About

This spreadsheet implements the Radiant Time Series Method for a simple building. The spreadsheet will handle up to 4 walls, each with a window and a roof. It may be readily extended by the user. The building that is entered in the spreadsheet now is described in Chapter 8, Sectio 8.14 of Heating, Ventilating, and Air Conditioning -- Analysis and Design, 6th Edition, F.C. McQuiston, J.D. Parker, and J.D. Spitler, New York: Wiley. 2004.

It relies on a number of functions written in Visual Basic for Applications (VBA). These may be viewed, and even modified(!) by the user by going to Tools -> Macro -> Visual Basic Editor.

Periodic response factors for walls and roofs may be determined with:1) HvacLoadExplorer, which comes with the McQuiston, Parker and Spitler textbook.2) PRF-RTF Generator, which may be downloaded (gratis) from the OSU Building and Environmental Thermal Systems Research Group web site:www.hvac.okstate.edu3) Software that comes with the book Cooling and Heating Load Calculation Principles, by C.O. Pedersen, D.E. Fisher, J.D. Spitler, R.J. Liesen 1998.(Atlanta, Georgia: ASHRAE).4) PRFs for a range of sample walls and roofs have been tabulated in the paper: Spitler, J.D., D.E. Fisher. 1999. Development of Periodic Response Factors for Use with the Radiant Time Series Method. ASHRAE Transactions. Vol. 105, No. 2, pp. 491-509.

Radiant Time Factors, the coefficients of the radiant time series, may be generated with the software items 1-3, above.

Ex. 8-16This spreadsheet calculates cooling loads for a zone with the ASHRAE RTS Procedure.Data that is entered by the user is shown highlighted.Design ConditionsIntermediate VariablesLocationDes MoinesDay number202Latitude41.53EOT-6.1MinutesLongitude93.7Std. Meridian90DegreesTime Zone6(5=Eastern TZ, 6= Central TZ, 7= Mountain TZ, 8=Pacific TZ)A346.6Daylight Savings Time1(0 = standard time; 1=daylight savings time)B0.186Month7(1=Jan ... 12=Dec; 21st of the month is assumed)C0.14Outdoor Design Temperature90Degrees FDecl.20.64DegreesDaily Range18.5Degrees FIndoor Air Temperature72Degrees FClearness Number1Ground reflectance0.2Surface DataSurface NameS WallRoofSurface Number12345Surface Area (sq. ft.)280000900Facing direction (deg)18001802700(0=N,90=E,180=S,270=W)Tilt (deg 0=horiz. Up;9009090090=vertical; 180=horiz. Down)Solar absorptivity0.90.90.90.90.9Outside surface conductance44444Direct (Beam) Solar IrradiationHourSolar TimeS wall Incident Flux (Btu/hr-ft2)Incident Flux (Btu/hr-ft2)Incident Flux (Btu/hr-ft2)Incident Flux (Btu/hr-ft2)Roof Incident Flux (Btu/hr-ft2)1-0.340.00.020.660.00.031.660.00.042.660.00.053.660.00.064.660.00.075.660.035.986.660.0100.697.660.0162.3108.6635.3216.5119.6667.0259.91210.6689.6289.61311.66100.5303.61412.6698.5301.01513.6683.7281.91614.6657.9247.81715.6624.2200.71816.660.0143.71917.660.080.52018.660.017.12119.660.00.02220.660.00.02321.660.00.02422.660.00.0Diffuse Solar IrradiationHourSolar TimeS wall Incident Flux (Btu/hr-ft2)Incident Flux (Btu/hr-ft2)Incident Flux (Btu/hr-ft2)Incident Flux (Btu/hr-ft2)Roof Incident Flux (Btu/hr-ft2)1-0.340.00.020.660.00.031.660.00.042.660.00.053.660.00.064.660.00.075.6610.835.986.6623.9100.697.6634.7162.3108.6644.0216.5119.6651.6259.91210.6656.9289.61311.6659.5303.61412.6659.0301.01513.6655.6281.91614.6649.5247.81715.6641.3200.71816.6631.5143.71917.6619.680.52018.665.917.12119.660.00.02220.660.00.02321.660.00.02422.660.00.0Total Solar IrradiationHourSolar TimeS wall Incident Flux (Btu/hr-ft2)Incident Flux (Btu/hr-ft2)Incident Flux (Btu/hr-ft2)Incident Flux (Btu/hr-ft2)Roof Incident Flux (Btu/hr-ft2)1-0.340.00.020.660.00.031.660.00.042.660.00.053.660.00.064.660.00.075.6610.835.986.6623.9100.697.6634.7162.3108.6679.3216.5119.66118.6259.91210.66146.6289.61311.66160.0303.61412.66157.5301.01513.66139.3281.91614.66107.4247.81715.6665.5200.71816.6631.5143.71917.6619.680.52018.665.917.12119.660.00.02220.660.00.02321.660.00.02422.660.00.0Air and Sol-Air TemperaturesHourAir T (F)Sol-Air T (F)Sol-Air T (F)Sol-Air T (F)Sol-Air T (F)Sol-Air T (F)173.973.966.9273.073.066.0372.272.265.2471.771.764.7571.571.564.5671.971.964.9772.875.273.9874.579.890.1976.984.7106.41079.697.5121.41182.8109.5134.31285.7118.7143.91388.0124.0149.31489.4124.9150.21590.0121.3146.41689.4113.6138.21788.2102.9126.31886.193.2111.41983.788.194.82081.382.678.22179.379.372.32277.477.470.42375.975.968.92474.874.867.8Periodic Response FactorsS wallRoof10.0001560.00000420.0056000.00065830.0147950.00427040.0144410.00775750.0096280.00825960.0054140.00691570.0027860.00511680.0013630.00352790.0006470.002330100.0003010.001498110.0001390.000946120.0000630.000591130.0000290.000366140.0000130.000225150.0000060.000138160.0000030.000085170.0000010.000052180.0000010.000032190.0000000.000019200.0000000.000012210.0000000.000007220.0000000.000004230.0000000.000003240.0000000.000002Conduction Heat Gains, Btu/hrS wallRoof111260728036135717943846523-52611-12573-17885-209925-1881066-6811134175122435251338294514524138915642181116718216817738242518699255719611255120499240421390212522293174323214132024155928Windows (same orientation as above)Frame area (sq. ft.)10.52Frame U-factor (Btu/hr-sq.ft.-F)1.04SHGCf0.063Glazing area (sq. ft.)69.48Glazing SHGC (q=0o)0.65Glazing SHGC (q=40o)0.64Glazing SHGC (q=50o)0.62Glazing SHGC (q=60o)0.56Glazing SHGC (q=70o)0.43Glazing SHGC (q=80o)0.23Glazing SHGC (diffuse)0.57Glazing U-value (Btu/hr-sq.ft.-F)0.42HourSolar Timeq (deg)1-0.3428.120.6628.931.6634.242.6642.253.6651.664.6661.575.6671.486.6680.997.6689.8108.6697.7119.66104.11210.66108.61311.66110.71412.66110.31513.66107.41614.66102.31715.6695.41816.6687.11917.6678.02018.6668.32119.6658.42220.6648.62321.6639.62422.6632.2At present, this spreadsheet does not account for exterior shading. It assumes there is no shading.Eqn. 7-32 is used assuming the entire glazing and frame are sunlitHourSolar TimeWindow Solar Heat Gains, Btu/hr1-0.34020.66031.66042.66053.66064.66075.6643686.6696197.661396108.661796119.6621231210.6623521311.6624621412.6624421513.6622931614.6620301715.6616781816.6612671917.667872018.662382119.6602220.6602321.6602422.660Window Conducted Heat Gains, Btu/hr1760.02390.03100.04-130.05-200.06-50.07320.08990.091950.0103070.0114330.0125510.0136410.0147000.0157220.0167000.0176480.0185660.0194700.0203730.0212920.0222170.0231580.0241140.0Sensible Internal Heat Gains, Btu/hrNameLightsPeopleEquipmentFraction radiative0.70.70.21921.20614.12921.20614.13921.20614.14921.20614.15921.20614.16921.20614.17921.20614.18921.20614.194605.925003070.6104605.925003070.6114605.925003070.6124605.925003070.6134605.925003070.6144605.925003070.6154605.925003070.6164605.925003070.6174605.925003070.618921.20614.119921.20614.120921.20614.121921.20614.122921.20614.123921.20614.124921.20614.1Heat Gain SummaryWall ConductionRoof ConductionWindow SHGWindow ConductionLightsPeopleEquipmentInfiltrationRadiativeConvectiveRadiativeConvectiveRadiativeConvectiveRadiativeConvectiveRadiativeConvectiveRadiativeConvectiveRadiativeConvectiveConvectiveBtu/hrBtu/hrBtu/hrBtu/hrBtu/hrBtu/hrBtu/hrBtu/hrBtu/hrBtu/hrBtu/hrBtu/hrBtu/hrBtu/hrBtu/hr170.441.4509.899.50.00.048.228.3644.8276.40.00.0122.8491.3193.2250.729.8303.059.20.00.024.814.5644.8276.40.00.0122.8491.399.4335.821.0150.329.30.00.06.13.6644.8276.40.00.0122.8491.324.3424.014.138.67.50.00.0-8.0-4.7644.8276.40.00.0122.8491.3-31.9514.48.4-43.6-8.50.00.0-12.6-7.4644.8276.40.00.0122.8491.3-50.766.84.0-104.6-20.40.00.0-3.3-1.9644.8276.40.00.0122.8491.3-13.272.11.2-149.3-29.1392.443.620.111.8644.8276.40.00.0122.8491.380.683.32.0-175.6-34.3865.096.162.236.5644.8276.40.00.0122.8491.3249.5916.09.4-158.1-30.91256.6139.6123.072.23224.21381.81750.0750.0614.12456.5493.41041.524.4-57.0-11.11616.1179.6193.1113.43224.21381.81750.0750.0614.12456.5774.81184.549.6147.028.71910.7212.3272.6160.13224.21381.81750.0750.0614.12456.51093.712153.390.0441.186.12117.2235.2347.4204.03224.21381.81750.0750.0614.12456.51393.913240.8141.4794.0155.02216.2246.2403.5237.03224.21381.81750.0750.0614.12456.51619.014330.1193.91167.2227.92197.7244.2441.0259.03224.21381.81750.0750.0614.12456.51769.115404.7237.71521.4297.02063.7229.3455.0267.23224.21381.81750.0750.0614.12456.51825.416452.1265.51821.0355.51827.4203.0441.0259.03224.21381.81750.0750.0614.12456.51769.117464.8273.02037.0397.71510.1167.8408.2239.83224.21381.81750.0750.0614.12456.51637.718440.6258.82148.1419.41140.6126.7356.8209.5644.8276.40.00.0122.8491.31431.419385.1226.22142.8418.4708.678.7296.0173.8644.8276.40.00.0122.8491.31187.520314.6184.82019.1394.2214.623.8235.2138.1644.8276.40.00.0122.8491.3943.621245.6144.21785.2348.50.00.0183.8107.9644.8276.40.00.0122.8491.3737.222184.5108.31463.7285.80.00.0137.080.5644.8276.40.00.0122.8491.3549.623134.879.21108.4216.40.00.099.658.5644.8276.40.00.0122.8491.3399.52497.557.3779.7152.20.00.071.542.0644.8276.40.00.0122.8491.3287.0Radiant Time FactorsNon-solarNon-solarNon-solarNon-solarNon-solarNon-solarNon-solar10.24623910.24623910.24623910.24623910.24623910.24623910.246239110.246239120.16073640.16073640.16073640.16073640.16073640.16073640.160736420.160736430.11923880.11923880.11923880.11923880.11923880.11923880.119238830.119238840.091855840.091855840.091855840.091855840.091855840.091855840.0918558440.0918558450.072335050.072335050.072335050.072335050.072335050.072335050.0723350550.0723350560.057780950.057780950.057780950.057780950.057780950.057780950.0577809560.0577809570.046613570.046613570.046613570.046613570.046613570.046613570.0466135770.0466135780.037865910.037865910.037865910.037865910.037865910.037865910.0378659180.0378659190.030915160.030915160.030915160.030915160.030915160.030915160.0309151690.03091516100.025331050.025331050.025331050.025331050.025331050.025331050.02533105100.02533105110.020813990.020813990.020813990.020813990.020813990.020813990.02081399110.02081399120.0171350.0171350.0171350.0171350.0171350.0171350.017135120.017135130.014125740.014125740.014125740.014125740.014125740.014125740.01412574130.01412574140.011658440.011658440.011658440.011658440.011658440.011658440.01165844140.01165844150.0096264930.0096264930.0096264930.0096264930.0096264930.0096264930.009626493150.009626493160.0079526730.0079526730.0079526730.0079526730.0079526730.0079526730.007952673160.007952673170.0065712830.0065712830.0065712830.0065712830.0065712830.0065712830.006571283170.006571283180.0054337780.0054337780.0054337780.0054337780.0054337780.0054337780.005433778180.005433778190.0045017450.0045017450.0045017450.0045017450.0045017450.0045017450.004501745190.004501745200.003726190.003726190.003726190.003726190.003726190.003726190.00372619200.00372619210.0030792540.0030792540.0030792540.0030792540.0030792540.0030792540.003079254210.003079254220.0025458590.0025458590.0025458590.0025458590.0025458590.0025458590.002545859220.002545859230.0021051260.0021051260.0021051260.0021051260.0021051260.0021051260.002105126230.002105126240.0017404230.0017404230.0017404230.0017404230.0017404230.0017404230.001740423240.001740423Cooling LoadsWall ConductionRoof ConductionWindow SHGWindow ConductionLightsPeopleEquipmentInfiltrationTotalRadiativeConvectiveRadiativeConvectiveRadiativeConvectiveRadiativeConvectiveRadiativeConvectiveRadiativeConvectiveRadiativeConvectiveConvectiveBtu/hrBtu/hrBtu/hrBtu/hrBtu/hrBtu/hrBtu/hrBtu/hrBtu/hrBtu/hrBtu/hrBtu/hrBtu/hrBtu/hrBtu/hrBtu/hr1183.341.41120.399.5364.20.0158.028.31016.5276.4252.20.0193.6491.3193.24418.12156.529.8946.159.2299.00.0131.314.5950.8276.4207.60.0181.1491.399.43842.93132.621.0781.629.3246.00.0106.53.6897.1276.4171.20.0170.9491.324.33351.84111.514.1631.87.5202.80.084.1-4.7853.0276.4141.30.0162.5491.3-31.92939.7592.88.4498.5-8.5167.30.065.8-7.4816.8276.4116.70.0155.6491.3-50.72622.9676.54.0381.6-20.4138.10.053.7-1.9786.9276.496.40.0149.9491.3-13.22419.2762.51.2280.2-29.1210.243.649.411.8762.3276.479.70.0145.2491.380.62465.1851.82.0194.6-34.3368.796.155.236.5741.9276.465.90.0141.3491.3249.52736.9946.39.4131.4-30.9570.0139.672.872.21356.51381.8482.9750.0258.42456.5493.48190.31047.524.4104.6-11.1798.6179.6101.2113.41754.21381.8752.7750.0334.12456.5774.89562.21157.849.6128.728.71034.4212.3139.9160.12047.71381.8951.8750.0390.02456.51093.710883.11281.090.0210.886.11257.2235.2185.3204.02273.01381.81104.7750.0433.02456.51393.912142.713117.8141.4349.3155.01447.5246.2231.5237.02450.01381.81224.8750.0466.72456.51619.013274.514165.0193.9534.3227.91588.4244.2274.5259.02591.11381.81320.5750.0493.52456.51769.114249.715216.6237.7750.3297.01667.4229.3310.0267.22704.71381.81397.6750.0515.22456.51825.415006.816265.5265.5978.1355.51677.9203.0333.9259.02797.01381.81460.2750.0532.82456.51769.115485.817304.9273.01196.9397.71619.4167.8345.2239.82872.21381.81511.3750.0547.12456.51637.715701.218329.2258.81386.7419.41497.3126.7343.1209.52302.4276.41124.70.0438.6491.31431.410635.519335.6226.21529.9418.41312.478.7328.9173.81941.5276.4879.80.0369.8491.31187.59550.220325.8184.81612.6394.21065.123.8305.7138.11678.2276.4701.10.0319.7491.3943.68460.321304.3144.21626.1348.5839.20.0277.7107.91477.7276.4565.10.0281.5491.3737.27477.122275.8108.31568.5285.8673.60.0246.880.51321.2276.4458.90.0251.7491.3549.66588.323244.379.21450.8216.4545.70.0215.558.51197.0276.4374.60.0228.0491.3399.55777.224212.857.31294.1152.2444.80.0185.842.01097.3276.4307.00.0209.0491.3287.05057.0Wall(all)RoofLightsPeopleEquip.InfiltTotalBtu/hrBtu/hrBtu/hrBtu/hrBtu/hrBtu/hrBtu/hr1775.01219.91292.9252.2684.9193.24418.12631.11005.31227.2207.6672.499.43842.93509.7810.91173.4171.2662.224.33351.84407.8639.41129.4141.3653.8-31.92939.75326.9490.01093.1116.7646.9-50.72622.96270.4361.11063.396.4641.2-13.22419.27378.7251.01038.679.7636.580.62465.18610.3160.31018.365.9632.6249.52736.99910.3100.52738.31232.92714.9493.48190.3101264.693.53136.01502.72790.6774.89562.2111654.1157.43429.51701.82846.51093.710883.1122052.9297.03654.81854.72889.51393.912142.7132421.5504.33831.81974.82923.21619.013274.5142725.0762.23972.92070.52950.01769.114249.7152928.31047.44086.52147.62971.71825.415006.8163004.91333.64178.82210.22989.31769.115485.8172950.01594.64254.02261.33003.61637.715701.2182764.61806.12578.81124.7929.91431.410635.5192455.61948.32217.9879.8861.11187.59550.2202043.22006.81954.5701.1811.0943.68460.3211673.41974.61754.0565.1772.8737.27477.1221385.01854.31597.5458.9743.0549.66588.3231143.21667.21473.3374.6719.3399.55777.224942.71446.31373.6307.0700.3287.05057.0

&C&A&CPage &P

Ex. 8-16000000000000000000000000

Time (hrs)Load (Btu/hr)Zone Sensible Cooling Load

Tables000000436.0351081393961.16152419561396.17400305551795.61171779112122.97850954312352.42292692742462.45166775082441.93669698222292.98868504862030.42884167021677.83855585811267.383691017787.2892864237238.43615454270000

Transmitted SHGAbsorbedHourSHG (Btu/hr)Solar Heat Gain

00000000000010.828768931235.947203841523.8700871943100.59242558834.6734595095162.262972742679.2731799499216.5216471224118.6002721182259.896161218146.5716369626289.5601406371160.0156961713303.557078728157.5090223997300.958664386139.313123892281.9374487409107.3822234763247.75345853465.4783407464200.654759730931.4750002488143.693538794519.552035158580.51496109695.921472776317.094152089900000000

S wall Incident Flux (Btu/hr-ft2)Roof Incident Flux (Btu/hr-ft2)Time (hr)Flux (Btu/hr-sqft)Incident Solar Irradiation

73.90573.90566.90572.9872.9865.9872.2472.2465.2471.68571.68564.68571.571.564.571.8771.8764.8772.79575.231473009573.883120864374.4679.830769618790.093295757376.86584.6665283896106.374168867179.6497.4764654887121.357370602582.785109.4700612266134.26163627485.745118.7236183166143.896031643487.965123.9685316385149.265342713889.445124.8845300399150.160699486990121.3454528757146.435925966789.445113.6060002822138.189528170288.15102.8826266679126.297320939586.11593.196875056111.446046228883.7188.109207910794.825866246881.30582.637331374778.151184220279.2779.2772.2777.4277.4270.4275.9475.9468.9474.8374.8367.83

Air T (F)Sol-Air T (F)Sol-Air T (F)HourTemperature (F)Air Temperature and Sol-Air Temperatures

0.0001560.0000040.00560.0006580.0147950.004270.0144410.0077570.0096280.0082590.0054140.0069150.0027860.0051160.0013630.0035270.0006470.002330.0003010.0014980.0001390.0009460.0000630.0005910.0000290.0003660.0000130.0002250.0000060.0001380.0000030.0000850.0000010.0000520.0000010.00003200.00001900.00001200.00000700.00000400.00000300.000002

S wallRoofHourPRFPeriodic Response Factors

111.7751085925606.87182016180.4346057538360.766593374856.8285965223178.905399236538.057673484245.90155809722.7803078738-51.947582046910.8348892693-124.53727776723.2555899082-177.71952649585.2708199068-209.001088425525.4242537575-188.207258356265.8517137463-67.8047179192134.057371865175.0034770757243.3614601624525.1427836381382.2100773864945.210634621524.03995485121389.4825372583642.35537669541811.187932101717.55349133422167.8966298054737.79923852172424.9955072209699.37304180582557.3098971666611.26647808332550.9451487202499.37374591962403.748038505389.83894844952125.2074983694292.79535016711742.5091205768213.99831268581319.5464741134154.8121369684928.1963605601

S wallRoofHourHeat Gain (Btu/hr)Conduction Heat Gains

000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Wall(all) Btu/hrRoof Btu/hrLights Btu/hrPeople Btu/hrEquip. Btu/hrInfilt Btu/hrTotal Btu/hrHourLoad (Btu/hr)Cooling Loads

Table 8-27 Radiative Portion of Heat Gains for Example 8-16HourWallRoofPeople (Btu/hr)Lights (Btu/hr)Equipment (Btu/hr)Window Conduction (Btu/hr)Window SHG (Btu/hr)Conduction (Btu/hr)Conduction (Btu/hr)1.070.4509.80.0644.8122.848.20.00.2462392.050.7303.00.0644.8122.824.80.00.1607363.035.8150.30.0644.8122.86.10.00.1192394.024.038.60.0644.8122.8-8.00.00.0918565.014.4-43.60.0644.8122.8-12.60.00.0723356.06.8-104.60.0644.8122.8-3.30.00.0577817.02.1-149.30.0644.8122.820.1392.40.0466148.03.3-175.60.0644.8122.862.2865.00.0378669.016.0-158.11750.03224.2614.1123.01256.60.03091510.041.5-57.01750.03224.2614.1193.11616.10.02533111.084.5147.01750.03224.2614.1272.61910.70.02081412.0153.3441.11750.03224.2614.1347.42117.20.01713513.0240.8794.01750.03224.2614.1403.52216.20.01412614.0330.11167.21750.03224.2614.1441.02197.70.01165815.0404.71521.41750.03224.2614.1455.02063.70.00962616.0452.11821.01750.03224.2614.1441.01827.40.00795317.0464.82037.01750.03224.2614.1408.21510.10.00657118.0440.62148.10.0644.8122.8356.81140.60.00543419.0385.12142.80.0644.8122.8296.0708.60.00450220.0314.62019.10.0644.8122.8235.2214.60.00372621.0245.61785.20.0644.8122.8183.80.00.00307922.0184.51463.70.0644.8122.8137.00.00.00254623.0134.81108.40.0644.8122.899.60.00.00210524.097.5779.70.0644.8122.871.50.00.001740Table 8-29 Cooling Loads due to Radiative Portion of Heat Gains for Example 8-16HourWallRoofPeople (Btu/hr)Lights (Btu/hr)Equipment (Btu/hr)Window Conduction (Btu/hr)Window SHG (Btu/hr)Conduction (Btu/hr)Conduction (Btu/hr)11831120252101719415836421579462089511811312993133782171897171106246411163214185316284203593499117817156661676763829678715054138763280807621454921085219566742141553699461314831357258735701047105753175433410179911581299522048390140103412812111105227343318512571311834912252450467232144814165534132125914942741588152177501398270551531016671626697814602797533334167817305119715112872547345161918329138711252302439343149719336153088019423703291312203261613701167832030610652130416265651478281278839222761569459132125224767423244145137511972282165462421312943071097209186445Table 8-30HourWallRoofWindow Conduction (Btu/hr)Window SHG (Btu/hr)People (Btu/hr)Lights (Btu/hr)Equipment (Btu/hr)Infiltration (Btu/hr)Total (Btu/hr)(Btu/hr)(Btu/hr)12251220186364252129368519344184418.1212893806218610051462992081227672993843315481111024617111736622433524126639792031411129654-3229405101490581671171093647-51262368036152138961063641-1324197642516125480103963681246585416092465661018633249273795610114571012332738271549381901072942159781503313627917759562111071573001247170234292847109410883121712973891492185536552889139412143132595044691694197538322923161913275143597625331833207139732950176914250154541047577189721484087297218251500716531133459318812210417929891769154861757815955851787226142543004163815701185881806553162411252579930143110635195621948503139188022188611187955020511200744410897011955811944846021449197538683956517547737377477223841854327674459159874355065882332316672745463751473719400577724270144622844530713747002875057