角度测量水的测量全册课程随堂练习题.docx

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)=20L=20*6-3=117on=INT(118o45/3+1)=401=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L428m,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：l=1.124-1.428=-O.3O4Hb=20.016-0.304=19.712wB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。=61.819-57.967=3.852mEhB=4.363+2.413-3.121+1.263+2.716-3.715=3.919wfh=3.919-3.852=0.067mfh=±127+3+4+5+6+8=±68wnH1=H4+/1,+v1=57.967÷4.363+-0067×7=62.316mIA<1I33H,=H1+¼+v0=62.316+2.413+-0067×3=64.723/n2-233H3=H2+3+v3=64.723-3.121+×4=61.594wH4=H3+¼+v4=61.594+1.263+-67×5=62.847wH5=H4+5+v5=62.847+2.716+67×6=65.55IwH6=H5+6+v6=65.551-3.715+三×8=61.820/?8、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=-0.025mmfh=±1210÷8+8+ll÷12=±84mmH1=H10+1+v1=44.330+1.224+×10=45.559wH2=H1+¼+v2=45.5591.424+x8=44.139M49H3=H2+z3+v3=44.139+1.781+×8=45.924zH4=H3+A4+v4=45.924-1.714+×ll=44.216nH10=H4+A5+v5=44.216+0.108+12=44.330n10、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a1=l.321m,B点尺上的读数b1=l.117m；仪器搬至B点附近，又测得B点尺上的读数b2=L466n,A点尺上读数a2=L695m。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？%=1.321-1.117=0.204？%,=1.695-1.466=0.229？%b*%4=1.466+0.204=1.67Om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0左A002001201624120161224<40wB1201824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145.690叽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？Dar=232.355-232.340=0.015mDab=(232.355+232.340)/2=232.348w1_D_0.015_K-KJ-232.34815400ADCD=145.682-145.690=-0.008Dcd=(145.682+145.690)/2=145.686m1D0.0081KDcd145.686182007、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+=64o20,+3'=64o23zAw=A-=64o23,-(-2)=64o44,第六章测量误差的基本理论5、函数z=zr2,其中z=x+2y,z2=2-y,X和y相互独立，其m1=my=m,求叫。z=z1÷z2=x+2y+2x-y=3x+ytn.=±y9m2x+mj=yWm6、进行三角高程测量，按h=Dtan计算高差，已知=20°,Ina=±1',D=250m,InD=±0.13m,求高差中误差fflh。mh=±(tana)2w+(Dsec2a)2m1=±J(tan20)2×0.132+(250×sec220)2×(60-)2V206265=±0.094机7、用经纬仪观测某角共8个测回，结果如下：56°32,13",56°32z2,56°32'17",56°32,14",56°32z19",56°32,23",56°32,21",56°32,18",试求该角最或是值及其中误差。X=B=56"32'18.25nV=X-/v1=5.25v2=-2.75v3=1.25v4=4.25v5=1.25v6=4.75,%=-2.75",也=0.25"8、用水准仪测量A、B两点高差9次，得下列结果(以In为单位)：L253,1.250,1.248,1.252,1.249,1.247,1.250,1.249,1.251,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+1.251八X=.25079v1=-0.003w,v2=Sn,v3=0.002m,v4=-0.002zn,v5=0.00tn,v6=0.003m,v7=0m,v8=0.00lm,v9=-0.00mmx=-j=±0.6346如Wln9、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？第七章控制测量3、已知A点坐标XA=437.620,yA=721.324；B点坐标x=239.460,y三=196.450o求AB之方位角及边长。4=196.450-721.324=-524.874n,X=239,460-437.620=-198.164<0,X<0-524874aAB=180+arctan=180+690l859.6=249ol8'59.6"-198.16Dab=561.035m4、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=87o512ff+150o20,12*+l25o06,42ff÷87029,12+89l3'42"-(5-2)×l80o=87051'12"-12"=87°5OO*,2=150°20'12'-12"=150°20'00'=125o06,42*r-12ff=125o06r30*=87029,12ff-12ff=87o29W;=89°13'42-12=89°13'30%=126o45W23=12+180o-=126o45W+180o-150o20W=156o25,00*4,=%3+180°-,y=156o25W+180°-125o0630ff=21IoI830*a45=a34+180o-=21lol8,30ff+180°-87o29,00*=303o49,30ff51=a45+180o-凤=303o49,30ff+180o-89°13'30"=34°36'00"a12=a51+180°-;=34o36W+180o-87o500zr=126o45'00"X12=D12CoSal2=-64.386,12=D12Sina已=86.223X23=D23COSa23=-66.390,K23=D23sina23=28.982X34=Dy4CoSa34=-153.721,AL4=。34Sina34=-93.494X45=D45COSa45=99.853,匕$=D45sincr45=-149.018X51=D51cosa51=184.794,Y51=D51sina51=127.481/=-64.386-66.390-153.721+99.853+184.794=0.15fy=86.223+28.982-93.494-149.018+127.481=0.174f=+"=0.152+0.1742=0.230IJ=0230_11Kr-D763.8533002000X1,2=X12+-×D12=-64.386-×107.61=-64.4071212D12763.85-f0174K1;=K2+-×Di2=86.223一一:×107.61=86.198,2,2ZD12763.85%23=-66.404,K2r3=28.965,X=-153.756,;=-93.535,X：5=99.818,Ay4;=-149.059,X；1=184,750,5,1=127.430,X2=X1+X；2=500-64.407=435.593Y2=Y+K12=500+86.198=586.198X3=369.189,Y3=615.163,X4=215.433,Y4=521.628,X5=315.25l,y5=372,569,X1=500.001,K1=499.9995、附合导线的已知数据及观测数据列入表7-31,计算附合导线各点的坐标。f=aAB-aCD+4x80°-=54ff=120o30,14ff,/?;=212o15W,=145°10'13",设=170o19z0al=«4+180°-,ft=04"29'46"a12=72°14'02",%c=107°03'49",s=116°44'48"Xl=Dbicosal=297.26XCOSlo4"29'46"=-74.408肛A。1=287.797,X12=57.307,K12=178.853,X2c=-27.407,Kzc=89.288,fx=-74.408+57.307-27.407-(155.37-200.00)=0.122mJy=-0.122m/=0.173,D=297.26+187.81+93.40=578.471/1D-33002000f0122X'=Xi+上XDRl=-74.408:×297.26=-74.47lw,r=287.860见例Md例578.47例X1,2=57.267w,F12=178.893w,X;c=-27.427w,c=89.308wX1=X+X；1=200.00-74.471=125.529*=487.860,X2=182.796/n,Y2=666.753m,Xc=155.369m,Y2=756.061m,第八章大比例尺地形图测绘4、某地的纬度=34°10',经度=108°50',试求该地区划1：1000000、1：1000001：100OO这三种图幅的图号。答：1-49,1-49-62,1-49-62-(30)5、用视距测量的方法进行碎部测量时，已知测站点的高程Hm=400.12m,仪器高i=L532m,上丝读数0.766,下丝读数0.902,中丝读数0.830,竖盘读数L=98°32,48“，试计算水平距离及碎部点的高程。(注：该点为高于水平视线的目标点。)D=kncos2a=100×(0.902-0.766)cos2(98032,48*-90o)=13.30机H=H+-Sin2a-vi-I2=400.12+；XloOX(0.902一0.766)sin2X(98°32'48"-90°)+1.532-0.830=402.82/n第十一章道路中线测量3、已知路线导线的右角(1)=210o42,$(2)=162o06,。试计算路线转角值，并说明是左转角还是右转角。(1) =210°42'-180°=30°42'路线为左转角(2) =1800-162W=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：= 102°29'06"32。的00+172。1832-32。4()族)6、已知交点的里程桩号为K4+300.18,测得转角左=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-=500×tan=76.957机22JTJTL=Raj=500X17°30'×-=152.716机180180E=R(Sec-l)=500×(sec-1)=5.888m22D=2T-L=l9SmZy=Jo-T=K4+223.22YZ=ZY+L=K4+375.94QZ=Zy+=K4+299.58JD=Z+y=T4+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()圆心角(外)Xi(m)(m)ZYK4+223.2200°00'00"00+24016.781055'22"16.780.28+26036.784°12,5336.751.35+28056.786030,23”56.663.22QZK4+299.58+30075.948o42,08"75.655.76+32055.946024,3755.823.13+34035.944007'06"35.911.29+36015.941。49,36w15.940.25YZK4+375.9400000'00"007、已知交点的里程桩号为K10+110.88,测得转角左=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：计算圆曲线测设元素a24°18'T=/?tan-=400tan=86.12(tn)22JTTT1.=Ra=4×24o18,×=169.65(n)180180°E=/?fsecy-IJ=4Xsec-H=9.16(w)D=2T-L=2×S62-69.65=2.59(机)计算主点桩里程JDK10+110.88-)T86.12ZYK10+024.76+)L169.65YZK10+194.41-)L284.825QZ+)D2K10+109.5851.285(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Ii(m)偏角值Of"偏角读数O/ft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=30°12,2=32o18',AB=387.62m,主曲线半径R2=300m.试计算复曲线的测设元素。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。AB-R2 tan-QnoI R, 387.62-300 tan- 2a. tan 2tan30。12,2=1114.61 Z13、已知交点的里程桩号为K21+476.21,转角fi=37°16',圆曲线半径R=300m,缓和曲线长h=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。解:24R60224x300= 0.5240R2 一万击L99180。602× 300=5。43,46 /3AfVX0=1S=60=59.9440R240×3002R6020nn3,n=2.0006R6x300"OX9Th=(R+p)tan+=(300+0.5)tan+29.99=131.3IznJTJT1.h=R(a-20)-2ls=300×(37ol6,-2×5o43¼6ff)+2×60=255.13/n1.=Rg-20o)念=300×(37o16,-2×5°43'46")念=135.13wEh=(R+p)secy-/?=(300+0.5)secy-300=17.12mDH=TrH-LH=2×131.31-255.13=7.49hZH=JD-Th=K21+476.21-131.31=K21+344.90HY=ZH+ls=C21+344.90+60=C21+404.90YHHY+L=K21÷404.90+135.13=/C21+540.03HZ=YH+ls=K21+540.03+60=C21+600.03QZHZ-K21+600.03一255.13/2=K21+472.465JD=QZ+-=K2+472.465+7.49/2=Xr21+476.2114、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（In）圆心角值°'wX(m)y(m)ZHK21+344.90000K21+36015.1015.100.032K21+38035.1035.0960.400K21+40055.1055.0611.549HYK21+404.906059.942.00K21+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)CZHK21+344.900000K21+36015.100.0320071715.10K21+38035.0960.4000391135.10K21+40055.0611.5491364155.083HYK21+404.9059.942.001544059.97K21+42074.9203.8842580475.02K21+44094.5807.5364332094.88K21+460113.95312.48961516114.63QZK21+472.465K21+480118.67413.90864103119.49K21+50099.3858.6364575899.76K21+52079.7884.6623203879.92K21+54059.9692.0021544360.00YllK21+540.0359.942.001544059.97K21+56040.0220.594051Ol40.03K21+58020.0300.0740124220.03K21+6000.03000.03HZK21+600.030016、第14题在算出各桩坐标后，前半曲线打算改用极坐标法测设。在曲线附近选一转点ZD,将仪器置于ZH点上，测得ZH点至ZD的距离S=15.670m,切线正向顺时针与S直线的夹角=15°10'12"。试计算各桩的测设角度和距离。由题可知，ZD在以ZH点为原点的相对坐标系中的坐标为：Xzd=Ssin=4.101Yzd=SCOSa=I5.124前半曲线各桩在上述相对坐标系中的坐标在第13题中已知，则以ZD为测站点，以ZH为后视点，可以计算出各桩与S顺时针夹角和星巨离：桩号(部分)测设角度距离(m)K20+555.018(ZH)OOO000'00"15.670K20+600158°35'59"30.021K20+615.018(HY)162°08'41”44.865K20+700172°58'00"128.345K20+800183°099'19223.236K20+900193°58'03311.951K20+957.693(QZ)198°40,06”360.144第十二章路线纵、横断面测量4.中平测量记录计算表表12-6测点水准尺读数(m)视线高程(m)高程(m)备注后视中视前视BM51.426419.054417.628K4+9800.87418.18K5+0001.56417.49+0204.25414.80+0401.62417.43+0602.30416.75ZD10.8762.402417.528416.652+0802.42415.11+092.41.87415.66+1000.32417.21ZD21.2862.004416.810415.524+1203.15413.66+1403.04413.77+1600.94415.87+1801.88414.93+2002.00414.81BM62.186414.624基平BNU高程为414.635