测量学课后练习题计算答案

第一章绪论7、某点的经度为118°45,，试计算它所在6°带及3°带的带号，以及中央子午线的经度是多少？答：N=INT(118°45//6+1)=20 L=20*6-3=117° n=INT(118°45//3+1)=40 l=40*3=120°第二章水准测量1、设A为后视点，B为前视点；A点高程是20.016m。当后视读数为1.124m，前视读数为1.428m，问A、B两点高差是多少？B点比A点高还是低？B点的高程是多少？并绘图说明。答：hB=1.124-1.428=-0.304mHB=20.016—0.304=19.712mB点比A点低7、调整表2-3中附合路线等外水准测量观测成果，并求出各点的高程。h=61.819-57.967=3.852m£h=4.363+2.413-3.121+1.263+2.716-3.715=3.919mfh=3.919-3.852=0.067mf=±12v7+3+4+5+6+8=±68mmhH=H+h+v=57.967+4.363+-0.067x7=62.316mTOC\o"1-5"\h\z1a1 1 33H=H+h+v=62.316+2.413+-0.067x3=64.723m2122 33H=H+h+v=64.723-3.121+-0.067x4=61.594m233 33H=H+h+v=61.594+1.263+-0.067x5=62.847m3 4 4 33H=H+h+v=62.847+2.716+-0.067x6=65.551m455 33H=H+h+v=65.551-3.715+-0.067x8=61.820m566 338、调整图2-40所示的闭合水准路线的观测成果，并求出各点的高程。fh=£h=1.224-1.424+1.781-1.714+0.108=-0.025mmf=±12<10+8+8+11+12=±84mmf〈fh，H=H+h+v=44.330+1.224+竺竺x10=45.559mTOC\o"1-5"\h\z10 1 1 49H=H+h+v=45.559-1.424+0025x8=44.139m122 49H=H+h+v=44.139+1.781+0025x8=45.924m233 49H=H+h+v=45.924-1.714+0025x11=44.216m344 49H=H+h+v=44.216+0.108+0025x12=44.330m10 4 5 5 4910、设A、B两点相距80m，水准仪安置于中点C，测得A点尺上读数a:1.321m，B点尺上的读数b『1.117m；仪器搬至B点附近，又测得B点尺上的读数4=1.466皿，A点尺上读数%=1.695皿。试问该仪器水准管轴是否平行于视准轴？如不平行，应如何校正？h=1.321-1.117=0.204mha=1.695-1.466=0.229mabh、牛hababa'=1.466+0.204=1.670m2水准管轴和视准轴不平行。校正方法：调节微倾螺旋使读数为1.670m,调节管水准器一端的调节螺旋使水准管气泡居中。第三章角度测量5、整理表3-5测回法观测水平角的记录手簿。水平角观测记录（测回法）测站盘位目标读数半测回角值平均角值备注O左A002001201624120161224〃<40〃B1201824右A18002061201600B3001806第四章距离测量和直线定向3、用钢尺丈量AB、CD两段距离，AB往测为232.355m，返测为232.340m；CD段往测为145.682m，返测为145.690m。两段距离丈量精度是否相同？为什么？两段丈量结果各为多少？AD=232.355-232.340=0.015mAB(232.355+232.340)/2=232.348mABAB1_|AD|_0.015_ 1K―D~2—232.348—15400AD=145.682-145.690=-0.008mCD(145.682+145.690)/2=145.686mCDCD1_|AD|_0.008_ 1K—D~―145.686—18200CD7、已知A点的磁偏角为西偏21',过A点的真子午线与中央子午线的收敛角为+3',直线AB的坐标方位角a=64°20',求AB直线的真方位角与磁方位角。A=a+y=64o20'+3'=64。23aA=A-6=64o23'-(-21)=64。44'第六章测量误差的基本理论5、函数z=Z]+z2，其中zjx+2y,z2=2x-y,x和y相互独立，其m=m=m,求m。z=z+z=x+2j+2x-j=3x+jm=±：9m2+m2=、；10mz xJ6、进行三角高程测量，按h=Dtana计算高差，已知&=20°,ma=±1',D=250m,mD=±0.13m,求高差中误差%m=±、((tana)2m2+(Dsec2a)2m2, 60=±n,(tan20)2x0.132+(250xsec220)2x( )2206265=±0.094m7、用经纬仪观测某角共8个测回，结果如下：56°32'13〃，56°32,21〃，56°32'17〃，56°32’14〃,56°32'19〃，56°32,23〃，56°32,21〃，56°32'18",试求该角最或是值及其中误差。x=」=56。32'18.25〃nv=x-lv=5.25〃,v=—2.75〃,v=1.25〃,v=4.25〃v=1.25〃,v=—4.75〃,v=—2.75〃,v=0.25〃m=±dvvf=±3.515〃，m=m==±1.24〃Vn-1 xnn8、用水准仪测量A、B两点高差9次，得下列结果(以m为单位)：1.253,1.250,1.248,1.252,1.249,1.247,1.250,1.249,1.251,试求A、B两点高差的最或是值及其中误差。1.253+1.250+1.248+1.252+1.249+1.247+1.250+1.249+1.251x= =1.250m9v=-0.003m,v=0m,v=0.002m,v=-0.002m,v=0.001m,v=0.003m,v=0m,v=0.001m,v=-0.001m6…89m=士. =±1.90mmn--1m—==±0.6346mm-n9、用经纬仪测水平角，一测回的中误差m=+15〃，欲使测角精度达到m=±5〃，需观测几个测回?m=m,5=-15,n=9xnn nn第七章控制测量3、已知人点坐标x『437.620,y「721.324；B点坐标x『239.460,y『196.450。求AB之方位角及边长。AY=196.450-721.324=-524.874m,AX=239.460-437.620=-198.16AY<0,AX <0-524.874 . .a=180+arctan =180+69。18'59.6〃=249。18'59.6〃ab -198.16D=561.035mAB4、闭合导线1-2-3-4-5-1的已知数据及观测数据列入表7-30,计算各导线点的坐标。f°=87o51'12〃+150o20'12〃+125o06'42〃+87o29'12〃+89o13'42''-(5—2)x180o=1'P'=87o5112''-12〃=87o51'00〃P'=150o2042''-12''=150o20'00〃2P'=125o06'42''-12''=125o06'30''3P'=87o2942''-12''=87。29’00''4P'=89o13'42''-12''=89o13'30''5a=126o45'00''12TOC\o"1-5"\h\za=a+180o-P'=126o45'00''+180o-150o20'00''=156o25'00''23 12 2a=a+180o-P'=156o25'00''+180o-125o06'30''=211o18'30''34 23 3a=a+180o-P'=211o18'30''+180o-87o29'00''=303o49'30''45 34 4a=a+180o-P'=303o49'30''+180。-89o13'30''=34o36'00''51 45 5a=a+180o-P'=34o36'00''+180o-87o5100''=126o45'00''AX =D cosa =-64.386,AY =D sina =86.223AX =D cosa =-66.390,AY =Dsina =28.982AX=Dcosa=-153.721,AY=Dsina=-93.494AX =D cosa =99.853,AY =D sina =-149.018AX =D cosa =184.794,AY =D sina =127.481f=-64.386-66.390-153.721+99.853+184.794=0.15Xf=86.223+28.982-93.494-149.018+127.481=0.174f=、;f2+f2=v0.152+0.1742=0.230120001_f_0.230_1K―而一763.85=12000AX'=AX+工xD=-64.386-0.15x107.61=-64.40712 12 £D 12 763.85TOC\o"1-5"\h\z-f 0174AYf=AY+—^yxD=86.223--x107.61=86.19812 12 £D12 763.85AX'=-66.404,AYf=28.965,AX'=--153.756,AYf=-93.535,23 23 34 34AX'=99.818,AYf=-149.059,AX'=184.750,AYf=127.430,45 45 51 51X=X+AX'=500-64.407=435.5932 1 12Y=Y+AY'=500+86.198=586.1982 1 12X=369.189,Y=615.163,X=215.433,Y=521.628,X=315.251,Y=372.569,X=500.001,Y=499.9995、附合导线的已知数据及观测数据列入表7-31,计算附合导线各点的坐标。f°=aAB-aCD+4x180o—邓=54〃TOC\o"1-5"\h\zB'=120o30'14〃,3'=212o15'44〃,3,=145o10'13〃,3,=170o19'01〃B 1 2 Ca=a+180o-p'=104o29'46〃B1 AB Ba=72o14'02〃,a=107o03'49〃,a=116o44'48〃12 2C CDNX=Dcosa=297.26xcos104o29'46〃=-74.408m,AY=287.797,AX=57.307,AY=178.853,AX=-27.407,AY=89.288,f=-74.408+57.307-27.407-(*5.37-200.00);0.122m,f=-0.122mx yf=0.173,£D=297.26+187.81+93.40=578.471f1-1==<K £D 33002000TOC\o"1-5"\h\zf 0.122AX'=AX+二xD=-74.408- x297.26=-74.471m,AY'=287.860m,B1 B1 £D B1 578.47 B1AX'=57.267m,AY'=178.893m,AX'=-27.427m,AY'=89.308m12 12 2C 2CX=X+AX'=200.00-74.471=125.529m,Y=487.860,1B B1 1X=182.796m,Y=666.753m,X=155.369m,Y=756.061m,22 C2第八章大比例尺地形图测绘4、某地的纬度=34°10',经度=108°50',试求该地区划1:1000000、1:100000、1：10000这三种图幅的图号。答：1-49,1-49-62,1-49-62-(30)5、用视距测量的方法进行碎部测量时，已知测站点的高程H造400.12m,仪器高i=1.532m,上丝读数0.766,下丝读数0.902,中丝读数0.830,竖盘读数L=98°32'48〃，试计算水平距离及碎部点的高程。(注：该点为高于水平视线的目标点。)D=kncos2a=100x(0.902-0.766)cos2(98。32'48〃-90。)=13.30mH=H+1knsin2a+i-12=400.12+1x100x(0.902-0.766)sin2x(98o32'48〃-90o)+1.532-0.8302=402.82m第十一章道路中线测量3、已知路线导线的右角B：(1)0=210°42'；(2)B=162。06'。试计算路线转角值，并说明是左转角还是右转角。a=210o42'-180o=30o42'路线为左转角a=180o-162o06'=17o54'路线为右转角4、在路线右角测定之后，保持原度盘位置，如果后视方向的读数为32°40'00〃，前视方向的读数为172°18'12〃，试求出分角线方向的度盘读数。答：分角线方向的度盘读数为：32o40'00〃+172°1812—32°4000=102o29'06〃

6、已知交点的里程桩号为K4+300.18,测得转角a左=17°30',圆曲线半径R=500m,若采用切线支距法并按整桩号法设桩，试计算各桩坐标。并说明测设步骤。T=Rtan—=500xtan"°3°=76.957m2 2L=R•—•土=500x17o30'x-=152.716m180 180— 17o30'E=R(sec--1)=500x(sec 1)=5.888m22D=2T-L=1.198mZY=JD-T=K4+223.22YZ=ZY+L=K4+375.94QZ=ZY+L=K4+299.58JD=QZ+DD=k4+300.18切线支距法计算表 表11-5桩号各桩至ZY或YZ的曲线长度（/j圆心角（①.）Xi(m)yi(m)ZYK4+223.2200°00,00〃00+24016.781°55,22〃16.780.28+26036.784°12,53〃36.751.35+28056.786°30，23〃56.663.22QZK4+299.58+30075.948°42，08"75.655.76+32055.946°24，37〃55.823.13+34035.944°07,06〃35.911.29+36015.941°49，36〃15.940.25YZK4+375.9400°00，00〃007、已知交点的里程桩号为K10+110.88,测得转角a左=24°18',圆曲线半径R=400m,若采用偏角法按整桩号法设桩，试计算各桩的偏角和弦长（要求前半曲线由曲线起点测设，后半曲线由曲线终点测设），并说明测设步骤。解：①计算圆曲线测设元素— — 24°18' 一一T=Rtan—=400tan =86.12（m）22TOC\o"1-5"\h\z兀_ _ _.兀 _ _L=R———=400x24°18'x——=169.65(m)180 180°24°18'2、24°18'2、-1=9.16(m)7Rsec--1=400xseck 2 7 kD=2T-L=2x86.12-169.65=2.59(m)②计算主点桩里程

JD-)TK10+110.8886.12ZYK10+024.76+)L169.65YZK10+194.41-)L/284.825QZK10+109.585+)D/21.285(校核)JDK10+110.88(计算无误)偏角法计算表桩号各桩至ZY或YZ的曲线长度li(m)偏角值°， 〃偏角读数°， 〃相邻桩间弧长(m)相邻桩间弦长(m)ZYK10+024.760000000000000+04015.24105291052915.2415.24+06035.2423126231262020+08055.2435723357232020+10075.2452319523192020QZK10+109.585+12074.415194535440152020+14054.413534935606112020+16034.412275235732082020+18014.4110155358580514.4114.41YZK10+194.4100000000000008、什么是正拨？什么是反拨？如果某桩点的偏角值为3°18,24〃，在反拨的情况下，要使该桩点方向的水平度盘读数为3°18,24〃，在瞄准切线方向时，度盘读数应配置在多少？答：由于经纬仪水平度盘的注字是顺时针方向增加的，因此测设曲线时，如果偏角的增加方向与水平度盘一致，也是顺时针方向增加，称为正拨；反之称为反拨。对于右转角(本例为右转角)仪器置于ZY点上测设曲线为正拨，置于YZ点上则为反拨。度盘读数应配置为 6°36,48〃10、什么是复曲线？如图11-23复曲线，设a130°12',a2=32°18',AB=387.62m,主曲线半径R2=300m。试计算复曲线的测设元素。 1 2 2答：复曲线是由两个或两个以上不同半径的同向曲线相连而成的曲线。a. 32。18'AB—Rtan-387.62—300tan R= 2 2= 2—=1114.61m2 .a 30。12'tan于 tan 2

13、已知交点的里程桩号为K21+476.21,转角a右=37°16',圆曲线半径R=300m,缓和曲线长l=60m,试计算该曲线的测设元素、主点里程，并说明主点的测设方法。 S1213、已知交点的里程桩号为K21+476.21,转角a右=37°16',圆曲线半径R=300m,缓和曲线长l=60m,试计算该曲线的测设元素、主点里程，并说明主点的测设方法。 S12-S-解：24R 24x3001s13 60 603q=——s—=—— 2240R2 2 240x3002=29.991 180。—―- 2R兀602x300180•—=5o43'46〃兀x=1-l3=60——60—=59.940s40R2 40X3002126026R6x300=2.00TOC\o"1-5"\h\z=(R+p)tan-+q=(300+0.5)tan37016-+29.99=131.31m^2 ^2L=R(a-2p)-^+21=300x(37。16'-2x5。43'46〃)-^+2x60=255.13mH 0180。 s 180。L=R(a-2p)^—=300x(37。16'-2x5。43'46〃)-^=135.13my 0180。 180。E=(R+p)seca-R=(300+0.5)sec371^--300=17.12mH2 2DH=2TH-LH=2x131.31-255.13=7.49mZH=JD-T=K21+476.21-131.31=K21+344.90HY=ZH+1=K21+344.90+60=K21+404.90YH=HY+L=K21+404.90+135.13=K21+540.03HZ=YH+1=K21+540.03+60=K21+600.03sQZ=HZ-LH=K21+600.03-255.13/2=K21+472.465JD=QZ+=K21+472.465+7.49/2=KJD=QZ+14、第13题在钉出主点后，若采用切线支距法按整桩号详细测设，试计算各桩坐标。切线支距法计算表桩号各桩至ZH(HY)或HZ的曲线长度1((m)圆心角值。’ 〃x(m)y(m)ZHK21+344.90000K21+36015.1015.100.032K21+38035.1035.0960.400K21+40055.1055.0611.549HYK21+404.906059.942.00

K21+42015.108364874.9203.884K21+44035.1012255994.5807.536K21+46055.10161510113.95312.489QZK21+472.465K21+48060.03171140118.67413.908K21+50040.0313222999.3858.636K21+52020.039331879.7884.662K21+5400.035440759.9692.002YHK21+540.036059.942.00K21+56040.0340.0220.594K21+58020.0320.0300.074K21+6000.030.030HZK21+600.0300015、第13题在钉出主点后，若采用偏角法按整号详细测设，试计算测设所需要的数据。偏角法计算表桩号x（m）y（m）8CZHK21+344.900000K21+36015.100.0320071715.10K21+38035.0960.4000391135.10K21+40055.0611.5491364155.083HYK21+404.9059.942.001544059.97K21+42074.9203.8842580475.02K21+44094