東北大學(xué)計(jì)算題

計(jì)算題(共30題)已知某地某點(diǎn)的經(jīng)度久=112°47',試求它所在的6°帶與3°的帶號(hào)及中央子午線的經(jīng)度是多少？某工程距離丈量容許誤差為1/100萬,試問多大范圍內(nèi),可以不考慮地球曲率的影響。根據(jù)下表中的觀測數(shù)據(jù)完成四等水準(zhǔn)測量各測站的計(jì)算。測點(diǎn)編號(hào)占八、、號(hào)后尺下絲上絲-刖尺下絲上絲方向及尺號(hào)水準(zhǔn)尺中絲讀數(shù)K+黑八、、減紅咼差中數(shù)備注后視距前視距黑八、、(m)紅(m)視距差d￡d1BM11.5710.793后51.3846.171K5=4.787K6=4.6871ZI)11.1970.417前60.5515.239后一前2ZD12.1212.196后61.9346.621111￥1.7471.821前52.0086.796后一前4.調(diào)整下列閉合水準(zhǔn)路線成果,并計(jì)算各點(diǎn)高程。水準(zhǔn)測量成果調(diào)整表測點(diǎn)測站數(shù)咼差值高程m備注觀測值m改正數(shù)mm調(diào)整值m

BM1NNNNBM]￡實(shí)測高差￡h= 已知高差=H-Ha=0終始 ,_高差閉合差fh= 容許閉合差fh容=士Wn=h h容一個(gè)測站的改正數(shù)=工n5．完成下表測回法測角記錄的計(jì)算。測站測回?cái)?shù)盤位目標(biāo)水平度盤讀數(shù)°/〃水平角草圖半測回值°/〃一測回值°/〃平均值°/〃O1左A01200ABVOB914500右A1801130B27145002左A901148B1814454右A2701212B145126.完成下表豎直角測量記錄計(jì)算。測站目標(biāo)豎盤位置豎盤讀數(shù)°/〃半測回角值°/〃一測回角值°/〃指標(biāo)差豎盤形式OM左811842全圓式順時(shí)針注記右2784130N左1240330右23556547．丈量兩段距離，一段往測為126.78米，返測為126.68米，另一段往測、返測分別為357.23米和357.33米。問哪一段丈量的結(jié)果比較精確？為什么？兩段距離丈量的結(jié)果各等于多少？

8．一根名義長為30米的鋼尺與標(biāo)準(zhǔn)長度比較得實(shí)際長為30.012米，用這根鋼尺量得兩點(diǎn)間距離為264.580米，求經(jīng)過尺長改正后的距離。4224a=126°18’28〃422412卩=134°34’26〃1卩=57°32’46〃2卩=61°17’20〃3卩=61°09’54〃4R=23R=34R=4211.設(shè)丈量了兩段距離，結(jié)果為：l=528.46m±0.21m；l=517.25m±0.16m。試比較這兩段距離之和及之差的精度。12.如圖所示，三角形的三個(gè)觀測值列于圖上，已知：acb=124°15',求aba和aCA13?閉合導(dǎo)線的觀測數(shù)據(jù)和已知數(shù)據(jù)如表所示，試求B、C、D三點(diǎn)的坐標(biāo)。(取為至cm)點(diǎn)號(hào)坐標(biāo)方位角距離(m)增量計(jì)算值(m)改正后增量(m)坐標(biāo)值△x△y△x△yxyA125°30'30〃105.22500.000500.000B53°18'43〃80.18C306°19'15〃129.34D215°53'17〃78.16A￡輔助計(jì)算：f=Xf=yfD=K=X牛A「B

02〃，試計(jì)算附合導(dǎo)線各邊的方位D14.如圖，已知aA=150°30’42〃，a“=28°44’AB CDlMah15.如圖，儀器安置在A點(diǎn)，要測定M點(diǎn)的距離和高程，今測得仰角a=17°02’，視距間隔nD14.如圖，已知aA=150°30’42〃，a“=28°44’AB CDlMah16.已知下列左角和右角，試計(jì)算線路的轉(zhuǎn)角a，并說明路線是左轉(zhuǎn)角還是右轉(zhuǎn)角。1)左角:B=170°24’30〃；2)右角:B2=165°25’36〃；17.完成下表中平測量記錄的計(jì)算。測點(diǎn)水準(zhǔn)尺讀數(shù)(m)視線高程(m)高程(m)備注后視中視前視BM51.426417.628K4+9800.87K5+0001.56+0204.25+0401.62+0602.30ZD10.8762.402+0802.42+092.41.87+1000.32ZD21.2862.004+1203.15+1403.04+1600.94+1801.88+2002.00ZD 3 2.18618.已知交點(diǎn)的里程為K3+182.76，測得轉(zhuǎn)角ay=25°48’，圓曲線半徑R=300m，求曲線測設(shè)元素及主點(diǎn)里程。19.設(shè)擬測設(shè)AB的水平距離D°=18m，經(jīng)水準(zhǔn)測量得相鄰樁之間的高差h=0.115m。精密丈量時(shí)所用鋼尺的名義長度L0=30m，實(shí)際長度L=29.997m,膨脹系數(shù)a=1.25X10-5，檢定鋼尺時(shí)的溫度t=20°C。求在4°C環(huán)境下測設(shè)時(shí)在地面上應(yīng)量出的長度D。 rv —20.已知MN—300°25’17〃，X=14.228m，Y=77.564m，X=47.337m，Y=73.556m，試計(jì)MMAA算置儀器于M點(diǎn)，用極坐標(biāo)法測設(shè)A點(diǎn)所需的數(shù)據(jù)。21計(jì)算水準(zhǔn)測量觀測高差及B點(diǎn)高程。表2-4水準(zhǔn)測量觀測記錄手薄測站占八、、號(hào)水準(zhǔn)尺讀數(shù)(m)咼 差(m)高程(m)備注后視前視IBM.A1.87422.718已知TP.10.919IITP.11.727TP.21.095

IIITP.21.186TP.31.823wTP.31.712B1.616計(jì)算檢核￡￡a-￡b=￡h=22.在表2-5中進(jìn)行附合水準(zhǔn)測量成果整理，計(jì)算高差改正數(shù)、改正后高差和高程。表2-5附合水準(zhǔn)路線測量成果計(jì)算表點(diǎn)號(hào)路線長L(km)觀測咼差h(m)i咼差改正數(shù)v(m)hi改正后咼差h(m)i高程H(m)備注BM.A1.5+4.3627.967已10.6+2.41320.8-3.12131.0+1.26341.2+2.7165BM.1.6-3.71511.819已￡f=￡h—(H—H)= f=+40+'L=h 測 B A h容—fv 二 ￡V=1km 乙L h23.按I1ABI2法檢校水準(zhǔn)儀i角，用鋼尺量得Di=5.8m,D2=40.9m。安置水準(zhǔn)儀在［點(diǎn)，得A尺讀數(shù)a=1207mm,B尺讀數(shù)b=1139mm,然后搬水準(zhǔn)儀至I點(diǎn)，又讀A尺上讀數(shù)a=11221466mm,B尺上讀數(shù)=1382mm,問：水準(zhǔn)管軸是否平行于視準(zhǔn)軸？如果不平行，當(dāng)水準(zhǔn)管氣泡居中時(shí)，視準(zhǔn)軸是向上傾斜還是向下傾斜？i角值是多少？如何進(jìn)行校正？24.已知A點(diǎn)和B點(diǎn)的坐標(biāo)，計(jì)算各邊的坐標(biāo)方位角心=節(jié)"開他人=代4.7冊(cè)陀兀=365.192m?7E=11^-771mo現(xiàn)測得各轉(zhuǎn)折角為:負(fù)=3孔"1巧仁以=73°08^40；/?2=68°39f56；^=295°44f36；

25.按表的數(shù)據(jù)，計(jì)算閉合導(dǎo)線各點(diǎn)的坐標(biāo)值。已知九宀=±40"*n,—=1/2000。閉合導(dǎo)線坐標(biāo)計(jì)簟 容點(diǎn)號(hào)角度觀測值(右角)°/〃坐標(biāo)方位角°/〃邊長(m)坐標(biāo)x(m)y(m)12000.002000.00694500103.8521390500114.5739415 54162.464883636133.5451223930123.68195233026附合導(dǎo)線AB123CD中A、B、C、D為高級(jí)點(diǎn)，已知aAB=48°48'48〃,x=1438.38m，y=4973.66m,a廠門=331°25'24〃，x=1660.84m,y=5296.85m；B B CD C C測得導(dǎo)線左角ZB=271°36'36〃，Zl=94°18'18〃，Z2=101°06'06〃，Z3=267°24'24〃，ZC=88°12'12〃。測得導(dǎo)線邊長：D=118.14m，D=172.36m,B1 12D=142.74m，D=185.69m。計(jì)算1、2、3點(diǎn)的坐標(biāo)值。已知f=±40%；，23 3C B容K=1/2000。容27．整理表中的四等水準(zhǔn)測量觀測數(shù)據(jù)。表四等水準(zhǔn)測量記錄整理測站編號(hào)后尺下絲、八刖尺下絲方向及尺號(hào)標(biāo)尺讀數(shù)K+黑減紅咼差中數(shù)備考上絲上絲后視前視后距前距黑面紅面視距差d￡d119790738后171864050K=4.6871K=4.787214570214-前04765265-252.252.4后-前+1.242+1.140+21.2410

-0.2-0.2227390965后2461724721830401-刖06835370后-前319181870后1604629112901226-刖15486336后-前410882388后0742552803961708-刖20486736后-前檢查計(jì)算巴= 為后視= 以="D= 》前視= Eh =b 平均Ed= E后視—E前視= 2Eh =平均28,已知a=300004z00〃，x=14.22m,y=86.71m；x=34.22m,y=66.71m；x=54.14m,ABAA112y=101.40m。試使用CASIOfx-3950P計(jì)算器編程計(jì)算儀器安置于A點(diǎn)，用極坐標(biāo)法測設(shè)1與2點(diǎn)的測設(shè)數(shù)據(jù)及檢核角Y、檢核長度L，并簡述測設(shè)點(diǎn)位過程。29已知圓曲線交點(diǎn)JD里程樁號(hào)為K2+362.96，右偏角t右為28°28’00〃，欲設(shè)置半徑為300m的圓曲線，計(jì)算圓曲線諸元素T、L、E、D，并計(jì)算圓曲線各主點(diǎn)的里程樁號(hào)。30據(jù)表中所列數(shù)據(jù)，試進(jìn)行閉合導(dǎo)線角度閉合差的計(jì)算合調(diào)整，并計(jì)算各邊的。坐標(biāo)方位角。點(diǎn)號(hào)觀測左角改正數(shù)改正角坐標(biāo)方位角°/〃〃°/〃°/〃

A14500001102175321044429386113041235904A12246261Z輔助計(jì)算f=pf=±60〃n= p容 答案1.6°帶：N=19,入=111°；3°帶：N=38,入=114°。2．半徑在10km的范圍內(nèi)，可以不考慮地球曲率的影響計(jì)算結(jié)果如下表：測點(diǎn)編號(hào)占八、、號(hào)后尺下絲-刖尺下絲方向及尺號(hào)水準(zhǔn)尺中絲讀數(shù)K+黑八、、減紅咼差中數(shù)備注上絲上絲后視距前視距黑八、、(m)紅(m)視距差d￡d1BM11.5710.793后51.3846.1710+0.832K5=4.787K6=4.6871ZI1)11.1970.417前60.5515.239-137.437.6后一刖+0.833+0.932+1-0.2-0.22ZD12.1212.196后61.9346.6210-0.0741A11.7471.821前52.0086.796-137.437.5后一刖-0.074-0.175+1-0.1-0.3計(jì)算結(jié)果如下表：水準(zhǔn)測量成果調(diào)整表測點(diǎn)測站數(shù)咼差值高程m備注觀測值m改正數(shù)mm調(diào)整值mBM1102.134+102.14444.313N146.45781.424+81.432N247.8898-1.787+8-1.779

N46.11011-1.714+12-1.702N44.40812-0.108+13-0.095BM]44.31349-0.051+510￡已知咼差=日終—H始=0終始 「實(shí)測咼差工h=-0.051m咼差閉合差f=-0.051mhf+51 1—h= ?+1一個(gè)測站的改正數(shù)二為n49mm容許閉合差f容許閉合差f二士 n=±70mmh容測站測回?cái)?shù)盤位目標(biāo)水平度盤讀數(shù)°’〃水平角草圖半測回值°’〃一測回值°’〃平均值°’〃O1左A01200913300913315913309ABVOB914500右A1801130913330B27145002左A901148913306913303B1814454右A2701212913300B145126.計(jì)算結(jié)果如下表:測站目標(biāo)豎盤位置豎盤讀數(shù)°’〃半測回角值°’〃一測回角值°’〃指標(biāo)差〃豎盤形式OM左8118428411884124+6全圓式順時(shí)針注記右278413084130N左1240330-340330-340318+12右2355654-3403067.相對(duì)誤差：kl=l/1200,k2=l/3590,因?yàn)橄鄬?duì)誤差kl>k2；所以第二段距離丈量比較精確。兩段距離丈量的結(jié)果分別為:d1=126.73m，d2=357.28m。D=264.686m。計(jì)算結(jié)果如下：a23=80°52’54〃a=260°3252’54〃R=80°2352’54〃NEa=199°3435’34〃a=19°4335’34〃R=19°3435’34〃SWa=318°422540〃a=138°242540〃R=41°4234’20〃NWa =89°20’30〃、a=313°20’10〃。ABED兩段距離的中誤差m1=m2=±0.26m。由于第一段距離比第二段長,所以第一段的相對(duì)中誤差小于第二段的相對(duì)中誤差。a=244°31’04〃；a=197°26’36〃。BACA計(jì)算結(jié)果如下表：占八、、號(hào)坐標(biāo)方位角距離(m)增量計(jì)算值(m)改正后增量(m)坐標(biāo)值△x△y△x△yxyABCDA125°30’30〃105.22-61.11+85.65-61.13+85.67500.000500.000438.87585.6753°18’43〃80.18+47.90+64.30+47.88+64.32486.75649.99306°19’15〃129.34+76.61-104.21+76.59-104.19563.34545.80215°53’17〃78.16-63.32-45.82-63.34-45.80500.000500.000￡392.90+0.08-0.08輔助計(jì)算：f=+0.08Xf=-0.08yfD=0.113K=1/3400XBa’=65°42’47〃 ；a=146°23’12〃 ；a=108°33112B1122C水平距離：D=125.24米；高程Hm=118.334米。a=9°35’30〃為左轉(zhuǎn)角；a=14°34’24〃為右轉(zhuǎn)角。計(jì)算結(jié)果如下表：測點(diǎn)水準(zhǔn)尺讀數(shù)(m)視線高程(m)高程(m)備注后視中視前視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+1000.32417.21ZDo1.2862.004416.810415.524+1203.15413.66

+1403.04413.77+1600.94415.87+1801.88414.93+2002.00414.81ZD3—2.186414.624T=68.71m；L=135.09m；E=7.77m；D=2.33m。JD=K3+182.76；ZY=K3+114.05；YZ=K3+249.14；QZ=K3+181.60；ZY=JD-T=K3+114.051YZ=ZY+L=K3+249.139QZ=YZ-L/2=K3+181.595JD=QZ+D/2=K3+182.76(校核)ry 25。48°T=Rtg—=300xtg- =68.709(m)22兀L= oR=135.088(m)180yE=R(sec-1)=7.768(m)D=-T-L=2.330(m)D=18.0051米。DMj=33.58m；°MN=353°05’52〃；P=52°40’35〃。21測站占八、、號(hào)水準(zhǔn)尺讀數(shù)(m)咼 差(m)咼程(m)備注后視前視IBM.A1.8740.95522.718已知TP.10.91923.973IITP.11.7270.632TP.21.09524.305IIITP.21.186-0.637TP.31.82323.668WTP.31.7120.096B1.61623.764計(jì)算檢核￡6.4995.453￡a-￡b=1.046￡h=1.04622點(diǎn)號(hào)路線長L(km)觀測咼差hj(m)咼差改正數(shù)v(m)h改正后咼差h(m)i高程H(m)備注BM.A1.5+4.362-0.015+4.3477.967已112.3140.6+2.413-0.006+2.407214.7210.8-3.121-0.008-3.129311.5921.0+1.263-0.010+1.253

412.8451.2+2.716-0.012+2.704515.5491.6-3.715-0.015-3.730BM.11.819已6.7f=￡h —(H—H)=+66mm f=±40YL=±104mmh 測 BA h容fv=—h=—9.85mm/km ￡v=-66mm1km ZL h23．由公式計(jì)算：(a—b)—(a—b)i=J2(i丄p〃—1.61x10-5?(D+D)=+46〃2(D—D) i221因i>20"，故水準(zhǔn)管不平行視準(zhǔn)軸。對(duì)于i角大于對(duì)于i角大于20"的水準(zhǔn)儀需要進(jìn)行校正。, A-Da=a— 2-2 2D—D21=1466—9=1457mm因a2<a2,說明視線向上傾斜。校正：水準(zhǔn)儀在I點(diǎn)處不動(dòng)，旋轉(zhuǎn)微傾螺旋，使十字絲中絲對(duì)準(zhǔn)A尺上的正確讀數(shù)a2(1457mm),此時(shí)符合水準(zhǔn)氣泡就不再居中了，但視線已處于水平位置。用校正針拔動(dòng)位于目鏡端的水準(zhǔn)管上、下兩個(gè)校正螺絲，使符合水準(zhǔn)氣泡嚴(yán)密居中。此時(shí)，水準(zhǔn)管軸也處于水平位置，達(dá)到了水準(zhǔn)管軸平行于視準(zhǔn)軸的要求。校正需反復(fù)進(jìn)行，使i角合乎要求為止。24^ =180+arctanba=91o18'AB X—XBAa二a+卩二91018'+33001236"—360=6103036"A1 ABAa=a+180—卩二6103036"+180—73。0840”=16802156"TOC\o"1-5"\h\z12 A1 1a=a—180+卩二16802156"—180+6803956"=5700152"23 12 2a=a—180+卩二5700152"—180+29504436"=17204628"34 23 325.閉合導(dǎo)線坐標(biāo)計(jì)算點(diǎn)號(hào)角度觀測值(右角)°/〃坐標(biāo)方位角°/〃邊長(m)坐標(biāo)計(jì)算x(m)y(m)

12-6〃13905003-6〃9415544-6〃8836365-612-6〃13905003-6〃9415544-6〃8836365-6〃12239301-6〃952330694500103.851104006114.571962418162.462874748133.543450824123.68694500638.102000.002000.002035.9412097.4511995.5002204.6701839.6492158.8191880.4602031.6952000.002000.00pfp容=±40〃"=±89〃"fp<fp容（合格）=+0?019m、J=-0.125mx yf=±0.126mDk-ID-0126一丄ED638.15064k<k容（合格）26.f卩=60〃、fp容二±4Zn二±89〃、f二偵師、=+0?101m、y'二±0.201mD合格）、ED=0.201/618.93=1/3080、k<k容合格）。X1=1347.281m，X=1446.876m，2X=1577.132m，3Y=5048.914m，Y=5189.593m，Y=5131.102m。12327.表四等水準(zhǔn)測量記錄整理測站編號(hào)后尺下絲、八刖尺下絲方向及尺號(hào)標(biāo)尺讀數(shù)K+黑減紅咼差中數(shù)備考上絲上絲后視前視后距前距黑面紅面視距差d￡d119790738后K171864050K=4.6871K=4.787214570214前k204765265-252.252.4后-前+1.242+1.140+21.2410-