Compression Estimation Using the McKee Formula

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The Boxcomp computer program will need various questions answered to calculate the required board grade for you.

The method of calculating a grade compression failure load (CFL, also sometimes noted as Box Compression Test Strength or BCT), used by this version of Boxcomp is the McKee formula. This formula was developed in the 1960's and is named after one of it's main inventors. Shown below is the shortend form of the formula, which is normally used in such calculations.

It should be noted that the McKee formula is being superseded by more accurate formulas developed in recent times. The programming code for Boxcomp is provided within the HTML page and is modular in nature, enabling not only other board materials to be added or substituted, but new calculation formulas to be used instead for McKee. However, for completeness, information on the McKee formula is provided below.

Accuracy of the McKee formula

An extract form "Box compression analysis of world-wide data spanning  years" by Urbanik and Frank:
Until recently, the state of the art of box com­pression estimation was the equation by McKee et  al.  (1963)  or various  modifications,  with  the assumption  that  Eq. provided  an  estimation that was accurate to within about 6% on average and  15%  for  the  majority  of  single-wall  boxes. In  reality,  we  see  that  for  a  broader  data  set  of single-wall  boxes,  the  McKee  equation  systematically  overestimates compression  strength.  It provides  an  estimate  within  about  11%  of  the true box compression value on average, and the strength  estimates  of  many  boxes  are  off  by more  than  20%.  The  estimated  strength of double-wall boxes and tube constructions can be off  by  even  more.

The shortend version of the McKee formula is:

CFL = 5.3 * ECT * $\sqrt{\mathrm{T * Z}}$

where:

ECT = edge crush test in Kpa/cm
T = thickness of the board in cm
Z = perimeter of the box in cm
CFL = Case failure load in Kpa

Or in SI-Units:

CFL = 53 * ECT * $\sqrt{\mathrm{T * Z}}$

where:

ECT = edge crush test in N/mm
T = thickness of the board in cm
Z = perimeter of the box in cm
CFL = Case failure load in N

The general full form of the McKee equation is:
CFL = a * ECT b * {$\sqrt{\mathrm{\left(DMDDCD\right)}}$}a-b * Z2b-1

where:

a & b = constants determined by experimentation
ECT = edge crush test
Z = perimeter of the box in cm
CFL = Case failure load in N
D = bending stiffness of the board
$\sqrt{\mathrm{\left(DMDDCD\right)}}$ = The Geometric Mean of the Machine Direction and Cross Machine Direction bending stiffnesses

CFL(lbs) = 2.028 * ECT 0.746 * {$\sqrt{\mathrm{\left(DMDDCD\right)}}$}0.254 * Z0.492