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竖曲线高程计算（fx-4800）（1）Lbl 0：H：B：R：I：J：{L}：T=R Abs(J-I) ÷2←C=B-L←I＜J=>F=1：≠=>I＞J=>F=－1△△←L≦0=>{HRBIJ}：Goto 0≠=>L＜B－T=>Z＝0：P=I≠=>L＜B=>Z=1：P=I：≠=>L＜B＋T=>Z=1：P=J：≠=>Z=0：P=J△△△G=H-CP+ZF(T-Abs C) ²÷2÷R▲Goto 0说明：H：变坡点高程B：变坡点里程L：线路上所求点里程I：前纵坡J：后纵坡T：竖曲线切线长竖曲线半径本程序可及计算范围（前竖曲线的终点至后竖曲线的起点），当L=0时可重新输入起算要素（H，B，R，I，J）进行下一段竖曲线和直线的高程计算。
边桩及路面以下任意厚度高程计算：变量变为：{LNM }主公式变为：G=H-N-CP+ZF（T-Abs C）²÷2÷R▲V=G+ME▲Goto 0N：路面至各施工层的厚度（m）M：中桩至边桩的距离E：路拱（路面横坡）V：左右边桩高程竖曲线高程计算（2）Lbl 1：{N }：N=1＝＞Goto 3：≠＝＞N=2＝＞Goto 4△←Lbl 2：{L}：T=R Abs(J-I) ÷2←C=B-L←I＜J=>F=1：≠=>I＞J=>F=－1△△←L＜3090=>Goto 1：≠=>L＜B－T=>Z＝0：P=I：≠=>L＜B=>Z=1：P=I：≠=>L＜B＋T=>Z=1：P=J：≠=>Z=0：P=J△△△G=H-CP+ZF(T-Abs C) ²÷2÷R▲Goto 1←Lbl 3：L≧3090＝＞H=563.532：B=3860：R=55000：I=0.025：K=4526：L=0.0175←L≧K＝＞H=580.157：B=4810：R=16000：I=0.0175：K=5503.582：L=-0.018←L≧K＝＞H=564.137：B=5700：R=10100：I=-0.018：K=6204：L=0.02089←L≧K＝＞H=579.599：B=6440：R=121193.615：I=0.02089：K=6676：L=0.017←L≧K＝＞H=589.119：B=7000：R=16000：I=0.017：K=7324：L=-0.0235←Goto 2←Lbl 4：L≧3090＝＞H=563.532：B=3860：R=56000：I=0.025：K=4649：L=0.0175←L≧K＝＞H=581.382：B=4880：R=12000：I=0.0175：K=5464.117：L=-0.021←L≧K＝＞H=564.162：B=5700：R=11100：I=-0.021：K=6204：L=0.0215←L≧K＝＞H=580.073：B=6440：R=104856.927：I=0.0215：K=6676：L=0.017←L≧K＝＞H=589.593：B=7000：R=16000：I=0.017：K=7324：L=-0.0235←Goto 2←。
竖曲线要素及变坡点处设计高程计算（1）竖曲线要素及变坡点处设计高程计算坡度计算: ①坡度=高差坡长%150.0-67.2553804.0-1==i %220.038.1833967.02==i②竖曲线类型：当1n n i i +-为正值时，为凹型竖曲线；当1n ni i +-为负值时，为凸型竖曲线。
③由厘米坐标纸上，经过反复试坡、调坡, 根据土石方填挖大致平衡和道。
设计规范中最小坡长等设计要求最后确定出变坡点: 变坡点1桩号:67.2550+K ，高程m 9404.0- 变坡点计算①变坡点一：桩号 67.2550+K , %150.0-i 1= %220.0i 2= R=21621.62m 变坡点高程：m 9404.0- A.计算竖曲线要素：=-=1i 2i ω0.37% 此时根据规范可知：该曲线为凹形曲线竖曲线几何要素中曲线长）（m R L 80%37.021621=?=?=ω竖曲线几何要素中切线长m L T 402802===竖曲线几何要素中外距m RTE 037.062.21621240222=?==B.计算竖曲线起终点桩号竖曲线起点桩号：67.2150+K竖曲线起点高程：m 8804.0-%15.0409404.0-=?+ 竖曲线终点桩号：67.2950+K竖曲线终点高程：m 8524.0-%22.0409404.0-=?+计算设计高程由110()H H T X i =-- H=H 1±hH 1:任一点切线的高程 x ：计算点到起点的距离 i 1：坡度H:任一点的设计高程曲线段内各点的设计高程： K0+220X=220-215.67=4.33m m Rxy 0004.022==切线高程：-0.8804-4.33×0.15%= -0.8869m 设计高程：-0.8869+0.0004= -0.8865m K0+240X=24.33m m Rxy 0137.022==切线高程：-0.8804-24.33×0.15%= -0.9169m 设计高程：-0.9169+0.0137= -0.9032mK0+260X=35.67m m Rxy 0294.022==切线高程：-0.8524-35.67×0.22%= -0.9309m 设计高程：-0.9309+0.0294= -0.9015m K0+280X=15.67m m Rxy 0057.022==切线高程：-0.8524-15.67×0.22%= -0.8869m 设计高程：-0.8869+0.0057= -0.8812m直线段内各点设计高程见下表：设计高程表桩号高程（m）桩号高程（m）K0+000 -0.56 +240.000 -0.9032 +20.000 -0.59 +260.000 -0.9015 +40.000 -0.62 +280.000 -0.8812 +60.000 -0.65 +300.000 -0.8361 +80.000 -0.68 +320.000 -0.7921 +100.000 -0.71 +340.000 -0.7481 +120.000 -0.74 +360.000 -0.7041 +140.000 -0.77 +380.000 -0.6601 +160.000 -0.80 +400.000 -0.6161 +170.000 -0.83 +420.000 -0.5721 +180.000 -0.86 +440.000 -0.5281 +200.000 -0.89+220.000 -0.8865。
Excel表格制作标高计算程序新建一个Excel文件，把Sheet1表重命名为“竖曲线”，把Sheet2表重命名为“设计标高”。
（1）在竖曲线表中的A1-E1（合并）单元格输入线路名称，在A2-E2单元格中分别输入“变坡点编号”、“变坡点里程”、“变坡点标高”、“曲线半径”和“切线长”,从第三行开始输入对应数据，（2）打开VB编辑器（Alt+F11），双击工程资源管理器中“设计标高”表图标，复制以下程序到界面上，保存后返回Excel窗口，在“设计标高”表中的第一列，从第二行开始输入要计算的里程桩号，完成后，在任一单元格中双击单元格，即可看见输入结果（在第二列），本程序默认遇到桩号列空单元格时不再向下计算。
Dim K As DoubleDim H As DoubleDim P1 As Double, P2 As Double, P3 As DoubleDim H1 As Double, H2 As DoubleDim R1 As Double, R2 As DoubleDim T1 As Double, T2 As DoubleDim D1 As Double, D2 As DoubleDim G1 As Long, G2 As LongPrivate Sub Worksheet_BeforeDoubleClick(ByVal Target As Range, Cancel As Boolean) On Error Resume NextDim i As LongDim hang As LongDim celln = 0For Each cell In Sheets("竖曲线").Range("a3:a65536")If cell.Value <> "" Thenn = n + 1ElseExit ForEnd IfNexti = 2flag:P2 = 0P3 = 0hang = 3If Sheets("设计标高").Cells(i, 1) <> "" ThenK = Val(Cells(i, 1))canshu:P1 = P2D1 = Val(Sheets("竖曲线").Cells(hang + 1, 2))D2 = Val(Sheets("竖曲线").Cells(hang + 2, 2))H1 = Val(Sheets("竖曲线").Cells(hang + 1, 3))H2 = Val(Sheets("竖曲线").Cells(hang + 2, 3))P3 = (H2 - H1) / (D2 - D1)D1 = Val(Sheets("竖曲线").Cells(hang, 2))D2 = Val(Sheets("竖曲线").Cells(hang + 1, 2))H1 = Val(Sheets("竖曲线").Cells(hang, 3))H2 = Val(Sheets("竖曲线").Cells(hang + 1, 3))R1 = Val(Sheets("竖曲线").Cells(hang, 4))R2 = Val(Sheets("竖曲线").Cells(hang + 1, 4))T1 = Val(Sheets("竖曲线").Cells(hang, 5))T2 = Val(Sheets("竖曲线").Cells(hang + 1, 5))P2 = (H2 - H1) / (D2 - D1)If K < D1 Then Sheets("设计标高").Cells(i, 3) = "超出": i = i + 1: GoTo flag If K > D2 And hang < n + 3 Thenhang = hang + 1GoTo canshuElseCall biaogaoSheets("设计标高").Cells(i, 2) = Round(H, 3)End IfElseEndEnd Ifi = i + 1GoTo flagEnd SubFunction biaogao() As DoubleOn Error Resume NextG1 = -1If P2 - P1 > 0 Then G1 = 1G2 = -1If P3 - P2 > 0 Then G2 = 1H = 0If K < D1 + T1 ThenH = H1 + (K - D1) * P2 + G1 * (D1 + T1 - K) ^ 2 / (2 * R1)ElseIf K <= D2 - T2 ThenH = H1 + (K - D1) * P2ElseIf R2 <> 0 ThenH = H2 - (D2 - K) * P2 + G2 * (K - (D2 - T2)) ^ 2 / (2 * R2)ElseH = H2 - (D2 - K) * P2End IfEnd IfEnd Function本程序只计算单一线路的中桩标高，若想把多个线路的参数放在同一个表中时，只需对以上程序稍加改动即可。
变坡点桩号变坡点高程R i1i2T L E 416.922240.64810000-3.714%-2.895%40.95081.90.084416.922240.64810000-3.714%-2.895%40.9581.90.084416.922240.64810000-3.714%-2.895%40.9581.90.084416.922240.64810000-3.714%-2.895%40.9581.90.084416.922240.64810000-3.714%-2.895%40.9581.90.084416.922240.64810000-3.714%-2.895%40.9581.90.084416.922240.64810000-3.714%-2.895%40.9581.90.084416.922240.64810000-3.714%-2.895%40.9581.90.084416.922240.64810000-3.714%-2.895%40.9581.90.084416.922240.64810000-3.714%-2.895%40.9581.90.084变坡点桩号变坡点高程R i1i2T L E 124102.532240.7915000-0.75%0.789%115.725231.450.446124102.532240.7915000-0.75%0.789%115.725231.450.446124102.532240.7915000-0.75%0.789%115.725231.450.446124102.532240.7915000-0.75%0.789%115.725231.450.446124102.532240.7915000-0.75%0.789%115.725231.450.446124102.532240.7915000-0.75%0.789%115.725231.450.446124102.532240.7915000-0.75%0.789%115.725231.450.446变坡点桩号变坡点高程R i1i2T L E 55530.442663000 2.439%-2.58%75.23150.450.943变坡点桩号变坡点高程R i1i2T L E 55460107.70512000 2.500%0.00%150.0003000.93855460107.70512000 2.50%0.00%150.0003000.93855460107.70512000 2.50%0.00%150.0003000.93855460107.70512000 2.50%0.00%150.0003000.93855460107.70512000 2.50%0.00%150.0003000.93855460107.70512000 2.50%0.00%150.0003000.93855460107.70512000 2.50%0.00%150.0003000.93855460107.70512000 2.50%0.00%150.0003000.93855460107.70512000 2.50%0.00%150.0003000.93855460107.70512000 2.50%0.00%150.0003000.93855460107.70512000 2.50%0.00%150.0003000.93855460107.70512000 2.50%0.00%150.0003000.938凹型竖------小桩号------55460107.70512000 2.50%0.00%150.0003000.93855460107.70512000 2.50%0.00%150.0003000.93855460107.70512000 2.50%0.00%150.0003000.93855460107.70512000 2.50%0.00%150.0003000.93855460107.70512000 2.50%0.00%150.0003000.93855460107.70512000 2.50%0.00%150.0003000.93855460107.70512000 2.50%0.00%150.0003000.93855460107.70512000 2.50%0.00%150.0003000.93855460107.70512000 2.50%0.00%150.0003000.93855460107.70512000 2.50%0.00%150.0003000.93855460107.70512000 2.50%0.00%150.0003000.938变坡点桩号变坡点高程R i1i2T L E55460107.70512000 2.500%0.00%150.0003000.93855460107.70512000 2.500%0.00%150.0003000.93855460107.70512000 2.500%0.00%150.0003000.93855460107.70512000 2.500%0.00%150.0003000.93855460107.70512000 2.500%0.00%150.0003000.93855460107.70512000 2.500%0.00%150.0003000.93855460107.70512000 2.500%0.00%150.0003000.93855460107.70512000 2.500%0.00%150.0003000.93855460107.70512000 2.500%0.00%150.0003000.93855460107.70512000 2.500%0.00%150.0003000.93855460107.70512000 2.500%0.00%150.0003000.93855460107.70512000 2.500%0.00%150.0003000.93855460107.70512000 2.500%0.00%150.0003000.93855460107.70512000 2.500%0.00%150.0003000.93855460107.70512000 2.500%0.00%150.0003000.93855460107.70512000 2.500%0.00%150.0003000.93855460107.70512000 2.500%0.00%150.0003000.93855460107.70512000 2.500%0.00%150.0003000.93855460107.70512000 2.500%0.00%150.0003000.93855460107.70512000 2.50%0.00%150.0003000.93855460107.70512000 2.50%0.00%150.0003000.93855460107.70512000 2.50%0.00%150.0003000.93855460107.70512000 2.50%0.00%150.0003000.938-----变坡点桩号变坡点高程R i1i2T L E55530.442663000 2.500%-2.576%76.140152.280.966 55530.442663000 2.50%-2.58%76.140152.280.966 55530.442663000 2.50%-2.58%76.140152.280.966 55530.442663000 2.50%-2.58%76.140152.280.966 55530.442663000 2.50%-2.58%76.140152.280.966 55530.442663000 2.50%-2.58%76.140152.280.966 55530.442663000 2.50%-2.58%76.140152.280.966前坡竖曲线起点竖曲线终点米数待求桩号变坡点桩号y 改正前高程375.970457.870-100.970275.000416.9200.0002235.377375.970457.870-99.970276.000416.9200.5002235.414375.970457.870-98.970277.000416.9200.4902235.451375.970457.870-97.970278.000416.9200.4802235.489375.970457.870-96.970279.000416.9200.4702235.526375.970457.870-95.970280.000416.9200.4612235.563375.970457.870-94.970281.000416.9200.4512235.600375.970457.870-93.970282.000416.9200.4422235.637375.970457.870-92.970283.000416.9200.4322235.674375.970457.870-91.970284.000416.9200.4232235.711后坡竖曲线起点竖曲线终点_X待求桩号变坡点桩号y 改正前高程123986.805124218.255104.505124113.750124102.5300.3642240.879123986.805124218.25589.505124128.750124102.5300.2672240.997123986.805124218.25574.505124143.750124102.5300.1852241.115123986.805124218.25559.505124158.750124102.5300.1182241.234123986.805124218.25544.505124173.750124102.5300.0662241.352123986.805124218.25535.505124182.750124102.5300.0422241.423123986.805124218.25525.785124192.470124102.5300.0222241.500前坡竖曲线起点竖曲线终点米数_X待求桩号变坡点桩号y 改正前高程55455.21555605.665 5.47555460.69055530.4400.005264.299前坡竖曲线起点竖曲线终点米数_X待求桩号变坡点桩号y 改正前高程55310.00055610.000146.50055456.555460.0000.894107.61855310.00055610.00050210.000510055460.000#########-1151.29555310.00055610.00050200.000511055460.000#########-1151.04555310.00055610.00050196.4405113.5655460.000#########-1150.95655310.00055610.00050170.000514055460.000#########-1150.29555310.00055610.00050160.000515055460.000#########-1150.04555310.00055610.00050153.000515755460.000#########-1149.87055310.00055610.00050148.000516255460.000#########-1149.74555310.00055610.00050125.000518555460.000#########-1149.17055310.00055610.00050117.000519355460.000#########-1148.97055310.00055610.00050111.000519955460.000#########-1148.82055310.00055610.00050110.000520055460.000#########-1148.795凹型竖曲线------小桩号（前坡）凹型竖曲线------大桩号（后坡）凸型竖曲线-----前坡凸型竖曲线-----前坡55310.00055610.000128.22755438.22755460.0000.685107.16155310.00055610.000137.44155447.44155460.0000.787107.39155310.00055610.000144.70055454.70055460.0000.872107.57355310.00055610.000137.15055447.15055460.0000.784107.38455310.00055610.000129.95055439.95055460.0000.704107.20455310.00055610.000123.00055433.00055460.0000.630107.03055310.00055610.000116.40055426.40055460.0000.565106.86555310.00055610.000109.95055419.95055460.0000.504106.70455310.00055610.000103.75055413.75055460.0000.449106.54955310.00055610.00097.70055407.70055460.0000.398106.39855310.00055610.000146.50055456.50055460.0000.894107.618后坡竖曲线起点竖曲线终点米数_X待求桩号变坡点桩号y 改正前高程55310.00055610.000143.62055466.3855460.0000.859107.70555310.00055610.00051560.000405055460.000#########107.70555310.00055610.00051517.000409355460.000#########107.70555310.00055610.00051510.000410055460.000#########107.70555310.00055610.00051507.2404102.7655460.000#########107.70555310.00055610.00051502.5004107.555460.000#########107.70555310.00055610.00051499.000411155460.000#########107.70555310.00055610.00051480.000413055460.000#########107.70555310.00055610.00051460.000415055460.000#########107.70555310.00055610.00051439.000417155460.000#########107.70555310.00055610.00051506.4404103.5655460.000#########107.70555310.00055610.00051503.5604106.4455460.000#########107.70555310.00055610.00051500.1374109.86355460.000#########107.70555310.00055610.00051504.2264105.77455460.000#########107.70555310.00055610.00051430.000418055460.000#########107.70555310.00055610.00051430.000418055460.000#########107.70555310.00055610.00051460.000415055460.000#########107.70555310.00055610.00051460.000415055460.000#########107.70555310.00055610.00051460.000415055460.000#########107.70555310.00055610.00051460.000415055460.000#########107.70555310.00055610.00051460.000415055460.000#########107.70555310.00055610.00051460.000415055460.000#########107.70555310.00055610.00051460.000415055460.000#########107.705后坡竖曲线起点竖曲线终点米数_X待求桩号变坡点桩号y改正前高程凸型竖曲线-----后坡凸型竖曲线-----后坡-----直坡上55454.30055606.58055611.73055530.4400.000263.906 55454.30055606.58055606.93055530.440264.030 55454.30055606.58055611.7355530.440263.906 55454.30055606.58055626.7355530.440263.520 55454.30055606.58055641.7355530.440263.133 55454.30055606.58055653.7355530.440262.824 55454.30055606.58055665.155530.440262.531改正后高程桩号外边缘标高2235.377275.0002235.1922235.914276.0002235.7292235.941277.0002235.7562235.968278.0002235.7832235.996279.0002235.8112236.023280.0002235.8382236.051281.0002235.8662236.079282.0002235.8942236.106283.0002235.9212236.134284.0002235.949改正后高程桩号2241.243124113.7502241.0582241.264124128.7502241.0792241.300124143.7502241.1152241.352124158.7502241.1672241.418124173.7502241.2332241.465124182.7502241.2802241.522124192.4702241.33755419.95055426.400改正后高程桩号55447.150264.29455460.69055454.700155439.95055433.00055413.750改正后高程桩号106.72355456.500106.908##########5100.000#########(106194.904)50356.500 ##########5110.000#########(106152.817)50346.500 ##########5113.560#########(106137.836)50342.940 ##########5140.000#########(106026.604)50316.500 ##########5150.000#########(105984.550)50306.500 ##########5157.000#########(105955.117)50299.500 ##########5162.000#########(105934.096)50294.500 ##########5185.000#########(105837.426)50271.500 ##########5193.000#########(105803.812)##########5199.000#########(105778.605)##########5200.000#########(105774.404)106.47655438.227106.661106.371106.60455447.441106.789106.499106.70055454.700106.885106.595 1.800 106.60055447.150106.785106.4959.350 106.50055439.950106.685106.39516.550 106.40055433.000106.585106.29523.500 106.30055426.400106.485106.19530.100 106.20055419.950106.385106.09536.550 106.10055413.750106.285105.99542.750 106.00055407.700106.185105.89548.800 106.72355456.500106.908106.6180.000改正后高程桩号路面边沿高程106.84655466.380106.711##########4050.000###################4093.000###################4100.000###################4102.760###################4107.500###################4111.000###################4130.000###################4150.000###################4171.000###################4103.560###################4106.440###################4109.863###################4105.774###################4180.000###################4180.000###################4150.000###################4150.000###################4150.000###################4150.000###################4150.000###################4150.000###################4150.000#########改正后高程桩号263.90655611.730264.091 264.03055606.930264.215 263.90655611.730264.091 263.52055626.730263.705 263.13355641.730263.318 262.82455653.730263.009 262.53155665.100262.716。
一、设置竖曲线的要求铁路线路所包含的坡度除平坡外，有上坡、下坡。
所谓坡度，即铁路线路的高程变化率，用千分率表示，就是每1000m水平距离高程上升或下降的数值，通常用符号“+、-、0”依次表示上坡、下坡或平坡。
在进行纵断面设计时，相邻两坡段的交点叫变坡点，两变坡点之间的水平距离叫坡段长度。
《铁路线路设计规范》规定：工、Ⅱ级铁路相邻坡段坡度的代数差大于3％0和Ⅲ级铁路相邻坡段坡度的代数差大于4‰时，需用竖曲线连接。
竖曲线的形状主要分为圆曲线形和抛物线形两种。
《新建客货共线铁路设计暂行规定》规定：纵断面宜设计为较长的坡段，相邻坡段的连接宜设计为较小的坡度差。
旅客列车设计行车速度为200 km／h的路段，最小坡段长度不宜小于600m，困难条件下最小坡段长度不应小于400m，且最小坡段长度不得连续使用2个以上。
旅客列车设计行车速度为160km／h的路段，最小坡段长度不宜小于400m，且最小坡段长度不宜连续使用2个以上。
竖曲线不得与缓和曲线、相邻竖曲线重叠设置，也不得设在明桥面和正线道岔内。
二、竖曲线的计算方法1.圆曲线形竖曲线计算《铁路线路设计规范》规定：Ⅰ、Ⅱ级铁路竖曲线半径为10000m Tv=5 X △i ，Ⅲ级铁路竖曲线半径为5000m。
Tv=2.5 X △i(1)竖曲线的切线长Tv=Rv ×tan a/2 = Rv/2 ×tan a= Rv/2000 × △i △i=△i2-△i1 的绝对值Tv－竖曲线的切线长(m)；Rv--竖曲线半径，a----竖曲线转角，△i－相邻坡段坡度的代数差(‰)。
(2)竖曲线的曲线长C≈2T。
(3)竖曲线的纵距竖曲线的纵距即竖曲线上任意点与切线上相邻点的标高差，用y表示，即y=x2/2Rv式中Y－竖曲线的纵距(m)；x－竖曲线上任意点距竖曲线始点或终点的距离(m)；(4)竖曲线标高H=Hp±y 式中H－竖曲线标高(m)；Hp－计算点坡度线标高，【例题】某一级铁路，有一圆曲线形竖曲线(如图3－20所示)，竖曲线中点里程为K24+400，标高为65.7 m，上坡i1=+2‰，下坡i2=-4‰，试计算竖曲线上每20 m点的标高。
精心整理竖曲线要素及变坡点处设计高程计算坡度计算:①坡度=高差坡长②竖曲线类型：当1n n i i +-为正值时，为凹型竖曲线； 当1n n i i +-为负值时，为凸型竖曲线。
③由厘米坐标纸上，经过反复试坡、调坡,根据土石方填挖大致平衡和道。
设计规范中最小坡长等设计要求最后确定出变坡点:变坡点1桩号:67.2550+K ，高程m 9404.0- 变坡点计算 ①变坡点一：桩号67.2550+K ,%150.0-i 1=%220.0i 2=R=21621.62m 变坡点高程：m 9404.0- A.计算竖曲线要素：=-=1i 2i ω0.37%此时根据规范可知：该曲线为凹形曲线竖曲线几何要素中曲线长）（m R L 80%37.021621=⨯=⨯=ω 竖曲线几何要素中切线长m L T 402802=== 竖曲线几何要素中外距m R T E 037.062.21621240222=⨯==B.计算竖曲线起终点桩号 竖曲线起点桩号：67.2150+K竖曲线起点高程：m 8804.0-%15.0409404.0-=⨯+ 竖曲线终点桩号：67.2950+K竖曲线终点高程：m 8524.0-%22.0409404.0-=⨯+计算设计高程由110()H H T X i =--H=H 1±h H 1:任一点切线的高程 x ：计算点到起点的距离 i 1：坡度H:任一点的设计高程曲线段内各点的设计高程：K0+220X=220-215.67=4.33m m Rx y 0004.022== 切线高程：-0.8804-4.33×0.15%=-0.8869m 设计高程：-0.8869+0.0004=-0.8865m K0+240X=24.33m m Rx y 0137.022== 切线高程：-0.8804-24.33×0.15%=-0.9169m 设计高程：-0.9169+0.0137=-0.9032m K0+260X=35.67m m Rx y 0294.022== 切线高程：-0.8524-35.67×0.22%=-0.9309m 设计高程：-0.9309+0.0294=-0.9015m K0+280X=15.67m m Rx y 0057.022== 切线高程：-0.8524-15.67×0.22%=-0.8869m 设计高程：-0.8869+0.0057=-0.8812m 直线段内各点设计高程见下表：设计高程表 桩号 高程（m ） 桩号 高程（m ） K0+000 -0.56 +240.000 -0.9032+20.000 -0.59 +260.000 -0.9015 +40.000 -0.62 +280.000 -0.8812 +60.000 -0.65 +300.000 -0.8361 +80.000 -0.68 +320.000 -0.7921 +100.000 -0.71 +340.000 -0.7481 +120.000 -0.74 +360.000 -0.7041 +140.000 -0.77 +380.000 -0.6601 +160.000 -0.80 +400.000 -0.6161 +170.000 -0.83 +420.000 -0.5721 +180.000 -0.86 +440.000 -0.5281+200.000 -0.89 +220.000 -0.8865。
竖曲线高程计算通常涉及到纵坡设计，可以用于计算道路或其他线性结构的竖向变化。
如果你想创建一个Excel表格来进行竖曲线高程计算，以下是一个简单的步骤指南：
1. 打开Excel
首先，打开Microsoft Excel软件。
2. 创建表格
在Excel中创建一个新的工作表。
在这个表中，你可以创建两列，一列是里程（或水平距离），另一列是高程。
3. 输入已知数据
在里程列中输入已知的里程点，在对应的高程列中输入相应里程点的高程。
4. 使用公式进行计算
对于每个里程点，你可以使用以下公式来计算其高程：
(H = H_{0} + i \times d)
其中：
•(H) 是当前里程点的高程。
•(H_{0}) 是前一个里程点的高程。
•(i) 是纵坡的坡度（单位为米/米或米/公里）。
•(d) 是当前里程与前一个里程之间的水平距离。
你可以在每个里程点的高程单元格中输入这个公式，并使用拖放功能将公式应用到其他里程点。
5. 保存和分享表格
完成计算后，保存你的Excel表格。
你可以将这个表格分享给其他人，或者将其导入到其他软件中进行进一步的分析和可视化。
示例：
假设你有以下里程和对应的高程数据：
你可以在里程为1和2的单元格中使用上述公式来计算对应的高程。
然后，使用拖放功能将这个公式应用到其他里程点。
