A lifting line theory for a three-dimensional hydrofoil

Abstract

Prandtl's lifting line theory was generalized to the lifting problem of a three-dimensional hydrofoil in the presence of a free surface. Similar to the classical lifting theory, the singularity distribution method was utilized to solve two-dimensional lifting problems for the hydrofoil beneath the free surface at the air-water interface, and a lifting line theory was developed to correct three-dimensional effects of the hydrofoil with a large aspect ratio. Differing from the classical lifting theory, the main focus was on finding the three-dimensional Green function of the free surface induced by the steady motion of a system of horseshoe vortices under the free surface. Finally, numerical examples were given to show the relationship between the lift coefficient and submergence Froude numbers for 2-D and 3-D hydrofoils. If the submergence Froude number is small free surface effect will be significant registered as the increase of lift coefficient. The validity of these approaches was examined in comparison with the results calculated by other methods.

Probe Into the Scheme of the Structural Design of Stereoscopic Garage

“…The center of this kind of parking spot on both sides has a stacking machine,and the whole garage operation all be done by stacking machine. It parked on stage when the cars comeing, then the cars has been taken by stacker in tunnels.The car will be carried by stacker walking within the roadway,ascension,and put into a specify layer beside the car parking, then the car will be push into a parking spot by stacker [6]. The process of picking up a car is just the sane but opposite in direction.…”