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CommNet
CommNet is a relay and control communication system implemented first in KSP 1.2 prerelease. Probes now have limited altitude and thrust control if they are not linked back to Kerbin or a control point via a relay antenna. ^{[1]} Antennae have limited range from which control and transmission of science data is possible.
Antenna Type  Tracking Station Level (Rating)  

1 (2G)  2 (50G)  3 (250G)  






























Please Note: The above table presumes only 1 antenna/relay is used on a vessel signalling back to Kerbin's DSN.
Contents
Range Calculation
Each antenna has a "power rating" (measured in unitless number). It ranges from 5k for the integrated CommandModule antenna available in every spacecraft, to 100G for the largest dishes. A connection can be established between two stations (craft to ground, or craft to relay) when the square root of the product of the strength ratings is greater than the distance between the two objects. When a craft has multiple, combinable antennas, the antenna's power ratings stack in a way that provides a diminished return using the following formula:
 Vessel Antenna Power = Strongest Antenna Power * ( Sum of Antenna's Powers / Strongest Antenna Power ) ^ ( Average Weighted Combinability Exponent for Vessel )
The range can then be calculated as stated above by taking the square root of the product of the two Antenna Strength ratings
 Range = SQRT ( Antenna Strength 1 * Antenna Strength 2 )
The Average Weighted Combinability Exponent for the Vessel can be thought of as the average of the sum of the combinability exponents of all combinable antennas on the vessel when weighted proportionally against their respective power level. This can be shown in the following way:
 SUM (( Antenna 'n' Power * Antenna 'n' Exponent ) : ( Antenna 'n+1' Power * Antenna 'n+1' Exponent )) / SUM ( Antenna 'n' Power ) : ( Antenna 'n+1' Power )
i.e. A vessel with a Comm 8888 (100e9 @ 0.75) and also a Comm 16 (500e3 @ 1.00) would have the following:
 (( 100e9 * 0.75 ) + ( 500e3 * 1.00 )) / ( 100e9 + 500e3 ) = 0.75000125 ... being the Weighted Average Combinability Exponent for the Vessel.
Please Note: All Antennas and Relays have a Combinability Exponent value of 0.75 except for the Communotron 16 having a value of 1 and the Communotron 16S having a value of 0. These values can be found in the part config files.
Signal Strength
To obtain your signal strength for a link at any given distance between the two points it is mostly the relative distance between the two points. The true calculation requires plotting the relative distance on a Bezier curve with they keys '0 0 0 0' and '1 1 0 0' to obtain the true Signal Strength. This can be calculated as follows:
 1  ( Distance away from 'Link Point' / Max Range of Antenna Link ) = 0 < x < 1 (as a fractional percentage)
 Substitute the result above into the Bezier Curve equation (Cubic derivation) of y = 2x³ + 3x² = (32x)x²
This will give you the Signal Strength between the link at your specified distance.
Example
Calculating the Signal Strength between a Level 3 DSN Tracking Center and a probe around Jool at a distance of 73.4Gm from Kerbin with two Communotron 8888 antennas.
 Max Power of Lvl 3 DSN connection: 250,000,000,000
 Max Power of Probe: 100,000,000,000 * (200,000,000,000 / 100,000,000,000)^0.75 = 168,179,283,051
 Max Range of Connection: SQRT( 2.5E11 * 1.68E11 ) = 205,048,337,625m
 Relative distance between Link Points: 1  ( 73.4 / 205 ) = 0.642
 Signal Strength: y = (32x)x² = (32(0.642))*(0.642)² = 0.707 = 71%
Therefore the Signal Strength for this connection would be 71%.
Connections through Relays
When considering the antenna power of your vessel, Direct Antennas and Relay Antennas combine to give you a 'Power' to calculate Signal Strength back to the KSC, however, if a different vessel is connecting through you to communicate with the KSC the Direct Antennas are disregarded in any calculations made.
Example
 A vessel with a Communotron 8888 Direct Antenna and a RA100 Relay Antenna orbiting around Eeloo at a distance of 105Gm from the KSC, with a Level 3 DSN, will connect back to the KSC with a Signal Strength of 48% as both antennas combine to give an increased antenna 'Power' for its own direct connection.
 A vessel rendezvoused with the above craft with a measly Communotron 16 will have to communicate back to the KSC through the relay as its antenna is not strong enough to communicate with the KSC directly. As this small, probe craft will only consider the RA100 Relay Antenna on the relay craft when calculating its connection back to the KSC, the power rating of the relay vessel drops and therefore the Signal Strength will drop to 26% (please note the calculations for these numbers have been obfuscated from the example for easy understanding of the concept).
Please keep the above in mind when creating relay vessels for you other craft to connect through in the depth of space.
DSN Strength
Each upgrade of the tracking center improves the strength of Kerbin's terrestrialbased Deep Space Network (DSN). Based on the provided figures, the Level 1 tracking station has an antenna strength of 2G, Level 2 is 50G, and Level 3 is 250G.
Science Transmission
The same document from the KSP developers states that science returned via a relay satellite will have a bonus applied (some fraction of the difference between the recovery and transmission science potential). The exact amount of the bonus depends upon signal strength. The amount of available Science Points you can transmit back to the KSC depends on your Signal Strength and the total potential value of the experiment.
Any experiments transmitted will be multiplied by the percentage of your connection, therefore an EVA Report high over the Mun (24 Science) at a Signal Strength of 68% would allow you to transmit a total of 16 Science points back to the KSC.
Difficulty Settings
Range Modifier = The value of this slider is a multiplier value that is applied to the power levels of all Antenna and Relay parts.
DSN Modifier = The value of this slider is a multiplier value that is applied to the power level of the DSN Network.
Tutorials, Calculators and Examples
A Google Sheets document that can help calculate Signal Strength and Ranges for you can be found here: CommNet Signal Strength Calculator & Antenna Selector
Example orbits for setting up a planetary network can be found at: Tutorial:Ideal Orbits for Communication Satellites
One method of setting up a fullsystem network can be found at Tutorial:Setting up a CommNet system.