Convex Rails With the NGL-60 Prototype Railgun

At the French-German Research Institute of Saint-Louis (ISL), railguns are investigated with respect to military scenarios. Currently, different railguns installed at ISL use rails with a flat contact surface. For lateral guidance of the armarture, the barrel is equipped with guiding bars made of reinforced plastic mounted on the sides of the rails. This solution is prone to damage of the guiding bars. In this investigation, rails with a convex-shaped contact surface are installed and used in a 2-m-long railgun. It is experimentally shown that using these modified rails, the guiding bars can be eliminated from the barrel setup, thus simplifying the barrel. Furthermore, in a comparison to launches with flat rails, the convex rail implementation is more efficient, resulting in a higher armature velocity at the same primary energy. Additional improvement was obtained by an armature modification.


I. INTRODUCTION
R AILGUNS are electrical accelerators that allow large muzzle velocities and energies.At ISL, the largest capacitor bank has a nominal 10-MJ energy content and can deliver gigawatt power levels.Using this power supply and a 6-m launcher of 40-mm caliber, c-shaped aluminum armatures were launched to velocities above 3000 m/s [1].At that time, further improvements with respect to the launch efficiency were made in experiments with hybrid armatures.By basically eliminating the rail/armature losses, overall launch efficiencies (E kin /E capacitor ) of above 30% were demonstrated.After this, the next logical step toward the military application was to develop a launch package.This 1.3-kg heavy launch package including a simple kinetic energy projectile was accelerated at 4.2-MJ initial electrical energy to 1230 m/s [2].Currently, the railguns at ISL use rails which have a flat armature-rail contact surface.To prevent the armature or the launch package from lateral movement during its acceleration, guiding bars are mounted on both sides of at least one rail.These bars are usually made out of fiber-reinforced plastic.They show a tendency for damage after a couple of shots-a behavior being more severe at high velocity.The intention of this investigation concerning the rail surface modification is to guide the armature by the rail surface geometry and thus eliminate the need for the guiding bars.In this article, we describe experiments performed with a 2-m-long, 60-mm square caliber railgun.A series of launches with increasing energy were performed using rails with a flat and with a convex contact surface.It was found that the convex rail shots do perform better in terms of end-velocity at the same initial energy.Furthermore, the c-shaped armature for the convex rails was modified by introducing a slit into the rear part of the armature legs and the performance was compared with the normal, not-modified armatures.

II. NGL-60 PROTOTYPE
The experiments in this investigation were performed using the NGL-60 prototype railgun [3].This railgun is a 2-m-long, 60-mm square caliber, open barrel setup.It is connected to 48 capacitor modules, corresponding to 2.4 MJ of primary energy at full charge.At a maximum current of just above 2 MA, aluminum c-shaped armatures with a mass of 770 g are accelerated to 1130 m/s [3].In Fig. 1, the different components are shown.The rails are mounted on a plastic body, separating these from the steel support on the top and bottom of the barrel.Distance tubes with steel bolts inside mechanically connect the steel supports and define the caliber.The current injection allows to connect the coaxial cables from the power supply unit to the rails.Mounted on the side walls of the rails are the guiding bars made of fiber-reinforced plastic.In the figure, the rails have a flat contact surface, and therefore the guiding bars are required to prevent the horizontal balloting of the armature or launch package during acceleration.These bars are prone to damage, especially when performing highenergy shots.Fig. 2 shows such damage (dashed circle) as it typically appears after several shots.For further operation, the barrel needs to be opened to access the rails and exchange the guiding bars.This is a tolerable situation in a laboratory environment, but not acceptable in a fieldable railgun.One possibility to improve on this situation is by integrating the armature guiding function into the rails and thus eliminate the need for guiding bars.By changing the rail contact surface to concave or convex shape, the rails should be able to ensure the guiding functionality and thus allow to simplify barrel construction.

III. RAIL SURFACE MODIFICATION
A change in the contact surface of the rail not only influences the mechanical behavior of the armature/rail contact but also alters the current density distribution.To get a qualitative, visual impression of this change, a COMSOL [4] simulation was programmed and executed.When an armature progresses through the barrel, the current in the rail in front of the armature is ramped up during a time that typically corresponds to the passage time of the length of the contact elements of the armature.In a square caliber railgun, a characteristic length is 0093-3813 © 2024 IEEE.Personal use is permitted, but republication/redistribution requires IEEE permission.
Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.the caliber and a typical time scale can be calculated by dividing the caliber by the velocity.In a simplified simulation, this typical time scale can be used to determine a corresponding ac frequency.For the NGL-60 and velocities of 500 m/s a frequency of 8 kHz is calculated.At this frequency, current concentration in the rails is strongly pronounced, and for a better visualization, a frequency of only 100 Hz was used.For the flat rails, the result of the simulation is shown in Fig. 3.The uneven current distribution is evident, the main body in the center of the rail caries only very little current, while the outer corners are subjected to a much higher current density.For elevated current amplitudes, such a distribution will cause local heating and in turn erosion.When using an appropriate shaped convex curved surface for the rails, the current distribution becomes more evenly distributed over the contact area of the rails, as shown in Fig. 4. Basically, the whole inner rail surface contact area has a current density close to the maximum.Comparing both the figures, the beneficial difference in electrical property for the convex rail surface modification becomes obvious.A concave surface modification leads to an even stronger current density concentration in the exposed outer corners when compared with the flat rails.Therefore, such a modification is discarded without further investigation.Following the publication [5], an elliptical surface shape was chosen by scaling the parameters from that paper to the rail size of the NGL-60 prototype.Optimally, the surface shape of the rails should closely follow the magnetic field lines next to the rail surface, but in practice such a fine-tuned optimization by simulation is not required.When doing the simulation using ac current, the situation in the experiment is  anyway different-the simulation does not include the effects of armature motion, such as the velocity skin effect or local contact losses and plasma development.From a practical point of view, the convex rails for the experiments with the NGL-60 prototype were produced using the flat rail geometry as a basis.From these flat rails, material was removed to form the convex, elliptical-shaped surface.The mounted, convex rails therefore have the flat rail caliber along the center line, and a slightly larger and increasing rail-to-rail distance from the center to the rail edges.

IV. EXPERIMENTS WITH CONVEX RAILS
The convex rail surface requires an adoption of the armature to this geometry.In Fig. 5, the corresponding armature with bore rider is shown.Clearly visible is the milled groove along the axis of movement in the contact surface of the armature arms.The black bore rider is 3D-printed using reinforced plastic material.The total mass of this setup is 737 g.Table I summarizes the key parameters of the performed launches.The first shot used a stored energy of 0.8 MJ, and for the subsequent shots, this energy was increased up to 2.2 MJ.The armature velocity increased from 495 to 995 m/s.For the last shot at 10 kV, at least one capacitor module did not perform correctly, and therefore not the full primary energy was used for the acceleration of the armature and the measured velocity was below the velocity expected from previous shots, as, for example, presented in [3].Fig. 6 presents the results of the shot at 8-kV charging voltage.The peak current reaches 1.6 MA.The velocity is measured by b-dots (shown as gray dots) and reaches 770 m/s.The continuously drawn gray line is the velocity evaluated from the action integral.The muzzle voltage indicates excellent contact behavior during the full   launch.For the five shots, the maximum current amplitude ranged from 1.2 to 1.925 MA.For all of them, the electrical contact was excellent and the armature showed no signs of wear on the X-rays taken directly after muzzle exit.

V. COMPARING FLAT AND CONVEX RAIL PERFORMANCE
During the experiments with the NGL-60 prototype, several launches with flat rail surfaces were performed.Some of these were made with armatures of a slightly different mass or a different cabling to the capacitor banks.Nevertheless, the performance of the different launches can be compared using the well-known railgun force law Integrating the formula (1) leads to where I 2 dt is the so-called action integral.When plotting the mass-scaled velocity [the left-hand side of formula (2)] versus

TABLE II PARAMETERS FOR SLITTED ARMATURE SHOTS
the action integral, a linear regression can be used to access the effective inductance gradient (L ′ eff ) as the slope of this regression.Using the action integral instead of the charging voltage of the capacitors eliminates also the uncertainty in this parameter.The charging of the capacitors is done manually and the end-voltage cannot be read very accurately.Another uncertainty is the different time in between charging and triggering of the launch-a variation in this time will lead to different discharges of the waiting capacitor banks.The results of a comparison of the five shots with convex rails and ten shots with flat rails are shown in Fig. 7.The linear regression is a good fit for each group of the launches and results in a value of L ′ eff = 0.393 µH/m for flat rails and L ′ eff = 0.439 µH/m for the convex rails.By equipping the NGL-60 prototype with convex rails, the inductance gradient increased by close to 12%.Qualitatively, this increase in the inductance gradient can be understood by the larger rail-to-rail distance (on average over the surface), as explained in Section III.In a railgun, an increase in caliber results in an increase in the inductance gradient.As the experiments showed, the new configuration of the NGL-60 prototype with convex rails is not only able to mechanically guide the armature through the barrel and thus eliminate the need for guiding bars but also does this more efficient in terms of acceleration by 12%.

VI. ARMATURE OPTIMIZATION
During the launch process, strong electromagnetic forces act on the armature and its trailing arms.As a result, above a certain value of the current, the current carrying arms are strongly pressed against the rail surface.This ensures a good electrical contact, but will also induce a certain amount of Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.friction reducing the propelling force. 1 The shape of the convex rail and armature contact surface ensures guidance, but there will be, at least slightly, armature motion perpendicular to the direction of acceleration.This horizontal movement leads to a degraded fit of the contact zone and increases the mechanical friction.As a result of this, small gaps in the contact zone will appear, which in turn will lead to local plasma contact.It is likely that more flexible armature arms could help in mitigating these adverse effects.To test this hypothesis, the armature was modified by introducing a central slit in both the trailing arms.This modification is shown in Fig. 8.A series of launches with increasing primary energy were performed with slitted armatures.The results are tabulated in Table II.At 8 kV, a shot was repeated, to investigate the reproducability of the results.Fig. 9 shows comparison of the results of these experiments to the launches with the normal, unmodified convex rail armature.From the fit values of L ′ eff = 0.448 µH/m and L ′ eff = 0.439 µH/m, it can be calculated that the effective inductance gradient is by 2.1% larger for the slitted armature.

VII. SUMMARY AND CONCLUSION
The railguns at ISL are usually of the open barrel type.When using rails with a flat contact surface, a guiding structure is required.Up-to-now guiding bars made out of glass-fiberreinforced plastic are mounted on both sides of at least one rail.During launches, especially at higher energy, these bars are often damaged.Using rails with a convex contact surface and correspondingly adopted armatures, it was shown experimentally that this surface modification allows to securely guide armatures through the 2-m-long barrel of the NGL-60 prototype railgun.When comparing the acceleration forces in between a barrel being equipped with flat rails versus rails with a convex surface, the convex rails performed by 12% more efficient.In a further modification, a slit was introduced in the trailing arms of the armature.This modification made the armature more compliant and allowed a further improvement of 2.1% when compared with the "normal" convex rail armature.In the near future, the experiences gained with the NGL-60 prototype setup will be transferred to the full 6-m-long NGL-60 railgun and experiments with convex rails will be performed.

Fig. 7 .
Fig. 7. Mass-scaled velocity versus action integral for experiments with flat and convex rails.
Manuscript received 11 April 2023; accepted 30 November 2023.Date of publication 23 January 2024; date of current version 1 February 2024.This work was supported by the French and German Ministries of Defense.The review of this article was arranged by Senior Editor F. Hegeler.

TABLE I PARAMETERS
FOR CONVEX RAIL SHOTS