Question E3A11:
What is a typical range for tropospheric duct propagation of microwave signals?  

Choices:  
A: 10 miles to 50 miles  
B: 100 miles to 300 miles  
C: 1,200 miles  
D: 2,500 miles    

Correct Answer is  B: 100 miles to 300 miles  

To understand tropospheric ducting: temperature inversions in the lower atmosphere can trap VHF/UHF/microwave signals and guide them well beyond normal line-of-sight. Typical duct paths are a few hundred miles.

Why B (100 miles to 300 miles) is correct
- Tropospheric ducts commonly extend signals a few hundred miles. For microwave bands, typical duct-assisted paths are on the order of 100–300 miles, sometimes a bit more, depending on duct strength and path geometry.

Why the other choices are incorrect
- A: 10 miles to 50 miles  
  That’s within or only slightly beyond normal line-of-sight for microwave links. It does not reflect the extended ranges caused by ducting.
- C: 1,200 miles  
  This is possible only in rare, strong maritime “superduct” events. It’s not typical.
- D: 2,500 miles  
  Extremely rare for tropospheric ducts; distances like this are more associated with ionospheric propagation, not typical tropospheric ducting.

Useful formulas and rules of thumb
- Normal (non-ducted) radio horizon distance:
  - In kilometers (heights in meters):  
    $$d_{km} \approx 3.57\left(\sqrt{h_t} + \sqrt{h_r}\right)$$
  - In miles (heights in feet):  
    $$d_{mi} \approx 1.23\left(\sqrt{h_t} + \sqrt{h_r}\right)$$
  These typically yield tens of miles for common tower heights, showing why 10–50 miles is normal LOS, not ducting.
- Ducting occurs with strong temperature inversions and a steep negative refractivity gradient, which bends rays and extends ranges to a few hundred miles typically (100–300 miles), with occasional longer paths in exceptional conditions.