CASIO-fx4800P型計(jì)算器連續(xù)計(jì)算線路高程、坐標(biāo)及放樣程序劉宗遠(yuǎn)2007-11-24(定稿)【簡(jiǎn)述】為了適應(yīng)現(xiàn)場(chǎng)快速、準(zhǔn)確、靈活的放樣要求，作者根據(jù)線路施工測(cè)量特點(diǎn)，運(yùn)用計(jì)算器的編程功能，使整條線路的施工測(cè)量計(jì)算數(shù)據(jù)能連續(xù)快速的計(jì)算，只要把整條線路各個(gè)交點(diǎn)處的計(jì)算要素輸入子程序中，你便擁有整條線路的“數(shù)據(jù)庫(kù)〞。在忙碌的施工現(xiàn)場(chǎng)，你不必?cái)y帶大量的施工圖和資料來(lái)查找平面、縱斷面的設(shè)計(jì)要素，更不必?fù)?dān)憂設(shè)計(jì)要素的輸入錯(cuò)誤，從而使得計(jì)算和放樣輕松、方便、快捷?！居?jì)算范圍】坐標(biāo)局部包括：各等級(jí)公路和高速路的直線段、圓曲線段、加對(duì)稱緩和曲線的圓曲線段中、邊樁坐標(biāo)及放樣計(jì)算。高程局部包括：各等級(jí)公路和高速路的直線段、豎曲線段、緩和超高段中、邊樁高程及放樣計(jì)算。一、坐標(biāo)及放樣程序【起算數(shù)據(jù)】：交點(diǎn)里程樁號(hào)、交點(diǎn)坐標(biāo)、前直線方位角、交點(diǎn)轉(zhuǎn)角、圓曲線半徑、緩和曲線長(zhǎng)〔一〕主程序：XYFY2Fix4M"Xc=":P"Yc="＇如須放樣輸入測(cè)站坐標(biāo)值,否那么輸入0Lbl0{HS}:H"K0+0":S"B=(-B,0,B)":Prog"A"＇變量輸入和聲明S=0=>E=0:≠>E=90＇求邊樁坐標(biāo)時(shí)的偏角值判定L=πRN÷180+V＇含有緩曲線的曲線總長(zhǎng)T=(V÷2-V^3÷(240R^2))+(R+(V^2÷(24R)-V^4÷(2688R^3)))tan(N÷2)＇切線長(zhǎng)A=Q-T:B=A+V:D=A+L:C=D-V＇A-ZH(ZY)點(diǎn)樁號(hào),B-HY點(diǎn)樁號(hào),C-YH點(diǎn)樁號(hào),D-HZ(YZ)點(diǎn)樁號(hào)Rec(T,F+180)＇求ZH(ZY)點(diǎn)的坐標(biāo)增量Z[1]=W+I:Z[2]=K+J＇ZH(ZY)點(diǎn)坐標(biāo)值Rec(T,F+GN)＇求HZ(YZ)點(diǎn)的坐標(biāo)增量Z[3]=W+I:Z[4]=K+J＇HZ(YZ)點(diǎn)的坐標(biāo)值Lbl1U=S÷(Abs(S+10E-19)):S=AbsS＇左右偏角每件判定H<A=>Goto2:≠>＇第一直線上坐標(biāo)計(jì)算判定H<B=>Goto3:≠>＇第一緩和曲線上坐標(biāo)計(jì)算判定H<C=>Goto4:≠>＇凈圓曲線上坐標(biāo)計(jì)算判定H<D=>Goto5:≠>Goto6⊿⊿⊿⊿＇第二緩和曲線和第二直線上坐標(biāo)計(jì)算判定Lbl2Rec(Q-H,F+180)＇第一直線上中樁坐標(biāo)增量計(jì)算X=W+I:Y=K+J＇中樁坐標(biāo)值計(jì)算Rec(S,F+180-(180-E)U)＇第一直線上與中樁同一斷面的邊樁增量計(jì)算X=X+I:Y=Y+J＇邊樁坐標(biāo)值計(jì)算S=SU＇邊長(zhǎng)條件判定Goto8Lbl3＇進(jìn)入第一緩曲線段計(jì)算Z=H-A＇待求點(diǎn)至ZH點(diǎn)的距離O=90Z^2÷(πRV)＇所求點(diǎn)緩曲線對(duì)應(yīng)的圓心角X=Z-Z^5÷(40R^2V^2)+Z^9÷(3456R^4V^4)＇緩曲線上ZH點(diǎn)至待求的支距X坐標(biāo)Z=Z^3÷(6RV)-Z^7÷(336R^3V^3)+Z^11÷(42240R^5V^5)＇緩曲線上ZH點(diǎn)至待求點(diǎn)的支距Y坐標(biāo)Lbl7Rec(X,F)X=Z[1]+I:Y=Z[2]+JRec(Z,F+90G)＇把中樁支距坐標(biāo)轉(zhuǎn)換成測(cè)量統(tǒng)一坐標(biāo)X=X+I:Y=Y+JRec(S,F+OG+EU)＇曲線邊樁坐標(biāo)增量計(jì)算X=X+I:Y=Y+J＇坐標(biāo)計(jì)算結(jié)果S=SU＇邊長(zhǎng)條件Goto8Lbl4＇進(jìn)入主圓計(jì)算局部Z=H-A-V÷2＇曲線上待求點(diǎn)到HY點(diǎn)的里程O(píng)=180Z÷(Rπ)＇待求點(diǎn)方位角所對(duì)應(yīng)的圓心角X=RsinO+(V÷2-V^3÷(240R^2))Z=R(1-cosO)+(V^2÷(24R)-V^4÷(2688R^3))＇主圓局部待求點(diǎn)支距坐標(biāo)XYGoto7Lbl5＇進(jìn)入第二緩和曲線計(jì)算Z=D-H＇曲線上待求點(diǎn)到HZ點(diǎn)的里程O(píng)=90Z^2÷(πRV)＇待求點(diǎn)方位角所對(duì)應(yīng)的圓心角X=Z-Z^5÷(40ZR^2V^2)+^9÷(3456R^4V^4)Z=Z^3÷(6RV)-Z^7÷(336R^3V^3)+Z^11÷(42240R^5V^5)＇待求點(diǎn)支距坐標(biāo)XYRec(X,F+GN+180)X=Z[3]+I:Y=Z[4]+J＇把中樁支距坐標(biāo)轉(zhuǎn)換成測(cè)量統(tǒng)一坐標(biāo)Rec(Z,F+GN+180-90G)X=X+I:Y=Y+JRec(S,F+GN+180-OG-(180-E)U)＇曲線邊樁坐標(biāo)增量計(jì)算X=X+I:Y=Y+J＇坐標(biāo)計(jì)算結(jié)果S=SUGoto8Lbl6＇進(jìn)入第二直線段計(jì)算局部Rec(H-D+T,F+GN)＇中樁坐標(biāo)增量計(jì)算X=W+I:Y=K+J＇中樁坐標(biāo)計(jì)算結(jié)果Rec(S,F+GN+EU)＇邊樁坐標(biāo)增量計(jì)算X=X+I:Y=Y+J＇邊樁坐標(biāo)計(jì)算結(jié)果S=SUGoto8Lbl8X=X◢＇顯示坐標(biāo)計(jì)算結(jié)果Y=Y◢M≠0=>Goto9:≠>Goto0⊿Lbl9＇進(jìn)入放樣局部計(jì)算Pol(X-M,Y-P)＇增量計(jì)算J<0=>J=J+360:≠>J=J⊿J"A"=IntJ+0.01Int(60FracJ)+0.006Frac(60FracJ)◢＇方位角計(jì)算結(jié)果〔此顯示值為度分秒格式〕I"L"=I◢＇極距計(jì)算結(jié)果Goto0(二)子程序:AH≤ZY2(ZH2)=>Q=JD1:W=X1:K=Y1:R=R1:F=F0:N=N1:V=Ls1:G=1(-1):=>H≤ZY3(ZH3)=>Q=JD2:W=X2:K=Y2:R=R2:F=F1:N=N2:V=Ls2:G=1(-1):=>H≤ZY4(ZH4)=>Q=JD3:W=X3:K=Y3:R=R3:F=F2:N=N3:V=Ls3:G=1(-1):=>H≤ZY5(ZH5)=>Q=JD4:W=X4:K=Y4:R=R4:F=F3:N=N4:V=Ls4:G=1(-1):=>……………H≤ZYn+1(ZHn+1)=>Q=JDn:W=Xn:K=Yn:R=Rn:F=Fn-1:N=Nn:V=Lsn:G=1(-1)注:H—待求點(diǎn)樁號(hào)ZYn+1(ZHn+1)—后曲線起點(diǎn)樁號(hào)Q—本曲線交點(diǎn)樁號(hào)W—本曲線交點(diǎn)X坐標(biāo)K—本曲線交點(diǎn)Y坐標(biāo)R—本曲線內(nèi)圓曲線半徑F—前直線方位角N—本交點(diǎn)轉(zhuǎn)角V—本曲線內(nèi)緩和曲線長(zhǎng)G—線路轉(zhuǎn)向符,左轉(zhuǎn)角-1,右轉(zhuǎn)角為+1二、高程及放樣程序【起算數(shù)據(jù)】：變坡點(diǎn)樁號(hào)A、變坡點(diǎn)高程B、前后縱坡CD、豎曲半徑R、橫坡度F、最大超高橫坡度G、ZH點(diǎn)樁號(hào)、YH點(diǎn)樁號(hào)、HZ點(diǎn)樁號(hào)、施工層厚度N、視線高W〔一〕主程序：GCFYW"SXG="：N＇常量輸入〔視線高程、施工層厚度〕Lbl1｛LО｝:L"K0+0"：О"B=":Prog"B"＇變量輸入及聲明K=C-D＇坡度差及豎曲線偏角K>0=>J=-1:≠>J=1⊿＇凹凸豎曲線判斷條件T=Abs(RK)÷2＇豎曲線切線長(zhǎng),如需顯示那么在后面加上◢H=A-T＇豎曲線起點(diǎn)ZY樁號(hào),如需顯示那么在后面加上◢X=A+T＇豎曲線終點(diǎn)YZ樁號(hào),如需顯示那么在后面加上◢M=L-A＇待求點(diǎn)至變坡點(diǎn)的距離L≤H=>P=B+MC-N-W:≠>＇前縱坡直線段中樁高程計(jì)算L≤A=>P=B+MC+J(T-AbsM)2÷(2R)-N-W:≠>＇前縱坡豎曲線中樁高程計(jì)算L≤X=>P=B+MD+J(T-AbsM)2÷(2R)-N-W:≠>＇后縱坡豎曲線中樁高程計(jì)算L>X=>P=B+MD-N-W⊿⊿⊿⊿⊿＇后縱坡直線段中樁高程計(jì)算E=0=>Goto2＇直線局部中、邊樁計(jì)算判斷條件≠>L≤E=>Goto2＇直線局部中、邊樁計(jì)算判斷條件≠>L>V=>Goto2＇直線局部中、邊樁計(jì)算判斷條件≠>L>E=>Goto3＇前緩曲超高局部中、邊樁計(jì)算判斷條件≠>L>U=>Goto4⊿⊿⊿⊿＇后緩曲超高局部中、邊樁計(jì)算判斷條件Lbl2O=0=>Z“H〞=AbsP◢＇顯示直線局部中、邊樁高程計(jì)算結(jié)果≠>Y“HB〞=Abs(P-OF)◢不需放樣顯示高程,否那么顯示放樣水準(zhǔn)尺計(jì)數(shù)⊿Goto1Lbl3S=〔L-E〕〔F+G〕÷〔V-U〕-F＇前緩曲線超高橫坡度計(jì)算S≤F=>Goto5：≠>S≤G=>Goto6＇超高起點(diǎn)(終點(diǎn))至零界面、零界面至全超高及全超高≠>Goto7⊿⊿局部的計(jì)算判斷條件Lbl4S=〔V-L〕〔F+G〕÷〔V-U〕-F＇后緩曲線超高橫坡度計(jì)算S≤F=>Goto5：≠>S≤G=>Goto6＇超高起點(diǎn)(終點(diǎn))至超高變坡零界面、零界面至全≠>Goto7⊿⊿超高、全超高局部計(jì)算判斷條件Lbl5O=0=>Z“H1”=AbsP◢＇≠>Y“H-D1”=Abs(P-OF)◢Q“H-G1”=Abs(P+OS)⊿Goto1Lbl6O=0=>Z“H2”=AbsP◢＇≠>Y“H-D2”=Abs(P-OS)◢Q“H-G2”=Abs(P+OS)⊿Goto1Lbl7O=0=>Z“H3”=AbsP◢＇≠>Y“H-D3”=Abs(P-OG)Q“H-G3”=Abs(P+OG)⊿Goto1注：W“SXG〞-視線高N-施工層厚度L"K0+0"-待求點(diǎn)樁號(hào)О"B="-中樁至邊樁距離〔二〕子程序：BL≤ZY2=>A=JD1:B=H1:C=I0:D=I1:R=R1:F=Ih:E=ZH1:U=YH1:V=HZ1:G=Imax1:≠>L≤ZY3=>A=JD2:B=H2:C=I1:D=I2:R=R2:F=Ih:E=ZH2:U=YH2:V=HZ2:G=Imax2:≠>L≤ZY4=>A=JD3:B=H3:C=I2:D=I3:R=R3:F=Ih:E=ZH3:U=YH3:V=HZ3:G=Imax3:≠>L≤ZY4=>A=JD3:B=H3:C=I2:D=I3:R=R3:F=Ih:E=ZH3:U=YH3:V=HZ3:G=Imax3:≠>……L≤ZYn+1=>A=JDn:B=Hn:C=In-1:D=In:R=Rn:F=Ih:E=ZHn:U=YHn:V=HZn:G=Imaxn注:ZYN+1:-下一個(gè)豎曲線起點(diǎn)樁號(hào)〔如：變坡點(diǎn)2的計(jì)算范圍為前豎曲線終點(diǎn)YZ1至后豎曲線起點(diǎn)ZY3，那么在程序中“L≤ZY3”就應(yīng)輸入ZY3的里程樁。同理，程序中“L≤ZY4”就應(yīng)輸入ZYA:-變坡點(diǎn)樁號(hào)〔在程序中輸入時(shí)以實(shí)際的變坡點(diǎn)里程樁號(hào)值替換程序中的JD1字符，以下同〕B:-變坡點(diǎn)高程C:-前縱坡度〔輸入帶符號(hào)〕D:-后縱坡度〔輸入帶符號(hào)〕F:-橫坡度R：-豎曲線半徑E:-ZH點(diǎn)樁號(hào)U:-YH點(diǎn)樁號(hào)V:-HZ點(diǎn)樁號(hào)G:-最大超高橫坡度例如如下列圖平曲線要素表交點(diǎn)樁號(hào)交點(diǎn)坐標(biāo)前直線方位角F轉(zhuǎn)角NRLs要素樁號(hào)XY°′″°′″ZY(ZH)YZ(YH)QDK84+000.00048344.94088997.968JD5K85+596.96048615.60087430.200297474213294850000K84+999.32K86+177.13JD6K87+964.81048461.98885055.84526617542126372000250K87+460.89K88+459.41ZDK88+800.00048719.33684251.499一、平面坐標(biāo)及放樣數(shù)據(jù)計(jì)算以方案二程序?yàn)槔?、首先根據(jù)設(shè)計(jì)圖紙整理平曲線計(jì)算工素填入要素表中方便在程序中輸入。2、子程序A的輸入：H≤87460.89=>Q=85596.96:W=48561.6:K=87430.2:R=5000:F=297°47′42″:N=13°29′48″:V=0:G=-1:=>H≤88800=>Q=87964.81:W=48461.988:K=85055.845:R=2000:F=266°17′54″:N=21°26′37″:V=250:G=13、運(yùn)行主程度XYFY21)計(jì)算右邊樁按“EXE〞鍵，顯示“XC=？〞輸入測(cè)站X坐標(biāo)，48580.155，無(wú)須放樣輸入0。按“EXE〞鍵，顯示“YC=？〞輸入測(cè)站Y坐標(biāo)，88196.234，無(wú)須放樣輸入0。按“EXE〞鍵，顯示“K0+0？〞輸入待求點(diǎn)樁號(hào)84800。按“EXE〞鍵，顯示“B=〔-B，0，+B〕？〞輸入中樁至邊樁距離14。(左邊樁-B，中樁0，右邊樁+B)按“EXE〞鍵，顯示“I？〞不輸入，計(jì)算器內(nèi)部計(jì)算增量。按“EXE〞鍵，顯示“J？〞不輸入，計(jì)算器內(nèi)部計(jì)算增量。按“EXE〞鍵，顯示右邊樁坐標(biāo)X=48494.835按“EXE〞鍵，顯示右邊樁坐標(biāo)Y=88212.012按“EXE〞鍵，顯示右邊樁放樣方位角A=169.3123〔此值為度分秒格式，即169°31′23″以下同〕按“EXE〞鍵，顯示右邊樁放樣距離L=86.76652)計(jì)算中樁按“EXE〞鍵，顯示“K0+0？〞輸入待求點(diǎn)樁號(hào)84800。按“EXE〞鍵，顯示“B=〔-B，0，+B〕？〞輸入中樁至邊樁距離0。(左邊樁-B，中樁0，右邊樁+B)按“EXE〞鍵，顯示右邊樁坐標(biāo)X=48481.0391按“EXE〞鍵，顯示右邊樁坐標(biāo)Y=88209.630按“EXE〞鍵，顯示右邊樁放樣方位角A=172.1810按“EXE〞鍵，顯示右邊樁放樣距離L=100.01713)計(jì)算左邊樁按“EXE〞鍵，顯示“K0+0？〞輸入待求點(diǎn)樁號(hào)84800。按“EXE〞鍵，顯示“B=〔-B，0，+B〕？〞輸入中樁至邊樁距離-14。(左邊樁-B，中樁0，右邊樁+B)按“EXE〞鍵，顯示右邊樁坐標(biāo)X=48467.2432按“EXE〞鍵，顯示右邊樁坐標(biāo)Y=88207.2482按“EXE〞鍵，顯示右邊樁放樣方位角A=174.2543按“EXE〞鍵，顯示右邊樁放樣距離L=113.4477計(jì)算下一樁號(hào)數(shù)據(jù)按“EXE〞鍵，顯示“K0+0？〞輸入待求點(diǎn)樁號(hào)84850。重復(fù)以上步驟,中、邊樁的計(jì)算順序不限，只是邊樁輸入時(shí)注意左負(fù)右正。樁號(hào)輸入不限制，可以是整樁號(hào)或非整樁號(hào)。放樣轉(zhuǎn)站時(shí)須重新啟動(dòng)程序，輸入測(cè)站坐標(biāo)后可繼續(xù)進(jìn)行計(jì)算。本程序遇對(duì)稱性緩和曲線時(shí)可連續(xù)計(jì)算，不必分段計(jì)算，這也是本程序的一個(gè)特點(diǎn)。二、高程及放樣數(shù)據(jù)計(jì)算1、首先根據(jù)設(shè)計(jì)圖紙整理豎曲線要素，填入如上格式表中。2、將要素輸入子程序B中：L≤85196.4=>A=84800:B=60.04:C=0.005:D=0.0116:R=20000:F=0.02:E=0:U=0:V=0:G=0:≠>L≤85878.8=>A=85470:B=67.81:C=0.0116:D=-0.034:R=12000:F=0.02:E=0:U=0:V=0:G=0:≠>L≤86649.5=>A=86000:B=49.79:C=-0.034:D=-0.0037:R=8000:F=0.02:E=0:U=0:V=0:G=0:≠>L≤87510=>A=86750:B=47.02:C=-0.0037:D=0.003:R=30000:F=0.02:E=87460.89:U=88209.41:V=88459.41:G=0.03:≠>L≤88800=>A=87750:B=50.02:C=0.003:D=-0.003:R=80000:F=0.02:E=87460.89:U=88209.41:V=88459.41:G=0.033、運(yùn)行主程序GCFY1〕無(wú)超高段高程放樣輸入與顯示如下:按“EXE〞鍵，顯示“SXG=？〞輸入測(cè)站視線高程63.1(無(wú)須放樣輸入0)。按“EXE〞鍵，顯示“N=？〞輸入施工層厚度0.5,〔如水穩(wěn)層、面層等〕。按“EXE〞鍵，顯示“K0+0？〞輸入待求點(diǎn)里程樁號(hào)84850。按“EXE〞鍵，顯示“B=？〞輸入中樁至邊樁的距離。求中樁輸入0。按“EXE〞鍵，顯示“H=2.974”中樁放樣水準(zhǔn)尺計(jì)數(shù)。按“EXE〞鍵，顯示“K0+0？〞輸入待求點(diǎn)里程樁號(hào)84850。按“EXE〞鍵，顯示“B=？〞輸入中樁至邊樁的距離。求邊樁輸入14。按“EXE〞鍵，顯示“HB=3.254”按“EXE〞鍵，顯示“K0+0？〞輸入待求點(diǎn)里程樁號(hào)…………重復(fù)以上步驟繼續(xù)計(jì)算下一樁號(hào)數(shù)據(jù)。2〕進(jìn)入超高段高程放樣輸入與顯示如下：超高起點(diǎn)(終點(diǎn))至超高變坡零界面路段按“EXE〞鍵，顯示“SXG=？〞輸入測(cè)站視線高程51.5(無(wú)須放樣輸入0)。按“EXE〞鍵，顯示“N=？〞輸入施工層厚度0.5,〔如水穩(wěn)層、面層等〕。按“EXE〞鍵，顯示“K0+0？〞輸入待求點(diǎn)里程樁號(hào)87500。按“EXE〞鍵，顯示“B=？〞輸入中樁至邊樁的距離。求中樁輸入0。按“EXE〞鍵，顯示“H1=2.73按“EXE〞鍵，顯示“K0+0？〞輸入待求點(diǎn)里程樁號(hào)87500按“EXE〞鍵，顯示“B=？〞輸入中樁至邊樁的距離。求邊樁輸入14。按“EXE〞鍵，顯示“H-D1=3.01”降低按“EXE〞鍵，顯示“H-G1=2.9”按“EXE〞鍵，顯示