The formula, in words
- The bottom carton carries everything above it, and only what is above it. A carton in a layer carries the cartons standing in its own column, which is one for every layer above it. Ten layers put nine cartons on the bottom one, and nine cartons at 15 kg is 135 kg, which at 9.81 metres per second squared is 1,324 newtons. Nothing about how the layer was arranged changes that figure, because arranging a layer moves no mass.
- The pattern changes the strength, not the load. A layer of identical cartons all facing one way stands corner on corner, and the whole of the rating is available. Turn the layers so they tie into each other and some of those corners land on panels instead, and only part of the rating is available. How much is a figure from testing the built unit, and this page takes it from you rather than deriving it, because the geometry does not determine it.
- Fitting more into a layer is not carrying more on a pallet. The turned pattern here takes ten cartons to a layer against nine and covers the deck exactly instead of leaving a strip bare. It also has 1,050 newtons to work with instead of 1,500, so it stops at eight layers where the other could take eleven. Eighty cartons against ninety, and the pattern with more in each layer is the one holding less.
- Three ceilings, and the lowest one is not always the same one. The height allows a number of layers, the aligned pattern's strength allows another, and the turned pattern's strength allows a third. Here they are ten, eleven and eight. The roof stops one pattern and its own strength stops the other, and a page that reported only the smallest of the three would hide which limit you would have to move.
A worked example
The inputs. Carton 400 by 300 by 200 mm at 15 kg. Deck 1,200 by 1,000 mm, 150 mm high. Ten layers. Compression limit 1,500 N for one carton. Seventy percent retained when the layers are turned. One hundred and fifty millimetres of handling clearance in 2,400 mm of height. Gravity at 9.81 metres per second squared.
The aligned layer. Length along the deck gives, each division rounded down: So there are 9 cartons. Width along gives: So there are 8. Nine cartons cover 1,080,000 of 1,200,000 square millimetres, which is 90.0%, and a strip 1,200 by 100 mm is bare. The turned layer. Cut the 1,000 mm width at 600 mm. The first 1,200 by 600 block takes 3 by 2, which is 6 cartons. The second 1,200 by 400 block takes 4 by 1, which is 4. Ten cartons cover 1,200,000 square millimetres, exactly 100.0% of the deck.
The turn. Rotate that arrangement 180 degrees about the deck centre. Block 1 moves from the 0 to 600 band into the 400 to 1,000 band and block 2 moves the other way, so the joints move. Not every joint moves, which is exactly why the strength retained is a typed figure and not something the drawing can tell you.
The load down the stack. One carton weighs, in newtons, its mass times gravity: From layer 1 to layer 10, the loads are 1,324.35, 1,177.20, 1,030.05, 882.90, 735.75, 588.60, 441.45, 294.30, 147.15 and 0 N. The bottom carton carries 1,324 N whichever pattern built the layer. The strength and the margin. Aligned strength is 1,500 N. Turned strength, in newtons: The aligned margin under its limit, in newtons: That prints as 176 N and 11.7%. The turned margin over its limit, in newtons: That prints as 274 N over and 26.1% over. The three ceilings. The height allows a number of layers: Aligned strength allows another: Turned strength allows a third: The height stops the aligned build at 10 and its own strength stops the turned build at 8. The handling envelope. Built height, in millimetres: Residual height, in millimetres: The rule reserves 150 mm, so 100 mm remain above the rule. At eleven layers the build is 2,350 mm and 100 mm into the reserved band. The turned pattern fits one more carton to a layer and carries ten fewer on the pallet. Ten a layer against nine, and 80 cartons against 90, because it stops at eight layers and the other stops at ten. Fitting more into a layer is not carrying more on a pallet.
The margin on one carton is 176 N, which is 11.7% of a figure the visitor typed. It is not a test result, it carries no condition, and the pallet it describes has never existed. A positive arithmetic margin is not approval.
The load becomes 1,030 N. The aligned margin is 31.3% and the turned margin is 1.9%, which is 19 N on one carton. The built height is 1,750 mm and 500 mm remain above the reserved band.
Check it yourself
Both patterns then allow eleven layers, the roof stops both of them at ten, and the turned pattern's extra carton a layer becomes ten extra cartons on the pallet for nothing. Every word this page has to say about the choice between the two patterns lives inside that one percentage, and the page cannot tell you what yours is.
What this does not model
Humidity, which is the largest single influence on how much load board actually takes; standing time and creep under a constant load; the variation between one carton and the next; vibration, shock and the forces of being lifted, set down and driven; the alignment a packing line actually achieves against the alignment drawn; overhang of any kind, which is refused rather than priced; the strength of the deck itself and its deflection under load; slip sheets, caps, collars, corner boards, wrap and strapping, none of which appear in the arithmetic and none of which substitute for carton strength; mixed cartons on one pallet; part layers and uneven builds; the pallet's own mass, which the bottom carton does not carry; the order the layers are built in; and what happens to any of this when the unit is broken down at the other end, which is a separate question about a separate envelope.