tl/dr versionrough approximation of elm-2032 fire control radar in fa-50 gives an air-to-air range performance of ~80 km (with the high-power transmitter configuration) using a 16" antenna size...
an old (2013-ish) KAI video (from the old forum) indicated a slightly less than ~100 km range which would mean an antenna slightly under 20" in size...
full versionwatching the vids of the new fa50 pair as well as the older vids of the initial pair in the Balikatan exercise, it struck me that all these hidef vids of the fa50 carrying external fuel tanks would allow one to approximate the diameter of the fa50 radome, from which one can then gauge the antenna size of it's elm-2032 fcr and with a little math approximate it's range performance as compared to public domain data and the manufacturer's catalog info...
as it happens, in a post in the "A2A refueling options for the FA-50" thread (
http://defenseph.net/drp/index.php?topic=820.msg2078#msg2078), @horge mentioned that the 150-gallon external fuel tank (Aero-1C) which the fa50 uses is around ~21.7" or so in diameter...
using that info and looking at stills from the fa50 hidef vids, the radome would appear to be around ~18.6" in diameter... now for argument's sake let's just say the antenna of the elm-2032 is only slightly smaller than that at around 16" in diameter...
from the IAI Elta catalog (
http://www.iai.co.il/sip_storage/files/0/38030.pdf) we know that the performance of the largest antenna size and highest transmitter power rating is given as ~148 km range in air-to-air mode (ie. from the catalog: 80 nm air-to-air, 80 nm air-to-ground, 160 nm air-to-sea)...
now in Friedman's "World Naval Weapon Systems", the elm-2032 is listed as having a 75 cm diameter antenna size as the maximum... now because both Friedman and the Elta catalog list the maximum weight as 100 kg (where weight depends on antenna configuration), it's possible that the 75 cm maximum diamter also applies to the catalog specs, so we make the assumption that the 75 cm antenna size applies to the ~148 km range performance...
so what we now have is: maximum antenna size of ~29.5" (ie. 75 cm) gives ~148 km range performance (at the same target rcs as used in the catalog)... and we also approximated the fa50 antenna size to be ~16"...
now from radar engineering we know that a slotted planar array antenna (like that used by the elm2032) has a range performance which is proportional to the fourth-root of the product of the antenna area and antenna gain (holding all other factors constant; see ref: "Radar Systems", Skolnik)... and we also know that the antenna gain is directly proportional to it's area... hence range is proportional to the fourth-root of the antenna area squared (again holding all other factors constant)...
given the maximum antenna diamter of 29.5", we thus get a maximum antenna area of ~684.8 sqin... and given an fa50 antenna diameter of ~16", we thus get an fa50 antenna area of ~201.1 sqin... thus the ratio of antenna areas (ie. fa50 to maximum) is ~0.294, which when squared gives ~0.086... and finally, taking the fourth-root of this squared ratio gives ~0.542
when we apply this ~0.542 scaling factor to the maximum range performance of ~148 km (since this range value is what is applicable to the maximum antenna size of ~29.5"), we get ~80.2 km as our approximation for the ~16" antenna size in the fa50...
so given ~148 km as the maximum air-to-air range for a full-size elm2032 antenna, we approximate the fa50 version as having a ~80 km air-to-air range performance (again this is with respect to the same target rcs used in the catalog)...
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(note 1)there is actually one further scaling factor we could apply (as was mentioned briefly early on), and this is the transmitter power... this is because range is also proportional to the fourth-root of the transmit power...
now the catalog only states the power draw as ranging from 2-3 KVa (depending on transmitter configuration)... this is not the same as the transmit power however but we can make the assumption that just as the power draw ranges from 0.67 to 1.0 (ie. normalized to the 3 KVa maximum value), we can suppose that the transmit power would also have a proportional range from 0.67 to 1.0 as well...
this means that if the fa50 fcr has a ~80.2 km range performance with the high-power transmitter configuration, then with the low-power transmitter configuration we would expect a range performance of ~72.5 km...
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(note 2)as to the question of what was the target rcs used in the Elta catalog, unfortunately it was not stated explicitly hence one could assume the ~148 km max range is the outright maximum performace of the fcr for that mode (ie. instrumented range in air-to-air mode), or one could assume it was based on a large rcs baseline target and scale ranges accordingly for other rcs targets (ie. knowing that range is directly proportional to the fourth-root of target rcs)...
one interesting thing to note is that Friedman gives the look-up air-to-air range as ~102 km (55 nm), which differs from the catalog maximum by a factor of ~0.687, this implies a fourth-power scaling of ~0.22 or roughly one-fifth... one could assume this means Friedman could have been using a target rcs of 1 sqm and the catalog used a target rcs of 5 sqm, or any other such combination preserving the roughly one-fifth relationship...
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(note 3)in an old (2013-ish) KAI video which I saw in the old forum, a reference was made to a slightly under 100 km range which would mean an antenna sized at slightly under 20" in diameter...
perhaps one day someone could actually measure the radome (or even antenna) of PAF's fa-50 to check how large (or small) it is...
