In “Marine Radio in the 1632 Universe” (GG 52) we took a broad look at what would be possible in the way of long-distance radio communication during the seventeenth century’s prolonged deprivation of high-frequency ionospheric skip. Much of the focus in that article was on northern Europe and the Atlantic.
Now our fictional universe has moved on to 1636, and the governments of the USE, Austria, Venice, and other potentially friendly powers can see trouble looming from the Ottoman Empire. Military services plan for foreseeable contingencies, and we authors and fans should do likewise. It’s time to take a more focused look at radio propagation in the Mediterranean region, and what would be feasible with equipment we can expect to be available from Grantville’s electronics industry by 1636.
The USE Navy could very well find it necessary to operate in the Adriatic. To begin with, seventeenth-century conditions favor seaborne logistics, which are always a concern to navies. The Adriatic, in particular, gives access to ports all along the Italian and Balkan states, and depending on Ottoman objectives, it could be a route to attack Venice or Venetian commerce. Then there are the implications for land campaigns. Trieste became important to the Austro-Hungarian Empire in the late nineteenth century, because there’s a fairly reasonable route between Trieste and Vienna that doesn’t cross high mountain passes. OTL Austria used it to build a railroad, and turned Trieste into the empire’s one real seaport. Even developed as a wagon road, either side in the coming struggle could find logistic uses for that route or want to deny it to the other.
The Aegean is a less likely theatre of operations, but not beyond the bounds of possibility. A naval threat to the Dardanelles could compel the Ottomans to pull back significant forces to guard the capital’s logistic lifeline, in the same way that the Doolittle bombing raid on Tokyo in 1942 did little actual damage, but forced the Japanese to bring some of their forces home.
The rest of the Mediterranean is the thoroughfare by which naval forces from the USE and possible allied powers would travel to their destinations and be supplied, and so itself could become a scene of conflict.
As we’ve seen in past novels and stories, radio is essential to the USE Navy’s effectiveness and is rapidly becoming so for the Kalmar powers and the Dutch. It’s time, then, to work out an estimate of what the capabilities and limitations of the navy’s radio communications might be, given the nature of the geography, the propagation modes available in the region, and the equipment and operator skills available as the time for action approaches. We also need to think about how far advanced the Venetians might be in radio by this date.
The military services and commercial interests are mostly interested in message-handling, so that’s what we’ll focus on. AM broadcasting uses the same propagation modes we’ll discuss here, but requires much more power, both because of the greater bandwidth of a voice signal and hence the more natural noise that will get through the receiver, and because a much better signal-to-noise ratio is needed to make out the subtle modulation of voices and music than to hear the full-on, full-off swings of Morse Code. But where communication stations lead the way, broadcasting will eventually follow.
So let’s look at what what might be possible in the Mediterranean region within the constraints of radio propagation physics and the Grantville electronics industry’s growing capabilities as the time for action approaches.
Communication routes and propagation modes
The Adriatic is a particularly likely place for naval conflict to occur; therefore it’s particularly relevant to run the numbers on what’s physically possible there, and what equipment and antennas would be needed for fleet communications and ship-to-shore work. As we shall see, the shape of the sea and the distances make it well-suited to ground wave propagation across salt water. That’s very fortunate, because ground wave at sea is only modestly affected by season, time of day, and weather.
The Aegean, being considerably smaller than the Adriatic, is even more favorable for regional ground wave communication.
Communication between the fleet (or a friendly shore station on Venetian territory) and the USE’s industrial base at home is a very different problem. That route crosses a considerable stretch of land. Ground wave losses are much higher across land than across salt water, especially across poorly conductive European land. That greatly limits ground wave’s range, and as we’ll see, the numbers don’t work for ground wave at this NTL date.
Communication direct from the USE or Venice to the Aegean is a similar problem. Either path would have to cross too much land, making ground wave an impractical proposition.
Ground wave isn’t the only propagation mode that’s useful across land, of course. Knife-edge diffraction is a major workhorse for land mobile communication. It works by bending a small portion of a signal’s power over the tops of mountain ranges. But it, too, has practical distance limitations, and Grantville’s electronics industry may not be making the high-frequency tubes it requires in time for the Ottoman attacks.
Of course, limited-range stations can be sited to form relay networks. Relaying over the Alps, however, would be a formidable problem at this period, both politically and logistically.
And that leaves us with skywave, available in quiet-sun years only on frequencies below the AM broadcast band, and mostly at night―the place in mid-hop where it bounces off the ionosphere needs to be in darkness for an hour or two before the path will open.
Published data shows a nightly opening lasting up to 8 hours. A single hop typically covers up to 2000 km with sufficient power; longer distances generally require multiple hops. When the intermediate ground reflection is off seawater, the losses are low enough to support paths of two or three hops in these medium- and low-frequency bands. Unfortunately, none of the routes we’re contemplating have large bodies of seawater in the right place to launch a second hop, so we’ll do only single-hop calculations.
To achieve high efficiency, these low frequencies require tall transmitting antennas and large radial ground wire arrays, which are expensive and time-consuming to erect and impractical to relocate. All this makes skywave good for logistic support and strategic communication, but not for operational command in real time. Battles will be commanded from the theatre of action, not from navy headquarters back home.
Onward to the numbers
The previous Marine Radio article covered a good deal of background information, terminology, and basic antenna math, which we won’t repeat here. We’ll just proceed to the noise, path loss, and power requirement calculations for our Mediterranean routes. As in the previous article, we’ll assume that the mission requirement is to handle Code message traffic reliably at 25 words per minute at any time of day or night, though not without making the radio operators work hard to hear the signal when the atmospheric noise is at its summertime worst.
At the distances we’re concerned with, there’s no need to consider the lowest radio bands, where full-size antennas are impractical even on land, and the less efficient shortened antennas are required. We’ll examine only the popular marine radio bands at 500 KHz, 2 MHz, and 4 MHz.
Electromagnetic noise is what a radio signal has to overcome. At the frequencies we’re examining, the earth’s atmosphere is the dominant RF noise source. The noise is generated mainly by thunderstorms, primarily in the tropics and in some continental interiors. The lightning bolt is both the RF source and the transmitting antenna, a miles-tall filament of ionized air powered by megavolts and kiloamps.
The noise level is reasonably uniform across the Mediterranean region, about 2 db stronger than in northern Europe, so that correspondingly more power is necessary to cover the same distance. (Strong local thunderstorms can blanket any man-made signal for a few hours; that could be a plot device.)
As before, for our purposes we’re concerned with the noise the receiving antenna will pick up in a 100 Hz bandwidth. That assumes a nearly ideal filter just wide enough to pass the signal, with a flat top and steep skirts. Can Grantville’s electronics industry produce that kind of an audio filter for the navy in time for the campaign? Maybe. If not, more noise will get through, and correspondingly more power will be required. But this gives us a theoretical limit.
From the noise level table in the previous article:
|Location||500 KHz||2 MHz||4 MHz|
|Mediterranean 35°-45°N, 5°W-35°E||-67 dbm||-85 dbm||-92 dbm|
Basic transmitting antennas
The basic full-size vertical antenna at 500 KHz and up is a quarter of a wavelength tall, centered on a ground plane of quarter-wavelength radial wires. At 500 KHz it would be 150 meters tall, which is just about the practical limit for an affordable wood lattice tower. That won’t fit on a ship, so a ship has to transmit on this band with a less efficient shortened vertical, with a wire top hat strung between the mastheads. But a quarter wave vertical at 2 MHz would be 37.5 meters high, and just under 19 meters at 4 MHz; a full-size ship’s mast can be lofty enough to support the former, and even a Wild-class courier schooner has masts tall enough for the latter.
The highest gain achievable in a one-piece vertical antenna occurs at a height of 0.64 wavelength. This is conventionally called a 5/8 wave vertical. A 5/8 wave antenna would be 96 meters high at 2 MHz, or 48 meters high at 4 MHz. These are certainly feasible on land.
For this analysis we’re ignoring sophisticated antenna arrays. It’s early days, and single-tower vertical antennas are what we can expect the industrial base to be able to build and get working properly.
Basic receiving antennas
The simplest thing to do is use the transmitting antenna for receiving. Ships almost always do this, except when using a direction-finding loop antenna for navigation purposes. At these frequencies, almost any antenna will pick up more noise from the atmosphere than the receiver generates. Antenna directivity will increase the received signal strength with little effect on the noise, however, assuming uniform spatial distribution of the noise.
Well-funded commercial and government shore stations can afford the space for large directional receiving antennas. In this article, however, we’ll assume that the shore stations we’re concerned with are temporary or recently established, and haven’t had time to build the complex antenna farms of mature split-site coastal stations.
Required signal-to-noise ratio
The Radio Propagation Handbook contains a table of signal-to-noise ratios relative to the noise in a 1 Hz bandwidth, recommended for different grades of service with several types of modulation used in commercial service. We’ll confine our analysis to Morse code, because that requires much less bandwidth than any form of voice communication and so demands much less transmitter power than any alternative available in the first decade of the NTL. For hand-sent Morse code the handbook gives +36 db for “operator-to-operator” service. But commercial Morse code at 25 WPM implies a typical receiver bandwidth of roughly 100 Hz, not 1 Hz, so the noise power passing through the filter is 100 times greater, or 20 db stronger. Hence, the signal-to-noise ratio in the actual bandwidth needed to achieve that grade of service is +16 db. A good operator could copy through a somewhat worse signal-to-noise ratio, but it would be tiring and probably result in errors and dropouts.
The same table recommends +45 db above the noise in a 1 Hz bandwidth for “good commercial service,” which would be +25 db above the noise in a 100 Hz channel.
We’ll use +16 db as the criterion for our basic power / path loss / antenna gain calculations.
Baseline case: MF/HF ground wave between fixed stations across salt water
The calculations underlying the following table are based on the following conditions:
- On the 500 KHz band, shore stations transmit with a quarter-wave vertical.
- On the 2 MHz and 4 MHz bands, shore stations transmit with a 5/8 wave vertical.
- The transmitting antennas are used for receiving.
- The criterion for successful communication is a +16 db signal-to-noise ratio in a 100 Hz bandwidth at the receiver terminals, after all gains and losses are accounted for.
Since the published propagation curves show the signal strength in terms of db relative to 1 microvolt per meter versus distance from a 1 KW transmitter using a short vertical antenna, we must first correct for the gain of the assumed transmitting antenna, then refer to the curves for converting field strength to the power an isotropic antenna will pick up at that wavelength, and correct for the gain of the receiving antenna. We can then compare the received signal power to the received noise power.
For each path we will show signal strength taken from the curves, then the power received at that wavelength taking into account the transmitting and receiving antenna gains, followed by the noise level, the resulting signal-to-noise ratio at that location, and finally the power needed to achieve a signal-to-noise ratio of just +16 db during the hours of highest noise.
We use the straight saltwater path from Venice to Corfu to represent the longest ground wave distance in the Adriatic. We don’t consider ground wave from Venice beyond that point, because the signal would run onto the Greek land mass, which weakens the signal rapidly. We also do the numbers for the short path across the Adriatic, which would be of interest for radio navigation using coastal beacons or direction-finding stations; a typical distance for that would be about 1.5 times the width of the sea.
John Harvell has pointed out that Corfu, at the entrance to the Adriatic, was a well-defended major Venetian naval base, making it a secure place to put an important radio station. George Iconomou drew attention to the strong Venetian positions on Cythera, Anticythera, Tinos, Kotor, and especially Crete. That raises the possibility of a ground wave relay chain running from Venice to Corfu, then Corfu to Crete with some loss crossing Greece, and possibly on to Tinos. Iver Cooper suggests a look at Malta. Malta wasn’t a Venetian possession, but it was under the control of the Knights of Malta, who had even more reason than the Venetians to oppose Ottoman expansion. While there isn’t an all-water path from Corfu to Crete, there is one from Corfu to Malta, and from Malta to Crete. So an alternate route for round-the-clock ground wave relay service is Venice to Corfu to Malta to Crete to Tinos. Without Malta, we run into the complication that the best place on Crete to cover the eastern Mediterranean is at the eastern end, but the only path to Corfu that doesn’t cross a long stretch of land is from the extreme southwest corner. (Also, Crete is long enough to lose a lot of signal strength on a lengthwise path, so the island would need two stations for optimum results in all directions. We’ll analyze all these paths and see what the numbers tell us.)
Taken together, stations at those places would give the navy and Venetian interests full-time radio communication over a large part of the Mediterranean.
- From Corfu: the Adriatic, the Ionian Sea, the “toe” of Italy and the southern Tyrrhenian Sea, and the central Mediterranean between Sicily and Greece across to Libya
- From eastern Crete: the Aegean and nearly all of the eastern Mediterranean except the region beyond Cyprus
- From Tinos: stronger communication into the northern Aegean; the ability to hear weaker ship transmitters
- From Malta: Sicily, Sardinia, Tunisia, and the passage between Sicily and Tunisia
- From Venice itself, not only the whole Adriatic, but limited coverage in the northern Tyrrhenian after land losses crossing Italy
Let’s look at the distances involved, and do the path loss and power calculations for the longest and shortest paths of interest. We’ll omit the calculations for some intermediate distances, since they’re bracketed by other calculated cases:
- Corfu to Malta, 636 km
- Malta to western Crete, 819 km
- Crete to Tinos, 262 km
The Corfu to Crete calculations are more complicated than the rest; they’re mostly over water, but the middle part is over land. The losses in the successive legs of a mixed path can’t be simply calculated as if they all started at the transmitter, because the path loss is the product of two different mathematical functions, which vary differently with distance and frequency. The geometric spreading factor follows an inverse square law modified by the earth’s spherical shape and is independent of frequency, while the resistive energy loss follows a decaying exponential function and degrades rapidly with frequency. Instead, each leg’s loss must be determined from the loss curve for the specific type of surface it crosses, over the specific portion of the path it covers between the transmitter and the receiver.
The path between Corfu and Crete that crosses the least land is from points on the extreme southwest of each island, from near Chalikounas to Elafonissi, just skimming the west coast of Greece for much of the way and occasionally crossing a short bit of projecting land.
On the other hand, the best place on Crete to cover the eastern Mediterranean and up into the Aegean by ground wave is on the eastern tip near Kato Zakros, but crossing much more land on the way across Greece.
We’ll calculate both paths and see what we get.
We won’t consider shore stations in the Aegean, because all the shores of that sea are in hostile territory. Defending a shore station there would be impractical.
|Path||Value, Units||500 KHz||2 MHz||4 MHz|
|Length of the Adriatic:
Venice to Corfu, 896 km
|E1KW, db µV/m||+29||+14||+2|
|Psignal, dbm||– 39||-61||-79|
|Pnoise, dbm||-67 dbm||-85 dbm||-92 dbm|
|Distance along the Italian coast:
Venice to Otranto, 756 km
|E1KW, db µV/m||+36||+24||+14|
|Pnoise, dbm||-67 dbm||-85 dbm||-92 dbm|
|S/N, db||+ 35||+ 33||+ 25|
|Width of the Adriatic:
Barletta to Dubrovnik, 211 km (131 mi)
|E1KW, db µV/m||+70||+67||+65|
|Pnoise, dbm||-67 dbm||-85 dbm||-92 dbm|
|Chalikounas, Corfu to Elafonissi, Crete,
568 km, consisting of:
Water: Chalikounas, Corfu to Ag Panteleimon, Greece, km 0-204
Land: Ag Panteleimon, Greece to Kalamata, Greece, km 204-333
Water: Kalamata, Greece to Elafonissi, Crete, km 333-568
E1KW, db µV/m
|Pant.-Kal. loss, db||-14||-19||-23|
|Kal.-E la. loss, db||-3||-15||-20|
E1KW, db µV/m
|Pnoise, dbm||-67 dbm||-85 dbm||-92 dbm|
|Chalikounas, Corfu to Kato Zakros, Crete, 745 km, consisting of:
Water: Chalikounas, Corfu to Limni Saltini, Greece, km 0-99
Land: Limni Saltini, Greece to Tolo, Greece, km 99-338
Water: Tolo, Greece to Kato Zakros, Crete, km 338-745
E1KW, db µV/m
|Lim.-Tol. loss, db||-31||-41||-47|
|Tol.-Zak. loss, db||-19||-29||-38|
E1KW, db µV/m
|Pnoise, dbm||-67 dbm||-85 dbm||-92 dbm|
Clearly, there’s no difficulty hearing a coastal station at either end of the Adriatic, anywhere in that sea. Further, at this distance there’s no need to resort to the 500 KHz band and the tall transmitting antenna it requires, if all we want to use is ground wave over salt water. In fact, if that band were used, a short antenna with its reduced gain and efficiency would be more than sufficient, without requiring a powerful transmitter.
If ground wave is all we’re interested in, all of these paths could reasonably be covered on 2 MHz, avoiding the need to build anything taller than a ship’s mast.
Ground wave ranges for ship transmitters
Next, we’ll calculate how far ships could hear each other above the noise level in the Mediterranean. They’re more limited in antenna space and transmitter power than shore stations.
In the non-canon vacuum tube timeline, it’s estimated that a 25-watt transmitting tube good up to perhaps 10 MHz could go into pilot production some time in 1635. That would be suitable for a ship’s transmitter running off batteries charged by a masthead wind generator, as depicted in “A Friend in Need.” A simple 250-watt tube could be available not too long afterward; four of these in a push-pull/parallel combination would make possible a 1 kilowatt transmitter, which would be manageable in ships with engines.
So let’s look at how far a marine transmitter could be heard at these two power levels. The following table assumes that:
- On the 500 KHz band, transmission is with a short vertical.
- On the 2 MHz band, the ship is large enough to mount a quarter-wave vertical; for example, a Fearless-class 100-foot escort schooner. Smaller vessels can use a short vertical, but we won’t make that calculation.
- On the 4 MHz band, all ships transmit with a quarter-wave vertical. (Higher vertical directivity might be possible on shipboard, but could actually be detrimental during severe rolling and pitching.)
- Ships receive with their transmitting antennas.
Ereqd here is the calculated signal strength in db relative to 1 microvolt per meter, required to produce a +16 db signal-to-noise ratio in a 100 Hz bandwidth at the stated regional noise level, at the given frequency. With that, we can apply the ground wave curves and antenna gain adjustments to determine the maximum range at the stated power.
|Value, Units||500 KHz||2 MHz||4 MHz|
|Ereqd, db µV/m||+15||+9||+8|
The major path distances of interest in these two seas are:
|Length of the Adriatic: Venice to Corfu||896|
|Width of the Adriatic: Barletta to Dubrovnik||211|
|Length of Aegean: Mykonos to Kavala||397|
Comparing, we see that ships can communicate with each other the length and breadth of either of these seas with a kilowatt on any of these bands. Furthermore, they can do it with 25 watts on 500 KHz, and not a great deal more than that on 2 MHz where the antennas are simpler and more efficient.
The one real reason to equip ships in this theatre with a top-hat antenna and an antenna tuner that can reach down to the 500 KHz band is to give them night-time seven-league boots, so they can reach out to distant ships and shore stations and over land obstacles.
Again, these numbers assume a signal barely strong enough to copy during the noisiest time of day and season, with some effort by the operators. Authors can adjust with higher power, better receiving antennas, more favorable hours, or shorter distances for more solid communication, or they can choose greater distances, lower power, and worse antennas if they want lower speeds, multiple attempts to get a message through, or chancier efforts. Or they can afflict their characters with a powerful thunderstorm at a critical moment or make a tube expire.
Communication isn’t the only use for these radio frequencies. As we saw in “Storm Signals,” radio signals can be used in many ways for navigation. For simple direction finding, two shore stations on bearings roughly 90 degrees apart as seen from the ship can provide a reasonably accurate position. The ship’s navigator can take bearings on two or three beacon stations using a direction-finding loop, or a couple of manned shore stations can take considerably more accurate bearings on the ship’s transmitter, undisturbed by pitching, rolling, and yawing.
A considerably better S/N ratio than +16 db would be desired for navigation, but as we can see, a 25-watt beacon or ship transmitter would be more than sufficient at the distances the Adriatic allows. Even 5 watts would put in a strong signal across the width of that narrow sea.
Two challenging cases: MF/HF ground wave between fixed stations across land
Before we go on to sky wave, there are two ground wave paths worth analyzing to see what we’d be up against if we want 24/7 communication. These are the USE-to-Venice route, and the shorter path from Corfu to the Aegean. For each of these cases, we’ll use the “poor earth” signal strength curves, but the same full-size fixed station antennas described above.
As canon has developed, there’s a good working relationship between the USE and the Venetian Republic. Even without a cooperative effort with the USE navy, Venetian merchant interests could well have a large MF station on the air by 1635, handling overnight commercial message traffic with the USE, the Netherlands, the Kalmar countries, and possibly France.
With all the chaos and war elsewhere in the Italies, mainland station sites anywhere south of Venice are a chancy proposition. That’s an issue for the mainline authors to wrestle with, however. But Corfu is ideally placed to punch a signal eastward across Greece to Velika on the Aegean coast and out to sea. The actual path is a short hop across water and then the long land leg, but nearly all of the loss will occur on the latter, so we’ll just do the simpler calculation for that, to get a ballpark estimate.
|Path||Value, Units||500 KHz
|Lübeck to Venice, 945 km||E1KW, db µV/m||-19||Off scale||Off scale|
|Psignal, dbm||-84||Off scale||Off scale|
|Pnoise, dbm||-67 dbm||-85 dbm||-92 dbm|
Corfu to Velika, 252 km
|E1KW, db µV/m||+24||-9||-23|
|Pnoise, dbm||-67 dbm||-85 dbm||-92 dbm|
Obviously, nobody in 1636 is going to be building a 2-megawatt transmitter. The 40 KW ganged alternator estimated to be necessary for the message from Vlissingen, Netherlands to Cantrell’s squadron in the West Indies was pushing it. So forget 24/7 ground wave contact between Venice and navy headquarters in Lübeck, for relay to the fleet. Even from further south in the USE, the power requirements would be unreasonable for the first decade NTL.
From Corfu to the Aegean, though, ground wave looks like a very practical proposition, if a 500 KHz antenna can be built there in time for the action. Driven with a kilowatt, ships anywhere in the Aegean should hear it, even behind islands. A ship would need about twice the power to cover the same path as a land station with a full-size antenna, or about 320 watts. Corfu should be able to hear a ship transmitting with a kilowatt, well out into the Aegean. It certainly adds to the strategic importance of Corfu.
MF Sky Wave
And so we come to sky wave at 500 KHz, to connect Venice with the rest of Europe’s growing radiotelegraph backbone―and USE Navy headquarters. As explained in the previous article, the low- and-medium frequency spectrum below about 700 KHz is where reliable nighttime sky wave will be found during the decades of the quiet sun. The 500 KHz region is something of a sweet spot for the mode: reasonably good propagation, moderate atmospheric noise levels, and near the practical limit for full-size vertical antennas supported by wood lattice towers. We can expect both the marine service and the fixed land communication service to make heavy use of that part of the spectrum in the late 1630s.
Sky Wave from Venice
There’s no question that Venice’s builders could put up a quarter-wave transmitting antenna for 500 KHz. Obtaining an unobstructed flat site big enough to accommodate the 300-meter diameter wire ground plane and defensible against pirate raids might complicate the task, of course. What’s more of a question is how powerful a transmitter they could bring in by the time the trouble starts. 100 watts should be easily obtainable by the middle of 1636; a kilowatt tube transmitter might be harder to get and harder to supply with power. (An RF alternator like the one built in 1633 in “Canst Thou Send Lightnings?” is a possibility, but not an easy one to operate and maintain.) So let’s see how far they could get out a usable signal, for each of the two vacuum tube cases.
As in the previous article, we have only the U.S. Navy curves for sky wave up to 200 KHz, so we must extrapolate to get an estimate for 500 KHz. One thing that helps is that whereas the published curves are for shortened vertical antennas, our hypothetical fixed station antennas at 500 KHz are full-size. The initial signal estimate in each case is for a 1 KW transmitter.
|Path||Value, Units||100 KHz
|Lübeck to Venice, 945 km
|Psignal, dbm||-7||-21||– 35?|
|Pnoise, dbm||-33||-49||– 81|
|S/N, db||+26||+28||+2 6?|
Why not do it at 200 KHz? That’s possible, but it would mean a shortened transmitting antenna, which requires a top hat to optimize the current distribution on the radiating wire. That requires a minimum of two towers to support the ends; three to six would be better. The BBC at 198 KHz uses two; NAA at Cutler, Maine around 20 KHz uses seven per antenna. A ship normally has two or three, the fore and mizzen masts supporting the top hat and the mainmast carrying the radiating wire.
Interestingly, these cases all come out with just about 10 db more signal than is needed to achieve the target +16 db S/N. If we look further at the 100 KHz and 200 KHz curves to find the distance where the loss is 10 db greater than it is at 945 km, which would take us down to that +16 db target with a 1 kilowatt transmitter, we find 2044 km (1270 mi) at 100 KHz and about 2012 km (1250) mi at 200 KHz. That relative relationship probably holds at 500 KHz as well, because the decrease in signal strength with distance on a single-hop path is mostly due to geometry. The path is through air, which is nearly lossless, and only the ionospheric reflection factor varies with frequency.
So if Venice gets a full-size transmitting antenna and a kilowatt to drive it, what else is within 2000 km, and should be able to hear its transmissions with a simple receiving antenna? Vaasa, Finland. Trondheim, Norway. The Shetland Islands. Lisbon, Portugal. St. Petersburg, Russia. Ankara, Turkey. All of the USE, the Netherlands, Bohemia, the Austro-Hungarian Empire, England, Scotland, Ireland, France, Spain, Switzerland, the Italies, Poland, Lithuania, Belarus, and Ukraine. Nearly all of the Mediterranean and a good stretch of North Africa. In short, Venice gets plugged into the European commercial message system and can manage its business affairs everywhere the net reaches.
Now, it also happens that Corfu is 1730 km from Lübeck. So if there is a fleet unit operating in the Aegean, with 24/7 ground wave contact with Corfu, Corfu will be able to relay message traffic direct to USE Navy headquarters as soon as night comes, without needing a relay through Venice.
Now, what if the transmitter puts out only 100 watts? Then, according to the sky wave propagation curves, the coverage zone at +16 db S/N is a ring, starting at about 200 km and ending at about 1000 km. (Sky wave skips over nearby terrain, because there’s very little power radiated off the end of the antenna, and because ionospheric reflection works best at shallow angles.) This tells us that to play in the sky wave arena at 500 KHz at all, anything under 100 watts is useless for reliable commercial service―unless we’re transmitting to a mature station with much more sophisticated receiving antennas, meaning large and expensive. That’s possible, but not likely by 1636.
Sky Wave Offshore
There’s one other interesting case to think about. What if there isn’t a shore station in Venice, but the USE does have a steamship in the northern Adriatic? The shortened 500 KHz ship antenna isn’t as good as a full-size antenna on a well-constructed ground plane ashore, but it isn’t dramatically worse. If we think a Venetian coastal station could reach Lübeck at night with 100 watts, a ship should be able to do it with 200 watts. A kilowatt should provide plenty of margin. So even in this case, the fleet could communicate at night with Navy headquarters.
Tactical voice communication
Up-time CB units would probably be hard to find by this time, even for the Navy. New-build short-range tactical voice transmitters and receivers wouldn’t strain Grantville’s tube production; it’s more a question of whether the industry’s very limited technical manpower would have time to design and debug all the necessary components in time for the Mediterranean campaign. This could lead to voice radio equipment being in short supply and temperamental, forcing the fleet to fall back to 4 MHz Morse Code for urgent battle coordination. It’s another variable authors could manipulate for story purposes.
With the equipment coming out of Grantville’s industries by the time the fleet heads for the Mediterranean, they’ll be able to communicate. Within the theatre of operations, full-time Morse Code communication is easily feasible. Overnight communication is possible with home, at levels of difficulty that could be adjusted for story needs. Night-time communication back to the USE for ships in transit off the Atlantic coasts of France and Portugal may be more difficult, but should be possible. One-way transmissions from the high-powered station at Vlissingen, Netherlands could be heard far out to sea.