# Pkg Solutions

# The McKee formula for Compression Estimation

The style common method of calculating a grade compression failure load (CFL, also sometimes noted as Box Compression Test Strength or BCT), 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It should be noted that the McKee formula is being superseded by more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.

### 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 comĀpression 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

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:**

^{b}* {$\sqrt{\mathrm{(DMDDCD)}}$}

^{a-b}* Z

^{2b-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

$\sqrt{\mathrm{(DMDDCD)}}$ =
The Geometric Mean of the Machine Direction and Cross Machine Direction
bending stiffnesses

^{0.746}* {$\sqrt{\mathrm{(DMDDCD)}}$}

^{0.254}* Z

^{0.492}

For more information see:

Predicting Box Compression Strength

BOX COMPRESSION ANALYSIS OF WORLD-WIDE DATA SPANNING 46 YEARS

In its turn ECT can be calculated from the CCT (corrugated crush test) of the different components of the board in accordance with the following formula:

ECT = 0.86 * (CCT1 + d * CCTF + CCT2)

CCT1 = Kpa/cm edge crush resistance of a corrugated strip of liner 1

CCTF = Kpa/cm edge crush resistance of a corrugated strip of fluting
medium

CCT2 = Kpa/cm edge crush resistance of a corrugated strip of liner 2

d = the draw factor of the board's fluting