Positive Phase p-T Curves

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(1) Positive Phase p-T Curves.  For the positive phase of a blast
wave, it is suggested that a close approximation of the p-T curve can be
obtained by using the following relationship:
EQUATION:
Ps = Pso(1 - ts/to)e -[alpha](ts/to)
(13a)
where,
Ps
=
pressure at time ts
Pso
=
peak incident pressure
ts
=
positive phase time of interest
to
=
positive phase duration
[alpha]
=
constant that determines the form of the p-T curve
The values of [alpha] can be expressed as a function of constant, k, which,
in turn, is defined as:
EQUATION:
k = is/Psoto
(13b)
where is, Pso, and to are obtained from Figure 4-5 of NAVFAC P-397.
The numerical relationship between k and [alpha] is listed below:
k
0.70
0.60
0.50
0.40
0.30
0.20
0.10
[alpha]  - 0.93
- 0.52
0
0.71
1.77
3.67
8.87
To simplify the solution, normalized plots of the positive phase p-T curve
as a function of k values are presented in Figure 7a.  For pressures up to
10 psi, these curves are applicable to both incident and reflected
pressures.
(2) Negative Phase p-T Curves.  The negative pressure curve can be
approximated by a cubical parabola expressed as:
_
_
_
_
_
_
EQUATION:
Ps = Pso(6.75ts/to)(1 - ts/to)2
(14a)
where,
_
_
Ps
= negative pressure at time ts
_
Pso
= peak incident negative pressure
_
ts
= negative phase time of interest
_
to
= negative phase duration
2.08-19