Back to Basics – The Fundamentals of Blast Design

 

             This document was originally presented at the Chapter’s 1999 workshop. 

               It was revised and re-published as a newsletter supplement in 2008.

                       (Click on the above title to open a copy of the document.)

 

 

                              *      *      *      *      *      *      *      *      *        *      *      *     

 

 

        Understanding Blast Vibration and Airblast, Their Causes and Their Damage Potential

 

               Originally presented at the GW Chapter’s workshops in 2006 and 2007.

                               (Click on the title to open a copy of the document.)

 

 

*      *      *      *      *      *      *      *      *        *      *      *

 

 

 

Useful Calculations and Conversion Factors for Blasters:

 

 

Official Metric Equivalents (according to U.S. and Canadian law):

 

1 inch (in.)             =    25.4 millimeters (mm)                             

 

1 pound (lb.)         =    453.59237 grams (g)

 

 

 

Conversion Factors:

 

Distance:

feet (ft)

x

0.3048

=

meters (m)

 

meters

x

3.2808

=

feet

 

 

 

 

 

 

Weight:

pounds (lbs)

x

0.4536

=

kilograms (kg)

 

kilograms

x

2.2026

=

pounds

 

 

 

 

 

 

Peak Particle Velocity:

in/sec

x

25.4

=

mm/sec

 

mm/sec

x

0.3937

=

in/sec

 

 

 

 

 

 

Volume:

cubic yards (yd3)

x

1.308

=

cubic meters (m3)

 

cubic meters

x

0.7645

=

cubic yards

 

 

 

 

 

 

Powder Factor:

lbs/yd3

x

0.93

=

kg/m3

 

kg/m3

x

1.6863

=

lbs/yd3

 

 

 

 

 

 

Square Root Scaled Distance:

ft/lbs1/2

x

0.45236

=

m/kg1/2

 

m/kg1/2

x

2.2106

=

ft/lbs1/2

 

 

 

 

 

 

Cube Root Scaled Distance:

ft/lbs1/3

x

0.3965

=

m/kg1/3

 

m/kg1/3

x

2.5221

=

ft/lbs1/3

 

 

 

 

 

 

Pressure:

lbs/in2

x

0.145

=

Pascals

 

Pascals

x

6.895

=

lbs/in2

 

lbs/in2

x

.0000689

=

kilobars*

 

kilobars*

x

14504

=

lbs/in2

 

feet of water

x

0.434

=

lbs/in2

 

lbs/in2

x

2.31

=

feet of water

 

                                                                      *  1 Bar  =  14.5 lbs/in2

 

 

                                                                      *************

 

 

Other miscellaneous calculations:

 

 

Pounds of explosive loading per foot of borehole  =  D2  x  S.G.  x  0.34*

 

                                        Where: 

 

D       =   explosive diameter

 

S.G.   =   specific gravity of explosive (g/cc)

 

 

*   In the above formula, the factor 0.34 is used to convert g/cc to lbs/cu ft and to calculate the

          volume of the explosive charge.     It is the result of the equation,  

 

                              0.7854  x 12  x  62.4

                                         1728

 

                    where:                    0.7854 = ¼ of pi

                                        12 = the number of inches in a foot

                                        62.4 = the weight of 1 cubic foot of water in lbs (at approximately 45oF)

                                        1728 = the number of cubic inches in a cubic foot

                                                           

 

*************

 

Displacement of water in a borehole:         H  =  D2 / (D2 – De2)  x  h  

 

                                        Where:

 

                                        H  =   final height of water

                                       

                                        h  =   initial height of water

                   

                                        D  =   hole diameter

 

                                        De  =   explosive cartridge diameter

 

Determine H, the final height of water, and then divide H by the cartridge length to

determine the number of cartridges that will be required to build out of the water.

 

 

*************

 

 

Square Root Scaled Distance (Ds)    =    Distance / Explosive Weight1/2

 

 

*************

 

 

The following equations express the relationships between Velocity, Displacement,

 Frequency and Acceleration for sinusoidal waveforms.

 

 

V  =  2 π  f  D                or             V  =  386.1 Gs / (2 π f)

 

D  =  V  /  (2 π f)

 

A  =  2 π  f  V         or            Ag  =  (2 π  f  V) / 386.1

 

f  =  V / (2 π D)      or            f  =  A  / (2 π V)

 

 

Where:

 

                                        V  =  velocity in inches/second

 

                                        D  =  peak displacement in inches

 

                                        A  =  acceleration in inches/second/second (in/sec2)

 

                                        Ag  =  acceleration in Gs

 

                                        f  =  frequency in Hertz (cycles per second)

 

                                        π (pi)  =  3.14159….

 

 

*************

                   

                              Cole’s formula for determining peak pressure from an explosive charge detonating

                                        underwater (assumed TNT or its equivalent):

 

                                        P  =  2.25 x 104 (W1/3 / R) 1.14

 

                                        Where:

 

                                        P  =  peak pressure in psi

 

                                        W =  explosive charge weight in pounds

 

                                        R  =  distance in feet from the detonating charge

 

 

*************

 

 

                                                                                                                        iseegoldenwest.org