Ball velocity

Chapter 2.2, in m-ball due to the difference in linear rates of the polymeric chains links it is appeared the hydrod5mamic interaction which leads to the appearance of the additional to g local averaged upon w-ball velocity gradient of the hydrodynamic flow This local gradient gm acts not on the conformational volume of the /w-ball but on the monomeric framework of the pol5meric chains (the inflexible Kuhn s wire giodel [22]). That is why the endowment of gm into characteristic time ty depends on the volumetric part of the links into the conformational volume of w-ball, l e., C g + g fY -... 

This system has been modeled numerically and the results have been compared with the experimental data of Frey. The mesh was 0.05616 cm by 0.05 cm and the time step was 0.005 ps. The computational problem was 78 cells in height and 20 cells in width. Figure 5.29 shows the experimental data and the calculated results of a steel ball interaction with PBX-9404 or Composition B. The ball velocity loss is defined as the initial ball velocity less the penetration velocity. The agreement demonstrates that the model describes the important process of the explosive penetration. 

When the steel ball penetrates inert or nearly inert explosive, the penetration velocity could be described by the ideal model. When the ball velocity was just sufficient to cause propagating detonation, however, the observed and calculated penetration velocities were much less than predicted by the ideal model. 

As the ball velocity was increased, the difference between the actual and ideal velocities decreased. A summary of the ball penetration calculations is given in Table 5.2. 

As shown in Chapter 4, the Held experimental critical condition for propagating detonation of V d adequately describes the jet initiation of explosives. The steel ball must present an effective diameter to the explosive. The critical ball velocity for PBX-9404 shown in Figure 5.29 is 0.114 cm/ps. The V d (in mm) for PBX-9404 is 16.0 therefore, the ball has an effective diameter of 1.23 cm. This is, within the calibration error, not significantly different from the actual ball diameter of 1.30 cm. The critical ball velocity for Composition B shown in Figure 5.29 is 0.18 cm/ps. The V d (in mm) for Composition B is 29 therefore, the ball has an effective diameter of 0.9 cm. 

Figure 5.29 Initial ball velocity vs. the ball velocity loss for a 1.3 cm diameter ball penetrating PBX-9404 or Composition B.

Fig. 4 Breakthrough load for four titanium substrate-ion combinations. Pin, 5 mm (0.2 in.) mby ball velocity, 56.6 mm (2.23 in./ s).

In impact sports, often a performer consistently tries to minimize execution time in order to increase implement velocity to achieve maximum ball velocity and/or distance. In bowling, it is likely that expert bowlers vary their temporal and spatial parameters - in this instance especially their foot slide, to adjust their final body segments into correct positions prior to releasing the ball. These adjustments are necessary to attain maximum accuracy. 

What therefore has allowed this quantity of oil to enter die contact It might be speculated that the rig dynamics causes a rapid reduction in load at start of motion. This would reduce the contact area and cause lubricant to be drawn into the gap between the surfaces. Rapid re-imposition of the load would entrap this lubricant and could lead to films thicker than the steady state value. If the load fell to zero, the quantity of oil enclosed by the contacting bodies within the radius a would be equivalent to a uniform film of 0.47 pm over the Hertzian area. This mechanism (of transient load reduction) could therefore quite easily provide means for a film of 0.16 pm to develop. However the simplest explanation is (hat die kinematic configuration is somehow different to that measured. The disk used in the experiments is itself clamped to ensure it remains at rest [13]. Friction in the dry contact may be sufficient to cause stick between the surfaces initially, which gives way suddenly when sufficient torque is developed. This could result in an initial overspeed of the ball when motion commences and subsequent damped torsional vibration. This mechanism has, however, been considered and discounted by Glovnea and Spikes [1]. For such a speed variation mechanism to explain the variation in he shown in Figure 2 for the 50 m/s case, the ball velocity corresponding to the first peak would need to be 0.7 m/s compared to its final stearfy state value of 0.4 m/s. 

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