  # Number of Coils

What if you use a large number of coils?

For example, there is US patent 5,763,812 for a coilgun that uses 36 coils. Will it be, say, about twelve times better than only three coils?

Obviously, more coils means more speed. But is it worth it? That really depends on the incremental cost of adding coils.

That patent designer really put a lot of work into it. But it seems to me that it's un-economic to use that many. The basic equations of motion under linear acceleration dictate that doubling the number of coils will only improve speed by the square root of two (1.414). This is because the projectile spends progressively less time in each coil as it progresses. To be precise, the exit velocity v = sqrt(2*a*d) where 'a' is the acceleration and 'd' is the distance under acceleration.

Let's use this equation to find the increase in speed for any increase in length (ie, number of coils). We really need to find the ratio of two different velocities, v1 and v2, at two different distances, d1 and d2, of constant acceleration.  Suppose d2 is some multiple 'k' of d1, such that d2 = k*d1. If you solve the equations to find the ratio of v2 and v1, then you get v2/v1 = sqrt(k).

In our example, using 36 instead of 3 coils will yield sqrt(12) improvement, which is only 3.46 times the exit speed of three coils.

Have a look at my spreadsheet for a graph of exit speed compared to length.

## Other Consequences of More Coils

Note there are practical problems of precision of control with a greater number of coils and especially with higher speeds. It will need a rigid frame, and an accurate calibration procedure to set up all the detectors.

My design used very few coils, because it takes a lot of time to wind coils by hand. And it takes a lot more time to build the logic circuits by hand on a breadboard. Not to mention, I ran out of breadboard space. Also, I wanted to see how well it worked before investing a lot of effort.

If it were quick and simple to add coils, I would probably have more than three. But this machine is still quite experimental. Perhaps someone will offer PC board layouts to easily add more stages of coil timers. And perhaps we'll find a way to purchase pre-fabricated coils. Any volunteers?

The patent also describes a design to detect position by (basically) measuring the inductance of the coil to see when the projectile enters it. See my page on inductance and closed-loop control for more information.

## Reducing Number of Power Drivers

I noticed the patent's design saved money by using high- and low-side power output stages. There is a power output driver on both sides of every coil; they don't just gang together to a common ground (like mine). The 36 coils are wired in a grid of six-by-six. By selecting 1-of-6 high drivers along with 1-of-6 low drivers, just one coil is activated. This reduces the need for power output stages from 36 down to only 12. Good idea.

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