The rules given in GURPS Vehicles, Second Edition for radio ranges are at the best simplistic and at the worst unphysical. This document attempts to describe a more realistic and physically based method of calculating 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:
1. Determine the transmitted power of the transmitter. This is the power of its energy source, multiplied by its efficiency, as explained above.
2. 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 π (range)2, where the range is in metres (or yards, or whatever your "unit distance" is).
3. 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 θ by

S = 2 π [1 - cos (θ / 2) ]
Once 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 4π, and the formula reduces to the omnidirectional case above.

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 4π 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 4π 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.

Sorry, your browser does not support applets.

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).

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.

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.

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.

These rules are intended to replace the rules for Communicators listed on pages 47-48 of GURPS Vehicles, Second Edition. Refer to that section for general information on radios, but replace the description of the Options and the Communicators Table with the information given here.

Options

To simulate this option, buy only the receiver portion of the radio from the tables below. Power consumption of a receiver only is 1 watt per 100 square metres of antenna. This is negligible for all but enormous antennae.
Tight Beam
For this option, choose the opening angle of the radio beam. Any angle from 360 degrees down to 10 degrees is achievable at TL7 for the listed cost in the table. This minimum angle reduces by a factor of 10 for each additional TL up to TL10. At any given TL, a reduction of up to a factor of 100 may be achieved by increasing the cost by the same factor. The beam opening angle is fixed, unless the Variable Beam option, below, is purchased instead.
Variable Beam
This allows the beam opening angle to vary from 360 degrees down to a minimum angle as determined using the Tight Beam rules above.
VLF
For simplicity, this may be read as per GURPS Vehicles, Second Edition. If greater realism is desired, the received power of an underwater transmission will actually drop off with distance with an additional exponential decay term.
Cellular Phone
This option remains the same as described in GURPS Vehicles, Second Edition, except that the weight multiplier also vanishes at TL8+.
Sensitive or Very Sensitive
These options no longer exist. If you want higher sensitivity, choose either a cryogenically cooled receiver, a larger antenna area, or both.
This involves using liquid nitrogen or a cryogenic refrigeration system to lower the temperature of the receiver. By reducing thermal noise in this way, the receiver sensitivity can be increased substantially. At TL7 this involves a small tank of liquid nitrogen which must be replenished once per day, at a cost of \$1 per refill. At TL8+, this option may be taken as a built-in cryogenic refrigeration unit instead, which reduces the transmitter efficiency by 1%, or for a receiver only increases the power requirement from negligible to 0.01 kW.
Jammer
This option allows the transmitter to send continuous "white noise" across a large portion of the radio spectrum, drowning out nearby communications. The large spectral range covered means the efficiency in the desired frequency is quite low. To work out if a transmission is successfully jammed, calculate the received power of the transmission and the jammer signal at the receiver. If the jamming power is greater than the signal power, the signal is jammed and cannot be received correctly. Note that jamming signals can be beamed, in which case the jamming beam must be aimed at the intended receiver. A jammer cannot receive, nor transmit normal radio messages. If a combination normal radio/jammer is required, buy each component separately.
ELF
This option remains the same as described in GURPS Vehicles, Second Edition.
Laser
This option remains the same as described in GURPS Vehicles, Second Edition, with the additional note that a laser is beamed by default with an opening angle of 0.01 degrees. A lens may be used to spread the beam over any opening angle. A fixed lens, allowing the beam to be spread over one predetermined angle, costs \$10 and has negligible weight. A tunable lens, allowing the beam to be spread over any angle, costs \$1000 and weighs 1 pound. Note that laser communication is blocked by anything that blocks line of sight.
Neutrino, Gravity, FTL
These options remain the same as described in GURPS Vehicles, Second Edition. GMs are encouraged to modify these options to suit their campaigns.

Communicator Tables

Transmitter Table
TLWeightCostEfficiency
60.4\$4050%
70.2\$4090%
80.1\$2092%
90.05\$1094%
10+0.02\$596%
Options
Tight Beam*x5x5x1
Variable Beam*x10x10x1
VLFx10x10x1
Jammerx1x1x0.1
Cellular Phone**x1/x1.5x1/x2x1
Laserx1x5x1
Neutrinox120x400x0.1
Gravityx1x1x0.5
TLWeightCostThreshold
610\$200010-13W
75\$100010-14W
82\$50010-15W
90.5\$20010-16W
10+0.1\$10010-17W
Options
Cryogenicx2x2x0.1
VLFx10x10x1
ELFx100x100x1
Cellular Phone**x1/x1.5x1/x2x1
Laserx1x5x1
Neutrinox120x400x1
Gravityx1x1x1

Notes:

• A transmitter/receiver is built by buying the two components separately, though the actual device will be one physical unit.
• For the transmitter part, choose the power consumption in watts, then multiply the listed weight and cost by the power. If the power is greater than 1000 watts, multiply the cost by (900 + power/10) instead of the power. For the receiver part, choose the antenna area in square metres, then multiply the listed weight and cost by the area. If the antenna area is greater than 100 square metres, multiply the cost by (90 + area/10) instead of the area.
• * Refer to the descriptions of the Tight Beam and Variable Beam options for constraints on beam sizes and possible additional costs.
• ** Cellular Phone option is x1.5 weight and x2 cost at TL7, x1 weight and cost at TL8+.

Examples

1. We want to build a radio for the Kitty Hawk. We choose 10W of power consumption, which is 90% efficient at TL7. A cellular phone capability multiplies weight by 1.5 and cost by 2. We do not want beamed transmission, so take the omnidirectional default. The transmitter weighs 30 pounds, and costs \$800. We choose a standard-looking car aerial, with an area of 0.01 square metres, for the receiver, again with cell-phone option and a standard sensitivity. This adds 0.075 pounds weight and \$20 in cost.

The range of the Kitty Hawk's radio, transmitting to an identical radio receiver, is 846 kilometres, or just over 500 miles. However, the range will be limited by horizon considerations on Earth, unless shortwave frequencies are used.

2. We want a radio for a small TL10 "free trader" starship. We choose a 4 kW transmitter with variable beam option down to the default minimum opening angle of 0.01 degrees. The transmitter weighs 80 pounds and costs \$6500. We choose a non-cryogenic receiver with an antenna area of 10 square metres (covering a good portion of the ship's outer hull). The receiver weighs 1 pound and costs \$1000. The transmitter efficiency is 96% and the receiver theshold is 10-17 watts.

On omnidirectional broadcast, our ship can be heard by a similar receiver at a range of just under 17.5 million kilometres, or 11 million miles. The radio wave propagation time for this distance is about a minute. With a beamed transmission at an opening angle of 0.01 degrees, the range extends to 2689 astronomical units, or about 15.5 light days. A radiotelescope with an antenna area of a million square metres (a square kilometre) and cryogenic receivers could hear our ship at a range of 12.9 parsecs (though with a propagation delay of 40 years)!