J9

Therefore, for the surface duct

2 sin 9 r0

where r0 = H/(2sin 9) and 9 is the inclination angle at the source of the maximum trapped ray. The quantity r2 r/r0 indicates that the propagation to range r may be viewed as the result of spherical spreading out to a transition range r0, followed by cylindrical spreading from r0 to r. The range r0 also corresponds to the condition in which the vertical extent of the beam subtended by the angle 29 equals the duct thickness H. Ranges greater than r0 are generally considered to represent far-field conditions. When the attenuation due to absorption and leakage is added, the duct TL expression becomes

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