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Some math for the record in case anyone else wants to build one of these.... My 9" estimate on the arm length as usable was based on faulty premise.
I'm working on designing version #2 so wanted to at least improve the current design a little
. After having used it for a while LOMLs big complaint about the current version is that they are somewhat overly large and she isn't the tallest person ever so getting the yarn over the top and onto the swift somewhat challenging. The gal at the yarn store I have beta testing another one has the same complaint (being of a similar altitude). So I decided to sit down and figure out about how big they should be or at least could be and still work for most hanks of yarn. The problem is that the angle math on calculating the actual sizes plumb bamboozled me so I decided to take the more direct approach of measuring the current setup and dividing the measured usable circumference from the theoretical circumference if the arms spanned a complete circle of the current setup to get a "correction factor". This saves me from having to do a full mockup and gives some guidance one design parameters that a mockup wouldn't.
So without further ado here it is showing all my work like they taught in grade school.
Current Swift Specs:
Arm length (end connection point- end connection point): 17.5"
Diameter of center pivots to connection point on arms: 1.5"
Max "wingspan" if the arms could go out to full extension: (17.5*2 + 1.5): 36.5"
Theoretical circumference: (37.5 * pi): 114.7"
Actual measured usable circumference where the yarn sits: 89"
Correction factor between actual and theoretical circumference: (89 / 117.5) : 0.78
The correction factor is because you can't go to full extension with the wings (some designs go closer than others, mine has a bit of tension) and also the actual contact points are slightly in from the actual circumference. It would be slightly different depending on how flexible your connection points are and how many arms you have.
Max measured circumference of a hank of yarn: 60" (I did a sampling of a dozen or so in LOMLs workroom, the larger ones were all pretty close to the same - 28 or 29" * 2 halves, some smaller hanks were closer to 36" in circumference.).
We obviously want some margin of error, so lets say we want to be able to handle pieces of yarn up to 66" around.
back out correction factor: 66 / 0.78: 84.6"
calculate theoretical diameter: 84.6 / pi: 27"
Subtract the center pivot size: 27 - 1.5": 25.5"
Calculate desired arm length: 25.5/2: 12.75"
So I'm going to say arms of 13-14" in finished length would generally be fairly safe to actually work for 99.9% of all yarn unless you got some sort of HUGE hank. Even 12" arms would probably be generally ok, but I don't think I'd recommend going smaller than that.
The top of the current swift is 27" above the table. With 14" arms and tightening up some of the slack space in the current build I think I can get it to about 17" off of the table or a cool 10" shorter.
Other notes:
With some twiddling I was able to get the current swift out to 93" instead of 89" measured usable circumference (the difference is largely due to how I attached the arms together which binds slightly at near full extension so 89" is current usable but a better design could get 93" or maybe a smidge more)
At that extension the circumference around the arms themselves (measured point-point) was 104
and the diameter of the arms was 34"
A true circle at that diameter would be 106.8".
So we lost only 2.8" to the straight lines between the arms (with 6 arms) vs circle math. The majority (another 11" lost) really is in the difference between the end of the arms and the valley the yarn rides in (visually this makes sense looking at the swift but its nice to have the math confirm).
So absolute best case correction factor would be around 0.87 to 0.9ish. I think something between 0.75 and 0.85 is definitely in the right ballpark for most designs though. 0.75 would be fairly conservative if you're arm connections had a lot of slop, 0.85 would be more aggressive and if things didn't work out right your swift might be to small.
I'm working on designing version #2 so wanted to at least improve the current design a little
. After having used it for a while LOMLs big complaint about the current version is that they are somewhat overly large and she isn't the tallest person ever so getting the yarn over the top and onto the swift somewhat challenging. The gal at the yarn store I have beta testing another one has the same complaint (being of a similar altitude). So I decided to sit down and figure out about how big they should be or at least could be and still work for most hanks of yarn. The problem is that the angle math on calculating the actual sizes plumb bamboozled me so I decided to take the more direct approach of measuring the current setup and dividing the measured usable circumference from the theoretical circumference if the arms spanned a complete circle of the current setup to get a "correction factor". This saves me from having to do a full mockup and gives some guidance one design parameters that a mockup wouldn't.So without further ado here it is showing all my work like they taught in grade school.
Current Swift Specs:
Arm length (end connection point- end connection point): 17.5"
Diameter of center pivots to connection point on arms: 1.5"
Max "wingspan" if the arms could go out to full extension: (17.5*2 + 1.5): 36.5"
Theoretical circumference: (37.5 * pi): 114.7"
Actual measured usable circumference where the yarn sits: 89"
Correction factor between actual and theoretical circumference: (89 / 117.5) : 0.78
The correction factor is because you can't go to full extension with the wings (some designs go closer than others, mine has a bit of tension) and also the actual contact points are slightly in from the actual circumference. It would be slightly different depending on how flexible your connection points are and how many arms you have.
Max measured circumference of a hank of yarn: 60" (I did a sampling of a dozen or so in LOMLs workroom, the larger ones were all pretty close to the same - 28 or 29" * 2 halves, some smaller hanks were closer to 36" in circumference.).
We obviously want some margin of error, so lets say we want to be able to handle pieces of yarn up to 66" around.
back out correction factor: 66 / 0.78: 84.6"
calculate theoretical diameter: 84.6 / pi: 27"
Subtract the center pivot size: 27 - 1.5": 25.5"
Calculate desired arm length: 25.5/2: 12.75"
So I'm going to say arms of 13-14" in finished length would generally be fairly safe to actually work for 99.9% of all yarn unless you got some sort of HUGE hank. Even 12" arms would probably be generally ok, but I don't think I'd recommend going smaller than that.
The top of the current swift is 27" above the table. With 14" arms and tightening up some of the slack space in the current build I think I can get it to about 17" off of the table or a cool 10" shorter.
Other notes:
With some twiddling I was able to get the current swift out to 93" instead of 89" measured usable circumference (the difference is largely due to how I attached the arms together which binds slightly at near full extension so 89" is current usable but a better design could get 93" or maybe a smidge more)
At that extension the circumference around the arms themselves (measured point-point) was 104
and the diameter of the arms was 34"
A true circle at that diameter would be 106.8".
So we lost only 2.8" to the straight lines between the arms (with 6 arms) vs circle math. The majority (another 11" lost) really is in the difference between the end of the arms and the valley the yarn rides in (visually this makes sense looking at the swift but its nice to have the math confirm
).So absolute best case correction factor would be around 0.87 to 0.9ish. I think something between 0.75 and 0.85 is definitely in the right ballpark for most designs though. 0.75 would be fairly conservative if you're arm connections had a lot of slop, 0.85 would be more aggressive and if things didn't work out right your swift might be to small.
