Short Dipole Equation

The ARRL Antenna Handbook has an equation listed in the section on shortening a dipole with a loading coil. But it's a pretty messy equation and has no real explanation associated with it. There is also a variable (D) that is unexplained. So I am going to try and simplify the equation a bit and take a guess at the unexplained variable.

XL =
106
34·PI·f
×
M1
Ln
24·( 234/f - B )
D
- 1
×
N1
1 -
f·B
234
2
- 1
N2
234/f - B
D1
Ln
24·( A/2 - B )
D
- 1
×
N3
N4
f·A/2 - f·B
234
2
- 1
A/2 - B
D2
  • Equation M1 = 1314.342
  • Equation N1 = 8.716
  • Equation N2 = -0.281
  • Equation N3 = 8.01
  • Equation N4 = -0.825
  • Equation D1 = 27.851
  • Equation D2 = 13.75
  • Equation XL = 515.887
  • Equation L = 11.527
  • Equation F1 = 1314.342
  • Equation F2 = 8.716
  • Equation F3 = -0.281
  • Equation F5 = 8.01
  • Equation F6 = -0.825
  • Equation F4 = 27.851
  • Equation F7 = 13.75
  • Equation XL = 515.887
  • Equation L = 11.527
  • Equation C1 = 1314.342
  • Equation C2 = 8.716
  • Equation C3 = -0.281
  • Equation C5 = 8.01
  • Equation C6 = -0.825
  • Equation C4 = 27.851
  • Equation C7 = 13.75
  • Equation CXL = 515.887
  • Equation CL = 11.527