The mathematical model of crown height in hedgerow orchard on southern hill slope

In the hedgerow orchard of hilly land, the crown height changes with ground slope so as to meet the condition of the sun light. Using astronomical trigonometric formulas, this paper calculates solar position of the 40° north latitude in vernal equinox and autumnal equinox. At the same time, it calculates the shadow length of tree body, determines the shadow length coefficient y and drafts the chart of shadow top contour based on the solar azimuth angle A and the coefficient of shadow length γ. According to the design of the north-south direction, we take two lines of the hedge with the changing figure of the top contour of shadow and crown cross-section to get mathematical models which determine the crown height of different sections in different ground slope.