How can I estimate the path loss
The answer seems to be to pick one from a catalog of available path-loss models and apply the formula.
Here, I'd try using the Hata model for urban areas. The model was originally made for portable cellular systems, so it uses a bit different terminology.
The formula is not so complicated:
$$L_{50}
=69.55
+26.16 \cdot \log_{10}f
-13.82 \cdot \log_{10}h_b
-C_h
+(44.9-6.55 \cdot \log_{10}h_b) \log_{10}d$$
and for 2 m band the correction factor is
$$ C_h = 8.29(\log_{10}(1.54 \:h_m))^2 - 1.1 $$
and
- $f$ is the frequency in MHz
- $h_{b}$ is the height of the base station antenna in meters
- $h_{m}$ is the height of the mobile station antenna in meters
- $d$ is the distance between the base antenna and mobile receiver
antenna in kilometers
what do the numbers mean when I find them?
Basic formula for power at the receiver is:
$$ P_{rx} = P_{tx} - P_L $$
Where:
- $P_{rx}$ is the power received, and
- $P_{tx}$ is the transmit power, and
- $P_{L}$ is all losses (path loss, feedline loss, etc).
The Hata model I've shown here will provide path-loss estimate for 50% of locations on the diameter of the circle with center in the "base station" and radius $d$. I personally, as a rough guide, would just use that number as $P_L$.
Now let's try to calculate the number. I'll take the frequency to be 145.5 MHz, which is a bit below the optimal range for the use of this model. The given height is 3 stories plus roof, so I'll round that to 10 meters.
First, the correction factor:
$$ \begin{align}
C_h &= 8.29\left(\log_{10} \left(1.54 \cdot \frac{10 \ \mathrm{m}}{1 \ \mathrm{m}}\right)\right)^2 - 1.1 \\
&= 10.6 \ \mathrm{dB}
\end{align} $$
Next, the main formula:
$$ L_{50}
=69.55
+26.16 \cdot \log_{10}\left(\frac{145.5 \ \mathrm{MHz}}{1 \ \mathrm{MHz}}\right)
-13.82 \cdot \log_{10}\left(\frac{10 \ \mathrm{m}}{1 \ \mathrm{m}}\right)
-10.6
+\left(44.9-6.55 \cdot \log_{10}\left(\frac{10 \ \mathrm{m}}{1 \ \mathrm{m}}\right)\right) \log_{10}\left(\frac{7 \ \mathrm{km}}{1 \ \mathrm{km}}\right) $$
$$L_{50}=69.55+56.58-13.82-10.6+38.35 \cdot 0.85 $$
$$L_{50}=134.3 \ \mathrm{dB}$$
So what does this number give us and how is it helpful?
The antennas are given as 7 dB Yagi, so I'll take that to be 7 dBi and I'll assume that you have 10 m of say RG-8 coaxial cable (a calculator gives me 0.5 dB loss for that) and that you're transmitting at 35 W.
The transmitter EIRP would be then:
$$P_{tx}
=10 \cdot \log_{10}\left(\frac{35\mathrm W}{1\mathrm W}\right)
+7-0.5
=21.94\:\mathrm{dBW}
=51.94\:\mathrm{dBm}$$
Our estimate of path loss is 134.3 dB and we have a same Yagi at the receiver plus same coax losses. This gives us received power of:
$$P_{rx}=51.94-134.3+7-0.5=-75.86 \ \mathrm{dBm}$$
which should be above S9 at the receiver, if my calculations are correct and the S-meter is properly calibrated.
I hope that my description of the process will let you do your own more exact calculations and help you a bit.