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# Spider Coil Calculations

Spider Coils    Welcome to my spider coils page. As you might have noticed, this is my favorite coil. They are easy to make, adjust and to use. I have always preferred them to cylinder wound coils. Below I have the formulas for calculating your own coils, as well as some examples.

A cousin to these coils are the spider contra wound coils. They are somewhat difficult to understand at first, but they are a technological breakthrough. But for the meantime, please read on here. Spider Coil Calculations

To calculate your own coils, here is some information and a few tips.

The main formula is L=(r*n)^2 / (8r + 11b), with L = inductance, r = mean radius, n = number of turns and b = coil depth. The means the inductance is equal to the mean radius times the number of turns squared divided by 8 times the mean radius plus 11 times the coil depth.

On the face, this is a little hard to work with if you are making a coil. If you have a coil and want to find out the inductance, this formula is fine as all you need is a ruler and to count the turns.

For us radio builders, the best place to start is to input the number of turns, the inside diameter of the spider coil and wire diameter. There is a glitch that was found concerning litz wire diameters which I will discuss later.

A spreadsheet or a programmable calculator is very handy for calculating the coil. I used the Lotus 123 program to make my spreadsheet. Below are the values and relative cell values. All this is based on the original formula that is shown above. I am much better at winding coils than I am the math, so please check this out.

cell name formula ____ ____ _______ C4 Wire diameter Input this value C5 Number Turns Input this value C6 Inside Diameter Input this values C7 Coil Depth (C4*C5) C8 Mean Radius (C7+(C6*0.5)+(C6*0.5))/2 C9 Outside Diameter (C7*2)+C6 C10 Inductance (((C8*C5)^2)/((8*C8)+(11*C7))) [The main formula] C11 Wire Length (C5*C8*2*3.14)/12 [Add a little more wire for connections] Length measurements are in inches, inductance in µH.

When winding spider coils with thin wire strand gauge size such as the 660/46, there was a difference found between the calculated coil depth (wire diameter times number of turns) and what the coil actually turned out to be. This drove a couple of us nuts until it was discovered that when a spider coil with litz is wound, the windings are compressed at the crossing points.

It was found that the diameter worked out to 15 to 18 percent less than the manufacturers data. This is not a problem in cylinder coils, only the spider coils. So instead of using 0.055 inches as a diameter, 0.048 was used.

Reducing the value of the wire diameter by 15% will give you a closer value of the outside diameter of the coil and a closer tolerance on the coil. Plugging in the two values (.055 vs .048) only makes about a 1.5% difference in the coil inductance. The wire length and outside diameter change quite a bit using the different diameters. Make the spreadsheet and plug in the numbers and check it out for yourself.

In the few instances that I have wound the coils using the spreadsheet and comparing the results with the L/C meter, I found that the calculated value ends up very close with the real world value.

At this time I am keeping this page open. I invite comments and especially corrections to any data in this section.

Feedback E-Mail

Dave, I found your webpage while searching for a formula for determing the number of turns for a given inductance of a spider web coil. The formula on your page is fine but isn't too practical if you want to build a coil to a specific inductance. Well, I used your formula to derive a formula for determing the number of turns required. After some math manipulations I was able to get what I wanted. The formula was checked for accuracy throughout the range of 1uH to 2000uH. The results agreed with the original formula. At first glance, the formula looks overwhelming since it is a quartic equation ( a 4th degree polynomial), but with the "Quartic Equation Solver" available for use at www.akiti.ca/Quad4Deg.html, it is a piece of cake to solve.

The formula for determining the number of turns required for a given inductance of a spider web coil is: w^2x^4 + 4rwx^3 + 4r^2x^2 - 60Lwx - 32Lr = 0

Where x = number of turns to be determined w = diameter of wire (inches) r = inner radius of coi (inches) L = desired inductance of coil (uH)

Enter the values for w, r, and L in the above formula; do the indicated multiplications and the formula will then appear as: Ax^4 + Bx^3 + Cx^2 - Dx - E = 0

A, B, C, D, E represent the results of the multiplications. Now take these values (don't forget that D and E are negative) and plug them into the similarly labeled boxes in the quartic equation solver. Press the "calculate solutions" button and it will spew out the results. Since this is a quartic equation, there will be 4 answers displayed. The correct answer will be obvious since it is a positive number, the other 3 will be either negative or complex.  