The Beard and Chuang model is a well known and leading theoretical force balance model used to derive the rotational cross-sections of raindrops in their equilibrium state by employing Chebyshev polynomials in series.
where shape coefficients <math>c_n \cdot 10^4</math> are defined for the raindrops with different equivolumetric diameter as in following table
d(mm)
n = 0
1
2
3
4
5
6
7
8
9
10
2.0
-131
-120
-376
-96
-4
15
5
0
-2
0
1
2.5
-201
-172
-567
-137
3
29
8
-2
-4
0
1
3.0
-282
-230
-779
-175
21
46
11
-6
-7
0
3
3.5
-369
-285
-998
-207
48
68
13
-13
-10
0
5
4.0
-458
-335
-1211
-227
83
89
12
-21
-13
1
8
4.5
-549
-377
-1421
-240
126
110
9
-31
-16
4
11
5.0
-644
-416
-1629
-246
176
131
2
-44
-18
9
14
5.5
-742
-454
-1837
-244
234
150
-7
-58
-19
15
19
6.0
-840
-480
-2034
-237
297
166
-21
-72
-19
24
23
Applications
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 de-polarizing 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.
References
K. V. Beard and C. Chuang. A new model for the equilibrium shape of raindrops. Journal of the Atmospheric Sciences, 44:1509-1524, 1987.
