Kerbalism: Transmission Rate vs Signal Strength

[VMQ]

Update: With Kerbalism 3.15 the DataRateDampingExponent value changed, affecting the science rate. See section at the bottom of the post.

 

The following section is based on Kerbalism 3.14, but the math is still correct.

I tried to make sense of the data rates shown and used by Kerbalism, see science rate 300kB/s in first picture below.

Now, if you are not interested in the formulas, just go to [1.8.x-1.11.x] Kerbalism Companion Calculator (KCC) - An antenna planner for Kerbalism [v1.3.0] [29th November 2020] and use the mod. If you are interested in the underlying math, keep on reading. As a bonus you get my measurements and theory about how relays affect the total data rate. 

First thing, all credit goes to Valentin Bischof who wrote the mod. I just looked at his code and compared it with what Kerbalism shows. The data rate depends on the signal strength as shown in the upper left corner in map or vessel view. See Mike Aben’s excellent tutorial about signal strength Ranges and Signal Strength | KSP Let's Do The Math. 

There are two settings that change the data rate. The Antenna Bandwidth factor (Antenna Speed) in the Kerbalism(1) Science settings.  Mine is set to 150%, but yours may vary. Secondly there is a DataRateDampingExponent in Kerbalism’s settings.cfg. It seems to be set to 6 by default.

Combining Antennas

Combining antennas changes the signal strength, see Mike Aben's tutorial, but it also changes the data rate. The combined data rate of the antennas on the vessel is calculated through:

With ABf the Antenna Bandwidth factor and AntRate the data rates of the active antennas this is the geometric mean of the data rates of the antennas. Careful, do not combine strong and weak antennas. A Communitron 16 with 2.2kB/s and a Communotron DTS-M1 with 25kB/s combine to 7.42kB/s, or 11.12kB/s with ABf = 1.5.

Data Rate

The total distance dependent rate can now be calculated by using the following formula:

With signal the signal strength and D the DataRateDampingExponent (= 6). This formula lets the data rate quickly deteriorate for signal strengths less than 100%. See plot for the factor that is multiplied with the combined antenna rate.

For example, to have more than 0.5 of the maximum transmission rate, one should have at least 90% signal strength.

 

Relays

The following is only loosely tested, so please let me know if you get the same results.

When going through a relay, the minimum of the total distance dependent rate of the vessel and the total distance dependent rate*ABf of the relay satellites involved is used (ABf = 1.5). I tested this with a relay in Mun orbit with a HG-5 relay antenna at 100% signal strength with 14.49kB/s (including the ABf) data rate and a direct antenna HG-55 with 200kB/s on a vessel.  With direct sight, the vessel achieves a data rate of 300kB/s (including the ABf), but in the Mun’s shadow the data rate drops to 21.74kB/s when the relay is used.

This looks like a small bug as the ABf factor is applied twice to the relay (9.66*1.5*1.5=21.74).

In a second test I had a Communotron 16-S at 96.63% signal strength on the vessel and the same faster HG-5 antenna on the relay, see picture below. The data rate to the relay was 2.69kB/s (agreeing with the formula above).

Changes in Kerbalism 3.15 and newer

In the newer version the DataRateDampingExponent setting was removed from Kerbalism’s settings.cfg. Now settings.cfg says:

Kerbalism will calculate a damping exponent to achieve good data communication rates (see KSP.log, search for DataRateDampingExponent)

According to my KSP.log the new damping coefficient is 14.034, but yours might vary.

Calculated DataRateDampingExponent: 14.0340 (max. DSN range: 250000000000, strength at 2 AU: 0.967)

A damping coefficient of 14 instead of 6 leads to significantly reduced science data range, see pictures below for comparison (left: D = 14.034; right: D = 6).

For further comparison here is a data rate vs. signal strength plot for D = 14:

For example, to have more than 0.5 of the maximum transmission rate, one should have at least 95% signal strength.

Restore behavior from Kerbalism 3.14

To restore the previous science data rate behavior, uncomment and change the following line in Kerbalism’s settings.cfg:

DampingExponentOverride = 6

Hope this helps someone to calculate science data transmission rates in Kerbalism.

Edited November 22, 2022 by VMQ
New Kerbalism version