Numerical Simulations of the Slingatron

Abstract

The slingatron mass accelerator is described for several track configurations (shapes), and numerical simulations of this accelerating mass traversing a given track configuration are presented. The sled is modeled as a point mass that interacts with the slingatron track using both a conventional and a new empirical velocity dependent friction law. The closed loop circular slingatron was found to produce high maximum sled velocities provided the gyration angular speed is always increasing. In contrast several spiral shaped slingatron tracks reveal that high maximum sled velocities are obtainable with the gyration speed held constant. In fact, a slingatron constructed out of semi-circles is shown capable of generating high velocity sleds in such a way that no initial sled injection is necessary. Choosing the proper initial gyration phase with an empirically determined friction model allows the mass sled to gain ever-increasing velocities when placed in a semi-circle slingatron. The sled bearing pressure and its total acceleration are examined and presented.

A Study of the Phase-Lock Phenomenon for a Circular Slingatron

“…This is because as the gyration speed 2ttR\f f+ f ) increases, so must the mass gain speed = 2;rasin(0) (see equation [5] for 0 = constant) per turn. However, we choose, y/ = y/ 0 + 2xft + 7rft 2 , which causes the gyration speed to become large at large times. Thus, we have shown that the only way the mass can stay phase locked with this increasing gyration speed is to assume smaller values of 0 so that it does not gain too much velocity per turn.…”

Slingatron: A High Velocity Rapid Fire Sling

“…A more complete list of approximate formulas for the case m = constant has been given earlier [5], and exact equations and computer models for the dynamics in references [2,6,7] with [6] including discussion of projectile mass loss. Finally note that the guide tube has a radius of curvature R that goes from Rin for the inner turn to Rut for the outermost turn.…”

“…The relationship of 7c-1 ln(Vin/Vout) to lt follows from equation 1 (with v = 0) but generalized to include a drag term due to bearing gas accumulated on the projectile nose, and also to allow for projectile mass loss. Converting the time derivative d/dt to Vd/dx, and integrating along the projectile path around the semi-circle then gives, 71-lln(Vin/Vou,) = g -(27t)-lln(min/mout) + 0.257itd 2 R<Pnse/(mV 2 )> , (6) where the subscripts in and out indicate the projectile velocity or mass either entering or leaving the semicircular tube section, d is the projectile diameter, R the radius of the semicircular tube, Pnose the reverse pressure from the dusty gas mass that accumulates on Vi, kmnlsec the projectile nose, and <> represents an average value of the argument integrated around the semicircle. The left side of equation 6 is the quantity plotted in Figure 7, and it is only equal to the friction coefficient in the limit that there is zero ablated mass from the projectile and also zero snowplowed dusty gas accumulated on the projectile nose.…”

“…A mechanical mass accelerator concept called a slingatron has been proposed by the author [1][2][3][4][5] and computer models developed by Tidman [2], Cooper et al [6], and Bundy et al [7] for the dynamics of both spiral and circular versions of this machine. Here we first summarize the dynamics.…”

Study of the Phase-Lock Phenomenon for a Circular Slingatron

“…This accelerator can propel either a constant mass or an ablating mass sled along a guide tube forming the slingatron track [2]; several slingatron configurations have been examined [1,2]. A simple friction model is also used in which the friction force is assumed to be proportional to the normal force exerted by the track [2] on the moving sled.…”