I used math to see if I could scale my 3d print model and see if it could fit in my print bed diagnolly instead of laid horizontally and vertically. My math was wrong, I thought I could do it but I missed some numbers.
I use calipers and math to figure out how much filament is left on a spool.
For example, think of the filament as one solid ring of plastic. My example spool is 60mm wide, the inner radius (of the filament, not the spool) is 28mm, and the outer radius is 40mm. Subtract the volume of the empty cylinder in the center from the solid cylinder of PLA, then multiply by 0.7 to account for packing density, and boom, you have a volume of filament that’s accurate to within a few percent. Convert that volume into cubic centimeters, multiply by 1.24, and you have a weight. This estimate gives my sample spool around 133 grams of filament.
For a quicker, less accurate method, think of the filament as a collection of individual circles wound around the spool. My example spool is 60mm wide, so that’s around 34 strands of filament, and the filament is stacked 12mm deep, so that’s around 6 strands of filament (it’s safest to round down). 34x6=204, so the filament is wound around the spool 204 times.
The average radius of one circle around the spool is probably 34mm (right in between the inner and outer diameters), so good ol 2πr gives us an average circumference of 213mm. 213mm×204 windings is around 43,500mm of filament, or 43 meters. Multiply by 3 grams (roughly the weight of 1 meter of filament). This estimate gives my sample spool around 129 grams of filament.
It sounds very involved, but once you get the hang of it it’s very intuitive. You just have to know that
a circle’s circumference is 2π times the radius, or π times the diameter
I used math to see if I could scale my 3d print model and see if it could fit in my print bed diagnolly instead of laid horizontally and vertically. My math was wrong, I thought I could do it but I missed some numbers.
I use calipers and math to figure out how much filament is left on a spool.
For example, think of the filament as one solid ring of plastic. My example spool is 60mm wide, the inner radius (of the filament, not the spool) is 28mm, and the outer radius is 40mm. Subtract the volume of the empty cylinder in the center from the solid cylinder of PLA, then multiply by 0.7 to account for packing density, and boom, you have a volume of filament that’s accurate to within a few percent. Convert that volume into cubic centimeters, multiply by 1.24, and you have a weight. This estimate gives my sample spool around 133 grams of filament.
For a quicker, less accurate method, think of the filament as a collection of individual circles wound around the spool. My example spool is 60mm wide, so that’s around 34 strands of filament, and the filament is stacked 12mm deep, so that’s around 6 strands of filament (it’s safest to round down). 34x6=204, so the filament is wound around the spool 204 times.
The average radius of one circle around the spool is probably 34mm (right in between the inner and outer diameters), so good ol 2πr gives us an average circumference of 213mm. 213mm×204 windings is around 43,500mm of filament, or 43 meters. Multiply by 3 grams (roughly the weight of 1 meter of filament). This estimate gives my sample spool around 129 grams of filament.
It sounds very involved, but once you get the hang of it it’s very intuitive. You just have to know that
a circle’s circumference is 2π times the radius, or π times the diameter
filament weighs about 3 grams per meter of length
Because I am the turboest of nerds I have made this a spreadsheet as well. Can’t actually share it for privacy reasons, but it fits within a 4x5 set of cells if anyone wants to copy it. You don’t even need to know what the math is doing, just copy the green highlighted functions into the cells verbatim and it should work like a charm. Just remember you’re using radii, not diameters