# Hopkinson-Cranz Scaling Law (Cube-Root Scaling Law)

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R =
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cataustria.Hopkinson-Cranz Scaling Law (Cube-Root Scaling Law)
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924917cb-113e-11e5-a3bb-bc764e2038f2

The Hopkinson-Cranz Scaling Law Range calculator computes for the Range estimation (R) needed when dealing with ammunition management.

INSTRUCTIONS:  Choose the preferred units and enter the following:

• (z) Distance Coefficient (see below)
• (w) Weight of material stored.

Range Estimation: The calculator computes the range (R) in meters.  However, this can be automatically converted into other length units via the pull-down menu.

### The Science

Many States use rules based upon the explosives, their quantity, and the distance from the explosive to where people are at risk.  These rules are known as Quantity-Distance (Q-D) criteria, and are based on the approach derived from the Hopkinson-Cranz Scaling Law5 6, which is further amended by a range of coefficients.  It is the basis of much of the work on the estimation of appropriate quantity and separation distances.

### Distance Coefficient

Examples of ammunition distance coefficients used in the field:

•   8.0 - Used to predict separation distances between ammunition process buildings (APB) within an explosive storage area (ESA).
• 14.8 - Used to predict separation distances between an explosive storehouse (ESH) and a public traffic route with civilian access.
• 22.2 - Used to predict separation distances between an explosive storehouse (ESH) and a building inhabited by civilians.
• 44.4 - Used to predict separation distances between an explosive storehouse (ESH) and a vulnerable building inhabited by civilians (e.g. a school).