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posted 1y ago by Olin Lathrop‭  ·  edited 1y ago by Olin Lathrop‭

#3: Post edited by Olin Lathrop‭ · 2022-10-07T12:40:13Z (over 1 year ago)
• The relative volumes of cylinders with the same height are proportional to the square of their diameter. Hopefully you can see this is true without further explanation.
• The relative volume of wire on a full spool is therefore
• &nbsp; &nbsp; D<sup>2</sup> - D<sub>empty</sub><sup>2</sup>
• Now take the ratio of the current to the full wire volume using the above formula:
• &nbsp; &nbsp; Fullness = (D<sub>curr</sub><sup>2</sup> - D<sub>empty</sub><sup>2</sup>) / (D<sub>full</sub><sup>2</sup> - D<sub>empty</sub><sup>2</sup>)
• Note that D<sub>full</sub> and D<sub>empty</sub> are constants for your purposes. To get remaining length of wire from the fullness fraction only requires another constant. During use, you therefore only need to perform the calculation:
• &nbsp; &nbsp; WireLength = (D - K<sub>1</sub>)K<sub>2<sub>
• You can write K<sub>1</sub> and K<sub>2</sub> on each spool when you receive it full.
• The relative volumes of cylinders with the same height are proportional to the square of their diameter. Hopefully you can see this is true without further explanation.
• The relative volume of wire on a full spool is therefore
• &nbsp; &nbsp; D<sup>2</sup> - D<sub>empty</sub><sup>2</sup>
• Now take the ratio of the current to the full wire volume using the above formula:
• &nbsp; &nbsp; Fullness = (D<sub>curr</sub><sup>2</sup> - D<sub>empty</sub><sup>2</sup>) / (D<sub>full</sub><sup>2</sup> - D<sub>empty</sub><sup>2</sup>)
• Note that D<sub>full</sub> and D<sub>empty</sub> are constants for your purposes. To get remaining length of wire from the fullness fraction only requires another constant. During use, you therefore only need to perform the calculation:
• &nbsp; &nbsp; WireLength = (D<sup>2</sup> - K<sub>1</sub>)K<sub>2<sub>
• You can write K<sub>1</sub> and K<sub>2</sub> on each spool when you receive it full.
#2: Post edited by Olin Lathrop‭ · 2022-10-07T12:35:08Z (over 1 year ago)
• The relative volumes of cylinders with the same height are proportional to the square of their diameter. Hopefully you can see this is true without further explanation.
• The relative volume of wire on a full spool is therefore
• &nbsp; &nbsp; D<sup>2</sup> - D<sub>empty</sub><sup>2</sup>
• Now take the ratio of the current to the full wire volume using the above formula:
• &nbsp; &nbsp; Fullness = (D<sub>curr</sub><sup>2</sup> - D<sub>empty</sub><sup>2</sup>) / (D<sub>full</sub><sup>2</sup> - D<sub>empty</sub><sup>2</sup>)
• The relative volumes of cylinders with the same height are proportional to the square of their diameter. Hopefully you can see this is true without further explanation.
• The relative volume of wire on a full spool is therefore
• &nbsp; &nbsp; D<sup>2</sup> - D<sub>empty</sub><sup>2</sup>
• Now take the ratio of the current to the full wire volume using the above formula:
• &nbsp; &nbsp; Fullness = (D<sub>curr</sub><sup>2</sup> - D<sub>empty</sub><sup>2</sup>) / (D<sub>full</sub><sup>2</sup> - D<sub>empty</sub><sup>2</sup>)
• Note that D<sub>full</sub> and D<sub>empty</sub> are constants for your purposes. To get remaining length of wire from the fullness fraction only requires another constant. During use, you therefore only need to perform the calculation:
• &nbsp; &nbsp; WireLength = (D - K<sub>1</sub>)K<sub>2<sub>
• You can write K<sub>1</sub> and K<sub>2</sub> on each spool when you receive it full.
#1: Initial revision by Olin Lathrop‭ · 2022-10-07T12:28:21Z (over 1 year ago)
The relative volumes of cylinders with the same height are proportional to the square of their diameter.  Hopefully you can see this is true without further explanation.

The relative volume of wire on a full spool is therefore

&nbsp; &nbsp; D<sup>2</sup> - D<sub>empty</sub><sup>2</sup>

Now take the ratio of the current to the full wire volume using the above formula:

&nbsp; &nbsp; Fullness = (D<sub>curr</sub><sup>2</sup> - D<sub>empty</sub><sup>2</sup>) / (D<sub>full</sub><sup>2</sup> - D<sub>empty</sub><sup>2</sup>)