住宅间距与日照关系的初步数学分析

Preliminary Mathematical Analysis of the Relationship Between the Residential Interval and Sunlight

从日照的角度对住宅间距进行了初步数学分析。对影长的计算方法进行了整理,选取计算条件研究了一日不同时刻、正午时刻不同节气与影长的关系;建立了住宅间距的物理模型和数学模型,并对典型城市的日照间距系数与纬度的关系,不同住宅高度与日照系数的关系进行了研究;最后给出了典型城市的日照间距系数取值范围。结果表明:一日内太阳高度角和影子的长度随时间不同而不同,太阳高度角在正午时刻最大,影子的长度在正午的时刻最短。正午时刻一年内不同节气的太阳高度角和影子的长度是不一样的,太阳高度角在夏至时最大,冬至时最小;影子的长度在夏至时最短,冬至时最长。纬度不同,日照间距系数也不同,纬度越大日照间距系数越大,即所需的间距越大。楼层越高日照间距系数越大,即所需的间距越大。

The residential interval was discussed with preliminary mathematical analysis of sunlight. Calculation methods of shadow length were summarized and calculation parameters were selected to determine the influence of different times of one day and different solar terms at noon to the length of shadow. The physical model and mathematical model were established to study the relation between coefficient of sunshine spacing and latitude, and the relation between various residential height and sunshine coefficient in a typical city. Value range of sunshine distance was then provided. The result demonstrated that the solar elevation angle and the length of shadow vary with times of one day as well as solar terms at noon. The solar elevation angle reaches maximum at noon time while the length of shadow reaches the minimum. Also, the solar elevation angle reaches the maximum at the summer solstice and minimum at winter solstice, while the opposite applies to the length of shadow. The coefficient of sunshine distance increases with the increasing latitude as well as the height of building, resulting in the increase of spacing.