Calculating AM directional ERP based on field strength?

[pianoplayer88key]

Hi all...

Does anyone know how to calculate effective radiated power (or whatever the correct term is) for directional AM stations?

For example, using 1170 KCBQ as an example, I know the actual power is 50kW, the RMS field (assuming 50kW non-directional using their antenna system) is 2499.5mV/m, and the actual field at 187.3° is 3750mV/m (mentally approximating/interpolating between the 185° 3559.01mV/m and 190° 3935.08mV/m).  How would I calculate the power to produce that field?

I tried searching on google, but most of the results I found mention things about isotropic radiators, gain in dB, and that's not what I'm trying to calculate here.

[R. Fry]

Field intensity varies as the square root of radiated power.  If the field at 1 km increases by a factor of 3750 / 2499.5 = 1.5, then radiated power has increased by 1.5² = 2.25 times, which value is 50 kW x 2.25 = 112.5 kW.

[pianoplayer88key]

Thanks.

Now is there a formula to calculate approximate field strength at a given distance, assuming constant known ground conductivity?  Just eyeballing the charts doesn't quite cut it for me (and in some cases the numbers won't even be on the chart).
For example, taking that field of 3,750 mV/m at 1 km, how would I calculate the field at 15.05 km (my distance from KCBQ) assuming a conductivity of 8 (what the M3 map says for the path)?  I want to guess it would be somewhere north of 200 mV/m, probably not exceeding 500 mV/m, but I'm not sure.  (The indicated signal strength on my PL-606 is about 81 dBuV using its built-in 100mm ferrite loopstick, but you know how inaccurate that is, as you have a PL-310 that I've read in reviews is similar on AM.)

(I don't know if I've asked this before.  I'd use search, but I have had problems searching for posts from specific people for some reason.)

[R. Fry]

There is no simple, accurate way of calculating such values, unfortunately.

Using the FCC groundwave propagation charts for that frequency and ground conductivity, that radiated power will produce a field intensity of about 124 mV/m at a distance of 15 km.

[pianoplayer88key]

Interesting... only 124 mV/m?
Based on how some of my radios behave with that signal (blocking/desense - the PL-606 and PL-380 show 45 dBuV with no signal audible on 1150 and 1190, or splatter - it's heard just as loud 30 kHz off channel on at least one or two radios I have), I would have expected it to be quite a bit stronger.    Basically it seems to overload my radios' front ends, which I had hoped should only happen with a much stronger signal, either starting with the blanketing contour or the maximum permissible exposure contour.  (But, then, chances are my definition of front-end overload may be inaccurate - I consider it to be any trace of impairment of reception of weak signals (that would be detectable if the local pest wasn't on the air) as close as the first-adjacent (including IBOC hash - if you can detect it, it's FE overloading), in a nutshell.)
As an example, reception of 1180 KERN is extremely difficult here (impossible using just the radio's built-in antenna except when KCBQ is off the air, suspected carrier barely detectable using the Select-A-Tenna).  I'm 237 miles, 144° from KERN (ERP 64.56kW toward me), but asking you to help calculate the received field strength would be beyond the scope of this post due to the distance and varying ground conductivity.  Estimating from the radio-locator coverage map, though, I'm probably about 1.85-2x past their estimated 150µV/m contour.
So the formula from which the FCC groundwave propagation charts were calculated is not known?

[R. Fry]

#1:  I want to guess it would be somewhere north of 200 mV/m, probably not exceeding 500 mV/m, but I'm not sure.   #2  Interesting... only 124 mV/m?

Probably your estimate in quote #1 above was based on a perfect ground plane.  But the groundwave propagation loss over a path having a ground conductivity of 8 mS/m is greater than that for a perfect ground plane.

[pianoplayer88key]

#1:  I want to guess it would be somewhere north of 200 mV/m, probably not exceeding 500 mV/m, but I'm not sure.   #2  Interesting... only 124 mV/m?

Probably your estimate in quote #1 above was based on a perfect ground plane.  But the groundwave propagation loss over a path having a ground conductivity of 8 mS/m is greater than that for a perfect ground plane.

Actually it was more like a guess pulled out of thin air.  BTW V-Soft Zip Signal says for 92020 (I'm at the extreme southern tip) 1170 KCBQ is estimated at 235.64mV/m daytime, but it's probably sampling from a site a couple miles closer.

Until several years ago, KCBQ used to operate from a different site about 6 miles north of me with a slightly different 50kW pattern, and at that time had a powerful lobe aimed right at me (maybe 200-300kW but I'm not sure).  Is there any way to find historical station/pattern data so I could calculate what the signal would have been like then?  (Also being able to check historical V-soft or radio-locator sites, if possible, would be interesting, but I haven't had much success with that on the Internet Archive website.)

[R. Fry]

BTW V-Soft Zip Signal says for 92020 (I'm at the extreme southern tip) 1170 KCBQ is estimated at 235.64mV/m daytime, but it's probably sampling from a site a couple miles closer.

Using the 3750 mV/m field at 1 km (from your earlier post), that field at 15 km over a perfect ground plane would be 3750 / 15 = 250 mV/m.

But the FCC groundwave propagation chart for 1170 kHz shows that the field at 15 km for a conductivity of 8 mS/m is about 49.4% of the inverse distance field.  Doing the math:  250 x 0.494 =  123.5 mV/m.

The V-Soft number probably is based on a location in that ZIP code that is closer to the tx site, and more in the main lobe of the radiation pattern.

Until several years ago, KCBQ used to operate from a different site about 6 miles north of me with a slightly different 50kW pattern, and at that time had a powerful lobe aimed right at me (maybe 200-300kW but I'm not sure).  Is there any way to find historical station/pattern data so I could calculate what the signal would have been like then?  (Also being able to check historical V-soft or radio-locator sites, if possible, would be interesting, but I haven't had much success with that on the Internet Archive website.)

The data for their 50 kW daytime pattern of Sept 2005 from a site at 32 50.367 N 116 59.517 W shows a tri-lobe radiation pattern with maximum ERP at 154 degrees.  Another lobe was centered on 226 degrees towards San Diego, and there was a fairly deep null between them.

If you can post the distance and bearing from the old KCBQ site to your location then an estimate of their field could be made there.

[pianoplayer88key]

The V-Soft number probably is based on a location in that ZIP code that is closer to the tx site, and more in the main lobe of the radiation pattern.

Probably so.  Searching 92020 on Google Maps points to a location maybe 1.5-2 mi NNW of me.  KCBQ is 9.3mi N of me, and their main lobe is focused approximately southwest.

The data for their 50 kW daytime pattern of Sept 2005 from a site at 32 50.367 N 116 59.517 W shows a tri-lobe radiation pattern with maximum ERP at 154 degrees.  Another lobe was centered on 226 degrees towards San Diego, and there was a fairly deep null between them.

If you can post the distance and bearing from the old KCBQ site to your location then an estimate of their field could be made there.

Wow, no wonder it had such a huge blowtorch signal here back in the day!!  Distance and bearing from them to me was 9.818km (6.1mi), 153.62°.  So what would the day (and night - their drop was quite noticeable) field have been?

I suspect that even if I had a radio with good selectivity, midday reception of 1180 KERN (381.42km, 144.33° toward me) would have been impossible then... although if you know of an inexpensive portable (GE SuperRadio approx max size/price, maybe Sangean PR-D5(?) ok, prefer ultralight more like Sony SRF-59 but with digital tuner) that could do it without any splatter/blocking/desense from 1170 I wouldn't mind knowing which one(s).

Your mention of a tri-lobe pattern reminded me...  I remember I used to be able to hear them fairly well in the mountains north of San Bernardino near Crestline in the daytime when I'd go camping there, as well as at friends' houses near Riverside, Bloomington, etc.  Now it's a no-show, or at least very weak in Moreno Valley if there's any trace at all.
Is there any chance of some radio-locator style estimated coverage map existing for that previous pattern?

Oh...  and is there any chance you may be using the 4nec2 software to calculate those fields, or do the part 15 research you've posted in other threads?  I have downloaded it in the last few months, and was recently trying to figure out a few things (one being the behavior (field at specified distance, for example) of an electrically very short antenna with a short (or no) ground plane), but so far don't know much about how to use it yet.

[pianoplayer88key]

I ran out of edit time, but if possible I'm curious...  what possible signal levels do you think your PL-310 might have displayed with those former fields from KCBQ?  (My PL-606, which I've heard is comparable to the 310, displays a level of about 81/25 +/- a dBu on KCBQ's current day pattern.)