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

cataustria.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 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).

### 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/>.

**Hopkinson-Cranz Scaling Law (Cube-Root Scaling Law)**, is used in 1 calculator.

**Calculators**