水准测量的内业计算

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,*,五、水准测量成果的内业计算方法,1,、计算高差闭合差,f,h,定义：,观测总高差与其理论总高差之差。,公式：,f,h,=h,测,h,理,对于附合水准路线：,h,理,=H,B,-H,A,，,f,h,=h,测,(H,B,-H,A,),对于闭合水准路线：,h,理,=0,，,f,h,=h,测,对于支水准路线：,f,h,=h,往,+,h,返,2,、计算高差闭合差的容许值,f,h,容,平地：,f,h,容,=40 (mm),山地：,f,h,容,=12 (mm),说明：,(1),上述公式只适用于普通水准测量等级（等外、图根、五等）；,(2)L,为水准路线全长的千米数，只计单程，不足,1,千米按,1,千米计；,(3)n,为水准路线全长的测站数，只计单程；,(4),每千米的测站数超过,16,时为山地，否则为平地；,(5),f,h,容,计算至整数。,3,、计算观测高差的改正数,v,i,高差闭合差,f,h,的分配原则：,将高差闭合差,f,h,反号后按路线长度或测站数成正比例地分配到各观测高差中去，即得各观测高差的改正数,v,i,。,观测高差改正数,v,i,的计算公式为：,v,i,=(-,f,h,/n,),n,i,或：,v,i,=(-,f,h,/L),L,i,令：,v,站,=-,f,h,/n,，叫每测站改正数，因此，,v,i,=v,站,n,i,；,又令：,v,km,=-,f,h,/L,，叫每千米,(,单位长度,),改正数，因此，,v,i,=,v,km,L,i,。,观测高差改正数,v,i,的计算说明：,(1),中间量,v,站,、,v,km,计算至,0.0001m(0.1mm),；,(2),最后改正数,v,i,计算至,0.001m(1mm),；,(3),v,i,一定要等于,-,f,h,，否则，强制分,配使其相等。,4,、计算改正后高差,h,i,改,h,i,改,=,h,i,+v,i,说明：用,h,i,改,=,h,理,作为检核,!,5,、计算各未知点高程,H,i,H,i,=H,i-1,+h,i,改,说明：终点计算出的高程一定要等于其已知高程，即,H,终,(,算,),=H,终,(,已,),！,【,例题,1】,如下图所示，为一附合水准路线测量成果，已知数据和观测数据均列于图中，试求各未知点的高程,H,i,。,附合水准路线测量成果：,h,1,+1.575,h,2,2.036,h,3,1.742,h,4,1.446,n,1,8,L,1,1.0km,n,2,12,L,2,1.2km,n,3,14,L,3,1.4km,n,4,16,L,4,2.2km,BM,A,1,2,3,BM,B,HA=65.376m,HB=68,.,623,m,计算步骤如下：,1,、计算高差闭合差,f,h,f,h,=h,测,(,H,B,-H,A,),=+3.315-(68.623-65.376)=+0.068(m),2,、计算容许高差闭合差,f,h,容,f,h,容,=40 =405.8,96mm,因为,f,h,f,h,容,，故其精度符合要 求，可做下一步计算。,3,、计算高差改正数,v,i,v,i,=(-,f,h,/L),L,i,=,v,km,L,i,v,km,=-,f,h,/L=,-0.068/5.8=-0.0117m,v,1,=,v,km,L,1,=(-0.0117m),1.0,-0.012m=-12mm,v,2,=,v,km,L,2,=(-0.0117m),1.2,-0.014m=-14mm,v,3,=,v,km,L,3,=(-0.0117m),1.4,-0.016m=-16mm,v,4,=,v,km,L,4,=(-0.0117m),2.2,-0.026m=-26mm,检核,:,v,i,=,-,f,h,=,-68mm,无需作强制分配。,4,、计算改正后高差,h,i,改,各测段观测高差,h,i,分别加上相应,的改正数,v,i,，即得改正后高差,h,i,改,。,h,1,改,=h,1,+v,1,=+1.575-0.012=+1.563mh,2,改,=h,2,+v,2,=+2.036-0.014=+2.022m,h,3,改,=h,3,+v,3,=,-,1.742-0.016=,-,1.758mh,4,改,=h,4,+v,4,=+1.446-0.026=+1.420m,检核：,h,i,改,=H,B,-,H,A,=+3.247m,5,、计算各未知点高程,H,i,计算公式为：,H,i,=H,i-1,+h,i,改,H,1,=H,A,+h,1,改,=65.376+1.563=66.939m H,2,=H,1,+h,2,改,=66.939+2.022=68.961m H,3,=H,2,+h,3,改,=68.961+(,-,1.758)=67.203m H,B(,算,),=H,3,+h,4,改,=67.203+1.420=68.623m,H,B(,算,),=H,B(,已知,),=68.623m,（检核）,表格计算如下：,测段,编号,点名,距离,L,（,km,）,测站数,实测高差（,m,）,改正数,（,m,）,改正后高差（,m,）,高程,（,m,）,1,2,3,4,5,6,7,8,1,BMA,1.0,8,+1.575,-0.012,+1.563,65.376,1,66.939,2,1.2,12,+2.036,-0.014,+2.022,2,68.961,3,1.4,14,-1.742,-0.016,-1.758,67.203,3,4,2.2,16,+1.446,-0.026,+1.420,68.623,BMB,5.8,50,+3.315,-0.068,+3.247,辅助,计算,每千米测站数,=50/5.8,16,，因此为平地。,f,h,=+68mm L=5.8km -,fh,/L,=-11.7mm,fh,容,=96mm,【,例题,2】,如下图所示，为一闭合水准路线测量成果，已知数据和观测数据均列于图中，试求各未知点的高程,H,i,。,闭合水准路线的计算步骤与附合水准路线,基本相同，计算时应当注意高差闭合差的公式为：,f,h,=,测,。,计算步骤如下：,1,、高差闭合差,f,h,=h,测,=,-,0.017m=,-,17mm,2,、高差闭合差的容许值,f,h,容,=12n=1232=68mm,因为,f,h,f,h,容,，故其精度符合要求，可做下一步计算。,3,、计算高差改正数,v,i,v,i,=(-,f,h,/n,),n,i,=,v,站,n,i,v,站,=-,f,h,/n,=+17/32,+0.5(mm),v,1,=v,站,n,1,=+,0.5,11,+,6(mm)v,2,=v,站,n,2,=+,0.5,8,=,+4(mm)v,3,=v,站,n,3,=+,0.5,6=,+3,(mm)v,4,=v,站,n,4,=+,0.5,7,+4(mm),检核：,v,i,=,-,f,h,=+0.017m,。,无需作强制分配。,4,、计算改正后高差,h,i,改,h,1,改,=h,1,+v,1,=-1.352+0.006=-1.346(m),h,2,改,=h,2,+v,2,=+2.158+0.004=+2.162(m),h,3,改,=h,3,+v,3,=+2.574+0.003=+2.577(m),h,4,改,=h,4,+v,4,=-3.397+0.004=-3.393(m),检核：,h,i,改,=0,。,如不相等，说明计算,中有错误存在。,5,、各待定点高程计算,H,1,=H,A,+h,1,改,=51.732+(,-,1.346)=50.386mH,2,=H,1,+h,2,改,=50.386+2.162=52.548m H,3,=H,2,+h,3,改,=52.548+2.577=55.125m,H,A(,算,),=H,3,+h,4,改,=55.125+(-3.393)=51.732m,检核：,H,A(,算,),=H,A(,已知,),=51.732m,如不相等，说明计算 中有错误存在。,表格计算如下：,测段,编号,点名,测站数,实测高差（,m,）,改正数,（,m,）,改正后高差 （,m,）,高程,（,m,）,1,2,3,4,5,6,7,1,BMA,11,-1.352,0.006,-1.346,51.732,1,50.386,2,8,+2.158,0.004,+2.162,2,52.548,3,6,+2.574,0.003,+2.577,55.125,3,4,7,-3.397,0.004,-3.393,51.732,BMA,32,-0.017,0.017,0,辅助,计算,f,h,=-17mm n=32,f,h,容,=68mm -,f,h,/n,=+0.5mm,【,例题,3】,支水准路线的内业计算。,下图所示为一支水准路线的观测结果。已知水准点,A,的高程为,H,A,=68.254m,，往、返测站,各,16,站。已知：,h,往,=,-1.386m,，,h,返,=+1.399m,。,试求,1,点的高程,H,1,。,BMA,1,h,往,h,返,解：,1,、计算高差闭合差,f,h,f,h,=h,往,+h,返,=,-1.386m+1.399m=+0.013m=+13,mm,2,、计算高差闭合差的容许值,f,h,容,f,h,容,=12n=1216=48mm,因为,f,h,f,h,容,，故其精度符合要求，可做下一步计算。,3,、计算往测高差的平均值,h,往均,h,往均,=(h,往,-,h,返,)/2=(,-1.386-1.399)/2=-1.392(m),4,、计算未知点,1,的高程,H,1,H,1,=,H,A,+h,往均,=68.254+,(-1.392)=66.862m,