单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,房地产测绘,10/2/2024,第二章 房产控制测量,2.3,导线测量内业计算,内容提要,:,1,、导线的近似平差计算,10/2/2024,（一）几个基本公式,1,、坐标方位角的推算,注意：若计算出的方位角,360,，则减去,360,；若为负值，则加上,360,或：,10/2/2024,例题,:,方位角的推算,1,2,3,4,5,95,130,65,128,122,12,30,1,2,3,4,5,已知：,12,=30,0,，,各观测角,如图，求各边坐标方位角,23,、,34,、,45,、,51,解：,23,=,12,-,2,180,0,=80,0,34,=,23,-,3,180,0,=195,0,45,=247,0,51,=305,0,12,=30,0,（,检查）,10/2/2024,2,、坐标正算公式,由,A,、,B,两点边长,D,AB,和坐标方位角,AB,，,计算坐标增量见图有：,D,AB,AB,A,B,X,y,0,X,AB,Y,AB,其中，,X,AB,=X,B,-X,A,Y,AB,=Y,B,-Y,A,X,AB,=D,AB,cos,AB,Y,AB,=D,AB,sin,AB,10/2/2024,3,、坐标反算公式,由,A,、,B,两点坐标来计算,AB,、,D,AB,D,AB,AB,A,B,X,y,0,X,AB,Y,AB,AB,的具体计算方法如下：,（,1,）计算：,10/2/2024,（,2,）计算：,（,3,）根据,X,AB,、,Y,AB,的正负号判断,AB,所在的象限。
10/2/2024,（三）闭合导线平差计算步骤,1,、绘制计算草图，在图上填写已知数据和观测数据2,、角度闭合差的计算与调整115.10,100.09,108.32,94.38,67.85,A,1,2,3,4,X,A,=536.27m,Y,A,=328.74m,A1,48,.,43,18,S,A,1,2,3,4,112,.,22,24,S,97,.,03,00,S,105,.,17,06,S,101,.,46,24,S,123,.,30,06,S,（,1,）计算角度闭合差：,=,测,-,理,=,测,-(n-2),180,（,2,）计算限差：,10/2/2024,（,3,）若在限差内，则按反号平均分配原则，计算改正数：,115.10,100.09,108.32,94.38,67.85,A,1,2,3,4,X,A,=536.27m,Y,A,=328.74m,A1,48,.,43,18,S,A,1,2,3,4,112,22,24S,97,.,03,00,S,105,.,17,06,S,101,.,46,24S,123,30,06,S,（,4,）计算改正后新的角值：,10/2/2024,3,、按新的角值，推算各边坐标方位角。
4,、按坐标正算公式，计算各边坐标增量5,、坐标增量闭合差计算与调整,115.10,100.09,108.32,94.38,67.85,A,1,2,3,4,X,A,=536.27m,Y,A,=328.74m,A1,48,.,43,18,S,A,1,2,3,4,112,.,22,24S,97,.,03,00,S,105,.,17,06,S,101,.,46,24,S,123,.,30,06,S,10/2/2024,115.10,100.09,108.32,94.38,67.85,A,1,2,3,4,X,A,=536.27m,Y,A,=328.74m,A1,48,.,43,18S,A,1,2,3,4,112,.,22,24,S,97,.,03,00,S,105,.,17,06,S,101,.,46,24,S,123,30,06,（,1,）,计算坐标增量闭合差,：,导线全长相对闭合差：,导线全长闭合差,:,10/2/2024,（,2,）分配坐标增量闭合差若,K1/2000,（,图根级），则将,f,x,、,f,y,以相反符号，按边长成正比分配到各坐标增量上去并计算改正后的坐标增量115.10,100.09,108.32,94.38,67.85,A,1,2,3,4,X,A,=536.27m,Y,A,=328.74m,A1,48,.,43,18,S,A,1,2,3,4,112,.,22,24,S,97,.,03,00,S,105,.,17,06,S,101,.,46,24,S,123,.,30,06,S,10/2/2024,115.10,100.09,108.32,94.38,67.85,A,1,2,3,4,X,A,=536.27m,Y,A,=328.74m,A1,48,43,18,A,1,2,3,4,112,22,24,97,03,00,105,17,06,101,46,24,123,30,06,6,、坐标计算,根据起始点的已知坐标和经改正的新的坐标增量，来依次计算各导线点的坐标。
10/2/2024,K,=,=,f,D,1,4000,1,2000,例题：闭合导线坐标计算表,点号,转折角,(,右,),改正后,转折角,方向角,边 长,D,(,米,),坐 标,增量,(,米,),X,Y,改 正 后,增量,(,米,),X,Y,坐标,(,米,),X Y,点号,A,1,2,3,4,A,1,97 03 00,105 17 06,101 46 24,123 30 06,112 22 24,+12,+12,+12,+12,+12,48 43 18,131 40 06,206 22 48,284 36 12,341 05 54,48 43 18,485.47,+0.09,-0.08,f,x,=,0.09,f,y,=,-,0.08,f,=,(,f,x,+,f,y,),=,0.120,539 59 00,理,=,540,00,00,m,=,测,-,理,=-60,m,容,=,40,=,89,540 00,00,97 03 12,105 17 18,101 46 36,123 30 18,112 22 36,115.10,100.09,108.32,94.38,67.58,+75.93,-66.54,-97.04,+23.80,+63.94,+86.50,+74.77,-48.13,-91.33,-21.89,-2,-2,-2,-2,-1,+2,+2,+2,+1,+1,612.18,545.62,448.56,472.34,415.26,490.05,441.94,350.62,1,2,3,4,A,536.27,536.27,328.74,328.74,A,+75.91,-66.56,-97.06,+23.78,+63.93,+86.52,+74.79,-48.11,-91.32,-21.88,0 0,10/2/2024,（四）附合导线平差计算,说明：与闭合导线基本相同，以下是两者的不同点,:,1,、角度闭合差的分配与调整,（,2,）满足精度要求，若观测角为左角，则将,f,反符号平均分配到各观测角上；若观测角为右角，则将,f,同符号平均分配到各观测角上。
1,）计算方位角闭合差：,方法,1,：,10/2/2024,例题：附合导线的计算,124.08,164.10,208.53,94.18,147.44,AB,CD,X,B,=1230.88,Y,B,=,673.45,X,C,=1845.69,Y,C,=1039.98,43,.,17,12,S,4,16,00,S,180,.,13,36,S,178,.,22,30,S,193,.,44,00,S,181,.,13,00,S,204,.,54,30,S,180,.,32,48,S,B,1,2,3,4,C,A,B,5,6,7,C,D,8,(1),绘制计算草图,在表内填写已知数据和观测数据,(2),角度闭合差的计算与调整,(,3),各边方向角的推算,(4),坐标增量闭合差的计算与调整,(5),推算各点坐标10/2/2024,图表：附合导线坐标计算表,点号,转折角,(,右,),改正后,转折角,方位角,边 长,D,(,米,),坐 标,增量,(,米,),X,Y,改 正 后,增量,(,米,),X,Y,坐标,(,米,),X Y,点号,A,B,5,6,7,8,C,D,180 13 36,178 22 30,193 44 00,181 13 00,204 54 30,180 32 48,124.08,164.10,208.53,94.18,147.44,B,5,6,7,8,C,1230.88,673.45,1845.69,1039.98,+8,+8,+8,+8,+8,+8,180 13 44,178 22 38,193 44 08,181 13 08,204 54 38,180 32 56,1119 01 12,43 17 12,4 16 00,43 03 28,44 40 50,30 56 42,29 43 34,4 48 56,+90.66,+116.68,+178.85,+81.79,+146.92,+84.71,+115.39,+46.70,+107.23,+12.38,738.33,+614.90,+366.41,+614.81,+366.53,f,x,=-0.09,f,y,=0.12,f,=,(,f,x,+,f,y),=0.150,K,=,=,f,D,1,4900,1,2000,-2,-2,-2,-1,-2,+2,+3,+3,+2,+2,+12,-9,+90.64,+116.66,+178.83,+81.78,+146.90,+84.73,+115.42,+107.26,+46.72,+12.40,+614.81,+366.53,1321.52,1438.18,1617.01,1698.79,758.18,873.60,980.86,1027.58,1119 00 24,理,=1119,01,12,m,=,测,-,理,=4,8,m,容,=40,N,=,98,cd,测,=43,17,12+6*180-1119,00,24=41648,10/2/2024,。