Hot End Length Formula?

The recent thread about hot ends got me once again thinking about all that goes into making a good hot end.

While on ebay I saw a listing and in the description I read this:

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There are many other things to consider in nozzle tips besides just the opening size. If the minor diameter (opening) is too small or too long you will have too much restriction, making it VERY difficult to push the filament through. If the opening is to short, you end up with turbulence in the extrusion material. I think I have a good balance on all of my tips, making the restricted opening long enough to avoid turbulence, but short enough to have minimum pressure required to feed it.
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This leads me to wonder if there is an optimal formula to help build the "perfect" hot end.

If I read the above correctly, then there are more to hot ends that just drilling a 3mm hole down some random bit of brass, and making the tip pointy. If that is the case, is there a formula that says something like, at 3mm filament, you need 110 mm of length from cold end to hot end, and you must have a 45 degree etc etc

Regards

I think he's referring to the extrusion orifice, not the whole hot end. Though, i don't know what an optimal length would be. but i think some multiple of the extrusion width, like for .5 mm you might want 4x length, or 2mm.

There are a lot of variables:

plastics - diameter -quality
insulation on hot end
heater size and type
extrusion speed
heat sinks
nozzle size - length - width -wall thickness
material used for nozzle - brass - copper -steel - aluminum
fan cooled

So based of the above, it is tricky.

I just installed a new hotend from reprap-fab.org and have had problems getting it to work, solution was a heat sink and running at 252 for ABS - found through trail and error over several nights. switching to PLA would change the rules again, that is why I will build a printer/extruder for PLA only.

In an ideal extruder (no burrs, perfectly round) You want an extrusion orifice as short as possible without breaking from the internal pressure or possible head crash. Turbulence in the extruder flow is negligible because the fluid (abs/pla) is extremely viscous, and you are immediately squashing it into the part. 1:1 or 1:2 aspect ratios work pretty well for strength vs required pressure with stainless steel hot ends.

If you are not highly skilled and making one yourself, longer is easier to make since you have to worry less about running your 1.75mm drill bit through the end of the material.

While a longer orifice allows more die swell, you could simply change to a larger diameter hole for this same effect, which would require less extruder pressure.

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