Open Loop Pulse Triggering
Results
Coil Comparison
In
this section we'll look at how the coils compare in various ways. The first thing
we can consider is how the coils perform compared to simulated results. Fig 1
shows the forceposition curves for the four coils using a solid projectile. 4th
order polynomial trend lines are fitted to the data points. The equations can
be integrated to determine the energy transferred to the projectile, these can
then be used to calculate the speeds. Alternatively the data points can be imported
into Matlab and numerically integrated.
Fig
1. Force  Position curves for solid projectile
It's
important to choose the correct material when running a simulation, the results
can vary significantly even with similarly sounding materials. I ran these simulations
with 1006 steel which is a low carbon steel and should (I hope) be similar to
the mild steel I'm using in its magnetic properties. Table 1 below shows the measured
and simulated data.
Coil 
A Sim

A Real

B Sim

B Real

C Sim

C Real

D Sim

D Real

Kinetic Energy (mJ) 
587

298

859

506

1206

704

1323

802

Projectile Speed (m/s) 
9.6

6.8

11.6

8.9

13.8

10.5

14.4

11.2

Table
1.
There
is clearly a large difference in the simulated and measured data, although they
agree better than I expected. Five possibilities come to mind as reasons for these
discrepancies:

The 1006 steel
material is a poor match for the actual projectile material.

The actual current
curve is dynamic whereas the simulation uses a constant current.

The projectile
drives some eddy currents in the accelerator tube and so gains less energy.

The projectile
is retarded by the commutating current and loses energy.
 Friction reduces
the energy transfer to the projectile.
These
are the most obvious factors but there are probably others. I would say that the
commutating current interaction is probably the most significant with accelerator
tube eddy currents coming second. The rising edge of the current pulse probably
isn't that influential because the projectile is going slowly to begin with so
the current reaches its maximum before the projectile moves very far.
In
the theory section I derived an equation
which can be used to determine the wire diameter which will give the maximum current
density for a given set of coil dimensions and circuit resistance. If we put the
typical test coil dimensions into this equation and specify an R_{E} of
0.08
we get a optimal wire diameter of 1.57mm. This is really close to the wire used
in coil D which also is the best performer in terms of muzzle speed. There isn't
much point in plotting the current density vs wire diameter without more data
points. I may make up additional coils with larger wire diameters to try and establish
the actual optimal diameter.
