Table 8 Equations of the SF curves for each parameter \(\hbox{m}_i\) and shape factor sub-category
\(\hbox{L}/\hbox{h} \le 1\) | \(1 <\hbox{L}/\hbox{h}\le 2\) | \(2<\hbox{L}/\hbox{h} \le 3\) | \(\hbox{L}/\hbox{h} >3\) | |
|---|---|---|---|---|
\(m_i = 3\) | ||||
\(\text{SF} = 1\) | \(0.018\hbox{x}^3+0.0065\hbox{x}^2+1.42\hbox{x}+0.51\) | \(0.026\hbox{x}^3-0.068\hbox{x}^2+1.74\hbox{x}-0.2\) | \(0.015\hbox{x}^3+0.033\hbox{x}^2+1.63\hbox{x}-0.26\) | \(0.031\hbox{x}^3-0.11\hbox{x}^2+2.018\hbox{x}-0.44\) |
\(\text{SF} = 2\) | \(0.04\hbox{x}^3+0.18\hbox{x}^2+2.2\hbox{x}+0.84\) | \(0.061\hbox{x}^3-0.056\hbox{x}^2+2.95\hbox{x}+0.18\) | \(0.06\hbox{x}^3-0.033\hbox{x}^2+2.92\hbox{x}+0.13\) | \(0.064\hbox{x}^3-0.077\hbox{x}^2+3.06\hbox{x}+0.027\) |
\(\text{SF} = 3\) | \(0.064\hbox{x}^3+0.36\hbox{x}^2+3\hbox{x}+1.75\) | \(0.084\hbox{x}^3+0.13\hbox{x}^2+3.82\hbox{x}+0.8\) | \(0.083\hbox{x}^3+0.14\hbox{x}^2+3.85\hbox{x}+0.65\) | \(0.088\hbox{x}^3+0.085\hbox{x}^2+4.036\hbox{x}+0.48\) |
\(\text{SF} = 4\) | \(0.085\hbox{x}^3+0.6\hbox{x}^2+3.7\hbox{x}+2.81\) | \(0.1\hbox{x}^3+0.4\hbox{x}^2+4.51\hbox{x}+1.55\) | \(0.11\hbox{x}^3+0.28\hbox{x}^2+4.93\hbox{x}+1.11\) | \(0.11\hbox{x}^3+0.23\hbox{x}^2+5.12\hbox{x}+0.9\) |
\(\text{SF} = 5\) | \(0.11\hbox{x}^3+0.81\hbox{x}^2+4.44\hbox{x}+3.88\) | \(0.13\hbox{x}^3+0.57\hbox{x}^2+5.47\hbox{x}+2.2\) | \(0.13\hbox{x}^3+0.47\hbox{x}^2+5.92\hbox{x}+1.64\) | \(0.15\hbox{x}^3+0.29\hbox{x}^2+6.47\hbox{x}+1.21\) |
\(m_i = 8\) | ||||
\(\text{SF} = 1\) | \(-0.019\hbox{x}^3+0.49\hbox{x}^2+0.66\hbox{x}+1.13\) | \(-0.013\hbox{x}^3+0.4\hbox{x}^2+1.25\hbox{x}+0.336\) | \(-0.03\hbox{x}^3+0.534\hbox{x}^2+1.17\hbox{x}+0.29\) | \(-0.0007\hbox{x}^3+0.222\hbox{x}^2+2.12\hbox{x}-0.416\) |
\(\text{SF} = 2\) | \(0.065\hbox{x}^3+0.09\hbox{x}^2+3.66\hbox{x}+0.31\) | \(0.064\hbox{x}^3+0.082\hbox{x}^2+3.82\hbox{x}-0.072\) | \(0.062\hbox{x}^3+0.082\hbox{x}^2+3.9\hbox{x}-0.17\) | \(0.071\hbox{x}^3-0.0084\hbox{x}^2+4.116\hbox{x}-0.3\) |
\(\text{SF} = 3\) | \(0.11\hbox{x}^3+0.36\hbox{x}^2+4.73\hbox{x}+1.5\) | \(0.11\hbox{x}^3+0.3\hbox{x}^2+5.24\hbox{x}+0.66\) | \(0.11\hbox{x}^3+0.25\hbox{x}^2+5.43\hbox{x}+0.44\) | \(0.12\hbox{x}^3+0.18\hbox{x}^2+5.63\hbox{x}+0.27\) |
\(\text{SF} = 4\) | \(0.14\hbox{x}^3+0.81\hbox{x}^2+5.57\hbox{x}+2.9\) | \(0.14\hbox{x}^3+0.74\hbox{x}^2+6.32\hbox{x}+1.57\) | \(0.14\hbox{x}^3+0.73\hbox{x}^2+6.56\hbox{x}+1.14\) | \(0.14\hbox{x}^3+0.68\hbox{x}^2+6.81\hbox{x}+0.84\) |
\(\text{SF} = 5\) | \(0.17\hbox{x}^3+1.25\hbox{x}^2+6.54\hbox{x}+4.42\) | \(0.17\hbox{x}^3+1.17\hbox{x}^2+7.435\hbox{x}+2.55\) | \(0.18\hbox{x}^3+1.09\hbox{x}^2+7.9\hbox{x}+1.92\) | \(0.18\hbox{x}^3+1.04\hbox{x}^2+8.18\hbox{x}+1.54\) |
\(m_i = 16\) | ||||
\(\text{SF} = 1\) | \(0.03\hbox{x}^3+0.063\hbox{x}^2+2.31\hbox{x}+0.82\) | \(-0.055\hbox{x}^3+0.96\hbox{x}^2+0.41\hbox{x}+0.81\) | \(-0.066\hbox{x}^3+\hbox{x}^2+0.76\hbox{x}+0.37\) | \(-0.0009\hbox{x}^3+0.3\hbox{x}^2+2.78\hbox{x}-0.74\) |
\(\text{SF} = 2\) | \(0.072\hbox{x}^3+0.16\hbox{x}^2+4.61\hbox{x}-0.26\) | \(0.067\hbox{x}^3+0.24\hbox{x}^2+4.46\hbox{x}-0.52\) | \(0.028\hbox{x}^3+0.58\hbox{x}^2+3.7\hbox{x}-0.12\) | \(0.077\hbox{x}^3+0.105\hbox{x}^2+4.9\hbox{x}-0.75\) |
\(\text{SF} = 3\) | \(0.1\hbox{x}^3+0.74\hbox{x}^2+5.78\hbox{x}+1.32\) | \(0.11\hbox{x}^3+0.65\hbox{x}^2+6.33\hbox{x}+0.3\) | \(0.1\hbox{x}^3+0.68\hbox{x}^2+6.4\hbox{x}+0.15\) | \(0.11\hbox{x}^3+0.53\hbox{x}^2+6.86\hbox{x}-0.18\) |
\(\text{SF} = 4\) | \(0.16\hbox{x}^3+1.15\hbox{x}^2+7.58\hbox{x}+2.7\) | \(0.18\hbox{x}^3+0.87\hbox{x}^2+8.86\hbox{x}+0.9\) | \(0.18\hbox{x}^3+0.84\hbox{x}^2+9.17\hbox{x}+0.44\) | \(0.19\hbox{x}^3+0.76\hbox{x}^2+9.46\hbox{x}+0.15\) |
\(\text{SF} = 5\) | \(0.22\hbox{x}^3+1.67\hbox{x}^2+9.16\hbox{x}+4.36\) | \(0.24\hbox{x}^3+1.36\hbox{x}^2+10.74\hbox{x}+1.92\) | \(0.24\hbox{x}^3+1.25\hbox{x}^2+11.37\hbox{x}+1.15\) | \(0.25\hbox{x}^3+1.14\hbox{x}^2+11.73\hbox{x}+0.74\) |