Radio Ranges
The sensitivity of radio detectors is directly based on the size of the collecting area. Nothing is below an "absolute detection threshold" so long as you are willing to build a big enough detector. This is what radio astronomers do.
When determining at what range a given detector can "hear" a given transmitter, the following quantities need to be known:
- The power of the transmission from the source. This can conveniently be expressed as the product of the transmitter's power consumption and an efficiency factor. The efficiency is usually expressed as a percentage, and must lie between 0 and 100%. A realistic efficiency is probably around 90% or so (NB: this is a semi-educated guess, I don't claim to be an authority on radio transmission efficiency).
- The directionality of the transmitter. Some transmitters are omnidirectional, spreading their transmissions equally in all directions. Others are beamed, concentrating their output into a fairly narrow beam, hopefully pointed in the direction of the intended receiver.
- The sensitivity of the receiver. This can conveniently be expressed as a threshold power level. If the power received at the detector is greater than the threshold, the transmission is detected.
- The collecting area of the detector. The larger the area of the detector's antenna, the more of the transmitted power it will receive, thus improving the chance that any given transmission will be detected.
Omnidirectional Transmitters
To determine the range of an omnidirectional transmitter with a given detector, follow these steps:- Determine the transmitted power of the transmitter. This is the power of its energy source, multiplied by its efficiency, as explained above.
- Use the inverse square law to determine the power per unit area at
the detector's range. This is just the transmitted power divided by
4
(range)2, where the range is in metres (or yards, or whatever your "unit distance" is).
- Determine the detection threshold power of your detector. Multiply the received power per unit area from the transmitter by the detector's collector area and see if it is above or below the detection threshold.
Omnidirectional transmissions get poor range compared to beamed transmissions, but are useful when broadcasting to many distributed receivers, or when sending distress messages.
Beamed Transmitters
The range of a beamed transmission is considerably longer than that of an omnidirectional one. Exactly how much longer depends on how much solid angle the beam subtends from the source. Every beam will spread out a little, and the solid angle measures the area covered by the beam at unit distance from the source.
If the beam is circular in cross-section, the solid angle S is
related to the opening angle of the beam
by
S = 2Once you have the solid angle, the power per unit area at the detector is the transmitter power divided by the solid angle, divided by the square of the distance. Note that if the opening angle equals 360 degrees, the solid angle is 4/ 2) ]
Note that real transmitters cannot confine 100% of their transmitted power into a narrow beam - there is low level signal leakage in almost all directions. This can be accounted for by reducing the effective transmitter efficiency slightly.
In some cases, the transmitter will beam in other patterns. For example,
terrestrial radio and TV transmissions are beamed mostly in a horizontal
plane, so that most of the power goes to reaching antennae at or near
ground level, and little is wasted into the sky or ground. If you
desire a transmitter with an unusual beaming pattern, simply assign a
reasonable amount of solid angle to the transmission, remembering
that 4 is omnidirectional.
Beamed transmissions are also good to prevent unintended receivers from
receiving your message. If interception of messages becomes important
in a game, assume that the slight leakage of signal into directions
outside the beam provides 1% of the total power to be spread over
4 of solid angle (i.e.
omnidirectionally), and calculate the detection range accordingly.
The only problem with beamed transmission is that the intended receiver needs to be in the beam! If you know the relative position of your intended receiver, and have some means of keeping track of it if it or you are moving (e.g. with reference to star positions, by using a GPS system, etc), then a computerised tracking system will easily be able to keep the beam on target.
If a beam needs to be aimed manually for any reason, require a skill roll against Electronics Operation (Communications), with a -1 penalty for every degree of opening angle less than 10 degrees. If the beam opening angle is less than 1 degree, only a critical success will succeed. Each attempt takes 3d seconds, and repeated attempts may be made with no penalty. Once a beam is aimed manually, it may be locked in place, assuming appropriate equipment and no relative motion of transmitter and receiver. GMs should rule on the stability of locked beams. Aiming a beam from an ocean liner to a lighthouse should be okay, while even momentary aiming from a speeding off-road vehicle should be almost impossible.
If you don't know where your intended receiver is, you can either aim at random, or use an omnidirectional transmission. If you have an idea of the general direction, you could aim a wide beam that way. How wide is up to the discretion of the person transmitting. The GM should rule on how far off target the beam is aimed and if the beam is wide enough to include the receiver.
Plugging it all in
The collecting area of any given detector needs to be decided when the receiver is designed. This size is usually determined by constraints imposed by whatever is carrying the receiver.You can get an idea of a realistic threshold detection limit from the technical specs of a radiotelescope (which I just happen to have handy)... The Parkes radiotelescope in Australia can detect roughly 10-15 watts. That's using cryogenically cooled detectors to reduce thermal noise, so at room temperature you're probably looking at a limit of about 10-14 watts using state-of-the-art TL7 equipment. Of course there's nothing to stop you using cryogenics to get down to the lower limit if you want. It would be reasonable to assume that TL9+ spaceships would routinely have cryogenic radio receiver systems.
I do not know what a typical civilian radio broadcast power is - a few tens of watts? If we take 10 watts of transmitted power (i.e. after efficiency losses), a detector area of a square metre, and a 10-14 watts threshold, the omnidirectional range turns out to be 8920 kilometres. Assuming no atmospheric effects.
The following applet calculates this range for you. Be careful to enter data in the correct units. Reasonable defaults for the efficiency of the transmitter and the detector threshold are given. The default opening angle corresponds to an omnidirectional transmitter. The range is displayed in kilometres, astronomical units, or parsecs, as appropriate.
To compare to figures given in GURPS Vehicles, 2nd Edition, consider an Extreme Range Radio Communicator, which has a vacuum range of 5,000,000 miles (about 8,000,000 km), for a power consumption of 4 kW. Using the range calculations given here, and assuming omnidirectional broadcast, 90% efficiency, and a detector threshold of 10-15 W, this range is achieved for a detector area of about 225 square metres, or an antenna 15 metres by 15 metres square (or a circular dish 17 metres in diameter). This seems reasonable for a large spaceship, but is oversized for a small vehicle. If the transmitter is beamed with an opening angle of 5 degrees, the detector antenna size shrinks to a tenth of a square metre, which is reasonable for almost any purpose.
Other Considerations
Frequency and Bandwidth
If you want to be more realistic, you can define the bandwidth of the transmitter and the transmitted power per hertz, then define the reception frequency and bandwidth and only count the power in the overlapping frequency ranges. This is probably too much bother for gaming purposes, unless different radio frequencies are important in the campaign (e.g. an alien species likes to use radio frequencies mostly outside normal human communication frequencies).Terrestrial Radio
All of the above discussion has assumed vacuum propagation of the radio waves. Travelling through air does not substantially affect radio waves, but the horizon distance and reflective properties of the ionosphere complicate matters for terrestrial radios.The horizon acts to limit some radio transmissions, because radio waves do not travel well through earth, rock, buildings, etc. The Earth's ionosphere is a layer of electrically charged particles (ions) in the upper atmosphere, some 100 kilometres from the surface. This layer can reflect radio waves in a certain frequency range.
On the Earth's surface (or any other planet) it is simplest to assume that medium and longwave transmissions are limited to "just over the horizon". Assuming the vacuum range calculations show that you are within range, then you will be able to detect a transmission only if you have a direct line of sight to the transmitter, or if you would have such a line of sight given enough extra height to get you above nearby trees, buildings, small hills, etc.
Shortwave radio (frequency 3-30 MHz) can be reflected by the ionosphere, and so has a much greater maximum range on Earth. For simplicity, assume a 200 kilometre additional distance to account for the trip to and back from the ionosphere, and if the total distance is less than the range, the shortwave radio transmission can be detected.
Note that ground-to-space communication by shortwave is hampered by the intervening ionosphere. Multiply effective range by 10 to account for this. The best solution is to use other frequencies, which can ignore this effect.
All of these considerations can be applied to other planets as well.
Satellite Communication
The horizon problems of terrestrial radio can be overcome by relaying messages via communications satellites. A network of three geostationary satellites, equispaced over the equator, will provide relaying capability between any two points on Earth. Such satellites orbit at an altitude of about 36,000 kilometres.If a satellite is used as a relay, the range problem must be tackled for both legs: transmitter to satellite, and satellite to receiver. These can both be solved using the methods given above.
Submarine Radio
Using radio for communication underwater has special difficulties. Sea water is a good electrical conductor, and conductors attenuate radio waves rapidly.Higher frequency waves are more severely affected, so much so that normal terrestrial radio frequencies cannot be used to communicate underwater. The only solution to this problem is to use ultra-low frequency radio waves.
Unfortunately, ultra-low frequency radio necessarily has a low bandwidth, and therefore cannot carry much information. Typically, submerged submarines can only send and receive morse code (or similar character encodings), since voice transmission requires more bandwidth than is available.
Propagation Time and FTL Radio
Radio waves travel at the speed of light, just under 300,000 kilometres per second. For ranges in excess of 300,000 kilometres, the time delay begins to be noticeable and annoying for two-way conversations.The propagation time for 1 astronomical unit is about 8 minutes and 20 seconds, and the propagation time for a parsec is 3.1 years. Conventional radio communication over more than a few AU is likely to take the form of monologues.
The rules above can be adapted to faster-than-light (FTL) radio as well, but individual GMs will need to make decisions about FTL radio availability, propagation speed, power efficiency, and detection thresholds, as well as any unusual effects such as "hyperspace interference", or odd geometrical effects. For example, FTL radio power may drop off as the inverse of distance, or inverse cube or some other power, instead of inverse square.