The water entry of slender axisymmetric bodies

Abstract

We present a study of the forces, velocities, and trajectories of slender (length/diameter = 10) axisymmetric projectiles using an embedded inertial measurement unit (IMU). Three nose shapes (cone, ogive, and flat) were used. Projectiles were tested at vertical and oblique impact angles with different surface treatments. The trajectory of a half-hydrophobic and half-hydrophilc case impacting vertically was compared to the trajectory of symmetrically coated projectiles impacting the free surface at oblique angles. The oblique impact cases showed significantly more final lateral displacement than the half-and-half case over the same depth. The amount of lateral displacement was also affected by the nose shape, with the cone nose shape achieving the largest lateral displacement for the oblique entry case. Instantaneous lift and drag coefficients were calculated using data from the IMU for the vertical, half-and-half, and oblique entry cases. Impact forces were calculated for each nose shape and the flat nose shape experienced the largest impulsive forces up to 37 N when impacting vertically. The impact force of the flat nose decreased for the oblique entry case. The location of the center of pressure was determined at discrete time steps using a theoretical torque model and values from the IMU. Acoustic spectrograms showed that the sound produced during the water entry event predominately arises from the pinch-off for the cone and ogive nose shapes, with additional sound production from impact for the flat nose shape. Each test run was imaged using two Photron SA3 cameras.

Water entry impact dynamics of diving birds

“…Previous literature used cones as an approximation to bird heads [23]. Trends in impact acceleration noted by Bodily et al [9] for projectiles with conical and ogive noses resemble accelerometer results obtained for seabird models in this study.…”

“…This force arises as the impacting body experiences a net upward force upon impact due to the effects of momentum transfer to the liquid, surface tension, viscous drag and pressure forces [7]. Experimental studies of projectiles [3,4,8,9] show that the forces of blunt body water entry can be maximum anywhere between phases 1 and 5. Thus, the forces of the initial stages of impact must be measured in order to make estimates of the dynamic strength for a given structure [10].…”

“…Experiments performed with different projectile shapes [9] show that nose shape of the projectile has a major effect on the impact force during water entry. They used three different nose shapes: flat, cone and ogive.…”

The Hydrodynamics of High Diving

“…In this study, we investigate experimentally the dynamics of the jumper underwater and the hydrodynamic causes of injuries in a high dive, by monitoring one male top-level cliff diver, jumping from different heights during his habitual training with high-speed cameras both in air and underwater and with an accelerometer fixed on his body. The final goal of this work is to better understand the physics underlying high cliff diving as inspired by the studies of the water entry of projectiles [9][10][11] and to be able to protect divers by monitoring their dives with embedded sensors or by designing safety gear.…”

On the impact of a concave nosed axisymmetric body on a free surface

“…More recent studies on spheres and axisymmetric slender bodies have shown that some other parameters like surface properties and spin imparted to the object can have important influence on splash and cavity formation. [5][6][7][8][9] Other than the hydrodynamic features like splash and cavity formation, there is an important structural perspective to the water impact problem. The central ques- tion is what is the pressure experienced by the object at impact; the theoretical value is given by what is known as the "water hammer" pressure expressed as ρ w V 0 c w , where ρ w is the water density, V 0 is the impact velocity, and c w is the speed of sound in water.…”