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
Diffraction
Reflection
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 mode
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 mode
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.
Power levels
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 mig
ht 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
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.
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.
Grantville Gazette, Volume 73 Page 16
