As W. would say, "It's complicated."
I don't know if there are any recent threads on this already but I have a question. What is the power measured in and how far will the signals go depending on the power? For example: (below)
>>Pwr<<
250.000
^ ^ ^ ^
Power is usually measured in Watts, but power density can also be measured in dBW, dBm and uV/m. Power can also be measured in kilocalories. Laboratory grade watt meters, calorimeters, measure power in kCals.
You asked a very simple question that defies a simple answer. The short answer is: based on what you provided, it's impossible to tell. I'll do my best to try and explain why without writing a dissertation. Its gonna be long, anyway, but I hope it answers your question.
You need to know effective radiated power. This takes the output power and factors in the sum of losses and gains. Losses can be from coaxial jumpers, isolators/circulators, cavities, filters, duplexers, transmitter multicouplers, etc. Gains can be factored in from antennas (noting directional characteristics, polarization, azimuth, and horizontal beamwidth) and tower-mounted preamps. 250 W out can equal 8 W ERP or 2,000 W ERP based on the stuff in the middle.
Different wavelengths have different characteristics. You'd need to know frequency.
Frequency coordinators and radio engineers use propagation models and modeling utilities to predict how far a signal will go, and how reliable a signal will be. You can take a site and draw a circle around it (a "beer can plot"... kinda like what some RR map images show, and APRS PHG circles), but don't count on radial plots. They are absolutely inaccurate. We primarily use two different models: Carey curves (R-6602) to very quickly establish a service contour and interference contour, and Longley-Rice for more substantial coverage analysis.
Very simply, Carey uses effective radiated power (with any directionality factored in), height above average terrain, and reliability factors to calculate a contour. A frequency coordinator would use this as the first test of whether to select a frequency or not. This isn't very accurate, but it makes for a good GO/NO GO test.
Longley-Rice is based on irregular terrain and requires digitized terrain. Additionally, surface refractivity , soil permittivity, Koppen climate index, and time/location/situation variabilities must be plugged in. Most of the time default values suffice. Then, the program calculates a value for a given point based on the radial, terrain, and these other factors, then assigns a color, and plots it on the map based on limit filters. It's pretty involved, but it's computerized. The faster the computer, the quicker the info is crunched.
There are other models, like Okamura, that might be better predictive in urban areas, Hata, Davidson, and combinations. There are also proprietary voodoo plots (no one but the coder knows what fudge factors go in, but pretty pictures come out).
The vast majority of license applications and issued licenses are sloppy. The preparers don't want to spend a lot of time on them because they get paid by volume, and they are usually not the ones building the radio system or operating it. In reality, it's extremely rare to see accurate ERP values calculated and specified on the license, unless it's a knowledgeable applicant filling the form out, or someone has been challenged to protect an incumbent station, or maybe protect against a Canadian objection. For example, 40 W out almost never equals 40 W ERP. Cable loss factored in, the power arriving at the antenna would be less. Antennas achieve gain essentially by focusing energy away from a donut shape around the antenna to more like a pancake, usually directing power out toward the horizon (most cases, that's NOT where that power is needed, but...). Tower mounting can also factor gains and losses, depending on how the energy is blocked or reflected in a given direction. Gain is also achieved by reflecting the signal and focusing it, like a flashlight beam. In land mobile radio, we use dBd (decibels referenced to a dipole). In microwave and ham radio marketing, dBi is used (decibels referenced to a theoretical isotropic antenna). It's an apple against an orange, but the correction factor is 2.14 dB - the dBi value is 2.14 dB higher than the dBd value (don't you want to buy the higher gain antenna?). Still the laws of physics don't bend for marketing. And, many applications don't even have HAAT or ERP values calculated (HAATs are important and they absolutely factor in, but they're not a part of ERP - sorry Warren).
You didn't need them years ago, but you do need them now. We see a lot of those values added in when the applicants go to file to add narrowband emissions.
So, that's what goes into this sausage, and why it's not so easy to produce coverage plots. That 250 W can be eaten up in the combiner and cable to the point where there's only 3 watts getting to the antenna, and the 10 dBd antenna produces a 30 W ERP signal, possibly, or the 250 W station could be going into a unity gain antenna on top of a garage 12 feet off the ground, not to mention being in a valley with mountain ranges around it.
And, those are under normal conditions. Anomalous propagation, such as diffraction, scatter, tropospheric ducting, aurora, etc. can extend the signal much further, hundreds, if not thousands of miles.
