Squib Dynamics


From gravity:

1. ay = dvy/dt = - g + α v2

Rayleigh drag coefficient α for objects at high velocity v:

2. α = ρair ACd/2m 

ρair = air density = 1.293 kg/m3 at 1 atmosphere
        pressure and 0o C

A = area at the front of the moving material in the plume 

m = ejected material's mass = ρeject Al 

Cd = dimensionless drag coefficient 

Cd = 0.25 for sleek automobiles
        0.5 in our calculations

3. α = ( ρair/ ρeject) Cd/2l

Table: Values of α for selected material parameters

material

α (cm-1)

A/V (cm-1)

cement, glass

 0.001 0.08
0.003 0.25
0.01 0.8

steel

 0.001 0.22
0.003 0.7
0.01 2.2

4. vy(t)= -(g/α)1/2 tanh [(g α)1/2t]

5. y(t) = y(t=0) - (1/α) ln cosh [(g α1/2t]

6. ax = dvx/dt = - α v2

7. vx(t)= vo/(1 + α vot)

8. x(t) = (1/α) ln (1 + α vot)

REFERENCE

Crockett Grabbe, "Direct Evidence for Explosions: Flying Projectiles and Widespread Impact Damage," Journal of 911 Studies, Vol. 14, Aug., 2007. 

 http://www.Journalof911Studies.com