity

but as a set of sub explosions.

5.2.5 TNO Model

TNO model is based on the degree of confinement and is measured

on a scale of 1 to 10 (Beccantini 2007, Sochet 2010). The number 10

corresponds to index volume of congested areas i.e. strong detonation and 1

corresponds to uncongested areas, i.e. weak deflagration. It is based on the

assumption that blast is generated only when the explosive is partially

118

confined. The parameters that are measured are scaled distance, positive

overpressure, duration time and impulse (Melani et al 2009).

5.2.6 Scaled Distance

Scaled distance is a relationship used to relate similar blast effects

from various explosive weights at various distances. Scaled distance gives a

blaster an idea of expected vibration levels based upon prior blasts detonated.

The scaled distance is measured by,

r = r × (PE

) (5.5)

where, r is the distance from the charge (m), Pa is the ambient pressure (bar),

E is the heat of combustion (J g-1).

5.2.7 Positive Overpressure

The positive overpressure can be found by,

P = (P × P ) (5.6)

where, P is the positive overpressure (bar), Ps is the positive scaled

overpressure (bar), Pa is the atmospheric pressure (bar).

5.2.8 Positive Duration Time

The scaled duration time is given by,

T = T ×EP

/

×1a

(5.7)

where, T is the positive duration time (sec), Ts is the scaled positive duration

time, a0 is the sound velocity (343.2 m s-1).

119

5.2.9 Impulse

The impulse is given by,

I =12

× P × T (5.8)

where, T is the positive duration time (s), P is positive overpressure (bar).

5.2.10 BS/ BST Model

Baker-Strehlow-Tang model(Baker et al 1994, 1996, 1998) is based

on the Mach number. It presents a correlation between the reactivity of fuel,

density of obstacles, and confinement. Flame speed is an important parameter

in measuring the blast wave propagation in this model.

The relation is given by,

P PP

= 2.4M

1 + M(5.9)

where, Pmax is the maximum overpressure (bar), P0 is the ambient overpressure

(bar), Mf is the Mach number.

Mach number =Flame velocitySound velocity

(5.10)

The scaled distance is measured by,

r = r ×P

E(5.11)

where, r is the scaled distance from the charge (m), r is the distance from the

charge (m), Pa is the ambient pressure (bar), E is combustion energy (charge),

(J g-1).

120

The positive overpressure can be found by,

P = (P × P ) (5.12)

where, P is the positive overpressure (bar), Ps is the positive scaled

overpressure (bar), Pa is the atmospheric pressure (bar).

The positive scaled impulse is given by,

I =I × a

E × p(5.13)

Where, I is the positive impulse (bar.s), a is the speed of sound, (m s-1), E is

the combustion energy (fuel air mixture), (J g-1), p is the atmospheric

pressure, (bar).

The combustion energy of fuel-air mixture is given by,

(E) = 2 × E × V (5.14)

where, E is the heat of combustion (sample firework mixture), (J g-1), V is

the volume of the vessel (m3).

5.2.11 Micro Calorimetric Test Data for Estimating TNT Equivalence

The experimental methods to assess the thermal instability/runaway

potential are primarily based on micro Calorimetry. It is designed to model

the course of a large-scale reaction on a small scale. Adiabatic Calorimetry is

one of the main experimental tools available to study the self-propagating and

thermally-sensitive reactions. One of the versatile micro calorimeter

techniques known as “Accelerating Rate Calorimetry” has the potential to

provide time-temperature-pressure data during the confined explosion of

121

fireworks mixture. The principle behind Accelerating Rate Calorimeter and its

usefulness in estimating the explosive potential of fireworks mixture have

been dealt with in the previous chapter. The ARC experimentation is designed

to study the explosive characteristics of energetic materials. The sample

quantities in ARC experiments are restricted to a maximum of 1gm to avoid

physical explosion of the sample vessel, unlike the field explosion. When

explosion occurs within confinement, time temperature data can be measured,

which is not viable in actual explosion due to the involvement of large

quantity of samples. The time, temperature, pressure data and the vigour of

explosion can be scaled up to field conditions (Bodman and Chervin 2004,

Badeen et al 2005, Whitmore and Wilberforce 1993).

Esparza 1986, Ohashi et al 2002, Kleine et al 2003 described a

procedure to calculate the TNT equivalent by a pressure based concept. This

approach is based on knowledge of the shock radius- time of arrival diagram

of the shock wave for the explosive under consideration. These data are used

to calculate the Mach number of the shock and the peak overpressure as a

function of distance (Dewey 2005).

ARC characterisation data generated for atom bomb cracker,

Chinese cracker, palm leaf cracker, flowerpot tip and ground spinner tip

mixtures have been dealt. Here an attempt has been made to employ them to

calculate their TNT equivalence of explosion.

5.3 RESULTS AND DISCUSSION

5.3.1 TNT Equivalence Model for Constant Distance

The results have been analyzed using this model for various

firework mixtures. Three cracker samples and two tip samples have been

selected. The distance from the centre of the explosion to the extent at which

the explosion took place has been kept as 3m (for all mixtures). The weight of

122

the samples taken has been varied from 5-25 grams. The results are presented

in Table 5.1 and Figures 5.5-5.8.

Table 5.1 Calculation of scaled range and overpressure for fireworks

Sample name

Heat of reaction , Ec,

( J g-1)

Sample weight,

(g)

TNTEquivalence,

W (g)

Scaledrange ,Z,

(m)

Overpressure,P (bar)

Atom bomb

cracker504.2

5 0.06 7.99 0.5410 0.11 6.34 0.9015 0.16 5.52 1.2420 0.21 5.03 1.5625 0.26 4.67 1.87

Chinesecracker 443.67

5 0.04 8.34 0.4910 0.09 6.62 0.8215 0.14 5.80 1.1220 0.18 5.25 1.4025 0.23 4.88 1.69

Palmleaf

cracker294.99

5 0.03 9.55 0.3710 0.06 7.58 0.6015 0.09 6.62 0.8220 0.12 6.01 1.0225 0.15 5.58 1.21

Flowerpot tip 972.23

5 0.10 6.42 0.8810 0.20 5.10 1.5215 0.30 4.45 2.1220 0.40 4.04 2.7025 0.50 3.75 3.26

Groundspinner

tip961.46

5 0.10 6.44 0.8710 0.20 5.11 1.5015 0.30 4.47 2.0920 0.40 4.06 2.6825 0.50 3.77 3.23

123

5.3.1.1 Scaled range vs. TNT equivalence for crackers

From the Figures 5.5 and 5.6 it is evident that the scaled range

decreases as the TNT equivalence increases for crackers and tip mixtures.

Figure 5.5 Scaled range vs. TNT equivalence for crackers (Atom bomb cracker ( ), Chinese cracker ( ), Palm leaf cracker ( ))

Figure 5.6 Scaled range vs. TNT equivalence for tip mixtures (Flowerpot tip ( ), Ground spinner tip ( ))

0

2

4

6

8

10

12

0 0.05 0.1 0.15 0.2 0.25 0.3

TNT Equivalence, (g)

3.5

4

4.5

5

5.5

6

6.5

7

0 0.1 0.2 0.3 0.4 0.5

TNT Equivalence, (g)

124

This is because TNT equivalence depends on the mass of the

sample taken. As the mass increases, TNT equivalence also increases. Hence

it can be inferred that the mass also has an effect over the scaled range. Thus

for tip samples, it can be observed that the effect of TNT equivalence over

scaled range resembles to the cracker samples due to similar mixture

composition.

5.3.1.2 Overpressure vs. TNT equivalence for firework mixtures

From the Figures 5.7 and 5.8, it can be observed that for the

crackers and tip mixtures the overpressure increases as the TNT equivalence

increases. This is because of the relationship between weight and TNT

equivalence. As the weight increases, TNT equivalence increases and since

overpressure and TNT equivalence have a direct correlation, the overpressure

increases. Thus, the weight is an important factor in determining the increase

or decrease of the overpressure.

Figure 5.7 Overpressure vs. TNT equivalence for crackers

(Atom bomb cracker ( ), Chinese cracker ( ), Palm leaf cracker ( ))

0

0.3

0.6

0.9

1.2

1.5

1.8

2.1

0 0.05 0.1 0.15 0.2 0.25 0.3

TNT Equivalence, (g)

125

Figure 5.8 Overpressure vs. TNT equivalence for tip mixtures

(Flowerpot tip ( ), Ground spinner tip ( ))

5.3.2 TNT Equivalence Model for Varied Distance

The results have been analyzed using this model for various

firework mixtures. Three cracker samples and two tip samples have been

taken. The distance from the centre of explosion to the point where the

explosion takes place has been varied as 3, 5, 10, 15, 20 m for each mixture

sample. The weight of the samples taken was 1g (constant for all mixture

samples). The results are presented in Table 5.2 and Figures 5.9-5.12.

0

0.5

1

1.5

2

2.5

3

3.5

0 0.1 0.2 0.3 0.4 0.5 0.6

TNT Equivalent, (g)

126

Table 5.2 Calculation of scaled range and overpressure for fireworks

Sample name

Heat of reaction , Ec, ( J g-1)

TNTEquivalence,

W, (g)

Distance,(m)

Scaledrange, Z,

(m)

Overpressure,P, (bar)

Atom bomb

cracker 504.2 0.01

3 13.67 0.18

5 22.77 0.11

10 45.55 0.05

15 68.32 0.03

20 91.09 0.02

Chinesecracker

443.67 0.009

3 14.26 0.17

5 23.76 0.10

10 47.53 0.05

15 71.30 0.03

20 95.06 0.02

Palm leaf cracker

294.99 0.006

3 16.34 0.13

5 27.23 0.08

10 54.46 0.04

15 81.69 0.02

20 108.92 0.02

Flowerpot tip

972.23 0.02

3 10.98 0.28

5 18.30 0.17

10 36.59 0.08

15 54.89 0.05

20 73.19 0.04

Groundspinner

tip961.46 0.02

3 11.02 0.28

5 18.36 0.16

10 36.73 0.08

15 55.09 0.05

20 73.46 0.04

127

5.3.2.1 Scaled range vs. Distance for firework mixtures

From the Figures 5.9 and 5.10, it can be observed that for crackers

and tip mixture the scaled range increases as the distance increases.

Figure 5.9 Scaled range vs. Distance for crackers

(Atom bomb cracker ( ), Chinese cracker ( ), Palm leaf cracker ( ))

Figure 5.10 Scaled distance vs. Distance for tip mixtures

(Flowerpot tip ( ), Ground spinner tip ( ))

0

20

40

60

80

100

120

0 5 10 15 20 25

Distance, (m)

0

20

40

60

80

0 5 10 15 20 25

Distance, (m)

128

This is because the weight of the sample is kept constant and thus

the TNT equivalence remains the same. Hence, the scaled range increases as

it holds a direct relation with distance.

5.3.2.2 Overpressure vs. Distance for firework mixtures

From the Figures 5.11 and 5.12, it can be observed that the

overpressure decreases as the distance increases for cracker samples and tip

compositions. This is because of the inverse relation between the distance and

the overpressure. Thus the overpressure value decreases for an increase in the

value of distance.

Figure 5.11 Overpressure vs. Distance for crackers

(Atom bomb cracker ( ), Chinese cracker ( ), Palm leaf cracker ( ))

0

0.05

0.1

0.15

0.2

0 5 10 15 20 25

Distance, (m)

129

Figure 5.12 Overpressure vs. Distance for tip mixtures

(Flowerpot tip ( ), Ground spinner tip ( ))

5.3.3 TNO Multi Energy Model

The results have been analyzed for this model using various

firework mixtures. The distance from the centre of the explosion to the point

where the explosion takes place is kept as 5-25 m (5, 10, 15, 20, 25 m

respectively). The ambient pressure is 1.0132 bar.

0

0.05

0.1

0.15

0.2

0.25

0.3

0 5 10 15 20 25

Distance, (m)

130

Table 5.3 Calculation of impulse for fireworks

Samplename

Heat of reaction

EC

( J g-1)

Positive scaled over

pressure Ps, (bar)

Scaled positiveduration

time Ts, (s)

Positive Over

pressure P, (bar)

Scaled distance

Positive durationTime, T

(s)

Impulse I,

(bar.s)

Atom bomb

cracker504.2 25.953 306.499 26.30

0.65

424.6 5583.5

1.30

1.95

2.60

3.25

Chinese cracker

443.67 16.732 163.197 16.95

0.68

216.65 1836.11

1.35

2.03

2.71

3.39

Palm leaf

cracker294.99 14.422 412.37 14.61

0.78

477.81 3490.40

1.55

2.33

3.10

3.88

Flower pot tip

972.23 30.156 967.6 30.56

0.52

1668.47 25954.2

1.04

1.57

2.09

2.61

Ground spinner

tip 961.46 2.354 1108.48 2.38

0.53

1904.31 2261.12

1.05

1.58

2.10

2.63

131

5.3.3.1 Scaled distance vs. Distance for fireworks

From the Figures 5.13 and 5.14, it can be observed that the scaled distance increases as the distance increases for cracker samples and tip

compositions.

Figure 5.13 Scaled distance vs. Distance for crackers (Atom bomb cracker ( ), Chinese cracker ( ), Palm leaf cracker ( ))

Figure 5.14 Scaled distance vs. Distance for tip mixtures (Flowerpot tip ( ), Ground spinner tip ( ))

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 5 10 15 20 25 30

Distance, (m)

0

0.5

1

1.5

2

2.5

3

0 5 10 15 20 25 30

Distance, (m)

132

This is because of the direct relation between the distance and the

scaled distance. It can also be inferred from this model that the value of

impulse largely depends on the positive overpressure and the positive duration

time. Larger the value of these parameters, higher is the impulse which is

nothing but the maximum peak overpressure. The value of impulse also varies

for different firework mixtures.

5.3.4 BS/BST Multi Energy Model

The results of this model have been analysed for various firework

mixtures. Three cracker samples and two tip samples have been used. The

ambient pressure is 1.0132 bar. The velocity of sound is 343.2 m s-1.

Table 5.4 Calculation of flame velocity

Sample name Peak overpressure,

Pmax ,(bar)

Machnumber, Mf

Flame velocity, (m s-1)

Atom bomb cracker 25.95 11.02 3783.57

Chinese cracker 16.74 07.34 2520.42Palm leaf cracker 14.43 6.37 2189.03Flower pot tip 30.15 12.91 4431.43Ground spinner tip 2.35 1.06 366.40

The Mach number ranges within 1.06 – 12.91. If the value falls

within this range, Scaled impulse can be deduced directly from the

characteristic curves depending upon the range of Mach number.

The distance from the centre of the explosion to the point where the

explosion takes place is taken as 5-25 m. The impulse and the positive

pressure values are obtained from Table 4.4. Volume of the obstructed area =

1 X 10-5m3.

133

Table 5.5 Calculation of positive scaled impulse for firework mixtures

Sample name

Heat of reaction

EC,( J g-1)

Volume of the

obstructed area V,

(m3)

Combustion energy E, (J g-1 m3)

Distance, (m)

Scaleddistance

, (m)

Positive scaled

impulse, I , (bar.s)

Atom bomb

cracker 504.2

1 × 10

0.010

5 23.24

8.810 46.4915 69.7320 92.9825 116.22

Chinesecracker

443.67 0.008

5 24.25

3.0210 48.5115 72.7720 97.0225 121.28

Palmleaf

cracker 294.99 0.005

5 27.79

6.5710 55.5815 83.3720 111.1725 138.96

Flowerpot tip

972.23 0.019

5 18.67

31.5710 37.3515 56.0220 74.7025 93.37

Groundspinner

tip961.46 0.019

5 18.74

2.8710 37.4915 56.2320 74.9825 93.72

134

From the Figures 5.15 and 5.16, it can be observed that the scaled

distance increases as the distance increases. This effect of tip mixture samples

is similar to that of the cracker samples. However, the curves of the two tip

samples are quite close. Since scaled impulse depends on the impulse,

indirectly the positive overpressure and the positive duration time has an

effect over the scaled impulse.

Figure 5.15 Scaled distance vs. Distance for cracker samples (Atom bomb cracker ( ), Chinese cracker ( ), Palm leaf cracker ( ))

Figure 5.16 Scaled distance vs. Distance for tip samples (Flowerpot tip ( ), Ground spinner tip ( ))

020406080

100120140160

0 5 10 15 20 25 30

Distance, (m)

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30Distance, (m)

135

5.4 SUMMARY

The TNT equivalence technique is used as a standard tool to

evaluate thermal explosion parameters. The Multi Energy Models are

alternative methods to TNT equivalence and a study of these models has been

conducted using the Thermal explosion data obtained from the Accelerating

Rate Calorimeter. TNT equivalence model compares the output of a given

explosive to that of TNT explosive. The TNO Multi energy model and

BS/BST model consider the obstacles or obstructions present within the

explosion region and have been applied as dust explosion models with the

available data. However, it is difficult to compare all the three models

directly, as they are based on different assumptions and the parameters vary

respectively. The overpressure and scaled distance are important parameters

in estimating the explosive potential of various firework mixtures. From this

study it has been observed that the firework mixtures, under certain conditions

can be equivalent to an explosive and hence have to be handled carefully. It

has also been observed that TNT equivalence model and TNO Multi energy

model do not consider the sound velocity, whereas the BS/BST model

depends on the sound velocity. All the three models can be applied to

determine the explosion limits. In summary,

Pressure rises due to thermal decomposition of fireworks.

Overpressure decreases with increase in distance.

TNT equivalence of fireworks mixture varies with different

weights.

The damage causing ability of the fireworks depends on the

initial mass and it decreases with distances.

The studies confirm that the damage causing ability of the blast

on structures due to explosive decomposition of fireworks

increases with increase in over pressure.