Two dimensional consideration about Plowbody (I)

Analytical representation of Plowbody curve

Abstract

(1) Two dimensional curve of plow-body is approximately represented by a sort of plane screw curves, that is r=r₀e^t(φ-α) where, r, r₀ are radius of curvature at any point of the curve and at share point respectively, φ, α are tangential angle at any point and at share point, and b is a constant.
(2) A curve decided by one const. b will be called simple curve. The radius of curvature of this curve simply increase or decrease, and is constant when b is O.
(3) When radius of curvature of a curve increase from share point to connecting point, then decrease from connecting point to end of breast, two const. b₁ and b₂, will be necessary to determine this curve. It will be called connected curve.
(4) By calculation of example, relations between b or b₁ and r₀, r₁, r₂, b₂ are shown in Fig. 2 and Fig 3.
(5) These constants are measured about real Japanese plows. The curve of a plow is neare simple curve and that of six plows are almost connected curve.
(6) Limit of radius of curvature at share point is decided by strain limit of compression side of curved fullow. For example, this is 45cm for Japanese common plow and 40cm for high breast plow.