Step 1: Governing Principles of Coil Gun Projectile Design
Through other peoples and my own research I have found that the projectile needs to be at least half the length of the coil and that longer projectiles leaning towards the length of but no longer than the coil perform best. This is because the projectile is only accelerated to the centre of the coil, if the projectile is less than half the length of the coil then when it is at the breach of the coil it has less distance to travel to reach the centre of the coil. If the projectile is longer than the length of the coil then some of the projectile is not being attracted into the coil usefully. This means that all the mass outside the coil when the projectile is centred in the coil is effectively dead weight.
The projectile diameter should be balanced with the strength of the magnetic field being produced. That is to say that if the capacitor bank is of a fixed size then the projectile should be paired with a coil that only just fully saturates all the magnetic material of the projectile.
If the projectile is too big then it will not fully saturate and so the extra mass in the projectile that is not magnetised is effectively dead weight. If the projectile is too small then it saturates too quickly and magnetic flux is not fully utilised to accelerate the projectile.
Projectile Length to diameter ratio
The projectile should follow good dimensions for ballistics. This means that the length of the projectile should be at least three times its diameter to reduce tumbling and no more than five times the length which is the upper limit for spin stabilised projectiles. Spin stabilisation is preferred because it stabilises the projectile without adding drag which lowers the projectile velocity and so kinetic energy.
The projectile must be made out of a Ferro-magnetic material. Aluminium does not work because it is designed to work as a reluctance launcher and not through induction. If the projectile is placed just of the centre of the coil then it should be inductively repelled out of the device but that would require longer pulse lengths and a conductive projectile so that a current can be induced in the projectile by the electromagnet and the projectile repelled. This introduces inductive losses that the reluctance set up does not have.
Soft iron is the best standard material as it gains and losses its magnetism easily and it is easy to shape as desired. Steel is a poor choice, the higher the grade of steel the worse the properties as it retains its magnetism after repeated shots and has a poor hysteresis reaction, also stainless steel is much less magnetic than iron if at all.
The optimal material for the projectile would be non-conductive, strongly ferromagnetic and have low hysteresis i.e. be able to gain and lose its magnetism very rapidly. Ceramic magnet composites are good but hard to work with as they are very brittle and still somewhat conductive typically in the range of 106 ohm.cm. (4) A good compromise is powdered iron matrix which can be easily manufactured using epoxy resin as a matrix but this offers a lower ferrous material density than a solid soft iron projectile.
The reduction of Eddie currents in the whole device improves performance as less energy is spent in resistive heating. Powdered Iron Matrix is one of the best options but has a lower magnetisable material concentration than the solid iron equivalent which negatively effects coil gun performance. Ceramic magnets or ferrites are a good solution as they are very resistive and hence reduce the Eddie current losses. The enclosure should also be conductive.
A more aerodynamic projectile will have a lower drag coefficient and hence slow down less over the distance it travels through the air but from a stabilisation point of view it needs to be spun and or have drag on the tail to stop it tumbling. Both of these options slow the projectiles velocity but increase the accuracy of the speed measurement via VUSAT as a point of impact can be identified rather than the potential for a side on impact which leaves an ambiguous impact location.
A flat ended solid cylinder is optimal for magnetic flux linkage. Any shape other than this leaves air gaps that reduce performance. The solution to this is to use magnetically inert tips such as Perspex, plastic or glass. Clear materials are preferred as they allow for optical triggering.
If a compromise must be made the ball ended is best or the projectile should be slightly lengthened if the tip is particularly pointed to maintain the same volume of magnetisable material in the projectile and the same mass. It would be interesting to see how longer, pointier projectiles perform where their mass is balanced by removing material from the tail by drilling it out. This may also help with stabilisation as the tail would be lighter than the nose.
The projectile position on the breach of the coil prior to firing can have a colossal effect on its exit velocity; this is down to pulse length and projectile acceleration/inertia. If the projectile is too far out of the breach then it will not be attracted into the coil fast enough so the current pulse is over before the projectile reaches the midpoint of the coil. If the projectile is too far into the breach of the coil then it will reach the centre of the coil before the current pulse is over and experience suck back and in some extreme cases fire out of the wrong end as the coil gun acts as an inductance launcher instead of a reluctance launcher.
Lower Mass projectiles will travel faster as KE=1/2mV^2. Unfortunately the material must be a ferrous/ferromagnetic one and so the weight is fairly set per unit volume. The mass is needed as it is the magnetisable mass that the coil gun uses to attract the projectile into the coil. If the projectile is too small the iron will ”saturate” meaning it is entirely magnetised and if a larger core was used more material could potentially be magnetised. Optimally, the coil gun should not saturate the projectile but come infinitely close to doing so.
Projectile Flux linkage
The projectile external diameter needs to be as close to the internal diameter of the coil as possible to reduce the air gap and maximise flux linkage. This means that he coil form tube needs to be as thin as possible and the projectile as snug a fit as can be achieved.
The projectile will tumble if left un-stabilised, this is undesirable as it increases drag on the projectile and reduces accuracy which means it will not land where you want it to and when it will take longer to do so delivering less force on impact. It also means that the force of impact could be spread down the length of the projectile shaft rather than concentrated at the tip. This can make calculation via horizontal VUSAT difficult due to ambiguous impact points.
The easiest way to stabilise it would be to use drag on the back of the projectile. This is usually done using flights or fins but they are hard to use when the projectile needs to be as snug a fit as possible in the barrel. Therefore the drag stabilisation must occur after the tail of the projectile, some wool or other flexible material would work and the stabilisers would look something like short streamers.
The best way of stabilisation is gyroscopically by adding a spin to the projectile, this possess a couple of small design problems to overcome in the coil gun design. Rifling would be a good solution but the wall thickness needs to be minimised to minimise the air gap and maximise flux linkage. Thin walls makes rifling hard and additionally in conventional weapons rifling cuts grooves into the projectile as it is forced out of the barrel, this is not a problem in a gun that works of compressed gasses such as gun powder but in a coil gun it would significantly slow the projectile down. The other method of rifling is to use a hexagonal barrel and twist it down its length by a finite degree but this introduces large air gaps which are undesirable.
A suitable solution would be to grab the projectile from the back and spin it with an electric motor prior to firing. This would work but the grabbing mechanism would need to be carefully timed to let go at the right time, this could be achieved by putting a small cone in the back of the projectile and putting an electromagnet in the reciprocating cone which is attached to the motor drive. This would require commutation to work though as the electromagnet would be rotating and the cone in the tail of the projectile is not optimal as it removes material.
It is possible to spin the projectile by making a multiple stage coil gun and winding the coils elliptically so each stage is slightly twisted from the last. This is hard to achieve though and is a suboptimal coil shape for magnetic flux density.
The projectile could theoretically be rotated inductively using an AC motor stator around the breach of the coil gun. This is probably the best solution but will most likely require complex modification of the projectile and introduce inductive losses if the projectile would otherwise be constructed from a non-conductive magnetic material such as a powdered Iron matrix.
The best solution for this experiment is to use a plastic tip to reduce front end drag and discourage tumbling, a plastic tail may be added at a future date to experiment with how aerodynamic spin stabilisation increases drag and if it is worth the loss in velocity.