Daytime vs Nightime Range

I reached out and asked chatGPT:

Part15 of FCC rules in U.S. allow for 100mW of power into a 3-meter antenna which provides a fully quiet daytime range of about 1.5 miles on the AM band. At night, however, skywaves from many full-power stations sharply reduce the range by interfering with the signal. How much added power would be needed to increase the fully quieting range with a 3-meter antenna at night?

The AI machine returned with this answer:

To estimate how much added power is needed to increase the fully quieting range at night, we need to understand how radio signal propagation works and the relationship between transmitter power and range.

Key Concepts:

1. Daytime Range: The range of the signal during the day is limited by groundwave propagation, which is primarily affected by power and antenna height.
2. Nighttime Range: At night, skywave propagation becomes more important due to ionospheric reflection, but it is also affected by interference from other stations (especially full-power stations) causing a reduction in the usable range.

The power-law relationship for radio signal propagation can be expressed as:

R∝P12R \propto P^{\frac{1}{2}}R∝P21​

Where:

• $R$ is the range.
• $P$ is the transmitted power.

This relationship means that doubling the power increases the range by a factor of about 2≈1.41\sqrt{2} \approx 1.412

Step-by-Step Calculation:

1. Daytime Range: At 100 mW of power with a 3-meter antenna, the fully quieting daytime range is about 1.5 miles.

2. Interference at Night: During the night, skywave propagation causes interference from other stations, reducing the quieting range.

   To estimate the amount of extra power needed to increase the range, we would assume that the interference limits the range and that more power would be required to overcome this.

   If we want to increase the range at night (under the condition of interference), we would need to overcome this interference by boosting the signal strength. However, the exact amount of additional power needed depends on how much the interference reduces the range at night, which can be complex and vary based on many factors (like local topography, atmospheric conditions, and the number of interfering stations).

   Assuming a simple case where a doubling of power results in a noticeable increase in range, we could estimate that increasing the transmitter power by a factor of 4 (quadrupling the power) would provide a range increase of about 2 times (doubling the range), which would likely be noticeable in improving the signal clarity despite the interference.

   Thus, quadrupling the power (from 100 mW to 400 mW) would likely increase the quieting range at night by a significant amount, potentially making it closer to 3 miles, depending on the level of interference.