Spreadsheet: 733939d1621922307-multi-dimensional-linear-interpolation-complex-interpolation
Sheet: Joseph

 |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  | x
 |  |  | Workings |  |  |  |  | Combined |  | β |  |  | 10 |  |  | 20 |  |  | 30 |  |  | 40
INPUT |  |  | Lookup | Match | Row | Column | Result | [NAME] |  | (φ'°) | B/H | b/B | NS |  |  | NS |  |  | NS |  |  | NS
 | (φ'°) |  |  |  |  |  |  |  |  |  |  |  | 0 | 2 | 4 | 0 | 2 | 4 | 0 | 2 | 4 | 0 | 2 | 4
 | β |  |  |  |  |  |  |  |  | 0 | 0.2 | 0 | 0.89 | 0.88 | 0.88 | 0.89 | 0.87 | 0.86 | 0.82 | 0.81 | 0.78 | 0.76 | 0.73 | 0.69
 | B/H |  |  |  |  |  |  |  |  |  |  | 0.5 | 0.97 | 0.96 | 0.96 | 0.95 | 0.93 | 0.91 | 0.92 | 0.89 | 0.87 | 0.86 | 0.83 | 0.76
 | b/B |  |  |  |  |  |  |  |  |  |  | 1.25 | 1 | 0.99 | 0.98 | 1 | 0.98 | 0.96 | 1 | 0.97 | 0.95 | 0.95 | 0.91 | 0.81
 | NS |  |  |  |  |  |  |  |  |  |  | 2.5 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0.97 | 0.84
 |  |  |  |  |  |  |  |  |  |  |  | 5 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0.89
 |  |  |  |  |  |  |  |  |  |  |  | 10 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1
OUTPUT (Interpolated) |  |  |  |  |  |  |  |  |  |  | 0.5 | 0 | 0.92 | 0.91 | 0.88 | 0.85 | 0.82 | 0.76 | 0.77 | 0.73 | 0.63 | 0.71 | 0.65 | 0.52
 |  |  |  |  |  |  |  |  |  |  |  | 0.5 | 0.96 | 0.95 | 0.89 | 0.92 | 0.89 | 0.78 | 0.87 | 0.84 | 0.68 | 0.83 | 0.76 | 0.56
 |  |  |  |  |  |  |  |  |  |  |  | 1.25 | 0.98 | 0.97 | 0.9 | 0.96 | 0.94 | 0.8 | 0.94 | 0.92 | 0.71 | 0.9 | 0.83 | 0.58
 |  |  |  |  |  |  |  |  |  |  |  | 2.5 | 1 | 1 | 1 | 1 | 1 | 0.86 | 1 | 1 | 0.79 | 1 | 0.93 | 0.68
 |  |  |  |  |  |  |  |  |  |  |  | 5 | 1 | 1 | 1 | 1 | 1 | 0.95 | 1 | 1 | 0.93 | 1 | 1 | 0.88
 |  |  |  |  |  |  |  |  |  |  |  | 10 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1
 |  |  |  |  |  |  |  |  |  |  | 1 | 0 | 0.87 | 0.84 | 0.75 | 0.87 | 0.79 | 0.56 | 0.8 | 0.66 | 0.42 | 0.73 | 0.56 | 0.33
 |  |  |  |  |  |  |  |  |  |  |  | 0.5 | 0.95 | 0.91 | 0.82 | 0.92 | 0.83 | 0.65 | 0.86 | 0.73 | 0.46 | 0.81 | 0.67 | 0.4
 |  |  |  |  |  |  |  |  |  |  |  | 1.25 | 0.97 | 0.94 | 0.83 | 0.95 | 0.87 | 0.67 | 0.92 | 0.81 | 0.5 | 0.89 | 0.76 | 0.46
 |  |  |  |  |  |  |  |  |  |  |  | 2.5 | 1 | 0.98 | 0.88 | 1 | 0.97 | 0.77 | 1 | 1 | 0.84 | 0.99 | 0.92 | 0.63
 |  |  |  |  |  |  |  |  |  |  |  | 5 | 1 | 1 | 0.95 | 1 | 1 | 0.9 | 1 | 1 | 0.84 | 1 | 1 | 0.83
 |  |  |  |  |  |  |  |  |  |  |  | 10 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1
 |  |  |  |  |  |  |  |  |  |  | 2 | 0 | 0.87 | 0.79 | 0.57 | 0.87 | 0.71 | 0.44 | 0.81 | 0.62 | 0.35 | 0.75 | 0.56 | 0.29
 |  |  |  |  |  |  |  |  |  |  |  | 0.5 | 0.97 | 0.93 | 0.65 | 0.94 | 0.79 | 0.49 | 0.89 | 0.72 | 0.42 | 0.85 | 0.69 | 0.37
 |  |  |  |  |  |  |  |  |  |  |  | 1.25 | 0.99 | 0.98 | 0.73 | 0.99 | 0.91 | 0.57 | 0.98 | 0.86 | 0.51 | 0.96 | 0.83 | 0.47
 |  |  |  |  |  |  |  |  |  |  |  | 2.5 | 1 | 0.99 | 0.82 | 1 | 0.96 | 0.69 | 1 | 0.95 | 0.64 | 1 | 0.95 | 0.61
 |  |  |  |  |  |  |  |  |  |  |  | 5 | 1 | 1 | 0.96 | 1 | 1 | 0.87 | 1 | 1 | 0.84 | 1 | 1 | 0.81
 |  |  |  |  |  |  |  |  |  |  |  | 10 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1
 |  |  |  |  |  |  |  |  |  | 20 | 0.2 | 0 | 0.9 | 0.89 | 0.9 | 0.75 | 0.73 | 0.72 | 0.62 | 0.59 | 0.56 | 0.52 | 0.49 | 0.45
 |  |  |  |  |  |  |  |  |  |  |  | 0.5 | 0.78 | 0.87 | 0.86 | 0.74 | 0.76 | 0.74 | 0.63 | 0.65 | 0.63 | 0.52 | 0.56 | 0.52
 |  |  |  |  |  |  |  |  |  |  |  | 1.25 | 0.86 | 0.92 | 0.92 | 0.83 | 0.84 | 0.83 | 0.74 | 0.75 | 0.74 | 0.63 | 0.66 | 0.63
 |  |  |  |  |  |  |  |  |  |  |  | 2.5 | 0.96 | 0.98 | 0.99 | 0.95 | 0.94 | 0.95 | 0.9 | 0.89 | 0.9 | 0.78 | 0.81 | 0.78
 |  |  |  |  |  |  |  |  |  |  |  | 5 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0.96 | 0.98 | 0.96
 |  |  |  |  |  |  |  |  |  |  |  | 10 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0.99 | 0.99 | 1
 |  |  |  |  |  |  |  |  |  |  | 0.5 | 0 | 0.86 | 0.86 | 0.84 | 0.73 | 0.7 | 0.67 | 0.62 | 0.56 | 0.51 | 0.52 | 0.45 | 0.39
 |  |  |  |  |  |  |  |  |  |  |  | 0.5 | 0.84 | 0.91 | 0.92 | 0.8 | 0.8 | 0.79 | 0.7 | 0.68 | 0.67 | 0.62 | 0.59 | 0.56
 |  |  |  |  |  |  |  |  |  |  |  | 1.25 | 0.88 | 1 | 0.97 | 0.85 | 0.88 | 0.86 | 0.76 | 0.75 | 0.75 | 0.68 | 0.66 | 0.64
 |  |  |  |  |  |  |  |  |  |  |  | 2.5 | 0.97 | 1 | 1 | 0.95 | 0.97 | 0.98 | 0.9 | 0.94 | 0.96 | 0.84 | 0.86 | 0.87
 |  |  |  |  |  |  |  |  |  |  |  | 5 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1
 |  |  |  |  |  |  |  |  |  |  |  | 10 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1
 |  |  |  |  |  |  |  |  |  |  | 1 | 0 | 0.85 | 0.82 | 0.78 | 0.72 | 0.64 | 0.58 | 0.61 | 0.5 | 0.42 | 0.52 | 0.39 | 0.3
 |  |  |  |  |  |  |  |  |  |  |  | 0.5 | 0.84 | 0.91 | 0.91 | 0.81 | 0.8 | 0.79 | 0.7 | 0.69 | 0.67 | 0.64 | 0.62 | 0.6
 |  |  |  |  |  |  |  |  |  |  |  | 1.25 | 0.87 | 0.95 | 0.96 | 0.85 | 0.85 | 0.85 | 0.76 | 0.76 | 0.75 | 0.71 | 0.7 | 0.69
 |  |  |  |  |  |  |  |  |  |  |  | 2.5 | 0.97 | 1 | 1 | 0.95 | 0.97 | 0.98 | 0.9 | 0.94 | 0.97 | 0.86 | 0.89 | 0.91
 |  |  |  |  |  |  |  |  |  |  |  | 5 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1
 |  |  |  |  |  |  |  |  |  |  |  | 10 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1
 |  |  |  |  |  |  |  |  |  |  | 2 | 0 | 0.9 | 0.9 | 0.9 | 0.87 | 0.86 | 0.84 | 0.84 | 0.81 | 0.78 | 0.81 | 0.77 | 0.74
 |  |  |  |  |  |  |  |  |  |  |  | 0.5 | 0.9 | 0.93 | 0.93 | 0.88 | 0.88 | 0.87 | 0.84 | 0.83 | 0.81 | 0.84 | 0.82 | 0.81
 |  |  |  |  |  |  |  |  |  |  |  | 1.25 | 0.92 | 0.97 | 0.99 | 0.9 | 0.92 | 0.92 | 0.86 | 0.86 | 0.86 | 0.85 | 0.85 | 0.84
 |  |  |  |  |  |  |  |  |  |  |  | 2.5 | 0.98 | 1 | 1 | 0.97 | 0.98 | 1 | 0.93 | 0.97 | 1 | 0.92 | 0.96 | 0.99
 |  |  |  |  |  |  |  |  |  |  |  | 5 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1
 |  |  |  |  |  |  |  |  |  |  |  | 10 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1
 |  |  |  |  |  |  |  |  |  | 30 | 0.2 | 0 | 0.93 | 0.92 | 0.91 | 0.65 | 0.64 | 0.63 | 0.51 | 0.5 | 0.48 | 0.4 | 0.37 | 0.36
 |  |  |  |  |  |  |  |  |  |  |  | 0.5 | 0.74 | 0.81 | 0.8 | 0.7 | 0.66 | 0.65 | 0.57 | 0.52 | 0.49 | 0.47 | 0.42 | 0.39
 |  |  |  |  |  |  |  |  |  |  |  | 1.25 | 0.78 | 0.85 | 0.86 | 0.74 | 0.73 | 0.72 | 0.63 | 0.6 | 0.59 | 0.54 | 0.5 | 0.47
 |  |  |  |  |  |  |  |  |  |  |  | 2.5 | 0.84 | 0.92 | 0.93 | 0.81 | 0.82 | 0.83 | 0.72 | 0.73 | 0.74 | 0.64 | 0.62 | 0.61
 |  |  |  |  |  |  |  |  |  |  |  | 5 | 0.95 | 1 | 1 | 0.93 | 0.98 | 1 | 0.88 | 0.95 | 1 | 0.8 | 0.85 | 0.87
 |  |  |  |  |  |  |  |  |  |  |  | 10 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1
 |  |  |  |  |  |  |  |  |  |  | 0.5 | 0 | 0.79 | 0.79 | 0.78 | 0.63 | 0.59 | 0.55 | 0.5 | 0.43 | 0.39 | 0.39 | 0.32 | 0.27
 |  |  |  |  |  |  |  |  |  |  |  | 0.5 | 0.76 | 0.87 | 0.87 | 0.72 | 0.71 | 0.7 | 0.58 | 0.56 | 0.54 | 0.49 | 0.46 | 0.43
 |  |  |  |  |  |  |  |  |  |  |  | 1.25 | 0.79 | 0.85 | 0.92 | 0.75 | 0.73 | 0.76 | 0.63 | 0.62 | 0.61 | 0.54 | 0.52 | 0.5
 |  |  |  |  |  |  |  |  |  |  |  | 2.5 | 0.87 | 0.91 | 1 | 0.84 | 0.85 | 0.9 | 0.74 | 0.78 | 0.8 | 0.67 | 0.7 | 0.71
 |  |  |  |  |  |  |  |  |  |  |  | 5 | 0.97 | 1 | 1 | 0.95 | 1 | 1 | 0.9 | 1 | 1 | 0.85 | 0.94 | 0.98
 |  |  |  |  |  |  |  |  |  |  |  | 10 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1
 |  |  |  |  |  |  |  |  |  |  | 1 | 0 | 0.79 | 0.75 | 0.73 | 0.63 | 0.53 | 0.49 | 0.55 | 0.41 | 0.35 | 0.48 | 0.33 | 0.26
 |  |  |  |  |  |  |  |  |  |  |  | 0.5 | 0.78 | 0.87 | 0.89 | 0.75 | 0.74 | 0.74 | 0.64 | 0.62 | 0.6 | 0.59 | 0.56 | 0.54
 |  |  |  |  |  |  |  |  |  |  |  | 1.25 | 0.81 | 0.9 | 0.91 | 0.78 | 0.78 | 0.78 | 0.68 | 0.67 | 0.66 | 0.64 | 0.62 | 0.61
 |  |  |  |  |  |  |  |  |  |  |  | 2.5 | 0.88 | 0.99 | 1 | 0.85 | 0.9 | 0.92 | 0.78 | 0.81 | 0.84 | 0.75 | 0.78 | 0.8
 |  |  |  |  |  |  |  |  |  |  |  | 5 | 0.97 | 1 | 1 | 0.96 | 1 | 1 | 0.92 | 1 | 1 | 0.89 | 0.98 | 1
 |  |  |  |  |  |  |  |  |  |  |  | 10 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1
 |  |  |  |  |  |  |  |  |  |  | 2 | 0 | 0.88 | 0.88 | 0.87 | 0.87 | 0.85 | 0.83 | 0.85 | 0.82 | 0.8 | 0.83 | 0.8 | 0.76
 |  |  |  |  |  |  |  |  |  |  |  | 0.5 | 0.89 | 0.91 | 0.91 | 0.89 | 0.89 | 0.87 | 0.88 | 0.86 | 0.84 | 0.87 | 0.85 | 0.82
 |  |  |  |  |  |  |  |  |  |  |  | 1.25 | 0.9 | 0.92 | 0.93 | 0.9 | 0.9 | 0.9 | 0.89 | 0.87 | 0.87 | 0.89 | 0.87 | 0.86
 |  |  |  |  |  |  |  |  |  |  |  | 2.5 | 0.97 | 1 | 1 | 0.96 | 0.97 | 0.98 | 0.92 | 0.94 | 0.96 | 0.91 | 0.92 | 0.94
 |  |  |  |  |  |  |  |  |  |  |  | 5 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1
 |  |  |  |  |  |  |  |  |  |  |  | 10 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1
 |  |  |  |  |  |  |  |  |  | 40 | 0.2 | 0 | 0.69 | 0.69 | 0.69 | 0.51 | 0.48 | 0.47 | 0.37 | 0.33 | 0.3 | 0.27 | 0.23 | 0.2
 |  |  |  |  |  |  |  |  |  |  |  | 0.5 | 0.65 | 0.73 | 0.71 | 0.6 | 0.55 | 0.53 | 0.64 | 0.38 | 0.35 | 0.34 | 0.29 | 0.25
 |  |  |  |  |  |  |  |  |  |  |  | 1.25 | 0.68 | 0.77 | 0.75 | 0.63 | 0.6 | 0.58 | 0.74 | 0.44 | 0.42 | 0.39 | 0.34 | 0.31
 |  |  |  |  |  |  |  |  |  |  |  | 2.5 | 0.72 | 0.83 | 0.84 | 0.68 | 0.68 | 0.68 | 0.87 | 0.53 | 0.53 | 0.45 | 0.43 | 0.41
 |  |  |  |  |  |  |  |  |  |  |  | 5 | 0.8 | 0.93 | 0.95 | 0.76 | 0.82 | 0.85 | 1 | 0.72 | 0.76 | 0.57 | 0.61 | 0.63
 |  |  |  |  |  |  |  |  |  |  |  | 10 | 0.94 | 1 | 1 | 0.91 | 1 | 1 | 1 | 1 | 1 | 0.76 | 0.93 | 1
 |  |  |  |  |  |  |  |  |  |  | 0.5 | 0 | 0.67 | 0.69 | 0.67 | 0.5 | 0.45 | 0.43 | 0.36 | 0.3 | 0.26 | 0.27 | 0.2 | 0.17
 |  |  |  |  |  |  |  |  |  |  |  | 0.5 | 0.68 | 0.81 | 0.81 | 0.63 | 0.62 | 0.61 | 0.47 | 0.44 | 0.41 | 0.39 | 0.35 | 0.32
 |  |  |  |  |  |  |  |  |  |  |  | 1.25 | 0.7 | 0.82 | 0.84 | 0.65 | 0.65 | 0.66 | 0.51 | 0.49 | 0.47 | 0.43 | 0.41 | 0.39
 |  |  |  |  |  |  |  |  |  |  |  | 2.5 | 0.76 | 0.92 | 0.96 | 0.72 | 0.77 | 0.8 | 0.59 | 0.62 | 0.63 | 0.54 | 0.56 | 0.56
 |  |  |  |  |  |  |  |  |  |  |  | 5 | 0.84 | 1 | 1 | 0.81 | 0.91 | 0.94 | 0.71 | 0.82 | 0.88 | 0.67 | 0.77 | 0.83
 |  |  |  |  |  |  |  |  |  |  |  | 10 | 0.96 | 1 | 1 | 0.94 | 1 | 1 | 0.89 | 1 | 1 | 0.86 | 1 | 1
 |  |  |  |  |  |  |  |  |  |  | 1 | 0 | 0.69 | 0.64 | 0.62 | 0.63 | 0.48 | 0.43 | 0.58 | 0.39 | 0.33 | 0.54 | 0.33 | 0.27
 |  |  |  |  |  |  |  |  |  |  |  | 0.5 | 0.77 | 0.81 | 0.82 | 0.75 | 0.73 | 0.72 | 0.71 | 0.66 | 0.62 | 0.68 | 0.62 | 0.57
 |  |  |  |  |  |  |  |  |  |  |  | 1.25 | 0.78 | 0.84 | 0.85 | 0.77 | 0.76 | 0.75 | 0.73 | 0.69 | 0.66 | 0.71 | 0.66 | 0.63
 |  |  |  |  |  |  |  |  |  |  |  | 2.5 | 0.83 | 0.92 | 0.95 | 0.81 | 0.85 | 0.87 | 0.76 | 0.78 | 0.79 | 0.75 | 0.76 | 0.77
 |  |  |  |  |  |  |  |  |  |  |  | 5 | 0.89 | 1 | 1 | 0.87 | 0.95 | 0.98 | 0.8 | 0.9 | 0.95 | 0.8 | 0.89 | 0.94
 |  |  |  |  |  |  |  |  |  |  |  | 10 | 0.98 | 1 | 1 | 0.97 | 1 | 1 | 0.94 | 1 | 1 | 0.93 | 1 | 1
 |  |  |  |  |  |  |  |  |  |  | 2 | 0 | 0.93 | 0.92 | 0.89 | 0.92 | 0.9 | 0.87 | 0.91 | 0.88 | 0.84 | 0.89 | 0.85 | 0.81
 |  |  |  |  |  |  |  |  |  |  |  | 0.5 | 0.93 | 0.95 | 0.93 | 0.93 | 0.92 | 0.9 | 0.92 | 0.89 | 0.87 | 0.92 | 0.89 | 0.86
 |  |  |  |  |  |  |  |  |  |  |  | 1.25 | 0.93 | 0.95 | 0.94 | 0.93 | 0.93 | 0.92 | 0.93 | 0.91 | 0.89 | 0.93 | 0.9 | 0.88
 |  |  |  |  |  |  |  |  |  |  |  | 2.5 | 0.94 | 0.99 | 1 | 0.94 | 0.98 | 0.98 | 0.94 | 0.97 | 0.97 | 0.94 | 0.96 | 0.96
 |  |  |  |  |  |  |  |  |  |  |  | 5 | 0.95 | 1 | 1 | 0.96 | 1 | 1 | 0.98 | 1 | 1 | 0.96 | 1 | 1
 |  |  |  |  |  |  |  |  |  |  |  | 10 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0.99 | 1 | 1