calculationsANCHOR CATENARY CALCULATIONMacro recorded April 2001 by John HoltropWater Depth (ft)28TYPICAL RODE DENSITIES, LBS/FOOTNylon Length (ft)120PlottedPlottedDistance fromNylon Density0.09Y, from surfaceDepthNylonChainKellet wt.Total wt.XBow, along rodesizechainnylon028.000.000.000.00.000Chain Length (ft)150.3327.670.090.000.00.10.943813/160.39Chain Density10.6627.340.090.000.00.21.887821/40.630.9927.010.090.000.00.32.832035/161.00Kellet Location (ft)701.3226.680.090.000.00.43.776543/81.400.04Kellet Weight (lbs)201.6526.350.090.000.00.54.721157/161.930.091.9726.030.090.000.00.55.665961/22.600.10Total Rode Length (ft)1352.3025.700.090.000.00.66.611075/83.800.13Scope (x:1)4.82.6325.370.090.000.00.77.556283/45.450.19calculated tension127.41653751962.9525.050.090.000.00.88.50179depth, error0.5201332083.2824.720.090.000.00.99.447310Horizontal Tension127.41653751963.6024.400.090.000.01.010.393211Computed Depth28.53.9324.070.090.000.01.111.339312Total Rode Weight (lbs)44.74.2523.750.090.000.01.212.285613Rode angle at surface (Deg)19.34.5723.430.090.000.01.313.2320144.9023.100.090.000.01.414.1787155.2222.780.090.000.01.415.1256165.5422.460.090.000.01.516.0727175.8622.140.090.000.01.617.0200186.1821.820.090.000.01.717.9675196.5021.500.090.000.01.818.9152206.8221.180.090.000.01.919.8631217.1320.870.090.000.02.020.8112227.4520.54924473940.090.000.02.121.7595237.7720.23249564140.090.000.02.222.7080248.0819.91634949120.090.000.02.323.6567258.4019.60080667220.090.000.02.324.6057268.7119.28586756730.090.000.02.425.5548279.0318.97153255910.090.000.02.526.5041289.3418.65780202950.090.000.02.627.4536299.6618.34467636040.090.000.02.728.4033309.9718.0321559330.090.000.02.829.35323110.2817.72024112820.090.000.02.930.30333210.5917.40893232630.090.000.03.031.25363310.9017.09822990750.090.000.03.132.20413411.2116.78813425130.090.000.03.233.15483511.5216.47864573680.090.000.03.234.10583611.8316.16976474290.090.000.03.335.05693712.1415.86149164780.090.000.03.436.00813812.4515.55382682950.090.000.03.536.95963912.7515.24677066530.090.000.03.637.91134013.0614.94032353230.090.000.03.738.86324113.3714.63448580710.090.000.03.839.81534213.6714.32925786570.090.000.03.940.76764313.9814.0246400840.090.000.04.041.72014414.2813.72063283710.090.000.04.142.67274514.5813.41723649980.090.000.04.143.62564614.8913.11445144660.090.000.04.244.57874715.1912.81227805130.090.000.04.345.53194815.4912.51071668730.090.000.04.446.48544915.7912.20976772780.090.000.04.547.43905016.0911.90943154520.090.000.04.648.39285116.3911.60970851160.090.000.04.749.34695216.6911.31059899870.090.000.04.850.30115316.9911.01210337760.090.000.04.951.25555417.2910.71422201910.090.000.05.052.21015517.5810.41695529330.090.000.05.053.16495617.8810.12030357020.090.000.05.154.11995718.189.82426721890.090.000.05.255.07505818.479.52884660830.090.000.05.356.03045918.779.23404210690.090.000.05.456.98606019.068.93985408230.090.000.05.557.94176119.358.64628290220.090.000.05.658.89776219.658.35332893340.090.000.05.759.85386319.948.06099254230.090.000.05.860.81016420.237.7692740950.090.000.05.961.76666520.527.47817395690.090.000.05.962.72336620.817.1876924930.090.000.06.063.68026721.106.89783006780.090.000.06.164.63726821.396.60858704530.090.000.06.265.59456921.536.46558527840.090.0020.026.366.58427021.686.32326840340.090.000.026.467.57407121.826.18163662460.090.000.026.568.56407221.966.04069014570.090.000.026.669.55407322.105.90042916930.090.000.026.770.54417422.245.76085389720.090.000.026.871.53437522.385.62196453030.090.000.026.872.52467622.525.48376126840.090.000.026.973.51507722.655.34624431060.090.000.027.074.50557822.795.20941385510.090.000.027.175.49617922.935.0732700990.090.000.027.276.48688023.064.93781323860.090.000.027.377.47768123.204.80304346940.090.000.027.478.46858223.334.66896098570.090.000.027.579.45948323.464.53556598110.090.000.027.680.45058423.604.40285864820.090.000.027.781.44168523.734.27083917870.090.000.027.782.43298623.864.13950776350.090.000.027.883.42428723.994.00886459220.090.000.027.984.41578824.123.8789098540.090.000.028.085.40728924.253.74964373670.090.000.028.186.39889024.383.62106642740.090.000.028.287.39059124.513.49317811230.090.000.028.388.38239224.633.36597897660.090.000.028.489.37429324.763.23946920450.090.000.028.590.36619424.893.11364897950.090.000.028.691.35829525.012.98851848380.090.000.028.692.35039625.142.86407789910.090.000.028.793.34259725.262.74032740570.090.000.028.894.33499825.382.61726718340.090.000.028.995.32739925.512.49489741070.090.000.029.096.319710025.632.37321826550.090.000.029.197.312310125.752.25222992430.090.000.029.298.305010225.872.13193256320.090.000.029.399.297710325.992.01232635690.090.000.029.4100.290510426.111.89341147950.090.000.029.5101.283410526.221.77518810380.090.000.029.5102.276410626.341.6576564020.090.000.029.6103.269510726.461.54081654510.090.000.029.7104.262610826.581.42466870320.090.000.029.8105.255910926.691.30921304560.090.000.029.9106.249211026.811.19444974050.090.000.030.0107.242611126.921.08037895520.090.000.030.1108.236011227.030.9670008560.090.000.030.2109.229611327.150.85431560820.090.000.030.3110.223211427.260.74232337630.090.000.030.4111.216911527.370.63102432370.090.000.030.4112.210711627.480.52041861290.090.000.030.5113.204611727.590.41050640540.090.000.030.6114.198511827.700.30128786180.090.000.030.7115.192511927.810.19206931820.000.000.030.7116.186612027.910.090568670.001.000.031.7117.181412128.00-0.00319571270.001.000.032.7118.177012228.09-0.08920680820.001.000.033.7119.173312328.17-0.16744895820.001.000.034.7120.170212428.24-0.23790788220.001.000.035.7121.167712528.30-0.30057069030.001.000.036.7122.165812628.36-0.35542589490.001.000.037.7123.164312728.40-0.40246342120.001.000.038.7124.163212828.44-0.44167461650.001.000.039.7125.162412928.47-0.47305225770.001.000.040.7126.161913028.50-0.49659055870.001.000.041.7127.161613128.51-0.51228517490.001.000.042.7128.161513228.52-0.5201332080.001.000.043.7129.161513328.52-0.5201332080.001.000.044.7130.161513428.52-0.5201332080.000.000.044.7131.161513528.52-0.5201332080.000.000.044.7132.161513528.52-0.5201332080.000.000.044.7133.161513528.52-0.5201332080.000.000.044.7134.161513528.52-0.5201332080.000.000.044.7135.161513528.52-0.5201332080.000.000.044.7136.161513528.52-0.5201332080.000.000.044.7137.161513528.52-0.5201332080.000.000.044.7138.161513528.52-0.5201332080.000.000.044.7139.161513528.52-0.5201332080.000.000.044.7140.161513528.52-0.5201332080.000.000.044.7141.161513528.52-0.5201332080.000.000.044.7142.161513528.52-0.5201332080.000.000.044.7143.161513528.52-0.5201332080.000.000.044.7144.161513528.52-0.5201332080.000.000.044.7145.161513528.52-0.5201332080.000.000.044.7146.161513528.52-0.5201332080.000.000.044.7147.161513528.52-0.5201332080.000.000.044.7148.161513528.52-0.5201332080.000.000.044.7149.161513528.52-0.5201332080.000.000.044.7150.161513528.52-0.5201332080.000.000.044.7151.161513528.52-0.5201332080.000.000.044.7152.161513528.52-0.5201332080.000.000.044.7153.161513528.52-0.5201332080.000.000.044.7154.161513528.52-0.5201332080.000.000.044.7155.161513528.52-0.5201332080.000.000.044.7156.161513528.52-0.5201332080.000.000.044.7157.161513528.52-0.5201332080.000.000.044.7158.161513528.52-0.5201332080.000.000.044.7159.161513528.52-0.5201332080.000.000.044.7160.161513528.52-0.5201332080.000.000.044.7161.161513528.52-0.5201332080.000.000.044.7162.161513528.52-0.5201332080.000.000.044.7163.161513528.52-0.5201332080.000.000.044.7164.161513528.52-0.5201332080.000.000.044.7165.161513528.52-0.5201332080.000.000.044.7166.161513528.52-0.5201332080.000.000.044.7167.161513528.52-0.5201332080.000.000.044.7168.161513528.52-0.5201332080.000.000.044.7169.161513528.52-0.5201332080.000.000.044.7170.161513528.52-0.5201332080.000.000.044.7171.161513528.52-0.5201332080.000.000.044.7172.161513528.52-0.5201332080.000.000.044.7173.161513528.52-0.5201332080.000.000.044.7174.161513528.52-0.5201332080.000.000.044.7175.161513528.52-0.5201332080.000.000.044.7176.161513528.52-0.5201332080.000.000.044.7177.161513528.52-0.5201332080.000.000.044.7178.161513528.52-0.5201332080.000.000.044.7179.161513528.52-0.5201332080.000.000.044.7180.161513528.52-0.5201332080.000.000.044.7181.161513528.52-0.5201332080.000.000.044.7182.161513528.52-0.5201332080.000.000.044.7183.161513528.52-0.5201332080.000.000.044.7184.161513528.52-0.5201332080.000.000.044.7185.161513528.52-0.5201332080.000.000.044.7186.161513528.52-0.5201332080.000.000.044.7187.161513528.52-0.5201332080.000.000.044.7188.161513528.52-0.5201332080.000.000.044.7189.161513528.52-0.5201332080.000.000.044.7190.161513528.52-0.5201332080.000.000.044.7191.161513528.52-0.5201332080.000.000.044.7192.161513528.52-0.5201332080.000.000.044.7193.161513528.52-0.5201332080.000.000.044.7194.161513528.52-0.5201332080.000.000.044.7195.161513528.52-0.5201332080.000.000.044.7196.161513528.52-0.5201332080.000.000.044.7197.161513528.52-0.5201332080.000.000.044.7198.161513528.52-0.5201332080.000.000.044.7199.161513528.52-0.5201332080.000.000.044.7200.161513528.52-0.5201332080.000.000.044.7201.161513528.52-0.5201332080.000.000.044.7202.161513528.52-0.5201332080.000.000.044.7203.161513528.52-0.5201332080.000.000.044.7204.161513528.52-0.5201332080.000.000.044.7205.161513528.52-0.5201332080.000.000.044.7206.161513528.52-0.5201332080.000.000.044.7207.161513528.52-0.5201332080.000.000.044.7208.161513528.52-0.5201332080.000.000.044.7209.161513528.52-0.5201332080.000.000.044.7210.161513528.52-0.5201332080.000.000.044.7211.161513528.52-0.5201332080.000.000.044.7212.161513528.52-0.5201332080.000.000.044.7213.161513528.52-0.5201332080.000.000.044.7214.161513528.52-0.5201332080.000.000.044.7215.161513528.52-0.5201332080.000.000.044.7216.161513528.52-0.5201332080.000.000.044.7217.161513528.52-0.5201332080.000.000.044.7218.161513528.52-0.5201332080.000.000.044.7219.161513528.52-0.5201332080.000.000.044.7220.161513528.52-0.5201332080.000.000.044.7221.161513528.52-0.5201332080.000.000.044.7222.161513528.52-0.5201332080.000.000.044.7223.161513528.52-0.5201332080.000.000.044.7224.161513528.52-0.5201332080.000.000.044.7225.161513528.52-0.5201332080.000.000.044.7226.161513528.52-0.5201332080.000.000.044.7227.161513528.52-0.5201332080.000.000.044.7228.161513528.52-0.5201332080.000.000.044.7229.161513528.52-0.5201332080.000.000.044.7230.161513528.52-0.5201332080.000.000.044.7231.161513528.52-0.5201332080.000.000.044.7232.161513528.52-0.5201332080.000.000.044.7233.161513528.52-0.5201332080.000.000.044.7234.161513528.52-0.5201332080.000.000.044.7235.161513528.52-0.5201332080.000.000.044.7236.161513528.52-0.5201332080.000.000.044.7237.161513528.52-0.5201332080.000.000.044.7238.161513528.52-0.5201332080.000.000.044.7239.161513528.52-0.5201332080.000.000.044.7240.161513528.52-0.5201332080.000.000.044.7241.161513528.52-0.5201332080.000.000.044.7242.161513528.52-0.5201332080.000.000.044.7243.161513528.52-0.5201332080.000.000.044.7244.161513528.52-0.5201332080.000.000.044.7245.161513528.52-0.5201332080.000.000.044.7246.161513528.52-0.5201332080.000.000.044.7247.161513528.52-0.5201332080.000.000.044.7248.1615135Y, from surfacePlottedNylonChainKellet wt.Total wt.PlottedDistance fromDepthXBow, along rode

calculations1

Distance from bow (ft)Depth (ft)Computed catenary

READ ME

The rode is limited to a total length of 250', any combination of nylon or chain.

Each time you enter a value the data base will recalculate a general solution. The final solution, however, is determined by varying the rode tension untill the computed and input depths agree. This can be accomplished by using use the "Calculate Tension" macro, Goal Seek (see tools menu), or manually by varying B18.

Fill in the required input fields (green) and then click the "calculate tension" button. If the "computed depth" (B19) is not close to the input depth (B3), then click the "calculate tension" button again. If the computed and input depths still do not match, use "goal seek" in the tools menu. B3 is the goal, vary B18 to get the answer.

input fields: greenoutput fields: yellow At the surface, the rode angle is:tan-1(total rode weight/horizontal tension). As the calculations progress down the rode, the rode weight term decreases.

Each step is one foot of rode length. Delta x and y are calculated using the sin and cosine of the rode angle.Straight line distance along the rode from the bow (ft). (gpl)The Computed Depth should be approx. equal to the input Water Depth (B3). If not, click the "Calculate" button again or see the READ ME notes below. (gpl)Assume: Water depth + freeboard depth (ft)(gpl)The straight line distance from the bow to the end of the rode.

Note that if Chain Length and Kellet Location are set to zero, values in columns I approach those in column J. (gpl)Actual distance from bow along rode based on modeled catenary (gpl).Depth from the surface or bow depending upon interpretation of "Water Depth" (B3). (gpl)computed as noted in READ ME notes. (gpl)Depth (ft) measured from the bottom to the waters surface or bow, depending upon interpretation of "Water Depth" (B3). (gpl)See http://en.wikipedia.org/wiki/Catenary for details and caveats as applied here.

In physics, the catenary (noun) is the curvature of a hanging flexible chain or cable when supported at its ends and acted upon by a uniform gravitational force (its own weight).

General equation: y = a cosh(x/a);

where a=T/ where T = the horizontal component of the line tension and = the weight per length unit.

In actuality, the rode suspended in air between the bow and the water's surface and the rode lying on the bottom will result in a curvature that is more complex than that modeled as a catenary. (gpl )modeledy = 9.4869x^1.9280R2 = 0.9986(gpl)modeledy = 9.4869x^1.9280R2 = 0.9986(gpl)