MNGN 444 – Blast Overpressure and Positive Pulse Duration Curves

Reference: P.Cooper, “Explosives Engineering”, Chapter 28, 1996.

MNGN 444 – Height of Burst Curves

Reference: M.Mellor, “Explosions and Snow”, Cold Regions Science and Engineering, Part III, Section 3A, 1965.

MNGN 444 – Equations I

Reference: G.F. Kinney, K.J.Graham, “Explosive Shocks in Air”, Second Edition, 1985.

Shock Velocity:

𝑼𝒙 = 𝑪𝒂 ∙ √𝟏 +𝟔𝑷𝒙

𝟕𝑷𝒂

Mach number:

𝑴𝒙 =𝑼𝒙

𝑪𝒂

Blast Overpressure:

𝑷𝒙 =𝟕(𝑴𝒙

𝟐 − 𝟏)

𝟔∙ 𝑷𝒂

Angle of incidence:

𝜷𝒎𝒊𝒏 =𝟏. 𝟕𝟓

(𝑴𝒙 − 𝟏)+ 𝟑𝟗

Mach stem number:

𝑴𝒔𝒕𝒆𝒎 =𝑴𝒊𝒏

𝒔𝒊𝒏 𝜷

Ca is speed of sound in air (sea level)

Pa is atmospheric pressure (sea level)

Subscript x means general (Incident/Mach Stem).

MNGN 444 – Equations II

Reference: P.Cooper, “Explosives Engineering”, Chapter 27, 1996.

Gurney Equation:

𝑽𝟎

√𝟐𝑬= (

𝑴

𝑪+

𝟏

𝟐)

−𝟏/𝟐

M: mass of metal cylinder (kg) C: mass of explosive (kg) √2E: Gurney constant (m/s)

Mott Equation:

𝒎 = [𝑴𝒌 𝒍𝒏 (𝑴𝟎

𝟐𝑴𝒌)]

𝟐

Mo: mass of metal cylinder (lb) Mk: distribution factor

𝑀𝑘 = 𝐵 ∙ 𝑡5/3 ∙ 𝑑1/3 ∙ (1 +𝑡

𝑑)

B: Mott coeficient for given explosive-metal pair T: wall thickness (in) D: inside diameter of metal cylinder (in)

Fragment Size:

Drag Attenuation Equation:

𝑽𝒔 = 𝑽𝟎 ∙ 𝒆−(

𝑨𝑾𝒇

)𝜸𝟎𝑪𝑫𝑹

or

𝑹 =𝒎

𝑨𝜸𝟎𝑪𝑫∙ 𝐥𝐧 (

𝑽𝟎

𝑽𝒔)

A: fragment area (m2) Wf: fragment mass (kg) γ0: specific weight of air (kg/m3) CD: Drag coefficient (0.6)

MNGN 444 – Blast Damage Curves

Reference: P.Cooper, “Explosives Engineering”, Chapter 28, 1996.

Lung Damage:

Ear Damage:

Secondary Blast Damage:

Tertiary Blast Damage: