Talk:Two-ray ground-reflection model

Variable undefined.

"Ground Reflection $\Gamma (\theta )={\frac {sin\theta -X}{sin\theta +X}}$

where $X_{v}=$${\sqrt {\varepsilon _{g}-{cos}^{2}\theta }} \over {\varepsilon _{g}}$

$X_{h}={\sqrt {\varepsilon _{g}-{cos}^{2}\theta }}$"

$X$ (with no subscript) is never defined. I'm guessing one of the values given is for the horizontally polarised case and the other for the vertically polarised case but nowhere is this spelt out. Furthermore $\varepsilon _{g}$ is never defined. Plugwash (talk) 13:39, 9 April 2014 (UTC)

$X_{v}$ is the vertically polarised component of the reflection and $X_{h}$ is the horizontally polarised component. $\varepsilon _{g}$ is the relative permittivity of the ground. This was all in the original text I'm afraid. My edits just made the derivation work; I haven't gone back and corrected or improved some of the basic equations, or specified the missing variables. Any help on this is much appreciated! Derekjc (talk) 10:14, 27 July 2016 (UTC)

Also $G_{g}r$ and $G_{l}os$ don't seem to be defined anywhere. Plugwash (talk) 13:57, 9 April 2014 (UTC)

$G_{*}$ is the antenna gain. As far as I understand Rappaport it's not so much a matter of $G_{los}$ $G_{gr}$, but rather $G_{t}$ (transmitter) $G_{r}$(receiver). @Plugwash: Should we just fix this? Currently it's rather wrong. CMorty (talk) 10:57, 24 March 2015 (UTC)

$G_{los}$ is the gain of the antennas (combined transmitter and receiver gains) in the direction of the line-of-sight (LOS) path and $G_{gr}$ is the combined antenna gains in the direction of the ground reflection (GR) path. Eventually we assume for the long distances (relative to antenna mast heights above the ground) the gains are approximately equal, therefore, $G_{los}\approx G_{gr}\approx G$. Derekjc (talk) 09:58, 27 July 2016 (UTC)

mathematical derivation

Mathematical derivation does not appear exactly in Rappaport's or Jake's reference even though it is referred. Could someone please give the correct reference for mathematical derivation? — Preceding unsigned comment added by 125.168.4.243 (talk) 04:15, 14 June 2018 (UTC)

Ground properties

It might be a great idea to also write about how the material the surface at the reflection point is made of will affect the formula. 2003:CA:9F0C:70F4:C0BB:6DEA:A5D6:EA63 (talk) 20:49, 19 November 2021 (UTC)

Path Loss equation is confusing

By convention, the term "path loss" (PL) means propagation loss between antennas, thus antenna gains should not be included. In that sense, the given PL equation with the factor G is misleading:

PL = 40 * log10(d) - 10 * log10(G * (ht)^2 * (hr)^2) [with antennas]

We can open up the last term as

10 * log10(G * (ht)^2 * (hr)^2) <=> 10 * log10(G) + 10 * log10((ht)^2 * (hr)^2)

Here, the term "10 * log10(G)" denotes the antenna gains in dB. This should be dropped away to produce path loss equation as it is conventionally understood:

PL = 40 * log10(d) - 10 * log10((ht)^2 * (hr)^2) [without antennas]

Jarmniku (talk) 11:49, 10 January 2025 (UTC)

Norton Ground Wave

I think it would be helpful to mention in this article that the two-ray propagation model loses accuracy as the transmitter and receiver heights approach zero. The two-ray propagation model predicts that the received power approaches zero in this limit. This is, of course, not correct (not what actually happens as the transmitter and receiver approach the surface). When the transmitter and receiver are both infinitesimally just above the surface of the earth, there is no longer a geometrical optics field (which is what the two-ray model is based on), but there is instead a lateral wave, which could also be called the "Norton ground wave" (https://en.wikipedia.org/wiki/Ground_wave). The lateral wave power decays as 1/d^4, but it is not described by the simple formula predicted by the two-ray propagation model (which goes to zero because of the term h_t*h_r). The lateral wave comes from the exact solution to the Sommerfeld problem of a dipole source over the earth, and it cannot be recovered from the two-ray propagation model. Elee1l5 (talk) 03:01, 24 May 2026 (UTC)

Criticial distance

There seems to have extra $\pi$, expected formula $d>d_{c}=4h_{r}h_{t}/\lambda$ ~2026-39267-49 (talk) 06:53, 11 July 2026 (UTC)