ORIGINAL: el cid again
The formula for the theoretical visual horizon is: 1.23 X SQRT(altitude in feet). So a plane flying at 500 feet has a visual horizon of 27.5 nm. But that is the theoretical range. The actual practical range is probably half that.
This is incorrect - in the sense the formula cannot be right - it is a useful rule of thumb for close in ranges. The USN does not teach this in this way - they make you memorize points in the function - and how to know where these points are.
News flash: The Earth is almost a sphere (very little distortion). So a linear function of altitude will not yield range. In fact, as you gain altitude, you gain range much faster than at a linear rate.
As a radar and countermeasures guy I got to do this sort of thing a good deal - because radar signals are almost like light (they actually bend slightly in some cases - but we pretend they are like light even then).
Further, I would always track everything in my neighborhood, by every means possible. I would have radar plot a track and then see if I (or an operator) could track entirely WITHOUT radar - single station passive detection INCLUDING ranging. To do that I had to use a German formula (published in a US technical intelligence document) which permits you to calculate range for altitude of the emitter (= observer if visual). I got to the point I could track an aircraft WITHOUT using radar and be within 10% of its real range - doing the calculations in my head in an era before calculators or computers like we have now. So trust me on this: the function is wrong. The earth really is curved, and range is not a linear function of observer altitude.
NEWS FLASH! Reread my post. We're talking visual horizon here. You know! That point where an object can no longer be seen due to the curvature of the earth! What the formula defines is a visual or radar SURFACE footprint from a given point of altitude. I said that the formula applied to determing the theoretical visual horizon, not omnidirectional range. And yes, the USN does teach this. Its where I learned it. It also applies to the radar horizon with a slight midification. I still have many of my training materials (the unclassified ones) from my A school. The Line of sight and radar horizons are virtually the same, the difference being you use 1.23 for LOS and 1.5 for radar. A fairly insignificant diifference.
A one hundred foot altitude yields a theoretical visual horizon of 12.3 nm. A 1000 foot altitude yields a theoretical visual horizon of 38.9nm. In case you don't understand what a theoretical visual horizon is, it is the maximum theoretical distance that an observer can see an object floating on the surface of the sea. If that object has height, for example it has a 100 foot mast, then add the two visual horizons together. If both are at 100 foot altitude, the maximum theoretical visual detection range is 24.6nm. This formula obviously does not take into account the size of the object to be detected. Its going to be much easier to detect a battleship than a periscope at those ranges.
So trust me on this: the function is correct. Range to the horizon is most certainly a linear function of observer altitude and is only limited by the curvature of the earth.
"single station passive detection INCLUDING ranging"
I assume you are using ESM as you used the term emitter. Exactly how are you computing the altitude and range if angle above the horizon and emitter power levels aren't known? Even if they were known, a good airborne radar operator can spoof the techique by varying output power or varying antenna tilt. Seems to me it mustn't have been very effective as the Navy doesn't teach this "ESP technique" to its AW operators.
Read my credentials at the bottom. I was an Aviation Warfare Electronics Operator for 26 years and am intimately familiar with airborne passive and active acoustic systems, radar (traditional and ISAR), ESM, MAD, IFF and IRDS. BTW, we're also taught to compute doppler, AOB and TMA values in our heads. I've also spent many a flight hour with my head pressed against the bubble observer windows in the P-3 searching for air and surface contacts in all kinds of weather conditions throughout the world.
So trust me once again here, I'm on very solid ground with this one.
Chez





