In “Marine Radio in the 1632 Universe” (Grantville Gazette 52) and “1636: Marine Radio in the Mediterranean” (Gazette 66) we explored the possibilities for communication across salt water. We also considered, briefly, a few overland paths of special interest to the Navy and commercial shipping interests.
Here, we’ll turn the focus to communication across land. As before, we’ll concentrate on reliable Morse code message-handling at commercial speeds and not other radio services such as broadcasting or navigation.
In the previous articles, there were certain routes of particular interest, for which we could calculate power requirements. It’s much less certain where military units will operate in the coming land campaigns, so instead we’ll estimate the distances achievable with the power levels and antennas most likely to be available. Where to apply those capabilities must be left to authors and their topographic maps.
Due to the complexity of the subject, this will be a simplified treatment of some representative cases. It would be impossible in a brief article to give thorough coverage to the motley menagerie of physical effects by which a radio wave can propagate across land. Not only are there entire books on the subject, but a thorough engineering analysis of any communication route requires topographic maps, ground conductivity maps, and local atmospheric data which neither we nor our fictional characters have.
Beyond those limitations, canon decrees a decades-long hiatus in the high frequency ionospheric skip by which hundred-watt ham stations in our own era are accustomed to reach halfway around the world. That leaves our down-time friends with a remaining menu of propagation modes for which there is little published performance data in the high frequency region. It’s possible to extrapolate from the handbook charts, but the uncertainties will be larger, and some useful physical effects may be overlooked altogether.
Fortunately, our purpose here is not to achieve the accuracy and certainty which professional communication systems engineers are called on to accomplish in the real world. That takes shelves of reference books, adequate time to collect and analyze field survey data, and years of experience. Our objective is to offer reasonable guidelines for plausibility in science fiction.
What we can do, then, is examine the major workhorses among the many land propagation modes and run the numbers for some representative cases. Those results can suggest when our characters could plausibly get a message through, when they couldn’t, and when communication could become marginal and intermittent.
Overview, for the non-technically inclined reader
Grantville Gazette readers and authors come from a wide variety of backgrounds. A few preliminary remarks may be helpful to orient those whose first language isn’t tech talk.
First, the folks who are faced with setting up radio communication, whether in the real world or in our fictional universe, have a variety of goals that revolve around what reliable range is achievable with what means and at what cost. The tradeoffs get tighter if the station must be mobile; limitations on equipment size, weight, and antenna height affect range. And, all of this is a moving target. The bounds of what is technically and economically feasible will expand, rapidly at times, as the electronics industry and the national economy mature.
Second, radio waves can travel from place to place by several different physical mechanisms, called “propagation modes” in tech jargon. They often occur in combination along different parts of a single geographic path. Each mode has its own quirks. The details of how a signal becomes weaker as it travels further from the transmitter determine what range is possible using a particular frequency, transmitter power, antenna design, and station location. We’ll examine three major propagation modes: ground wave, free space, and sky wave. We’ll also look at diffraction and reflection. Whether to think of the latter two as separate modes is as much a matter of semantics as anything else. They’re separate physical effects, but in practice they generally show up as part of a path that’s otherwise free-space.
Third, the variables that radio specialists juggle are station location, transmitter power, frequency, antenna design, the height of the antenna’s supporting structure, and the surrounding terrain. Location can be a compromise between where the communication is actually needed, and where it’s possible to get a signal out past terrain obstacles. Power and frequency both depend partly on the transmitter technology (tubes, electromechanical alternators, spark gaps).
The very longest ranges occur with night-time sky wave, largely limited by our period’s quiet sun to frequencies below 700 KHz (wavelengths greater than 428 meters). Consequently, maximum performance requires very tall and expensive antennas, and high power to overcome the strong natural noise at such low frequencies.
Conversely, mobile operations favor the smaller antennas that go with higher frequencies, and operate mostly by ground wave and diffraction-boosted free space modes. Ground wave ranges decrease with increasing frequency, but not in a linear fashion. Free space ranges depend almost entirely on antenna height above surrounding terrain, and diffraction is governed by bend angle over terrain obstacles.
Where we stand
By 1636, Grantville’s electronics industry is no longer strait-jacketed by the dwindling legacy of up-time parts. In the last year and a half, it has crossed the threshold of sustainability. It’s now manufacturing all the components for a simple but practical tube-based radio communication station. Production is still limited, but growing all the time.
The main focus here will be on the performance achievable with that equipment. However, we’ll also touch on the fairly numerous fractional-watt “tuna can” transceivers made earlier from salvaged up-time transistors.
Calculations will lean toward the conservative side. The criterion throughout is a reliable and predictable communication service for military and commercial needs, when conditions are at the unfavorable end of their natural range of variation. At other times, signals are likely to be stronger and easier to copy.
Supporting technical information
The Terminology section of the original article in the series “Marine Radio in the 1632 Universe” contains a good deal of background information, which readers may find helpful to review. Two of the definitions are ubiquitous in propagation and antenna calculations, and worth repeating here:
Decibels or dB: A logarithmic way to express a power gain or loss ratio P2/P1
The dB form of expression is very convenient. Gains and losses expressed in logarithmic form can be added up algebraically, instead of multiplying very large and small numbers. Gains are positive, losses are negative. For example, an increase in power by a factor of 10 is +10 dB, while a decrease by a factor of 1000 is -30 dB.
Absolute power levels can be expressed as dB relative to some stated reference level, such as one milliwatt or the thermodynamic noise floor of a reference antenna.
dBm: decibels relative to 1 milliwatt
1 W=+30 dBm
Fixed versus mobile stations
One very convenient way to classify radio stations and networks is by mobility.
1636 is a little early for the industry to achieve the miniaturization and the high frequencies best suited to mobile-in-motion operation.
In the context of 1636 logistics, a reasonable definition of a “mobile” land station is one that can be transported in any vehicle up to a horse-drawn heavy freight wagon or a river barge, and set up in the field in half a day or less. “Fixed” stations would be everything else.
Mobility has a major impact on the practical size of a station’s equipment and the amount of radio frequency power it can generate—and indirectly, on the frequency bands and propagation modes it can use most effectively. The lower the frequency, the longer the wavelength, and the larger an antenna must be if it is to deliver optimum results.
There are degrees of mobility. For a wagon-mobile station, the height of a tall tree is a practical limit for an antenna structure, whether actual trees or guyed poles are used to support the antenna. Sustained operation at up to fifty watts would be reasonably manageable for this kind of station. Anything more than that would present some difficulties.
Five watts and a wire antenna would be more reasonable for a station that must be transported in a mounted scout’s saddle bags.
A likely practical limit for a major fixed station in this period would be a single guyed tower 150 meters high, with steam or water power to run the transmitter. Depending on the transmitter technology and prime power source, a kilowatt or more would be possible.
Signal types and technologies
We can also classify communication stations according to the type of signal they can generate and receive. That, in turn, depends on the transmitter and receiver technology.
Tubes, transistors, and electromechanical alternators generate a fairly pure continuous sine wave, a “CW” signal. This concentrates the power into the minimum bandwidth necessary to contain the on-off keying of a Morse code signal—on the order of 100 Hz wide. Since the amount of natural noise that gets through the receiver is proportional to the bandwidth of the receiving filter, a narrow signal helps in maximizing the signal-to-noise ratio.
The CW signal has no modulation other than the keying. It must interact with a tube or transistor oscillator in the receiver to generate an audible tone. Again, this helps maximize the signal-to-noise ratio by not wasting power on a steady carrier wave that contains no information. On the other hand, it also means that Grantville-made components are required in the receiver as well as the transmitter.
Large fixed CW stations would start to appear toward the end of 1635. They would grow over the next few years into the backbone of Europe’s new communication infrastructure. Once that backbone is up and running, a mobile unit (or one station in a mobile net) would only need to set up where one of these big stations can hear it. From there, it could dispatch a message anywhere the net reaches. Think of the fixed stations as the late 1630s information superhighway.
Spark stations could be built nearly anywhere in Europe using down-time skills and materials, and they could be built long before Grantville learns how to make tubes. Rick Boatright has suggested that enterprising down-timers will get busy bringing up local spark nets and relay arrangements as soon as the cheat sheets appear.
Unfortunately, a spark transmitter’s output is a train of poorly-shaped short bursts of radio frequency power that repeat at an audio rate. This results in a low average power output and poor frequency control, spreading its limited power across a wide bandwidth.
Complementing the spark transmitter, a crystal set doesn’t require Grantville’s manufacturing facilities, either. It can receive the burst-modulated spark signal, but it has both wide bandwidth and no amplification. It lets a lot of atmospheric noise through, and it’s not very sensitive.
Consequently, spark stations make much less effective use of their power than CW stations. They’re far from useless, but their effective range is nothing like that of CW stations of similar power consumption and antenna design. Worse, far fewer of them can operate in a given frequency band without mutual interference, because of their broad signals.
Most of the calculations that follow will be for CW, which is much easier to describe mathematically as well as much more effective. We’ll get to spark, though.
Suitable frequency bands for land communication
For a given communication need, the choice of band depends on a variety of considerations. For any propagation mode, some bands work better than others, or reach further than others, or require less power than others, or are easier to build equipment for than others.
By 1636, we can expect a first-generation family of simple tubes that deliver reasonable efficiencies at frequencies up to perhaps 15 MHz, at power levels from under a watt to a few hundred watts. That isn’t everything the communication services would like to have, but it’s enough to accomplish quite a lot. It will be a couple more years before the industry can master the design, materials science, and manufacturing of the more complex and expensive tubes that will open up the higher frequencies.
Electromechanical alternators top out at around 600 kHz, but can reach tens of kilowatts.
On the other hand, 500 kHz is about as low in the spectrum as we can expect the early builders to construct full-size transmitting antennas, even at the largest fixed stations. A standard quarter-wave vertical antenna for that frequency requires a 150-meter tower centered on a radial-wire ground plane 300 meters across. (The radial wires need not impede farming or grazing if they’re buried or elevated.) Such an antenna could be externally tuned down to 400 kHz or so and still perform fairly well.
To get a feel for the size of this kind of structure at such a low frequency, look at this picture from the Wikipedia article on antennas: https://en.wikipedia.org/wiki/File:Sendemast_Hirschlanden.jpg. Even this example is slightly shortened from optimum height, with a small capacitive top hat.
Below that frequency we’d have to accept the engineering and cost tradeoffs of shortened antennas, which are both more expensive and less efficient. This picture from the Wikipedia article on T antennas is probably at about the maximum height that could be built with wood lattice towers: https://en.wikipedia.org/wiki/File:Antenna_of_WOR-AM.jpg.
Many low-frequency antennas are a lot more complicated and expensive than that. See this example: https://en.wikipedia.org/wiki/File:Grimetonmasterna.jpg. They’re technically possible, of course, but not likely to happen this early.
The cost and real estate of huge antennas isn’t the only obstacle to the early use of the favorable propagation characteristics at low frequencies, either. The atmospheric noise rises very rapidly below 500 kHz, requiring much more power to be heard at the greatest potentially possible distances. It’s doubtful that such super-powered transmitters would be feasible or affordable this early.
Bottom line: in this period, the most useful frequencies lie between about 400 kHz and 15 MHz.
Propagation across land often doesn’t lend itself to straightforward rules and calculations, because land isn’t a uniform medium. It’s not flat, the ground conductivity varies from place to place, and some locations are covered by lakes and swamps instead of low-conductivity dirt and rock.
Multipath effects are common. Signals can arrive at a receiver by multiple propagation modes, and along multiple terrain paths by the same propagation mode. They can add in phase, enhancing the signal strength by 3 to 6 dB, or add out of phase, causing deep cancellations of 20 dB or so. As the temperature and humidity distribution of the atmosphere changes, the arriving signals can drift in and out of phase, sometimes as rapidly as a couple of times a second.
Different parts of a single path often involve different propagation modes, making calculations complicated even where the detailed data exists to estimate path losses. This article will focus on conservative estimates for several fairly simple but common types of land paths.
As before, we’ll concentrate on propagation modes that can provide reliable day-in, day-out service at commercial Morse code speeds. Exotic modes that provide only sporadic openings are of interest to hams, but usually not to military services and businesses, unless an author wants to use a freak band opening as a plot device. (There are ways that can happen, especially in summer.) We’ll also leave out of the discussion potentially useful modes that would require hardware not yet available.
With the tubes and other radio parts expected to be in at least limited production by 1636, the USE and its partners could reasonably expect to exploit (or wrestle with) the following modes for land communication:
- Ground wave
- Free space propagation
- Sky wave
Ground wave mode
Ground wave is an interaction between a radio wave and the electrical conductivity of the earth. The traveling wave induces currents just below the surface, which cause it to deflect downward toward the surface so that it follows the curve of the earth. The path losses and power requirements are fairly simple to estimate with the aid of the graphs in the Radio Propagation Handbook. Land is much less conductive than salt water, particularly poorly conductive European land, so the propagation losses are far greater than we calculated in the marine radio articles. Therefore, the usable ranges are much shorter.
We can generally ignore topography for ground wave; it doesn’t have a strong influence at the frequencies where ground wave is usable. For that reason, ground wave range offers a conservative minimum level of performance that we can be reasonably confident will be available along any route, regardless of the intervening terrain. If the terrain is favorable, other modes may allow communication with smaller antennas and less power, but if not, ground wave will still be there.
Frequency selection for ground wave is a complicated tradeoff. The lower the frequency, the lower the propagation losses, and the greater the potential range. Unfortunately, the lower the frequency is, the taller the transmitting antenna must be to get reasonable efficiency and the low radiation angle needed to launch its power along the surface. And, the lower the frequency, the higher the atmospheric noise is, so low frequencies require more power to take full advantage of the superior propagation. In the OTL world, very low frequency ground wave signals have traveled to the far side of the world, at the cost of enormous transmitting antennas and colossal power.
With the power levels and antenna heights likely to be feasible by 1636, it would be impossible to exploit low-frequency (under 300 kHz) ground wave to its fullest. As we’ll see, though, what can be affordably achieved at practical frequencies is of great value.
Under these constraints, 500 kHz is something of a sweet spot for long-range ground wave. Therefore, we’ll calculate poor-earth ground wave ranges at that frequency. We’ll also do the calculations at 5 MHz and 15 MHz. Those frequencies are within the capabilities of the first generation of down-time tubes, and they’re better suited to the antenna dimensions and power levels of a land mobile station.
Free space propagation mode
Mathematically speaking, pure free space propagation is the simplest to analyze of all modes, and is by far the least lossy. “Path loss” for this mode doesn’t involve actual power dissipation along the propagation path at all. It’s just a mathematical expression of the continuous decrease in power density as the spherical wavefront expands away from the transmitting antenna and grows in frontal area—the classic “inverse square law” that follows from simple geometry and the capture area of the receiving antenna.
Unfortunately, that ideal can rarely be achieved in practice anywhere near the earth’s surface. Even at microwave frequencies, antennas can’t be made sufficiently directional to avoid reflections off the earth along point-to-point routes. Consequently, wave interference between direct and reflected paths is unavoidable. About the only place it could be applied in pure form is in high-angle communication with aircraft. That’s outside the scope of this article.
However, an approximation to free space propagation can occur over much of a path, if at least one end of the link is many wavelengths above nearby terrain, and the reflections are off lossy surfaces. A common practical case is communication between a hilltop base station and a mobile unit on flat land. While most of that type of path might be unobstructed, the last part of almost any terrestrial path comes within a wavelength or less of the earth as the wave leaves or approaches an antenna near ground level. That terminal portion of the path transitions into high-loss ground wave. The Rural Electrification Administration’s publication Power System Communications: Mobile Radio Systems has loss curves for that type of mixed path down to 40 MHz. With an adjustment for the larger capture area of an antenna scaled for 15 MHz, we can extrapolate path loss at the frequencies our 1636-period tubes can handle.
Diffraction is an electromagnetic phenomenon that causes a small portion of a radio wave’s power to re-radiate from the edge of an obstruction and propagate into the shadowed space beyond. It’s the reason you can hear an FM broadcast station when you’re behind a hill. Given the bend angle needed to reach the antenna behind the obstacle, the diffraction loss can be calculated and added to the rest of the path loss terms. With that number, it’s possible to calculate the increase in transmitter power needed to overcome the diffraction loss.
Diffraction very conveniently complements free space propagation. In a situation where a fraction of a watt might be enough to reach a receiver up in the clear on a hilltop, several watts to several tens of watts might be needed to be heard in the valley beyond. The synergistic combination of free space propagation and diffraction is a major workhorse of land mobile communication in our own era, and it will be in the 1630s as well—just at lower frequencies for the first decade or so. Interestingly, it will often work better at these lower frequencies, because the longer wavelength results in a larger effective capture area at the edge of the obstruction. Thus, more of the transmitter’s power is available to be re-radiated into the shadow.
Reflection can occur off any conductive surface. A bounce off a hillside can carry a signal around a mountain or down into a valley. In modern cities, the metal structures of buildings cause multiple reflections. The lead and copper roofs of large early modern buildings may offer some useful reflection paths at the higher frequencies, if the field teams can locate the hot spots by exploring for them. However, large expanses of metal can also cause radio shadows.
Sky wave mode
These first four modes are only modestly affected by weather, time of day, and season. With adequate receivers, transmitter power, and antennas, they offer very reliable full-time service over quite useful distances.
Sky wave, on the other hand, offers far greater range than any combination of these terrestrial modes, but only during the hours of darkness, and only below 700 kHz or so during the long quiet-sun decades of the seventeenth century. (At high latitudes, the summertime hours of darkness are very short, or even non-existent.)
In the marine radio articles, we looked extensively at sky wave at 500 kHz. For a single hop, it doesn’t make much difference whether the path is over sea or land, since the only bounce is off the ionosphere. As it happens, European land distances are mostly single-hop distances. We’ll repeat just a few key performance numbers here.
The earliest NTL-built CW transmitters were the “tuna can” transceivers, made from salvaged up-time solid-state parts. A quarter watt is a reasonable guess for typical output. Using transistors originally intended for receivers, audio equipment, and power supplies, operation to 15 MHz is within reason. Some units might be able to reach 30 MHz or higher.
The new electronics industry would put early effort into a 5-watt tube, to drive a receiver’s speaker. This would make a very useful low-power transmitting tube. A 25-watt tube would follow soon afterward. We could expect these two power levels to be fairly common for mobile transmitters. Their power demands would be a reasonable fit for transportable storage batteries and foot pedal generators.
The next priority for power tubes would probably be at about the 250-watt level, intended for fixed stations. An amplifier built around four of those tubes could deliver a kilowatt. We found in the marine radio calculations that 1 kilowatt at 500 kHz is sufficient to achieve the maximum possible range of a single sky-wave hop (in European noise levels), while 100 watts is the bare minimum to use sky wave at all.
We can assume that a 500-kHz station will be optimized for either marine ground wave or sky wave, or both, since that’s where its expensive antenna really pays off. Whatever land ground wave service it offers in the daytime will be within that power range. Still, it’s easy enough to do the calculations for the lower power levels typical of mobile stations and see what the results are. A mobile station could conceivably loft a 500-kHz wire antenna on a kite or a balloon and lay out a few radials on the ground, though that’s unlikely to be a common practice.
Signals and noise
Electromagnetic noise is an unavoidable fact of life in radio communication. Signal-to-noise ratio is central to the calculations and estimates that follow. It’s what determines whether a radio signal will be heard.
The earth’s atmosphere is the dominant RF noise source below 10 MHz. 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 writhing filament of ionized air powered by megavolts and kiloamps.
Atmospheric noise decreases rapidly with frequency, giving way to cosmic sources somewhere above 10 MHz.
In the VHF and UHF bands, cosmic noise in turn gives way to noise sources within the receiver, leading to an entirely different set of engineering tradeoffs. But in 1636 the electronics industry won’t be ready to go there.
As in the previous articles, our criterion for an adequate signal-to-noise ratio for Morse code communication at commercial speeds is +16 dB in a 100 Hz bandwidth.
The European regions where we’re likely to see land action in the next few novels fall roughly from latitude 45 to 55 degrees north and 0 to 30 degrees east. The intensities for this region taken from the noise maps in the Radio Propagation Handbook are selected for summer, 8 PM to 4 AM. This is the most unfavorable season and time of day. That choice is appropriate to our objective, a reliable full-time communication service with minimal outages.
As with season and time of day, we will apply the graphs for standard deviation in the most pessimistic way. Authors needing uncertain communication in more favorable circumstances can make more optimistic estimates for distance or power requirements.
As noted in the earlier article, the handbook’s data and text dealing with atmospheric noise include no term for the gain of the receiving antenna. The assumption made here is that antenna directivity enhances noise pickup from the favored direction to the same degree that it suppresses noise from the insensitive directions, provided the noise is spatially uniform. Thus, the following table represents the noise received on any efficient antenna.
(An inefficient receiving antenna, such as a Beverage wave antenna, would attenuate noise and signal by the same amount, so the S/N would be unchanged, as long as the noise from the antenna remains greater than the receiver’s internal noise At these frequencies, that would almost always be the case.)
Atmospheric noise in a 100 Hz bandwidth at selected frequencies, dBm
|500 kHz||5 MHz||15 MHz|
Basic land antennas
For each of these three bands, we’ll assume for simplicity that the transmitting antenna is a full-size quarter-wave vertical with a ground plane. There are several reasons for this choice.
A land station on the 500-kHz band in this early period would almost certainly construct this type of antenna. Anything with higher performance would be structurally unaffordable.
Furthermore, any station wanting to use ground wave requires a vertically polarized antenna. Ground wave and sky wave are the useful modes at 500 kHz.
A mobile unit, on the other hand, would usually prefer a vertical antenna because it’s omnidirectional and easy to erect. It could be a quarter-wave vertical with a ground plane, or an elevated half-wave antenna such as a coaxial sleeve vertical. For simplicity, the calculations will be for the quarter-wave case. A quarter wavelength at 5 MHz is 15 meters, and a quarter wavelength at 15 MHz is 5 meters. Either of these would be lightweight structures, easy to break down and transport. A unit traveling with a wagon could easily carry disassembled poles and guy ropes of those dimensions, or shoot cords over a tree limb with a slingshot to support a wire antenna. Or, a half-wavelength vertical wire antenna of similar performance could be hung inside a church tower, provided it’s higher than any nearby metallic structure.
We’ll assume that these communication stations use their transmitting antennas to receive. That will usually be true in the early years. Specialized 500 kHz directional receiving antennas that deliver improved signal-to-noise ratio may come later, but probably not in 1636.
This is not to say that our early modern radio technicians and operators couldn’t design and construct more sophisticated antennas. They certainly could, and the higher in frequency they go, the smaller the arrays would be, and the easier to manage. Grantville arrives in the seventeenth century with multiple editions of The ARRL Antenna Book, an excellent practical guide to the design and construction of antennas for 1.8 MHz and higher. The popular antenna analysis program EZNEC was available in the 1990s; one or more of the hams might have had copies. So, it’s possible that certain fixed stations intending to communicate with distant mobiles might install high-gain directional arrays for 15 MHz on tall poles, and even make them rotatable. Generally, the benefit would tend more toward working weak mobiles in unfavorable locations than toward dramatically increased range. For a mobile unit, though, it would usually be easier to set up on a hilltop than to cope with a bulky and awkward directional antenna.
As for the horizontally polarized antennas common in twentieth-century ham radio, they’re designed to make optimum use of ionospheric skip in the HF bands. There’s little sky wave skip in those bands during the seventeenth-century sunspot minimum. Therefore, we leave them out of consideration.
Ground wave communication ranges
For ground wave on European land we’ll use the published path loss curves for “poor earth.”
Ereqd in the following table 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, using the theoretical antennas on which the handbook’s charts are based.
G is the total gain of the two quarter-wave vertical antennas at the two ends of the link, relative to the theoretical antennas. The quarter-wave transmitting antenna has a gain of +3 dB compared to a short vertical, and the same antenna used for receiving has a gain of +5 dB relative to an isotropic antenna. Thus, the total antenna gain G=+8 dB. This term increases the signal power at the receiver without affecting the noise power. Conversely, it reduces the transmitter power required to achieve the target S/N of +16 dB. With that correction added, we can then apply the ground wave curves to find the maximum range at the stated transmitter power.
One limitation is that the handbook’s noise maps and ground wave loss curves only go to 10 MHz. Therefore, the figures for 15 MHz are extrapolated, and contain more uncertainty than those for 500 kHz and 5 MHz.
One caution that should be kept in mind when applying the maximum range estimates to story plotting is that they assume a receiver with an optimized narrow passband filter. The filters in the receivers built in the first few years won’t be that good; therefore, their working range will be somewhat less. This is particularly true of the little tuna-can transceivers. Nevertheless, they will be very useful for tactical field communications. The whole tuna-can outfit can be carried in a cavalry scout’s saddlebag, and set up in a few minutes. And, a regimental headquarters station with a good receiver would be able to hear it at the calculated range and answer with a hundred times the tuna can’s power.
|Value, Units||500 kHz||5 MHz||15 MHz|
|Ereqd, dB µV/m||+18||+18||+0.4|
|Ereqd-G, dB µV/m||+10||+10||-7.6|
There are some interesting observations here. We see that lower frequencies give much longer ground wave distances across poor earth. Although the losses are much greater at the higher frequencies suited to mobile use, even modest power offers very useful ranges for tactical operations or village-to-village local nets. And power requirements go up rapidly as distance increases, because of the exponential factor in ground wave path losses. That’s why quite useful range is available even at very low power levels.
This suggests creating a general-purpose communication infrastructure consisting of many low-cost stations providing local access for end users, all connected together through a backbone network of much larger stations on lower frequencies.
Pseudo free space communication ranges
There’s a rule of thumb that says free space propagation occurs between a base station antenna on a hilltop or tower and a mobile unit at that base station’s geographic horizon. This type of radio path is extremely reliable; it’s more likely to be interrupted by artificial interference than by any natural phenomenon.
For spherical earth, the range calculation is a straightforward exercise in trigonometry. At ordinary hilltop heights, the horizon distance can be approximated accurately enough by a simplified equation in the REA handbook:
Dfree=free space path distance in miles
H1=height of base station antenna above ground level in feet
H2=height of mobile station antenna above ground level in feet
In kilometers and meters, that would be
There’s also a rule of thumb that the distance to the radio horizon is about 4/3 the distance to the geographic horizon. That’s because of refraction due to the density gradient in the lower atmosphere. However, that effect can vary a lot with weather conditions, especially at microwave frequencies. Relying on over-the-horizon tropospheric bending can result in random outages.
With the free-space geographic range calculated, the curves in the REA handbook can then supply the path loss. The curves assume an antenna height of 6 feet at the mobile end. That’s a reasonable assumption for our wagon-mobile units if they don’t find a convenient hill or a tall tree. We’ll do the path loss and power calculations for 15 MHz only, extrapolated from the 40 MHz loss curves. That’s less of an extrapolation than doing it for 5 MHz as well; also, the noise is much lower at 15 MHz, so that band is a good choice for land mobile use anyway.
The free space distance equation obviously includes the case in which both station antennas are elevated, as in hilltop-to-hilltop operation between relay stations. The range between them is the sum of their horizon distances. Of course, this assumes no terrain obstacles tall enough to obstruct the direct path between the stations, and no interfering bounces off highly reflective surfaces. For that case, where the wavefront continues to expand and the power density declines after the wave passes the transmitting station’s horizon, the path loss is not the sum of the losses of the two separate paths from each station to a 6-ft high station at their mutual horizon. Instead, the inverse square law applies to the second part of the path. For the case of two stations at equal heights, the additional path loss would be -6 dB due to the quadrupling of the wave front’s area in the second half of the path. Quadrupling the transmitter power would compensate for that. For example, taking the case in the table below where a 250-mW transmitter on a 1600-ft hill could reach a 6-ft high antenna 60 miles away, 1 W would be sufficient to reach a station on another 1600-ft hill 120 miles away.
The REA curves show path loss at distances continuing well beyond the horizon (for a mobile station on flat ground), at which point the free space wave transitions into ground wave, and the losses increase. In other words, with increased power it’s possible to communicate reliably for some distance beyond the geographic horizon. We’ll explore the distances where the received power falls to the desired +16 dB S/N, for 25 W, 5 W, and ¼ W.
The curves assume a half-wave vertical at the base station and a quarter-wave vertical at the mobile. That’s a reasonable setup for a fixed base station communicating with a mobile unit. A quarter-wave antenna at a mobile set-up on a hilltop might send 3 dB less power toward the lower elevations.
For this calculation, we’ll use the assumed antenna combination, and add a correction for the 15 MHz receiving antenna’s larger capture area relative to the same antenna design at 40 MHz. That comes out to G=+8.5 dB.
As with the ground wave case at 15 MHz:
- Pnoise=-116 dBm
- Receiver Preqd=-100 dBm
In the following table
- Lfree is the path loss at Dfree
- G=+8.5 dB
- Pfree is the transmitter power required to achieve +16 dB S/N at Dfree
The published curves are drawn for eight base station heights given in feet, with distances in miles, so we’ll use those as the primary units and calculate the metric equivalents.
|6 (1.83)||6.9 (11.1)||-124.8||-116.3||0.042||10.6 (17)||20.5 (33)||28 (45)|
|25 (7.62)||10.5 (17)||-129.5||-121||0.126||12 (19.3)||23.5 (37.8)||32 (51.5)|
|50 (15.2)||13.5 (21.7)||-130||-121.5||0.141||15 (24.1)||28.5 (45.9)||38 (61.2)|
|100 (30.5)||17.6 (28.3)||-128||-119.5||0.089||20.5 (33)||37 (59.6)||47 (75.7)|
|200 (61)||23.5 (37.88)||-129.5||-121||0.126||27 (43.5)||45 (72.5)||57 (91.8)|
|400 (122)||31.7 (51.1)||-130||-121.5||0.141||35.5 (57.2)||57 (91.8)||70 (113)|
|800 (244)||43.5 (70)||-130.5||-122||0.159||47 (75.7)||71 (114)||90 (145)|
|1600 (488)||60 (96.6)||-132.5||-124||0.251||60 (96.6)||86 (138)||105 (169)|
In short, at any distance up to 60 miles, a quarter-watt tuna can transmitter is powerful enough to communicate by Morse code, as long as the station at the far end is on a high enough hill and has a receiving filter just wide enough to pass a CW signal.
With relatively simple first-generation tube equipment, five watts would be adequate to send messages over a 100-kilometer path, from even a fairly modest hilltop. Even a kilowatt wouldn’t be sufficient to do that by ground wave.
(Operators generally prefer not to select the narrowest possible filter that will pass the signal, unless they need it either to suppress noise or to separate closely-spaced signals in a crowded band. Given that mobile tube transmitters would usually fall into the 5- to 25-watt range, this propagation mode offers the less fatiguing sound of a somewhat wider filter.)
These examples demonstrate the great value of high locations for communication across land. With the coming of radio, mountaintops have become strategic terrain. That’s why the USE government maintains a major relay station on top of the Brocken in the Harz Mountains. Though canon doesn’t mention a permanent station atop the Großer Beerberg in the Thüringerwald, it’s reasonable to expect one there as well. Let’s look briefly at a few terrain altitudes of interest in the USE.
above 50 m
|North German plain, typical||80-250 (25-75)||–||Most regions north of Grantville|
|Brocken||3747 (1142)||89 (144)||118 km SW of Magdeburg|
243 km S of Hamburg
132 km N of Grantville
|Großer Beerberg||3222 (982)||82 (132)||37 km W of Grantville|
85 km N of Bamberg
140 km N of Nürnberg
216 km N of Ingolstadt
|Aircraft at 5000 ft||5000 (1524)||101 (164)|
|Aircraft at 14000 ft|
max altitude without oxygen
|14000 (4267)||170 (274)|
Calculating the additional path loss due to diffraction over an obstacle can be very complex. The Radio Propagation Handbook devotes an entire chapter to it, and we can’t do full justice to the topic here. What we can do is examine a few simple cases that a mobile communication crew is likely to encounter.
If a radio path that’s otherwise free-space or close to it is obstructed by higher terrain near one end, it can be modeled mathematically to a good approximation as an additional loss term added to the free space path loss. The diffraction loss can be compensated by increasing the transmitter power. That loss is a nonlinear function of the frequency and the angle through which the path must bend to reach the receiver. The handbook provides a nomograph for the purpose.
If both ends of the path are obstructed, then two diffraction loss terms must be added to the free space path loss.
The handbook says that diffraction is likely to dominate the path over the obstacle if the bend angle is less than 0.02 radian. That’s equivalent to a 2% grade, if the wave arrives at the obstacle parallel to the horizon. For example, that would be the case if there were a 50-meter-high ridge line 1 km from the receiver. If the angle is greater than that, the handbook indicates that other less lossy propagation mechanisms such as forward scatter might deliver a stronger signal to the receiver. However, the chapter is written with UHF and microwave signals in mind. At the wavelength of a 15 MHz signal (20 meters) other modes are less likely to be of much help, so we’ll make the pessimistic assumption that an obstructed station depends on diffraction.
|50 m Obstruction Distance|
|15 MHz Diffraction Loss|
|Transmitter Power Multiplier|
For example, a mobile unit communicating with a base station on a 30-meter hill 28 km away over an unobstructed path would require about 90 mW. But if the mobile’s path is blocked by a 50-meter ridge 1 km away, the route would require 12.6 times as much power, or 1.13 W. If both ends are similarly obstructed, 14.2 W would be needed.
50 watts should be sufficient to communicate over the majority of pseudo-free space paths where there’s a single obstruction at one end. Mobile-to-mobile paths where both stations have limited power and nearby obstructions tend to have significantly reduced range. That situation is common in hilly terrain. For that reason, there would be a tactical advantage to setting up a relay station or a command post on a high location, if one can be secured in the operation area.
Radio waves reflect from conductive surfaces and can bounce into shadowed areas. In up-time cites reflections off the metal structures of buildings are very common. In the seventeenth-century world it’s possible that 15 MHz signals might reflect from metal-roofed church spires or off steep cliffs. Otherwise, they’re not likely to be a frequent source of help to radio operators. The handbooks give little information on estimating their magnitude, except for billboard-sized metal mirrors used on microwave fixed routes and oriented with great care.
To recap very briefly the discussion in “1636: Marine Radio in the Mediterranean,” sky wave below the AM broadcast band is likely to be reliable while the ionospheric path is in full darkness. That lasts from about an hour after sunset at the west end of the path to an hour before sunrise at the east end. The range estimated in that article, using a standard full-size antenna on a single-hop path, came out to about 950 km with 100 watts, and 2000 km with 1 kilowatt.
Shorter ranges may be iffy. The published loss curves for 100 and 200 kHz show reasonable path losses down to 200 km or so, but this may not be reliable in the weak ionization conditions of the seventeenth century. A signal striking the ionosphere at a steep angle may not be bent enough to return to earth. The shallower incidence angles at longer ranges are more likely to be reflected back to the ground.
Thus, we could encounter a skip-over zone somewhere between 350 km where 24/7 ground wave becomes too weak to copy, and 500 km or so, where night-time sky wave first reaches the ground. Message traffic for that dead zone might have to be relayed by a station 1000 km away.
Interestingly, the “gray line” mode canonized in a number of places, beginning in 1632 itself, is a manifestation of sky wave, but at higher frequencies. The canon contacts made with this mode used unmodified up-time ham gear. Ham transmitters aren’t built to operate at 500 kHz and lower. Their lowest band starts at 1.8 MHz. At that frequency, the weak ionization of the seventeenth-century Maunder Minimum is barely enough to offer skip for a short period around twilight. Sky wave opens when the ionosphere’s high-loss lower layer fades shortly after sunset, allowing the signals to reach the higher layers where skip happens. But the higher-layer ionization degrades with time, too. The higher frequencies need stronger ionization to be bent back to earth, so the ham band opening fades quickly. The short duration of that opening limits communication to stations near the same longitude, hence the term “gray line.” But based on long historical experience, medium and low frequencies should be able to reflect off much weaker ionization than the ham bands need, and persist for many hours during the night.
Spark communication capabilities
Having covered with reasonable confidence what CW could do using the major propagation modes, it’s time to take a look at spark. Here, we’re on much shakier ground. In fact, any estimate of what could be done with spark verges on outright speculation. The problem is that most of the published material dealing with spark that can be easily found nowadays is more historical than technical. There are a great many unknowns.
We do have Rick Boatright’s spark article “Radio FAQ Part 1: Spark and Crystal Radios” posted at http://www.1632.org/1632tech/faqs/radio-rfe.html. We also have “The History of Amateur Radio, Part IV” at http://www.astrosurf.com/luxorion/qsl-ham-history4.htm. They’re in good agreement that after the U.S. 1912 Radio Act pushed hams above 1.5 MHz (200 meters), the working ranges were typically between 25 and 75 miles. That’s with 600 watts input, on ground wave across North American “good earth,” with the equipment and antenna a ham could set up at home. So, what should we expect in our early NTL years in Europe?
It’s a fair guess that anyone who doesn’t have access to tube gear probably won’t be getting power from a commercial electric utility, either. That’s doubly true for a mobile station. So, 20 or 30 watts from storage batteries or pedal generators is a lot more likely than 600 watts. Not to mention, components for that power level would be a lot easier to fabricate from materials generally available in early modern times, and a lot more reliable as well. And, as noted above, European soil is typically considered to be “poor earth” in the absence of specific data.
Going from 600 watts down to 30 watts is a change of -13 dB. We can look up the loss for ground wave propagation across 75 miles on good earth at 1.5 MHz, and then look up the distance on the poor-earth chart for 13 dB less loss at the same frequency.
All other things being equal, we get 13 miles (21 km).
But all other things may very well not be equal.
For a typical early twentieth-century ham living in a suburban lot with trees for antenna supports, a full-size antenna for 1.5 MHz was impossible, let alone an optimally constructed full-size antenna. That would be 50 meters high on a ground plane 100 meters in diameter. The obvious solution would be a “T” antenna. But there usually wasn’t the space or budget for that either.
What a ham in that period could usually put up would be a single wire going up at a roughly vertical angle to somewhere in a tree’s branches. A single horizontal wire from the top to another tree would provide some amount of capacitive top-loading, but the more-or-less vertical wire would connect to one end, not to the precise center. Then, instead of multiple radial wires at ground level for the return current to flow into with low resistive loss, there would usually be a clamp on a single water pipe running out to the water main in the street. Lacking city water, there would often be nothing more than an eight-foot metal rod driven into the ground outside the window, which might or might not reach the water table.
Everything is wrong with this. It’s a random shortened vertical, which has a broadened vertical radiation pattern to begin with. The antenna current is less than optimally coupled to the electromagnetic field; that requires the electrical resistances elsewhere in the RF circuit to be very low if the antenna is to be at all efficient. But the ground resistance is high, so power is wasted. Because the horizontal wire isn’t centered on the top of the vertical wire, horizontally polarized emission isn’t cancelled out, so some of the power is wasted in a horizontally polarized signal that can’t couple into the ground wave. The random-wire top loading is generally insufficient to resonate the antenna, so inductance must be added, but an imperfect inductor adds more resistance to the circuit and wastes more power. The tilt of the vertical wire further de-optimizes coupling into the ground wave.
It does radiate. Any conductor that carries RF current will radiate something. It just doesn’t do an efficient job of converting RF power into a ground wave signal.
A military communications detachment in the field, or a commercial enterprise with money to spend and the connections to obtain an unobstructed site, need not accept these limitations. They could locate where there’s room to put up a proper antenna for the band they’re using. (This becomes easier if they select a higher frequency, where antennas aren’t so large.)
Another limitation of the early ham station was the crystal set. A crystal set’s only source of power to drive the headset is the radio wave. The signal-to-noise ratio was not the only determinant of whether the signal could be heard; it was the absolute strength of the signal itself. The capture area and efficiency of the receiving antenna had as much to do with that as the transmitting antenna. (Not only that, the passive crystal set imposes an unfortunate trade-off between selectivity and sensitivity. The more tightly the resonant tank circuit is coupled to the antenna, the more signal can be passed through to the headset, but the broader its bandwidth becomes, and less effective it is in separating signals on nearby frequencies.)
Those limitations would be the case for most of the crystal sets in our fictional universe, but it need not be true for all of them. One of the pieces of bypassed technology, which is certainly known to Grantville’s radio scholars, is the electromechanical audio amplifier. In principle, it’s an earphone mechanically coupled to a carbon microphone. Drive one or two stages of audio amplification from a crystal set, and a weak signal could be brought up to audibility. Noise would again become the limitation.
Combine optimally designed and installed antennas with crude audio amplification, and perhaps that -13 dB could be made up. That doesn’t take deep knowledge and years of experience, it just takes money, materials, and manpower. Any army that’s had a spy in the libraries could at least optimize its antennas.
Which bands would likely be used for spark radio is another major area of uncertainty. 1.5 MHz is inside the upper end of the AM broadcast band. All the thousands of legacy up-time broadcast band receivers cover 530 kHz to 1.710 MHz with 10 kHz channel spacing. That’s a large enough installed base of equipment to permanently nail down that band for broadcasting. Spark would be most unwelcome there. Besides, an optimum antenna for such a low frequency is inconveniently large for most users, especially mobile stations. Broadcasting stations are few in number and commercially funded, hence can afford good antennas and enough power to reach crystal sets.
The next band up in the spectrum is the 160-meter ham band at 1.8 to 2.0 MHz, which has been in use for vital government and military communication almost from the time the up-timers arrived. The spectrum plot of a spark transmitter in Rick’s article shows most of the power concentrated in a 10 kHz bandwidth, but with splatter spreading out for 100 kHz on each side. That kind of interference would be even more unwelcome in this busy piece of spectrum.
Up-time band allocations place a marine band at 2.0 to 2.5 MHz, which appears in “Storm Signals” (Grantville Gazette 31). That’s a broad enough chunk of spectrum to accommodate at least one spark channel without seriously inconveniencing all the CW stations. The experimental spark transmitter Rick cites was tested at 2 MHz, so we know it’s feasible. It’s reasonable to expect some spark stations at somewhat higher frequencies as well, to take advantage of the smaller and less expensive antennas, the more modest demands on real estate, and the less demanding logistics.
Rational considerations don’t always govern in real life, though. A wide variety of individuals, associations, businesses, governments, and other entities are likely to get involved with radio in the early years. They’ll have wildly varying resources, sources of knowledge, locations, and willingness to cooperate with others. Given all that, spark stations are liable to show up anywhere in the low, medium, and high frequency bands. The efficiency and radiation pattern may be abysmal, but any antenna will put out some kind of a signal. Even if a random length of wire isn’t tuned to resonance, it will radiate something, if there’s any RF current flowing in it at all. Depending on the need of the moment, it might be enough.
So, things could get quite messy for quite a long time, until tube gear becomes a lot more plentiful. The hash and splatter from spark stations could be showing up in more places and on more frequencies as time goes on. CW operators with good receivers are likely to be very grateful for their narrow filters and noise blankers.
Saveskie, Peter N. Radio Propagation Handbook. Blue Ridge Summit, PA: Tab Books, 1980. ISBN 0-8306-9949-X, ISBN 0-8306-1146-0 pbk.
Rural Electrification Administration, U.S. Department of Agriculture REA Bulletin 66-8 Power System Communications: Mobile Radio Systems. U.S. Government Printing Office, 1978.
American Radio Relay League The ARRL Antenna Book. Various editions.
Boatright, Rick. “Radio FAQ Part 1: Spark and Crystal Radios” http://www.1632.org/1632tech/faqs/radio-spark-crystal.html
Boatright, Rick. “Radio FAQ Part 3: RF Environment” http://www.1632.org/1632tech/faqs/radio-rfe.html
Unidentified author. “The History of Amateur Radio, Part IV” http://www.astrosurf.com/luxorion/qsl-ham-history4.htm
Department of the Navy, Naval Electronic Systems Command. Naval Shore Electronics Criteria: VLF, LF, and MF Communication Systems. Washington: U. S. Government Printing Office, 1972. FSN 0280-901-1000 http://www.navy-radio.com/manuals/0101-1xx/0101_113-00.pdf through -08.pdf
Payne, Craig. Principles of Naval Weapon Systems. Annapolis, MD: Naval Institute Press, 2006. USBN 1-59114-658-5 books.google.com/books?isbn=1591146585
British Broadcasting Corporation, Research Department. “Low-frequency sky-wave propagation to distances of about 2000 km”, Report No. 1971/8. http://downloads.bbc.co.uk/rd/pubs/reports/1971-08.pdf
Maritime Radio Historical Society. “Reports from NMO” http://radiomarine.org/gallery/show?keyword=pt3&panel=pab1_8#pab1_8
Wikipedia “Antenna (radio)” https://en.wikipedia.org/wiki/Antenna_%28radio%29
Wikipedia “T-antenna” https://en.wikipedia.org/wiki/T-antenna