How much wire do I need?

Wire length estimation

The following tools estimate the length of wire needed to form common shapes for components. The accuracy of the estimates were tuned through experimentation. You may develop your own estimates and experiments. First estimate the length of wire needed to perform one or more steps you tend to perform often with different gauges or wire. Cut more wire than you need to an exact initial length. After performing the series of steps from one end, subtract the remaining unused length from the initial length and compare it to your estimate. If it is a simple series of steps you will want to perform over and over with different tool sizes and wire thicknesses, make a table to record your estimates and actual results. You can remove error trends by including tuning variables like padding and spacing.

Estimate wire length needed to form eyes

Eyes refer to small loops used to connect components together. Forming eyes is one of the most common steps in any design. Use the wire length estimator to the right to estimate how much wire you need to form an eye given wire thickness t (derived from wire gauge) and tool diameter d.

Circle Estimate = (d+t)𝝅

Teardrop Estimate = (d+t)(3/4𝝅+1)

Combined Estimate (50-50) = 3.25(d+t)

The combined estimate is a weighted sum of circular and teardrop shaped eyes. Eye Forming Experiment shows how a 50-50 combined estimate was found to work well.

Estimate wire length for loops

Use the wire length estimator to the right to estimate how much wire you need to form a loop. This is a simple circular estimate of one revolution around tool with diameter d, accounting for wire thickness t as including some padding p to remove error.

Loop Estimate = (d+t+p)𝝅

For larger loops or thinner wire, the wire tends to spring back and uncoil slightly which introduces error. Large Loop Spring Back Experiment shows how Padding p = 0.1 mm was found to be sufficient for tight closed loops or smaller (>= 10 mm diameter) open loops. For open loops larger than 10 mm, increase the padding to 0.6-0.8 mm and don't use wire thinner than 20ga.

Estimate wire length for coils

A coil is made of multiple revolutions of wire around a stem. If the coiling wire is wrapped tight around the stem, the estimate is n number of revolutions multiplied by the single loop estimate assuming coiling wire thickness t, stem diameter d, and some padding p.

Coil Estimate = n(d+t+p)𝝅

The stem is often another wire, so the estimator gives the option of specifying the gauge of the stem which is then converted to mm.

It also helps to know how long the coil will be after completing n rotations. Assuming that even a tight coil is going to have some space s in between coils, the estimator determines the coil length as l = n(t+s)

Sometimes you don't care how many rotations make up a coil as long as it covers some length of the stem. The estimator can determine the number of rotations needed to cover length l as n = l / (t + s).

Wire Coiling Experiment shows how Padding p = 0.1 mm and Spacing s = 0.05 mm works well.

Combining Estimates

S-links

S-links are made up of two eyes with no stem in between. In order for the ends to line up in a balanced figure-8, you also need to subtract the wire thickness t as illustrated to the right. Also pictured are sets of L6-1 and L6-2 s-links formed from a range of 20 ga wire lengths in 1 mm increments. L6-1 s-link length estimates are 2(eye) = 21.68 mm and 2(eye)-t = 20.87 mm. This suggests that 21 mm will results in the most balanced L6-1 s-link, and indeed it does. L6-2 s-link length estimates are 2(eye) = 26.3 mm and 2(eye)-t = 25.49 mm. This suggests that 25.5 mm would result in a perfectly balanced L6-2 s-link. Indeed, lengths of 25 and 26 mm produced the most balanced looking L6-2 s-links, and 25.5 mm would probably look even more balanced. This validates the 2(eye)-t estimation approach.

Wrapped Eye

Wrapped eyes start with the bend some length from the end. This length will need to take one tight loop around a small diameter tool and then coil a few rotations around a stem of same gauge. For example, let us assume we want a 20 ga wire L6-1 eye with 2 wraps. Because the coil starts on the front of the eye, if you want the end of the coil hidden in the back, 2 wraps is really more like 1.6 wraps. The 2.5 mm loop will take 10.72 mm wire according to the loop estimator plus 8.12 mm wire according to the coil estimator. So that first bend should be 18.84 mm from the end, but let's round up to 19 mm. If you want to account for an exact stem length between 2 wrapped eyes, remember to add the length of stem used by the wraps. For example, if we want to accommodate 6 mm of beads between 2 wrapped eyes in the earlier examples, we will need 21.55 mm for each eye plus 1.72 mm of stem covered by the wraps for each eye plus the 6 mm for the beads, totaling to 2(21.55+1.72)+6.00 = 52.54 mm. When making this component for the first time, round up the the wire length to 60 mm. Subtract the amount you end up trimming from 60 mm and use that new exact length to make any more of the same component.

Wrapped Frame

A wrapped frame is similar to the wrapped eye except the wire wraps around a larger mandrels before coiling around the stem. For a simple wrapped frame without beads on the stem, I usually place a centered eye at the other end. Let us assume we want a 20 ga wire LL-1 frame with 2 wraps and L6-1 centered eye at the other end. The 13.5 mm LL-1 loop will take 45.28 mm wire according to the loop estimator plus 10.83 mm wire according to the coil estimator. So the placing that first bend 56.11 mm from the end is perfect. The other side of the bend should include enough stem for the coil to wrap around (1.72 mm) and another 10.76 mm for the 2.5 mm eye totaling to 12.48 mm. Let's round it to 56.5 mm one one side of the frames side of the initial bend and 12.5 mm on the eye side totaling to 69 mm.

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