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{"sheet":"数値シミュレーション","index":0,"n_rows":596,"n_cols":20,"rows_kept":596,"cut":false,"hidden":false,"merged":[[92,13,92,15],[92,10,92,12],[92,16,92,17]]}
["ゴルフボールの運動"]
[null,null,null,null,null,null,null,null,null,null,null,null,null,null,"Sp＝(πdn/60)/u"]
["空力係数",null,null,null,null,null,null,null,null,null,null,null,null,null,"n",400]
["Sp","Cd","Sp","Cl","Sp","Cm",null,null,null,null,null,null,null,null,"d",0.05]
[0.01,0.21,0.03,0.1,0.01,1.1999999999999999E-3,null,null,null,null,null,null,null,null,"u",1,null,null,{"$f":"PI()*P$4*P$3/60/P5","v":1.0471975511965976}]
[0.03,0.21,0.03,0.1,0.2,2E-3,null,null,null,null,null,null,null,null,null,50,null,null,{"$f":"PI()*P$4*P$3/60/P6","v":2.0943951023931952E-2}]
[0.1,0.23400000000000001,0.06,0.14199999999999999,0.5,4.0000000000000001E-3,null,null,null,null,null,null,null,null,null,100,null,null,1.0471975511965976E-2]
[0.2,0.27800000000000002,0.1,0.17100000000000001,0.8,8.0000000000000002E-3]
[0.4,0.37,0.2,0.255,2,0.02]
[0.7,0.46800000000000003,0.4,0.36]
[1,0.51,0.7,0.42499999999999999]
[0.7,0.46800000000000003,1,0.46]
[1,0.51,0.7,0.42499999999999999]
[2,0.54,1,0.46]
[null,null,1.5,0.55000000000000004]
[null,null,2,0.55000000000000004]
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["計算式"]
[null,"u⇡＝(vx－vax、vy、vz－vaz) ：対気速度ベクトル"]
[null,"u＝|u⇡|＝√(ux^2＋uy^2＋uz^2)"]
[null,"ξ⇡＝u⇡/u ：対気速度方向単位ベクトル"]
[null,"η⇡＝ζ⇡×ξ⇡ ：揚力方向単位ベクトル"]
[null,"Sp＝(d/2)ω/u ：スピンパラメータ（ボール周速度と対気速度の比）"]
[null,"Cd＝cd(Sp) ：抵抗係数（スピンパラメータの多項式）"]
[null,"Cl＝cl(Sp) ：揚力係数（スピンパラメータの多項式）"]
[null,"Cm＝cm(Sp) ：モーメント係数（スピンパラメータの多項式）"]
[null,"q＝(1/2)ρu^2 ：動圧"]
[null,"D⇡＝qCdAξ⇡ ：抵抗ベクトル"]
[null,"L⇡＝qClAη⇡ ：揚力ベクトル"]
[null,"Dm＝qCmAd ：スピン減衰トルク"]
[null,"g⇡＝(0、g、0) ：重力加速度ベクトル"]
[null,"a⇡＝(－D⇡＋L⇡)/m－g⇡ ：ボールの加速度ベクトル"]
[null,"dω/dt＝－Dm/I ：スピン角加速度",null,null,null,null,null,null,null,"一般のExcel計算式と同様に、入力データを１つでも変更すると直ちにマクロが実行されます。"]
[null,null,null,null,null,null,null,null,null,"入力データを複数変更してから計算するには、［数式］タブ→［計算方法の設定］メニュー→［手動］を選択しておきます。"]
["初期値計算",null,null,null,null,null,null,null,null,{"$f":"exe(\"マクロ呼び出し（ここをダブルクリックしてEnter）\",\"golf\",G97:G103,G106:G133,J96:Q596)","v":"マクロ呼び出し（ここをダブルクリックしてEnter）"},null,null,null,null,null,null,"マクロは[標準モジュール]のMoｄule6に入っています。"]
[null,"v0⇡＝v0(cosθ、sinθ、0) ：ボールの初期速度ベクトル",null,null,null,null,null,null,null,"マクロは[標準モジュール]のMoｄule6に入っています。"]
[null,"r0⇡＝(0、0、0) ：ボールの初期位置ベクトル",null,null,null,null,null,null,null,"時間","速度",null,null,"位置",null,null,"スピン"]
[null,"ω0＝2πn/60 ：初期スピン角速度",null,null,null,null,null,null,null,"t","vx","vy","vz","x","y","z","ω","n","-z","z軸はy軸目盛で表示。"]
[null,null,null,null,null,null,null,null,null,"[s]","[m/s]","[m/s]","[m/s]","[m]","[m]","[m]","[rad/s]","[rpm]","[m]","ただし、ｚ＋がｙ－目盛になるので、符号反転。"]
["初期値",null,null,null,null,null,null,null,null,2.5000000000000001E-2,77.230665170378089,19.333771259038528,4.3901826556579038E-2,1.9356714339810535,0.48359943150501894,5.4989783511008887E-4,208.66746729105276,{"$f":"Q96/(2*PI())*60","v":1992.6275329102459},{"$f":"-P96","v":-5.4989783511008887E-4}]
[null,"初期速度ベクトルv0⇡",null,null,"vx0=v0cosθ",null,{"$f":"G111*COS(RADIANS(G112))","v":77.623658102079716},"m/s",null,4.9999999999999996E-2,76.84130523898628,19.311225694681745,8.7267875799468292E-2,3.8615635334106782,0.96666718677841801,2.1906265620422914E-3,207.9028183470684,{"$f":"Q97/(2*PI())*60","v":1985.3256733603396},-2.1906265620422914E-3]
[null,null,null,null,"vy0=v0sinθ",null,{"$f":"G111*SIN(RADIANS(G112))","v":19.353751647973418},"m/s",null,7.4999999999999997E-2,76.455541911360527,19.286163326525553,0.13010649593063395,5.7777666675186836,1.4491397431558757,4.9088964266537846E-3,207.1454695810194,{"$f":"Q98/(2*PI())*60","v":1978.093525374665},-4.9088964266537846E-3]
[null,null,null,null,"vz0=0",null,0,"m/s",null,0.10000000000000002,76.073339183142181,19.258631541158902,0.17242588031435677,7.6843703005317732,1.9309547749032989,8.6916244372124852E-3,206.39532866102007,1970.9302072486612,-8.6916244372124852E-3]
[null,"初期位置ベクトルr0⇡",null,null,"x0=0",null,0,"m",null,0.12500000000000003,75.694661438234476,19.228676762602387,0.21423407087352114,9.5814630014291282,2.4120511288730184,1.3525930536091279E-2,205.65230471862643,1963.8348512526065,-1.3525930536091279E-2]
[null,null,null,null,"y0=0",null,0,"m",null,0.15000000000000005,75.319473444881893,19.196344474197318,0.25553896139946802,11.469132453599943,2.892368800714376,1.939913385528369E-2,204.91630831858646,1956.8066033427542,-1.939913385528369E-2]
[null,null,null,null,"z0=0",null,0,"m",null,0.17500000000000007,74.947740351754504,19.161679239935502,0.2963483007779289,13.347465464402994,3.3718489116245109,2.6298749053611747E-2,204.18725142933854,1949.844622879614,-2.6298749053611747E-2]
[null,"初期スピン角速度",null,null,"ω0=2πn/60",null,{"$f":"2*PI()*G113/60","v":209.43951023931953},"rad/s",null,0.20000000000000009,74.579427684039402,19.124724725245933,0.33666969613347564,15.216547974628405,3.850433685625573,3.4212482733558633E-2,203.4650473942358,1942.9480823531635,-3.4212482733558633E-2]
[null,null,null,null,null,null,null,null,null,0.22500000000000012,74.214501339541357,19.08552371725408,0.37651061589484103,17.076465067861808,4.3280664273549743,4.3128229935718659E-2,202.74961090347574,1936.1161671147963,-4.3128229935718659E-2]
["入力データ",null,null,null,null,null,null,null,null,0.25000000000000011,73.852927584794472,19.044118144529044,0.4158783927833884,18.927300979751166,4.8046915003556938,5.3034070708914929E-2,202.0408579667149,1929.3480751158133,-5.3034070708914929E-2]
[null,"積分間隔",null,null,"Δt",null,1.2500000000000001E-2,"s",null,0.27500000000000002,73.494673051186709,19.000549096333202,0.45478022672693436,20.769139107176525,5.280254305854009,6.3918266754091166E-2,201.33870588634863,1922.6430166522603,-6.3918266754091166E-2]
[null,"質量",null,null,"m",45.93,{"$f":"F107/1000","v":4.5929999999999999E-2},"kg",null,0.29999999999999993,73.139704731098945,18.954856841388626,0.49322318770105694,22.602062017323064,5.7547012620123992,7.576925814013831E-2,200.64307323143768,1916.0002141159471,-7.576925814013831E-2]
[null,"慣性モーメント",null,null,"I",null,8.3626078377000005E-6,"kgm^2",null,0.32499999999999984,72.787989974060039,18.90708084617404,0.53121421849995387,24.426151456657831,6.2279797836457167,8.8575660089868891E-2,199.9538798122625,1909.4189017514593,-8.8575660089868891E-2]
[null,"ボールの直径",null,null,"d",42.67,{"$f":"F109/1000","v":4.267E-2},"m",null,0.34999999999999976,72.439496482919495,18.857259792765678,0.56876013743884768,26.241488359810553,6.7000382623890484,0.10232625983440322,199.27104665548811,1902.898325418998,-0.10232625983440322]
[null,"ボールの断面積",null,null,"A=(π/4)d^2",null,{"$f":"(PI()/4)*G109^2","v":1.4299971341046563E-3},"m^2",null,0.37499999999999967,72.094192310038935,18.805431596234921,0.605867640989872,28.048152858359021,7.1708260473060337,0.11701001353428014,198.59449597992216,1896.4377423628889,-0.11701001353428014]
[null,"打出し速度",null,null,"v0",null,80,"m/s",null,0.39999999999999958,71.752045853503787,18.751633421615246,0.64254330635331103,29.846224289519473,7.6402934259267159,0.13261604326565313,197.92415117284949,1890.0364209855932,-0.13261604326565313]
[null,"打出し角",null,null,"θ",null,14,"deg",null,0.42499999999999949,71.413025853356217,18.695901700450616,0.67879359396600414,31.635781204742571,8.1083916057043091,0.14913363406997812,197.25993676692721,1883.6936406270704,-0.14913363406997812]
[null,"ボールのスピン速度",null,null,"ｎ",null,2000,"rpm",null,0.4499999999999994,71.077101387850462,18.638272146937009,0.71462484994867159,33.416901378215456,8.5750726958805643,0.16655223106564446,196.60177841762481,1877.4086913493495,-0.16655223106564446]
[null,"スピン軸傾斜",null,null,"φ",null,5,"deg",null,0.47499999999999931,70.744241869731638,18.578779773668479,0.75004330849386036,35.189661815270497,9.0402896897497094,0.1848614366200432,195.94960288119404,1871.1808737261558,-0.1848614366200432]
[null,"スピン軸単位ベクトルζ⇡",null,null,"ztax=0",null,0,"ND",null,0.49999999999999922,70.414417042538801,18.517458906998769,0.78505509419615693,36.954138760701291,9.5039964473112075,0.20405100758060898,195.30333799315417,1865.0094986374593,-0.20405100758060898]
[null,null,null,null,"ztay=－sinφ",null,{"$f":"-SIN(RADIANS(G114))","v":-8.7155742747658166E-2},"ND",null,0.52499999999999913,70.087596976933298,18.454343202029097,0.81966622432626235,38.710407706986544,9.9661476783018692,0.22411085256341237,194.66291264727835,1858.893887068811,-0.22411085256341237]
[null,null,null,null,"ztaz=cosφ",null,{"$f":"COS(RADIANS(G114))","v":0.99619469809174555},"ND",null,0.54999999999999905,69.763752067053076,18.389465657232517,0.85388261105047381,40.458543402422542,10.426698925598085,0.24503102929791831,194.0282567750674,1852.8333699153306,-0.24503102929791831]
[null,"風速（追い風、向かい風）",null,null,"vax",null,4,"m/s",null,0.57499999999999896,69.442853026893729,18.322858628724841,0.8877100635970705,42.198619859164751,10.88560654897924,0.26680174202656504,193.39930132569788,1846.8272877902259,-0.26680174202656504]
[null,"風速（横風）",null,null,"vaz",null,4,"m/s",null,0.59999999999999887,69.124870886716991,18.254553844191836,0.92115429037105434,43.930710361179287,11.342827709243572,0.28941333895785393,192.77597824643149,1840.8749908377156,-0.28941333895785393]
[null,"空気密度",null,null,"ρ",null,1.2929999999999999,"kg/m^3",null,0.62499999999999878,68.809776989487233,18.184582416482115,0.95422090101865176,45.65488747210501,11.798320352668027,0.31285630977167705,192.15822046347338,1834.9758385502391,-0.31285630977167705]
[null,"重力加速度定数",null,null,"g",null,9.8066499999999994,"m/s^2",null,0.64999999999999869,68.49754298733653,18.112974856874846,0.98691540844293923,47.371223043026802,12.252043195803834,0.33712128317564366,191.54596186326731,1829.1291995898398,-0.33712128317564366]
[null,"抵抗係数 0次係数",null,null,"cd0",0.1923,{"$f":"F$136*F122","v":9.6149999999999999E-2},null,null,0.6749999999999986,68.188140838058857,18.039761088031138,1.0192432307719137,49.079788220160907,12.703955710599823,0.36219902451119979,190.93913727421599,1823.3344516136065,-0.36219902451119979]
[null,"抵抗係数 1次係数",null,null,"cd1",0.53939999999999999,{"$f":"F$136*F123","v":0.2697},null,null,0.69999999999999851,67.88154280163387,17.964970456637666,1.0512096932802881,50.780653452452938,13.154018109845643,0.38808043340836917,190.33768244881526,1817.5909811030665,-0.38808043340836917]
[null,"抵抗係数 2次係数",null,null,"cd2",-0.24990000000000001,{"$f":"F$136*F124","v":-0.12495000000000001},null,null,0.72499999999999842,67.577721436780536,17.888631745750875,1.0828200302662558,52.473888499089398,13.602191332927319,0.41475654148797297,189.74153404619108,1811.8981831974277,-0.41475654148797297]
[null,"抵抗係数 3次係数",null,null,"cd3",3.3500000000000002E-2,{"$f":"F$136*F125","v":1.6750000000000001E-2},null,null,0.74999999999999833,67.276649597541322,17.810773186849826,1.1140793868844254,54.159562436923402,14.048437031887762,0.44221851011021868,189.15062961502883,1806.2554615305653,-0.44221851011021868]
[null,"揚力係数 0次係数",null,null,"cl0",9.2999999999999999E-2,{"$f":"F$137*F126","v":7.4400000000000008E-2},null,null,0.77499999999999825,66.978300429896905,17.731422471605494,1.1449928209360951,55.837743667815346,14.492717557785026,0.47045762816857645,188.56490757688437,1800.6622280716522,-0.47045762816857645]
[null,"揚力係数 1次係数",null,null,"cl1",0.78790000000000004,{"$f":"F$137*F127","v":0.6303200000000001},null,null,0.79999999999999816,66.682647368411907,17.650606763374157,1.1755653046180001,57.508499925889424,14.934995947341347,0.49946530992789123,187.98430720986696,1795.1179029693449,-0.49946530992789123]
[null,"揚力係数 2次係数",null,null,"cl2",-0.52190000000000003,{"$f":"F$137*F128","v":-0.41752000000000006},null,null,0.82499999999999807,66.389664132911918,17.568352708422172,1.2058017262306315,59.171898284706579,15.375235909876134,0.52923309290570575,187.40876863268446,1789.6219143994247,{"$f":"-P128","v":-0.52923309290570575}]
[null,"揚力係数 3次係数",null,null,"cl3",0.12230000000000001,{"$f":"F$137*F129","v":9.784000000000001E-2},null,null,0.84999999999999798,66.099324725191948,17.484686446889377,1.2357068918471894,60.828005164354856,15.813401814516295,0.55975263579579704,186.83823278904114,1784.1736984158083,-0.55975263579579704]
[null,"モーメント係数 0次係数",null,null,"cm0",6.9999999999999999E-4,{"$f":"F$138*F130","v":6.9999999999999999E-4},null,null,0.87499999999999789,65.81160342575653,17.399633623497952,1.2652855269442114,62.476886338457788,16.24945867767747,0.59101571643295614,186.27264143237917,1778.7726988048398,-0.59101571643295614]
[null,"モーメント係数 1次係数",null,null,"cm1",7.3000000000000001E-3,{"$f":"F$138*F131","v":7.3000000000000001E-3},null,null,0.8999999999999978,65.526474790591621,17.313219398013558,1.2945422779948719,64.118606941101731,16.683372150809856,0.62301422979806431,185.71193711095481,1773.4183669427796,-0.62301422979806431]
[null,"モーメント係数 2次係数",null,null,"cm2",1.1999999999999999E-3,{"$f":"F$138*F132","v":1.1999999999999999E-3},null,null,0.92499999999999771,65.24391364796854,17.225468455465251,1.3234817140259321,65.753231473682888,17.115108508402535,0.65574018606254547,185.15606315324069,1768.1101616564042,-0.65574018606254547]
[null,"モーメント係数 3次係数",null,null,"cm3",0,{"$f":"F$138*F133","v":0},null,null,0.94999999999999762,64.963895095279881,17.136405016130471,1.3521083281392829,67.38082381167483,17.544634636240364,0.68918570867129814,184.60496365364602,1762.8475490866465,-0.68918570867129814]
[null,null,null,null,null,null,null,null,null,0.97499999999999754,64.686394495907606,17.046052845291353,1.3804265389989996,69.001447211317284,17.971918019907594,0.72334303246323284,184.05858345854628,1757.6300025551882,-0.72334303246323284]
[null,"慣性モーメント(均質な球)",null,null,"I",null,{"$f":"(2/5)*G107*(G109/2)^2","v":8.3626078377000005E-6},"kgm^2",null,0.99999999999999745,64.411387476123323,16.954435262768246,1.4084406922847961,70.615164316227066,18.396926733532638,0.75820450182856369,183.51686815261488,1752.4570024339369,-0.75820450182856369]
[null,"抵抗係数微調整用乗数",null,null,null,0.5,null,null,null,1.0249999999999977,64.13884992202081,16.861575152236281,1.4361550621127488,72.22203716393193,18.819629428768405,0.7937625689020259,182.979764045449,1747.3280360173126,-0.7937625689020259]
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[null,"技術的なご質問のみお受けします。"]
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