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Beard and Chuang model

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The description of raindrop shape has some rather practical uses. Understanding rain is particularly important with regard to the propagation of electromagnetic signals. A portion of atmosphere that has rain in it, or a rain cell, has the characteristic of attenuating and
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EM signals that pass through it. The attenuation of such a signal is approximately proportional to the square of the frequency of the signal, and the de-polarization is proportional to the shape distribution of raindrops in the rain cell.
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is a well known and leading theoretical force balance model used to derive the rotational cross-sections of
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are defined for the raindrops with different equivolumetric diameter as in following table
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K. V. Beard and C. Chuang. A new model for the equilibrium shape of raindrops.
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You can help Knowledge (XXG) by 130:Beard and Chuang model of raindrop 14: 302:{\displaystyle c_{n}\cdot 10^{4}} 794: 737: 31:relies largely or entirely on a 20: 253: 250: 241: 210: 201: 195: 163:in vertical angular direction 150: 144: 1: 259:{\displaystyle r(\theta )=a} 883: 789: 732: 156:{\displaystyle r(\theta )} 867:Atmospheric science stubs 269:where shape coefficients 59:"Beard and Chuang model" 176:{\displaystyle \theta } 749:-related article is a 303: 260: 177: 157: 131: 113:Beard and Chuang model 304: 261: 178: 158: 129: 121:Chebyshev polynomials 273: 189: 167: 138: 44:improve this article 804:atmospheric science 802:This article about 299: 256: 173: 153: 132: 819: 818: 762: 761: 725::1509-1524, 1987. 694: 693: 109: 108: 94: 874: 840: 833: 826: 798: 791: 783: 776: 769: 741: 734: 312: 308: 306: 305: 300: 298: 297: 285: 284: 265: 263: 262: 257: 231: 230: 182: 180: 179: 174: 162: 160: 159: 154: 104: 101: 95: 93: 52: 24: 16: 882: 881: 877: 876: 875: 873: 872: 871: 847: 846: 845: 844: 788: 787: 730: 728: 713: 699: 289: 276: 271: 270: 222: 187: 186: 165: 164: 136: 135: 105: 99: 96: 53: 51: 37: 25: 12: 11: 5: 880: 878: 870: 869: 864: 859: 849: 848: 843: 842: 835: 828: 820: 817: 816: 799: 786: 785: 778: 771: 763: 760: 759: 742: 727: 726: 714: 712: 709: 698: 695: 692: 691: 688: 685: 682: 679: 676: 673: 670: 667: 664: 661: 658: 654: 653: 650: 647: 644: 641: 638: 635: 632: 629: 626: 623: 620: 616: 615: 612: 609: 606: 603: 600: 597: 594: 591: 588: 585: 582: 578: 577: 574: 571: 568: 565: 562: 559: 556: 553: 550: 547: 544: 540: 539: 536: 533: 530: 527: 524: 521: 518: 515: 512: 509: 506: 502: 501: 498: 495: 492: 489: 486: 483: 480: 477: 474: 471: 468: 464: 463: 460: 457: 454: 451: 448: 445: 442: 439: 436: 433: 430: 426: 425: 422: 419: 416: 413: 410: 407: 404: 401: 398: 395: 392: 388: 387: 384: 381: 378: 375: 372: 369: 366: 363: 360: 357: 354: 350: 349: 346: 343: 340: 337: 334: 331: 328: 325: 322: 319: 316: 296: 292: 288: 283: 279: 255: 252: 249: 246: 243: 240: 237: 234: 229: 225: 221: 218: 215: 212: 209: 206: 203: 200: 197: 194: 172: 152: 149: 146: 143: 107: 106: 42:. Please help 28: 26: 19: 13: 10: 9: 6: 4: 3: 2: 879: 868: 865: 863: 862:Physics stubs 860: 858: 857:Precipitation 855: 854: 852: 841: 836: 834: 829: 827: 822: 821: 815: 813: 809: 805: 800: 797: 793: 784: 779: 777: 772: 770: 765: 764: 758: 756: 752: 748: 743: 740: 736: 731: 724: 720: 716: 715: 710: 708: 705: 704:de-polarizing 696: 689: 686: 683: 680: 677: 674: 671: 668: 665: 662: 659: 656: 655: 651: 648: 645: 642: 639: 636: 633: 630: 627: 624: 621: 618: 617: 613: 610: 607: 604: 601: 598: 595: 592: 589: 586: 583: 580: 579: 575: 572: 569: 566: 563: 560: 557: 554: 551: 548: 545: 542: 541: 537: 534: 531: 528: 525: 522: 519: 516: 513: 510: 507: 504: 503: 499: 496: 493: 490: 487: 484: 481: 478: 475: 472: 469: 466: 465: 461: 458: 455: 452: 449: 446: 443: 440: 437: 434: 431: 428: 427: 423: 420: 417: 414: 411: 408: 405: 402: 399: 396: 393: 390: 389: 385: 382: 379: 376: 373: 370: 367: 364: 361: 358: 355: 352: 351: 347: 344: 341: 338: 335: 332: 329: 326: 323: 320: 317: 314: 313: 310: 294: 290: 286: 281: 277: 267: 247: 244: 238: 235: 232: 227: 223: 219: 216: 213: 207: 204: 198: 192: 184: 170: 147: 141: 128: 124: 123:in series. 122: 118: 114: 103: 92: 89: 85: 82: 78: 75: 71: 68: 64: 61: –  60: 56: 55:Find sources: 49: 45: 41: 35: 34: 33:single source 29:This article 27: 23: 18: 17: 812:expanding it 801: 755:expanding it 744: 729: 722: 718: 700: 697:Applications 268: 185: 183:is equal to 133: 112: 110: 97: 87: 80: 73: 66: 54: 30: 851:Categories 711:References 100:March 2024 70:newspapers 287:⋅ 248:θ 220:∑ 199:θ 171:θ 148:θ 117:raindrops 40:talk page 747:physics 84:scholar 86:  79:  72:  65:  57:  806:is a 745:This 666:-2034 628:-1837 590:-1629 552:-1421 514:-1211 318:n = 0 315:d(mm) 91:JSTOR 77:books 808:stub 751:stub 669:-237 663:-480 660:-840 631:-244 625:-454 622:-742 593:-246 587:-416 584:-644 555:-240 549:-377 546:-549 517:-227 511:-335 508:-458 479:-207 476:-998 473:-285 470:-369 441:-175 438:-779 435:-230 432:-282 403:-137 400:-567 397:-172 394:-201 362:-376 359:-120 356:-131 111:The 63:news 690:23 684:-19 681:-72 678:-21 675:166 672:297 657:6.0 652:19 646:-19 643:-58 637:150 634:234 619:5.5 614:14 608:-18 605:-44 599:131 596:176 581:5.0 576:11 570:-16 567:-31 561:110 558:126 543:4.5 532:-13 529:-21 505:4.0 494:-10 491:-13 467:3.5 429:3.0 391:2.5 365:-96 353:2.0 348:10 46:by 853:: 723:44 721:, 687:24 649:15 640:-7 538:8 526:12 523:89 520:83 500:5 488:13 485:68 482:48 462:3 456:-7 453:-6 450:11 447:46 444:21 424:1 418:-4 415:-2 409:29 386:1 380:-2 371:15 368:-4 291:10 266:, 839:e 832:t 825:v 814:. 782:e 775:t 768:v 757:. 611:9 602:2 573:4 564:9 535:1 497:0 459:0 421:0 412:8 406:3 383:0 377:0 374:5 345:9 342:8 339:7 336:6 333:5 330:4 327:3 324:2 321:1 295:4 282:n 278:c 254:] 251:) 245:n 242:( 239:s 236:o 233:c 228:n 224:c 217:+ 214:1 211:[ 208:a 205:= 202:) 196:( 193:r 151:) 145:( 142:r 102:) 98:( 88:· 81:· 74:· 67:· 50:. 36:.

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