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[N6YWU]

Assuming propagation conditions allow, is there a rule-of-thumb for approximately how much more power it takes for an HF signal to travel two hops off of the ionosphere, versus one hop? (to provide approximately the same path loss and S/N to receive stations.)

I often see semi-circular arc patterns of one hop receptions from my 100 mW to 1 Watt FT8 and WSPR transmission on PSKreporter and wsprnet maps (different on different bands, different on 80M thru 10M, and varying with time-of-day, SFI, & etc.).  I'm wondering how much more Tx power (and/or antenna gain) I would need to see a second more distant arc of spots on the map.

[K1VSK]

Depends on conditions more than power or ERP. Also depends on mode, e.g., CW beats SSB anytime, noise floor at the receiving end and obviously frequency.

One of the (few) things I like about FT modes is the ability to quantify receive signal strength while varying transmit power but conditions change too rapidly to make any valid conclusion.

[N0GV]

The answer to this question is that the path determines the amount of reflection from the ionosphere and the ground.

Clearly a path to Alaska from Florida is a 3 - 4 hop path and all of the hops are ionosphere to soil. A similar distance is from Florida to Northern Europe but all of the hops are ionosphere to seawater. Clearly the expectation is that the European path will have a larger S/N ratio and this is bourne out quite clearly in the data and in experience.

Bottom line: no, there is no "simple" equation that will accomplish this.

Grover

[K6BRN]

One of the (few) things I like about FT modes is the ability to quantify receive signal strength while varying transmit power but conditions change too rapidly to make any valid conclusion.

Note that the receive report sent to you by the other station on FT8 is a signal to noise ratio metric, not signal strength.  It is very possible (and happens to me regularly) that a strong signal may have a poor S/N on my end due to crowded band conditions and even stronger signals nearby.  Similarly, when I follow the MUF down the bands during the day, a DX station very often will have a barely discernable trace on the waterfall, but an excellent S/N due to lack of interference.  The FT8 waterfall seems to approximately follow signal strength - but this metric is not numeric.

Brian - K6BRN

[K1VSK]

One of the (few) things I like about FT modes is the ability to quantify receive signal strength while varying transmit power but conditions change too rapidly to make any valid conclusion.

Note that the receive report sent to you by the other station on FT8 is a signal to noise ratio metric, not signal strength.  It is very possible (and happens to me regularly) that a strong signal may have a poor S/N on my end due to crowded band conditions and even stronger signals nearby.  Similarly, when I follow the MUF down the bands during the day, a DX station very often will have a barely discernable trace on the waterfall, but an excellent S/N due to lack of interference.  The FT8 waterfall seems to approximately follow signal strength - but this metric is not numeric.

Brian - K6BRN

Correct. The correlation isn’t linear. I was referring only to one receive point with presumably a constant noise floor over a short period within which various power level changes can be quantified.

[W1VT]

The lowest loss path is all water crossing the equator like Hawaii to the South Pacific.

The highest loss is traversing the North and South poles.

I can usually find a five minute band opening if the country has a lot of hams within a few months of looking at the optimum times on the easier bands like 40 through 17 meters.

I needed Indonesia on 30M and worked YB5QZ this past weekend.  As a bonus I worked 9V1XX five minutes earlier!  200W to wires in the trees.
Entities 266  and 267 on 30M.

[K4GTE]

Anywhere between 5-1500 watts, depending on propagation/conditions/equipment. There is no formula.

[W1VT]

https://www.voacap.com/itshfbc-help/method30.html#:~:text=APPROACH%3A%20Versions%20of%20VOACAP%20developed,short%20path%20model)%20are%20run.
How VOACAP does it calculations

[WA3SKN]

I think "Spinal Tap" said it best... "They were the loudest band because everyone else had a 1-10 level on their guitars while the had a 1-11 level on their knobs".
Do you really think that any of the "bar graph level" software meters are close to accurate? Or 50 microvolts  equals S9?
Propagation levels can vary over 100 dB in milliseconds.  It is "signal to noise ratio" that counts.
Remember the AGC standard of 100 dB variation at the receiver antenna input would cause a maximum variation of 6 dB at the speaker?
Bar graphs are "eye candy" and only meant to make you feel good.
73s.

-Mike.

[WB6BYU]

...I'm wondering how much more Tx power (and/or antenna gain) I would need to see a second more distant arc of spots on the map.

You can run those tests using VOACAP and see - it allows you to
enter the transmitter power.  There are a number of tools included
on the web site that give you a lot of information about the path.

Generally, however, it isn't that simple:  the coverage for a particular
path depends on the ionospheric conditions in the middle of a hop,
and a 2-hop path depends on conditions in two different locations both
being favorable at the same time.  And, of course, there are other
quirky modes that can confuse things, like ionospheric ducting, or
reflections off the top of the E-layer.

From here in Oregon, paths to W8 and vicinity are usually a long
single hop, but the East Coast generally requires 2 hops.  Sometimes
the time window is pretty narrow, but the 2-hop path may be easier
because it doesn't require as low of an angle of radiation. 

I have no problems covering either running 5W CW on Field Day, so I
suspect that such paths are well within the capabilities of the equipment
you are using.  It isn't just a matter of power output.

[N6YWU]

One of the (few) things I like about FT modes is the ability to quantify receive signal strength while varying transmit power but conditions change too rapidly to make any valid conclusion.

Changing conditions aren't a problem, as there are statistical tests that can tease out even the weakest of correlations from any physically real effect (transmit power, etc.) given enough data.

Those statistical tests used to require a supercomputer to crunch all the data, but nowadays, everybody's smart phone is a supercomputer.  And the various reverse beacon networks capture vast amounts of data to crunch.

But you are correct in that you can't draw conclusions from tiny sample sets, so a single S/N report is usually misleading.

[AF5CC]

The lowest loss path is all water crossing the equator like Hawaii to the South Pacific.

The highest loss is traversing the North and South poles.

The highest loss path usually seems to be the one coming out of my QTH!

73 John AF5CC

[AC7CW]

It seems the OP was asking for the time and he got a history of clocks instead. I used to know the typical path loss per hop but can't recall it and can't find it...

[KA4WJA]

Ron,
Wow!  What a great question!  This is a question that I started studying back in the early-to-mid 1970's!  (yes....a nerdy adolescent)   And, something I continue to study (and teach, from time-to-time)!

Assuming propagation conditions allow, is there a rule-of-thumb for approximately how much more power it takes for an HF signal to travel two hops off of the ionosphere, versus one hop? (to provide approximately the same path loss and S/N to receive stations.)

Fyi, there is a lot to all of this....but, the good news is that for most of my fellow hams, the simple quick-'n-dirty answer (rule-of-thumb) usually suffices! 


Please forgive me a brief preface (and tiny rant) here:

I'm sure someone will question my figures/numbers, and that's fine with me....especially if you have more accurate numbers / more scientific data!   So, if some would like to correct my numbers, please post your numbers, calculations, results, (and sources) and we will all learn more!  This is what life is about, you know...learning, etc. is a wonderful thing....and, the smartest people I know have two fine qualities --- they ask questions --- and they know that they don't know everything! 

However, if someone wishes to post contrary comments / opinion, without any facts / sources....or posts personal insults, etc....please do all of us (yourself included) a favor and just don't....you'll end-up proving ole' Teddy Roosevelt's quote (paraphrasing here: "credit goes to the man that tries....rather than the critic who sits on the sidelines"...)

Sorry about this preface, I realize it might sound a bit like a rant....but, I'm just getting tried of trying to help my fellow hams and being insulted and berated for it (usually from those actually unwilling to offer actual help, btw)


Okay, now that this out-of-the-way....here's the good stuff! 

1)  Of course, as others have mentioned, the short answer is..."it depends"....(but, if you want just a really quick-'n-dirty answer, figure on ~ 10 - 15dB...)

And, be aware that the RF wave's earth reflection losses, ionospheric refraction losses, ionospheric absorption losses, scattering losses, polarization losses, etc. for the most part are "mode independent", meaning all modes (CW, SSB, FSK, PSK, FT-8, etc.) are all effected the same / similarly (same amount of dB)....but.

But, reception of some modes / intelligibility of the information transmitted, can be better with some modes, as they better tolerate some fading/absorption/losses/phase changes/multipaths, etc., so there are additionally some "mode" variables that are more noticeable on multi-hop paths...

Further, there are so many variables across our amateur radio HF bands, communications paths, etc., as well as the variables of the ionosphere (and the earth) itself....due to all of those variables, in my experience (and study) there isn't just one specific answer...

But, if you want an approximate hard number (as oxymoronic as that may be), as I wrote above, the short answer is....in actual real-world HF comms (such as 20m SSB), the differences in overall path loss between a single-hop and double-hop QSO is ~ 10 - 20db....(although could be as little as 6db at some instances, most times it's typically in the 10 - 15db range...)

This means that if you're in QSO with one station that is a single-hop path, and another that is a double-hop path, and you wish to produce the same signal level (not S/N) at the more distant / double-hop path station's receive antenna, as you do at the other's.....then you'd need to increase your transmit ERP by approx. 10 to 15db when transmitting to the double-hop path station.  That is a significant increase in ERP, which could only be accomplished by serious increase in antenna gain (like going from a low, loaded dipole, etc. --- up-to a big yagi on a tall tower), and/or significant increase in transmit power (like going from your 50-100 watts ---- up-to ~ 1500 watts or so)....

When most folks see those numbers, they wonder if they're true how do they actually make long-range multi-hop contacts??  Fact is, they do....and fact is that sometimes the real strong (and real long) multi-hop contacts are in fact "ionospheric-ducting" being refracted/reflected along inside the ionosphere for a large portion of the path, and not being reflected multiple times back-n-forth from earth's surface and ionosphere but many times only once or twice...
(of course, other times we realize just how little signal is needed to actually accomplish the QSO...assuming low receive noise levels....and, now you see the other side of the situation --- the noise ---- and, now you see why just adding to the signal does not always work, 'cuz the other guy just might have too much noise.....if the guy more distant / on the double-hop path has a noise level 15dB lower [VERY possible....that's only the old-standard 2 or 3 S-units lower] than the guy who is closer / single-hop, you may in actual fact get a better S/N report from the more distant / double-hop station!  )

And, finally in a short answer, while sea water reflections almost always produce less loss than earth/dirt reflections, the differences are usually not as pronounced as first though, as the sea water reflection losses are typically only 5 to 6dB better....of course, "calm sea water" reflections are even better, but as an ocean sailor I can tell 'ya that this in unlikely to happen very often!

Please also note that mountainous terrain reflection losses are almost always worse than flat terrain reflections, mostly due to the scattering losses.



2)  A bit of clarification may be needed here...

I often see semi-circular arc patterns of one hop receptions from my 100 mW to 1 Watt FT8 and WSPR transmission on PSKreporter and wsprnet maps (different on different bands, different on 80M thru 10M, and varying with time-of-day, SFI, & etc.).  I'm wondering how much more Tx power (and/or antenna gain) I would need to see a second more distant arc of spots on the map.

Please be aware that while you can work (from your California locale) some single-hop comms in the US, most paths for you to the east coast are double-hop....and, of course just about all your DX paths (except for Canada, Mexico, etc.) are multi-hop paths (no matter how they are presented on the screen of some "reporter")....sure the "maximum" single-hop path is ~ 2000 - 2200 miles, but many paths of ~ 2000 -2200 miles are double-hop....{and, fyi, just as example, from East Coast US / Northeast US to Europe, while this is generally a triple-hop path and sometimes a double-hop path, there are times that both a double-hop path AND a triple-hop path exist at the same time!}


3)  The long answer (well, I'm not going to even try the long answer, 'cuz it would take pages....and, is well explained in various ITU and IEEE, etc. papers....but, I will give you a bit more):

To quote from an ITU paper (from decades ago):

In general, when an upgoing wave is incident on the ionosphere it leads to the excitation of an ordinary (0) and an extraordinary (X) wave. These two waves have different polarizations, etc. and may be regarded as propagating independently within the ionosphere, and are subject to different amounts of absorption. Although ground-reflection losses depend on wave polarization, here [for ease of initial calculation] values are taken for circularly polarized waves. So, polarization-coupling losses, multiple-hop ground losses and absorption losses are examined together.
<snip>
In the case of multiple-hop modes all the considerations given in for single-hop modes apply, but additional allowances should be made for the loss of power at ground reflection and for the effective transfer of power between the 0 and X waves on successive hops arising from the mode conversion which takes place at each entry to the ionosphere.

However, these calculations become rather lengthy [see Bradley and Bramley, 1971] and so in the present method only allowances for ground-reflection losses of circularly-polarized waves are included, together with the polarization-coupling losses calculated as for single-hop modes [these can then be added together, to calculate total losses].

As I wrote above, there is an awful lot to all of this....and, if you desire further discussion, I'm game...(but, I don't have too much time right now....but, I'll try!)

And I will also gladly provide some more info, including some papers you may find helpful....but, be forewarned some of these papers are quite long (4 to 79 pages) and have a lot of math to sort thru....which even I'm not up-to these days!   
 (gosh, I don't think I could solve multiple diffi-eq's or anti-diffi-eqs if you put a gun to my head....it's been decades!  hmm, I guess computers do these now-a-days, huh?) 

Aside from the original research (that I started learning from, in the early 1970's), the 44-page ITU doc (from the late 1970's), that I quoted above, is probably the best...

But, there is one recent 4-page paper, from 2018, that is pretty good, too. (but is mostly math, hi hi)

It's "conclusions" are rather obvious....kinda a "Duh!" moment....but, since it's written by students (?) at the School of Civil Engineering, Qinghai University....I'm not surprised...

Btw, it is nice to see though, that their results are backed up by the original research of ~ 50 years ago, and the ITU docs/papers from 40 some years ago....(surprise, surprise, Physics / Radiowaves are still the same....no matter how good we make our radios, computers, etc. mother nature / physics are still there, standing strong!)

3 Conclusions
(1) The characteristics of the reflecting surface determine the strength of the reflected wave and how far the signal will ultimately travel while maintaining useful signal integrity.
(2) The number of hops of radio waves on the ocean surface is greater than the number of hops on the surface of the land, that is, the loss of the signal strength of the ocean surface is less than the loss of signal strength on the land surface, and the loss of signal strength over the rugged terrain is greater than the loss of the signal strength of the smooth terrain.

Of course, there's 3 pages of math before that....so, if you want to do those equations, have fun! 


Anyway, I do hope this helps?

73,
John,  KA4WJA