No abstract

Investigations, carried out principally on the vertical water entry of steel spheres, are described. Graphs show the effect of several experimental parameters on the time and place of occurrence of various events in the life of the cavity which accompanies the entry. These parameters include the density and pressure of the atmosphere above the water, and the velocity, size, and nose shape of the missile. Froude-scaling is found to be a good first approximation in describing cavity behavior, and some improvement is effected by the pressure-density scaling of the atmosphere above the water. The energy lost by a missile during the open-cavity phase of its water entry is found to be used up principally in the formation of the cavity, and the cavity shape is not dependent on the nose shape of the missile for a given drag force.

An investigation of factors which influence the formation of a cavity when a sphere enters water vertically is described. It was found that cavities are formed at much lower entry speeds for contaminated spheres than for clean ones, but that there is little dependence on the type of the contaminant. In regard to the scaling of this effect, the tendency to form a cavity varies little with change of size or specific gravity of the sphere. Water-entry cavities are observed to form at velocities much lower than those required for incipient cavitation in the water tunnel; consequently, a relation between the two effects appears improbable. Some dependence of cavity formation on viscosity might be inferred from the observation that cavities were formed at lower entry speeds by spheres coated with liquids of high viscosity than by spheres without this coating.

Drag coefficients have been determined from high speed motion pictures for ¼-inch to 1½-inch steel spheres shot into water vertically with speeds from 25 to 208 ft./sec. These drag coefficients correspond to the entrance cavity phase and to the v-squared-law drag forces only, the immediate effects on the spheres of other forces being eliminated in the calculations. It is found that CD is a function of both the Reynolds and Froude Numbers. Within the range investigated, the dependence may be expressed by CD=0.0174 ln(RF½).

The manner in which a sphere behaves when it enters the water from air depends on the rate at which energy is taken from it, and most of this energy is utilized in setting water into motion. The virtual mass is a partial measure of this motion. An investigation of virtual mass for spheres shortly after vertical water entry is described. The spheres used had specific gravities between 1.06 and 16.77 and impact velocities ranged from 21 to 103 ft./sec. The value of the virtual-mass coefficient was found to be much smaller than had previously been estimated, an average value of 0.08 being obtained. The method used recognizes the dependence of CD on sphere speed and depth, and makes comparisons only where these parameters have the same value.