弓高弦长法测量直径中的最佳测量点的选择

The Selection of the Best Measuring Point for Measuring a civcle's Diameter with the Arch-Height and chord-Langth Method

弓高弦长法测圆直径的一个重要问题,是如何选取最佳测量点。本文从误差的传递着手,严密推证了弓高及弦长测量的标准差取不同值时最佳测量点的位置。在一般情况下弓高及弦长的标准差相同(σ_h-σ_s)时,最佳测量点的位置应为 h=(2^(1/2))/2S(=2/3D)处。值得注意的是用弓高弦长法对最佳测量点的测量,其标准差为直接测量直径时标准差的0.866倍。

It is an important problem to select the best measuring point for measuring a circle's diameter(D)with the arch—height(h)and chord—length(s)method.Eased on the theory of error,in this article,we stri otly deduce where is the best measuring point when the standard error of arch—height and that of chord—length are both befined.Generally,when the standard error of arch—height is egual to that of chord—length,the best mea- sting point is at h=(2^(1/2)/2_S(=-(2\3)-D),It is very interesting that the standard error of a diameter which is measured with the arch—height and the chord—le- ngth method is only 0.866times as much as that of the diameter which is measured direetly.