Optimum ratio of line width to layer thickness for overhang performance?

When I have overhangs in my model, Cura colors them red. However, I noticed if I make layer thickness thinner, the red area is reduced or disappears.

This could mean that thinner layer thickness is better for overhang, but it could also mean that a larger ratio of line width to layer thickness is better. It makes sense that if line width is 4X the layer thickness (such as 0.15 layers with 0.6 line width), overhang performance should be better than if line width is only 2X (such as 0.3 layers with the same 0.6 line width.

Is there a model that explains the optimum ratio of line thickness to layer height? Is only the ratio important, or is layer height also important by itself?

Cura high-lights overhangs in red if the printer would end up printing completely into thin air.

If your overhang is angled instead of being a purely vertical-to-horizontal transition, a much thinner layer height can increase the chances that enough of the prior layer exists to support the next layer being printed.

Basically, the thinner the layer (within reason), the greater the allowable angle of overhang that is safe to print.

A wide line works if there is something below it to squeeze the filament against, but if you don't have a full layer below it, it will stay thinner and it will droop. I would not use extreme ratios on overhangs. Still, do a parametric test: a overhang tower (a compact one) at different line widths and layer heights. If you test 3 layer heights and 3 line widths, it's only 9 short prints.

However, as you can see in filament reviews, different materials behave differently. I think there is no a priori optimal value.

In terms of Cura's model for showing overhangs, I'm nearly sure it's just the ratio - rise over run, or rather run over rise. And indeed that's what makes sense mathematically:

At least some portion of the wall extrusion in layer N+1 needs to sit on top of the corresponding wall extrusion in layer N. For a given 3D surface slope, the "run" - the distance the cross-section moves from one layer to the next, which needs to be bounded by some fraction of the line width - varies proportionally to the "rise" - the layer height.

• In that case, there seems to be little downside of maximizing the ratio. Are there any other downsides of wide lines, but thin layers? I think for me with a 0.4mm nozzle, that 0.1 layer and 0.7 line width would be the practical limit--a ratio of 7. May 14, 2020 at 4:45
• You can't actually make lines wider than your nozzle width without something to press down against under the nozzle orifice. You'll just extrude the nozzle width into thin air. May 14, 2020 at 10:21
• I routinely use 0.7mm line widths with my 0.4mm nozzle. I think the limit is related to the size of the flat area at the end of the nozzle. Sadly, nobody seems to specify the diameter of the flat area of nozzles, though it would seem to be a relevant parameter. May 14, 2020 at 14:23
• You can use 0.7 line width fine as long as there's either bed surface or existing printed material under a decent portion of the nozzle orifice. You can't when the nominal line only overlaps the one below it by 0.15 mm because there's no surface below the nozzle orifice to make the extrusion spread out to 0.7 mm. It'll just extrude 0.4 mm into thin air. Essentially, line width greater than nozzle size makes at best minimal improvement to ability to print overhangs May 14, 2020 at 15:44
• and adjusting the flow. Doing this all by hand for the layer height in effect is tedious and error-prone. Aside from the lifting part, I think it can be done with current slicers, but it's not automated at all. Jul 14, 2020 at 16:06