Tetrahedron

[Hotel26]

An idea in the back of my mind for a long time has been spurred by a post by Zaznaczony in KerbalX...  I didn't quite dare to implement this, but now I am ready.

You can see the idea very graphically in this video, I made a year ago for PROJECT BOOTSTRAP.  Four relays in tetrahedral flight, angled 109.5 degrees apart like the bonding the carbon atom adopts.

So here's the craft I have just built, based on components from my DSRN-V, Beep, Scout and Terrapin craft -- it's called Tetrahedron:

It's all ion-drive, naturally (vide Hotel26 avatar), and comes packaged in a fairing with my standard 2.5m dock for attachment to a lifter and transit power unit.  (NB, shot above shows craft after one RA-2 has already been discharged.)

So the plan is that:

1. Tetrahedron is delivered into a high, circular, equatorial orbit around the target planet or moon;
2. the Terrapin drives Tetrahedron into a low, circular orbit with altitude being equal to the intended periapsis, L, of all satellites, in highly-elliptical orbits (where a circular orbit at L has a period less than 1hour);
3. this orbital period is divided by 3, giving P₃.  At time intervals, 0, P₃ and 2P₃, each RA-2 separates and uses ion power to perform a modest 19.5-degree ascending inclination burn.  These 3 orbits are now phase-shifted by 120 degrees;
4. those 3 orbits are then circularized at altitude L;
5. the Terrapin then drives the DSRN-V (RA-100) into a polar orbit (90-degree inclination change) and it, too, circularizes at altitude, L;
6. next: each RA-2 in turn, reaching it's highest latitude (19.5 N), performs a burn to extend its apoapsis, H, nearly out to the SOI of the target body, producing the most elliptical orbit possible;
7. finally, the RA-100, reaching the south pole, is also boosted to its desired apoapsis, an equal altitude as the RA-2s, i.e. H.

The result is 4 satellites orbiting in sync like this (except in the video, I did not bother precisely with the sync of the polar relay).

The polar relay is the RA-100 (poking up out of the ecliptic plane (over moons etc) and it connects the target body to the Deep Space Relay Network (DSRN), and it also covers the northern hemisphere.

The 3 RA-2s comprise the three, lower lobes, covering the equator and south pole, connecting to each other and to the RA-100, forming the local network.

The typical period of coverage is many days (~41d for Kerbin) as all satellites spend most time at high-to-very-high altitudes.  All satellites then go effectively out of service for a couple of hours while they dip through their zenith nadir and then "reboot".  The system outage is predictable, short and easy to plan for.

If steps 6 and 7 above are all completed within an hour, the system synchronization will be such that downtime is only around that long.  In addition, if the orbital periods of each of the four satellites are tuned within a fraction of a second of each other (use 0.5% thrust on the ion engines) then the system will hardly drift at all, thereby remaining in sync for years.

I'll be reporting back here with results after a test.  IF this succeeds, the pay-off will be a lighter, more compact version of my Scout to send to each of the 16 satellites of Kerbol (including the 3 in the Kerbin system),

Edited February 25, 2021 by Hotel26

[Hotel26]

All went well and the video below was made of the results of the test on Kerbin.

I'll be appending detailed instructions in a subsequent note in this topic.

Deployment on Kerbin requires the RA-2s to go into extended, elliptical first, followed by the RA-100 last.  This is in order to maintain contact with ground-stations and to provide communication at the South Pole, which is where the RA-100 makes its final orbit change.

At other locations in the Kerbol system, the polar RA-100 will go elliptical early in order to connect home to Kerbin and broadcast down to the equator, where the RA-2s will perform their orbit extension maneuvers at 19.5N.

 

In the case that ground stations are not in use on Kerbin, the RA-2s will have to first go into a standard 120-degree separation equatorial orbit to provide comm to the RA-100 as it makes its 14-minute 90-degree inclination change.

Detailed instructions to follow.  The description given in the Original Post is pretty close to accurate, however.

 

Edited February 25, 2021 by Hotel26

[Hotel26]

Tetrahedron: Instructions For Use

Using Kerbin as an example:

1. mount Tetrahedron on your own lifter and launch and deliver the package to e.g. 400km above Kerbin
2. zero the inclination
3. stage RA-2 separation
4. rename relay components: e.g KR0 RA-100, KR1 RA-2, KR-2 RA-2, KR3 RA-2, and set KAC timers on each (allowing them to expire without deletion) so that you can easily switch between relays
5. Note the orbital period, P, which will be roughly 56m.  Divide this by 3, giving P₃, 18m40s.
6. Switch time display (top left) from MET to UT and set a schedule for each RA-2 relay: +0, +P₃, +2P₃.  In my case, I select 5:50:0 (hms), 0:08:40 and 0:27:20 for inclination change maneuvers for KR1, KR2 and KR3.
7. execute an ascending node (northward) inclination change on schedule, each RA-2 in turn, aiming for an inclination of 19.5 degrees [90 (east) + 19.5 = 109.5 degrees from the North pole].  Don't forget to switch to UT time, commencing each relay's maneuver.  Also note that you may use Alt-period to warp time with physics, to speed up the duration of the ion burn.  For final tuning to a precise, 19.5000d, set the Dawn ion engine thrust limiter to 0.5% (lowest +ve setting)
8. for each RA-2 satellite, I now found it useful to wait until each reaches 19.5S and perform a very minor retro burn to establish the periapsis on the opposite side of the orbit, at 19.5N.  This is a good way to precisely mark the highest latitude of the orbit in preparation for the Orbit Extension Maneuver.  It's important not to de-circularize the orbit too much and it's also important to ensure that all RA-2s (and, later, the RA-100) have the same periapsis.
9. now proceed to separation of the RA-100 (still attached to the Terrapin ion driver).  Operating solo, it has a dV in excess of 9 km/s.  Begin a 90-degree ascending inclination change.  This maneuver may still take more than one pass to complete, so be prepared to limit each brun within the range, say, of a 10S..10N range of latitudes.
10. when the RA-100 reaches 90N, execute a short retro burn to lower the periapsis (to match those of the RA-2s).  This is to mark the location of the South Pole in the orbit, as this is where the future Orbit Extension Maneuver needs to be performed.  (This may actually be difficult to do unless one of the RA-2s is north enough for contact and has ground-station connection to KSC, but it can skipped or awaited on a subsequent orbit, as desired).
11. as the first RA-2 approaches 19.5N (its periapsis, for convenience for creating a maneuver node), fire prograde and extend apoapsis to 80Mm (just inside Kerbin SOI).  Note the orbital period, P_s.
12. as each subsequent RA-2 approaches 19.5N, execute a similar prograde burn to around 80Mm, but this time, target the same orbital period, P_s.
13. finally, as the RA-100 approaches its southern (90S) periapsis, execute the similar prograde burn, extending its orbit to match the same period, P_s.

Congratulations!  Your first tetrahedral relay system is now in operation.

Notes:

• For Kerbin, I place a second RA-100 [DSRN-V] into a southern orbit, but entering circular polar orbit (same periapsis as before), waiting until the northern RA-100 reaches apoapsis; then waiting until the southern RA-100 reaches the South Pole and there extending its apoapsis toward the 80Mm mark until its orbital period is also, P_s.  Since the Kerbin "Polar Link" is crucial in connecting other planets and moons with the KSC, having a second polar RA-100 in operation and 180-degree out of phase with the first, provides continuous operation for the rest of the system.
• Using the instructions above for all other planets/moons, I extend the orbit of the RA-100 before the RA-2s in order to "connect home", to enable comms for the equatorial RA-2s before they perform their own maneuvers.

Edited August 8, 2020 by Hotel26

[Hotel26]

For future reference (for Kerbin):

0:
    SMA = 42162782
    ECC = 0.98387
    INC = 90
    LPE = 270
    LAN = 0
    MNA = 0
    EPH = 0
1:
    SMA = 42162782
    ECC = 0.98387
    INC = 19.5
    LPE = 90
    LAN = 0
    MNA = 0
    EPH = 0
2:
    SMA = 42162782
    ECC = 0.98387
    INC = 19.5
    LPE = 90
    LAN = 120
    MNA = 0
    EPH = 0
3:
    SMA = 42162782
    ECC = 0.98387
    INC = 19.5
    LPE = 90
    LAN = 240
    MNA = 0
    EPH = 0

 

Edited October 4, 2020 by Hotel26

[Azimech]

Strange nobody took an effort to compliment on your work. Maybe the community is on a decline?

I must admit though, first time in many months that I'm actually here.