,*,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,内容提要:,四、导线的内业计算,讲题:导线测量内业计算,内容提要:讲题:导线测量内业计算,1,四导线的内业计算,计算各导线点的坐标,（一）几个基本公式,1、坐标方位角(grid bearing)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：,四导线的内业计算计算各导线点的坐标（一）几个基本公式,2,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）,例题:方位角的推算1234595130651,3,2、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,2、坐标正算公式由A、B两点边长DAB和坐标方位角AB，计,4,3、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：,3、坐标反算公式由A、B两点坐标来计算AB、DAB DA,5,（2）计算：,（3）根据,X,AB、,Y,AB,的正负号判断,AB,所在的象限。,（2）计算：（3）根据XAB、YAB的正负号判断AB,6,1、,幸福的背后,2、吐鲁番的葡萄熟了,1、幸福的背后,7,（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(angle closing error)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,A,1,2,3,4,112,22,24,97,03,00,105,17,06,101,46,24,123,30,06,（1）计算角度闭合差：,=,测,-,理,=,测,-(n-2),180,（2）计算限差：,（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,8,（3）若在限差内，则平均分配原则，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,A,1,2,3,4,112,22,24,97,03,00,105,17,06,101,46,24,123,30,06,（4）计算改正后新的角值：,（3）若在限差内，则平均分配原则，计算改正数：115.10,9,3、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(closing error in coordination increment)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,A,1,2,3,4,112,22,24,97,03,00,105,17,06,101,46,24,123,30,06,3、按新的角值，推算各边坐标方位角。4、按坐标正算公式，计,10,115.10,100.09,108.32,94.38,67.85,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,（1）,计算坐标增量闭合差：,导线全长相对闭合差(relative length closing error of traverse):,导线全长闭合差:,115.10100.09108.3294.3867.85A1,11,（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,A,1,2,3,4,112,22,24,97,03,00,105,17,06,101,46,24,123,30,06,（2）分配坐标增量闭合差。若K1/2000（图根级,12,115.10,100.09,108.32,94.38,67.85,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。,115.10100.09108.3294.3867.85A1,13,K,=,=,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,x,=+0.09,y,=,0.08,=,x,+,y,=0.120,539 59 00,理,=540,00,00,=,测,理,=,60,容,=,40,5=,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,K=,14,例题：,用EXCEL程序进行闭合导线计算,例题：用EXCEL程序进行闭合导线计算,15,（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：,（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,16,方法2(*)：,（1）计算角度闭合差：,2、坐标增量闭合差的计算,（2）满足精度要求，将f,反符号平均分配到各观测角上。,右角：,左角：,其中，,的计算公式如下：,方法2(*)：（1）计算角度闭合差：2、坐标增量闭合差的,17,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,=1039.98,43,17,12,4,16,00,180,13,36,178,22,30,193,44,00,181,13,00,204,54,30,180,32,48,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。,例题：附合导线的计算124.08164.10208.5394,18,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,x,=+0.09,y,=,0.12,=,x,+,y,=0.150,K,=,=,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,=,测,理,=,48,容,=,40,6=,98,图表：附合导线坐标计算表点号转折角改正后方位角边 长 坐,19,例题：,用EXCEL程序进行附合导线计算,例题：用EXCEL程序进行附合导线计算,20,