Scaled distance Sachs

Once the energy quantities E and the initial blast strengths of the individual equivalent fuel-air charges are estimated, the Sachs-scaled blast side-on overpressure and positive-phase duration at some distance R from a blast source can be read from the blast charts in Figure 4.24 after calculation of the Sachs-scaled distance ... 

R = Sachs-scaled distance from charge center (-)... 

R Sachs scaled distance, defined by equation 6-25 (unitless)... 

Determination of the scaled distance (Sachs dimensionless scaled distance)... 

In the first place the Sachs scaled distance is calculated according to Eq. (10.167) to give... 

Because the curves depend on Sachs scaled distance, this can be taken over from Example 10.27. 

According to [66] the distance-dependent side-on peak overpressure in the far fleld (Sachs scaled distance according to Eq. (10.167) R > 2) can be calculated using the TNT equivalent model (vid. Sect. 10.6.3.1). For the near fleld the following relationship should be used (vid. [2])... 

FIGURE 3.4. TNO multi-energy model for vapor cloud explosions. The Sachs scaled side-on overpressure and positive-phase duration are provided as a function of the Sachs scaled distance (AlChE/CCPS, 1994). 

Sachs scaled distance A dimensionless distance used in blast modeling, defined by Equation (3.8)... 

Once estimated the explosion energy, the peak overpressure at a given distance can be derived from generalized graphs, where the normalized overpressure as a function of the non-dimensional distance is reported. The non dimensional distance is calculated using the Sachs scaling law (AIChE/ CCPS, 1999) ... 

The Universal Hopkinson-Cranz and Sachs Laws of Blast Scaling have both been verified by experiment. These laws state that self-similar blast (shock) waves are produced at idendcal scaled distances when two explosive charges of similar geometry and the same explosive composition, but of different size, are detonated in the same atmosphere [49]. 

The blast scaling law which is almost universally used to predict characteristics of blast waves from explosions at high altitude is that of Sachs (Reference 10). Sachs law states that dimensionless overpressure and dimensionless impulse can be expressed as unique functions of a dimensionless scaled distance, where the dimensionless parameters include quantities which define the ambient atmospheric conditions prior to the explosion. 

Characteristic Sachs dimension Re = [P/Pol was taken as a reference scale to neglect the shape of the explosive volume in determining the relative distance R =R/Re. That approach does not imply analysis of blast wave parameters at distances of 1 < P/Py < 3. In experiments described in [1], the radius of the cylinder filled with HAM was Py = 1.7 m. In mixtures with less than 28.7% H2 content the pressure and impulse values became lower. 

Let us point to the relation in the Sadovskiy-Hopkinson scaled distance A, relative distance RIRq and non-dimensional Sachs parameters. Thus, at Pq = 0.1 MPa it turns out that RIRq = 2.5A = 5.2 R. 

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