Plane Equilibrium Research Articles

Method for calculating two-dimensional supersonic flows of a chemically reacting inviscid gas

A numerical method is presented for calculating plane and axisymmetric equilibrium supersonic flows of a chemically reacting inviscid gas. The method is analogous to the method of integral relations for piecewise approximation of the integrands, but the streamlines are used as the lines which divide the flowfield into strips. The number of “strips” does not affect the form of the approximating equations and may be arbitrary.

Elastic equilibrium of an isotropic plane with a doubly periodic system of inclusions

Elastic equilibrium of an isotropic plane with a doubly periodic system of inclusions

Stability of the plane equilibrium form of multiply connected plates under the action of discrete loads

Stability of the plane equilibrium form of multiply connected plates under the action of discrete loads

The Role of the Fins in the Equilibrium of the Swimming Fish

ABSTRACT An attempt was made to determine the relationship of the fins to the equilibrium of the swimming dogfish. Two factors at least are involved in this equilibrium; passive mechanical forces and reflex motions of the fins themselves. The part played by the automatic (passive) components was estimated by experimenting on a model of Mustelus canis mounted in a wind tunnel tested at a suitable air speed. The equilibrium in the horizontal plane (yawing equilibrium--for turning movements) is unstable without fins, completely stable only in the absence of the first dorsal fin, and is neutral when all fins are present. In the vertical plane (pitching equilibrium--for rising and diving turns) the equilibrium is unstable without fins, and this instability is greatly increased by the presence of the pectorals. The pelvics have little or no effect. Stability and controllability are inversely related. The fish is comparatively stable in the horizontal plane, extremely controllable in the vertical plane. This fact is closely related to the flexibility of the body for lateral movements. The results obtained in the wind tunnel were confirmed by amputation of the fins of the living dogfish. The normal equilibrium of the swimming dogfish in the vertical plane is determined largely by the pectoral fins and the heterocercal tail. The relationship of these facts to the problem of the evolution of the swimming chordates is considered.