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Some filaments suggest "reducing cross-sectional area" of the print. Is this referring to the vertical plane or horizontal plane? In other words, if I were to print a rectangular prism, would I want the long side of it printed in the vertical direction or parallel to the print bed?

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Based on your link in the comment, the cross-sectional area is the one on the X-Y axis (horizontal). The least area, the least material there is "pulling up" (curling) the layer when the plastic cools down.

When it comes to your specific question:

if I were to print a rectangular prism, would I want the long side of it printed in the vertical direction or parallel to the print bed?

...the answer is not as simple as "long side vertical", as you want both little warping and strong parts and the two may be better achieved by differen orientations.

Personally I would base my choice on the intended application: as the difference between the Z and the X+Y axis is their behaviour under load is substantial. FDM artefacts are anisotropic: they resist very well to compression along the Z or tension along the X & Y axis, but are weak along the same axis if you invert the direction of the force applied. Again: this difference is not marginal but substantial.

Keep in mind that "area" is actually "printed area", so you could have a model with a large footprint but a small printed area (think to the bottom of a Tour Eiffel model, or to a pipe standing up).

Were I to experience warping or poor adhesion with a specific model, I would reduce the cross-sectional area in the model (by adding relief cuts and/or cavities) or in the slicer (by decreasing the density of the infill) or would tackle the issue fror another angle, for example by switching the bed material (some specialised surface with good adhesion for the type of filament in use) or creating the object I wanted with an assembly rather than in a solid piece... But again: it would be a second-order consideration for me, and I would worry about it only if the problem were actually manifesting for that specific model.

For example: say that I were to print the head of a hammer. I would print it with the surface that hits the nail parallel to the printing bed so that the compression force resulting from hitting a nail would be along the Z axis. The link of a chain? Flat on the bed, so that the pulling forces from stretching the chain would be aligned with the X and Y axis.

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My guess is, based on the fact that this is ABS and the same paragraph recommends an heated bed, that they mean you should avoid layers with large continuous areas because those can be problematic with ABS if your heat is not very well controlled.

Basically while you are printing the upper part the lower part is cooling, and ABS shrinks as it cools, short strands shrink by a little and apply little force to the print while long strands shrink by a lot (same percentage, but more length - because they are longer to begin with) apply a lot of force and pull the edges of the print of the bed

so they suggest the shorter sides be on the X and Y and the longer side be on the Z axis.

Note that this will make materials with high shrinkage and low bed adhesion like ABS easier to print - this will not make the resulting part stronger or in any way better

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