Pieces per Load

Two limits, two divisions, and you take the smaller. Cube allows $V_a / v_p$ pieces; payload allows $W_{max} / w_p$; the load has to satisfy both, so the answer is the minimum of the two. Satisfying one is no help whatever — a trailer that has room for another skid but no payload left is full, and so is one with payload to spare and no floor.

Take the floor, and then look at the fraction you discarded. You load whole skids, so 52.94 means 52 go on. But the 0.94 is worth reading rather than throwing away: it says a slightly lighter or slightly smaller piece would have earned another one aboard. When the remainder is close to a whole piece, small packaging changes have a step function waiting for them, and a two per cent reduction in piece weight can be worth a whole extra unit per load. When the remainder is near zero, that same two per cent buys nothing. The fraction is where the leverage lives.

It is also worth reading the two divisions against each other rather than only the smaller one. If cube allows 72 and weight allows 53, you are hauling nearly 1,100 ft³ of empty trailer on every trip — that is what weighing out looks like in cubic feet, and it is the number to bring to a conversation about smaller equipment or heavier-payload equipment. If the two come out close together, the freight sits near the equipment's crossover density and both limits are being used, which is the best outcome available.

This is a cube count, not a stacking plan. The arithmetic assumes the pieces tile the space, and real pallets do not. 48 × 40 inch skids leave waste across a 102 inch trailer interior no matter how they are turned. Product that cannot be double-stacked loses the entire upper half of the trailer regardless of what the volume arithmetic says — and in that case the honest input is not a smaller available volume but a piece volume measured to the full stack height the skid occupies, floor to roof, because that is the space it really takes. Load-planning software exists to do the tiling properly; this page gives you the ceiling that software will never beat.

The right order of work is: check the density against the crossover to learn which limit will bind, use this to get the count, take the floor, then check the cube and weight utilisations of the resulting load to see how much of each capacity you actually used. Four numbers, and between them they describe a truckload completely.