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

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

INSTRUCTIONS:  Choose units and enter the following:

• (z) Distance Coefficient (see below)
• (w) Weight of Explosive Material Stored

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

The Math / Science

The Hopkinson-Cranz Scaling Law Range formula is:

        `R = z * w ^(1/3)`

where:

• R = Hopkinson-Cranz Scaling Law Range
• z = distance coefficient (see below)
• w = weight of material stored

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). 

Resources:

• "Formulae for Ammunition Management." International Ammunition Technical Guideline. 1st ed. New York: UN, 2013. 2-3. UN SaferGuard. United Nations Office for Disarmament Affairs (UNODA), 20 May 2013. Web. 12 June 2015. <http://www.un.org/disarmament/convarms/Ammunition>.
• Salveson, Matthew Ward. "Chapter 1: Background and Motivation."Computational Methodologies for Blast and Shock Mechanics. N.p.: n.p., 2007. 2. Print.
• Florek, Jason F. STUDY OF SIMPLIFIED MODELS OF AIRCRAFT STRUCTURES SUBJECTED TO GENERALIZED EXPLOSIVE LOADING. Ann Arbor, MI: ProQuest LLC, 2008. Rutgers University Community Repository. ProQuest LLC, Oct. 2007. Web. 12 June 2015. <https://rucore.libraries.rutgers.edu/rutgers-lib/22849/pdf/1/>.