Taking a receiving station at TM194450 which has a reasonable line of sight to Sudbury
from Wolfbane BBC2 analogue from Sudbury has the following characteristics
TX e.r.p 250kW on channel 44 18 miles away (corroborated by http://www.bbc.co.uk/reception/tv_transmitters/tv_sudbury.shtml )
Convert these to standard units
TX power
p= 250000 W
Distance
multiply by 1.60943 to get km, multiply by 1000 to get metres
d=18*1.60943*1000
thus
d=28970 m
from Ref(1) formula(1)
where e is in V/m
thus
e = (sqrt(30*250000))/28970
e=0.095 V/m
Convert to dBuV/m (=20log10(e/1uV))
e=20log10(0.095/1e-6)
e=100 dbuV/m
Conversion of this into a signal strength
From Ref 2 the open-circuit voltage across the terminals of a half-wave dipole aligned for maximum signal in a field strength of e V/m
e * lambda
V = -------------
pi
where lambda is the wavelength and pi = 3.14159... The terminated voltage at the receiver is ½ this, as half is lost between the source impedance and the matched termination.
wavelength is related to frequency where
speed of light (3x108m/s) = frequency * wavelength
Deriving the frequency from the channel number. We know the channels are 8MHz wide, and channel 21 corresponds to about 470MHz. Channel 44 is therefore (44-21)*8 up on this
f = 8*(channel-21)+470 MHz
= 8*(44-21)+470 = 654MHz
lambda = 3*108/654*106 = 0.46 m
received signal voltage for a dipole
V = 0.5 * 0.095 * 0.46 / 3.14159 = 0.0069 V
Convert this to dBuV
V = 20log10(0.0069/10-6)
V = 77dBuV
This is now increased by the antenna gain. I am using a standard cheap and nasty Maxview 14 element aerial cited by Maplin at 7.3dB gain
so I expect a signal level of 77 + 7.3 = 84dBuV
Final received signal level = 84 dBuV
(the form above also allows for masthead amps and CT100 downlead, not accounted for here)
I measure 71-74dBuV for BBC2, a difference of 10-13dB. This seems reasonable to me, given the non-perfect roof mounted antenna
I don't know is the honest answer to that. The calculation up to field strength has been checked twice and independently calculated to arrive at the same result. CCIR rec 417-3 (now ITU BT417-5 but I'm not going to pay them to look at the update) quotes a minimum field strength of 65dBuV/m in band IV and 70dBuV/m in band V, in which case the test receiver would technically be outside the service area of Sudbury if the field strength were 62dBuV/m. All I can say is that the value I arrive at agrees reasonably with experiment in the test case.
Ref 1 ITU-R PN525-2 available here
Ref 2 RSGB Radio Communication Handbook p11.3