P3D Launch Sequence Study (Part I)

Started: September 1, 1996 -- Last Update: December 5, 1996

Viktor Kudielka (ÖVSV P3D Mission Analysis Project)

Introduction

This document is intended as a base for discussion of alternative launch sequences of P3D.

Start Data

Nominal DeltaV

  1. Arc-jet first: 4750 .9 ln(400/350) + 3000 .9 ln(350/200) = 571 + 1511 = 2082 m/s
  2. Bi-prop first: 3000 .9 ln(400/250) + 4750 .9 ln(250/200) = 1269 + 954 = 2223 m/s
  3. 1/2 arc-jet, 1 bi-prop, 1/2 arc-jet: 4750 .9 ln(400/375) + 3000 .9 ln(375/225) + 4750 .9 ln(225/200) = 276 + 1379 + 503 = 2158 m/s

Scenario A

Motto: ``Gut Ding braucht Weile'' == ``Rome wasn't built in a day''

This scenario represents a first attempt to design a proper sequence of orbital manoeuvers for achieving a satellite lifetime of 20 years and longer. The major challenge is to properly use the two very different propulsion systems for achieving this goal.

First Drift Phase

Without any major manoeuver (i.e. change of inclination) the perigee of the initial GTO will drift from its initial value of 178° through 180° and further on to 360°, with a rate of about 0.77°/day. We want to arrive at an orbit with a 16 hour period, an inclination of 60°(+/-3° depending on the then current longitude of the ascending node (RAAN)) and an argument of perigee (ArgP) of about 315°(see ``Drifting P3-D Orbits: Perigee at 225° or 315°?''). A major inclination change can be done with a minimum of deltaV only at apogee, that is, when the perigee is near 0° or 180°, and the orbital period as well as the eccentricity are as high as possible. Since an ArgP of 180° will be reached already within a few days after start, there will be not enough time to do orbit and attitude determination, checking all mechanical and electronic systems, adjusting attitude and spinning up the satellite. Consequently the inclination change has to be done near an ArgP of 0°/360° The final goal of ArgP=315° can be reached now faster, although with a higher total deltaV, than from an ArgP of 180°. Until ArgP=360° is reached, the orbital period can be increased in a step-wise fashion with the arc-jet. But with a major restriction. The sun angle of the satellite (with the solar panels still in the initial position) must be low enough for recharging the batteries. The example presented in this chapter relies on the following assumption:

The following example assumes a start date of April 21, 1997 and a GTO RAAN = 200°. In figure A.1.1A the usual four Kepler elements (inclination, eccentricity, argument of perigee, RAAN) are shown, figure A.1.1B includes diagrams of the sun angle, the orbital period and the current mass. In this example the initial conditions are such, that the orbital period can be increased up to the target of 16 hours only in two intervals, due to the unfavourable sun angle between day 70 and 180 after start. The first firing of the arc-jet is planned for orbit #51, assuming all initial testing, spinning up and adjusting the attitude has been done successfully. Before reaching the 16 hour orbital period, the last one or two burns of the arc-jet have to be very carefully timed, in order to achieve the exact orbital period. Otherwise a correction can be done later also.

The deltaV requirement is around 191 m/s, with the crude assumption of a .9 efficiency for the geometric misalignment at perigee for one hour burns.

Major Inclination Change

The major inclination change will take place near ArgP=360°. The example shows one initial small inclination change for calibration purposes, four inclination changes with equal deltaV, and one final adjustment to reach an inclination of 70°. All these motor burns are assumed to take place at apogee, with the attitude such that the total velocity is not changed and the geometry of the orbit (semi-major axis and eccentricity) remains the same.

The assumption is here, that orbit determination, attitude determination and attitude adjustment can be done within two orbital periods (two perigee passes). This is a very tight schedule and has to be verified.

Orbit ArgP sma ecc inc HeightPer HeightApo VPer VApo deltaV
# deg km deg km km m/s m/s m/s
550 359.09 32252 0.7826 07.64 632 51116 10068 1228 000
551 359.60 32252 0.7827 10.65 632 51116 10068 1228 064
553 000.15 32252 0.7826 23.66 633 51115 10067 1228 278
555 000.44 32252 0.7825 36.67 637 51111 10064 1228 278
557 000.59 32252 0.7823 49.67 643 51105 10059 1229 278
559 000.62 32252 0.7821 62.65 650 51098 10054 1229 278
561 000.58 32252 0.7820 70.02 654 51094 10050 1230 159

Total deltaV = 1335 m/s

For comparison changing inclination by 63° would need a single impulse of 1284 m/s, without changing height of perigee but with the risk of a fatal accident when the burn is interrupted.

Second Drift Phase

After reaching i=70°, ArgP will drift between -0.04 and -0.05°/day, depending on the actual value of RAAN. For the majority of cases the eccentricity will decrease continuously - with half-year periodic variations - until the target of ArgP=315° is reached. But for a certain range of RAAN the eccentricity will increase first before decreasing again. In the worst case encountered in simulations so far, the height of Perigee will drop from initially 500 km to less than 100 km before increasing again. This is certainly unacceptable. In case a similar situation will be caused by the start date and time, a higher perigee has to be achieved at the end of the inclination change. Inclination will change during this second drift phase between +4.5° and -1.0°, depending on the initial RAAN.

In our example the satellite will drift until an ArgP of 320° is reached at orbit #1915. The inclination has increased to nearly 74°.

Final Inclination Change

This inclination change (assumed to be done with the arc-jet) is even more dependent on the RAAN than the previous phases. The actual necessary change in inclination might be between -6° and -17°. Due to the ArgP around 315°, the required deltaV is higher than for similar inclination changes at ArgP=0° or 180°.

Simulation of other cases show, that we have to consider the major and the final inclination change, including the second drift phase, as a whole. When the final inclination change would be too high, the major inclination change has to be reduced. The second drift phase would then last longer. Another possibility is still, to increase the orbital period beyond 16 hours for the inclination changes. Also the ArgP at the beginning of the final inclination change can be properly chosen for an optimal final drift phase.

The major problem with this second inclination change is the mechanical configuration. After the major inclination change the satellite will be despun and the solar panels will be unfolded. The center of gravity will no longer be on the central axis aligned with the two motors. Some strategy, a combination of short arc-jet burns together with proper actions of the momentum wheels at the descending node and unloading the momentum wheels by magnetic torquing around perigee, has to be developed, considering also the power budget.

The considerations which led to the proposed ``final'' orbit are documented in ``Drifting P3-D Orbits: Perigee at 225° or 315°?'', which is the English version of an article which appeared in AMSAT-DL Journal, Vol.21, No.4, pp. 33-40, Dec. 1994. A slight modification of the proposal might reduce the deltaV requirements. The final inclination change could be done already around 325° or 320° and the inclination adjusted such that the ArgP drifts within a range from 330° and 300°. Examples for four different values of RAAN are shown in figures A.5.1 (RAAN = 0°), A.5.2 (RAAN = 90°), A.5.3 (RAAN = 180°), and A.5.4 (RAAN = 270°), with an assumed begin date of August 2000. From these examples it is evident, that the "optimal" inclination for the final drift phase should be reached with an accuracy of .1 ° or .2°.

In our specific example we start at an ArgP of 320° (orbit #1915) and assume half hour burns of the arc-jet at the descending node every orbit until orbit #2955, when we reach an inclination of 61°, a value chosen from different simulations for the begin of the final drift phase. The deltaV required for this final inclination change is 477 m/s.

We can show now diagrams for the whole period of propulsive action. In figure A.1.2A the four Kepler elements (inclination, eccentricity, argument of perigee, RAAN) are shown, figure A.1.2B includes diagrams of the sun angle, the orbital period, the current mass, and an expanded view of the ArgP at the major inclination change. Figure A.1.2C shows the height of perigee.

Final Drift Phase

The final drift phase is shown in figures A.1.3A and A.1.3B. We can expect an ArgP between 320° and 300° for nearly twenty years, and afterwards the ArgP will move to 270°, at least for stations in the northern hemisphere quite acceptable. And, since the height of perigee is increasing from 3000 km to over 14000 km, stations in the the southern hemisphere are also served.

Summary -- Scenario A

Scenario B

This scenario represents an attempt to reach the final drift phase much faster than with the approach of scenario A. The intent is to have a similar initial drift phase but only until an ArgP of around 315°. During this drift phase the orbital period will be increased stepwise to 16 hours. Then follows immediately the major inclination change at the descending node to the proper inclination for the final drift phase. This inclination change is, in terms of deltaV, much more expensive than at apogee. This will be the price for an earlier three-axis-stabilised operation.

Initial Drift Phase

A start date of April 21, 1997 is assumed, as in scenario A. Since the major inclination change will take place already at ArgP=315° and not at 360°, the increase of the orbital period has to be started earlier (orbit #25), leaving only about ten days for initial testing and spinning up the satellite. The deltaV requirement for the initial drift phase is identical to that of scenario A, 191 m/s. Figures B.1.1A and B.1.1B show the four Kepler elements (inclination, eccentricity, argument of perigee, RAAN) and sun angle, orbital period, and satellite mass for the initial drift phase.

Major Inclination Change

With orbit #429, on day 232, an ArgP of 315° is reached and the inclination change can begin. With three inclination changes of 3°, 28°, and 22°, which will need deltaV's of 118, 1127,and 938 m/s respectively, an inclination of 60° can be reached.

Final Drift Phase

The final drift phase is shown in figures B.1.3A and B.1.3B. Although the initial inclination for the final drift phase is most probably not yet "optimal", the overall trend can be seen. ArgP will increase for about three years and then decrease continuously, passing through 270° - after 14 years - and finally through 180°. The apogee will remain over the northern hemisphere for thirty years. The height of perigee will vary between 2000 and 12000 km.

Summary -- Scenario B

Although the total deltaV of this example is beyond the assumed capabilities and also the balance of the two motors/propellants is not achieved, this example will be a base for further refinements.

Scenario C

This scenario is intended to investigate possibilities to reduce the deltaV requirements of scenario B by moving the inclination change towards the apogee, to ArgP = 330°. This causes some deviation from the initially assumed target range for the ArgP of 315° +/-15°.

Initial Drift Phase

The initial drift phase is similar to that one of scenario B. Only the start of the orbit period changes can be delayed to orbit #45 (day 21).

Major Inclination Change

The major inclination change is done here in five steps like scenario A, compared to the three steps in scenario B. The direction of the impulses is assumed to have an along-track and an out-of-plane component only. Since the inclination change does not occur at 0° or180°, we get changes in eccentricity also.
Orbit ArgP sma ecc inc HeightPer HeightApo VPer VApo deltaV
# deg km deg km km m/s m/s m/s
459 330.13 32252 0.7847 7.108 565 51182 10122 1221 0
460 330.35 32252 0.7844 10.11 577 51170 10113 1222 95
462 330.22 32252 0.7846 24.83 891 50856 9864 1253 465
464 330.03 32252 0.7846 39.56 1214 50534 9625 1284 471
466 329.7 32252 0.7543 54.3 1545 50202 9394 1316 477
468 329.74 32252 0.7531 59.08 1584 50164 9368 1319 155

Total deltaV = 1663 m/s

Final Drift Phase

The final drift phase is shown in figures C.1.3A and C.1.3B. Due to the slightly different initial inclination compared to scenario B we get a drift of ArgP first to about 345° and then back to 270° after about 25 years.

Summary -- Scenario C

Scenario D

In scenarios B and C the inclination changes have been done by assuming along-track and perpendicular-to-orbit velocity changes only. This causes not only changes in inclination, but also minor changes in the other orbital elements, notably in eccentricity. To preserve the precise orbital configuration and change inclination only, also a small radial velocity change is necessary. Scenarion D implements such a more sophisticated manoeuver. The constant height of perigee (500 km) will improve the magnetic torquing manoeuvers for the neccessary attitude changes.

The major inclination change takes place at ArgP = 320°. This requires an earlier start of the orbit period changes and also an increased deltaV, compared to scenario C. The advantage is an earlier three-axis stabilised operation.

Initial Drift Phase

Orbit period changes start with orbit #15 (day 8).

Major Inclination Change

Orbit ArgP sma ecc inc HeightPer HeightApo VPer VApo deltaV
# deg km deg km km m/s m/s m/s
428 320.12 32248 0.7855 6.991 539 51201 10144 1219 0
429 320.49 32248 0.7855 10.00 540 51199 10142 1219 117
431 321.15 32248 0.7853 25.02 545 51195 10139 1219 576
433 321.64 32248 0.7851 40.03 550 51189 10134 1220 570
435 321.93 32248 0.7850 55.03 555 51185 10130 1220 566
437 322.02 32248 0.7849 59.03 558 51181 10128 1220 151

Total deltaV = 1980 m/s

Final Drift Phase

The final drift phase is shown in figures D.1.3A and D.1.3B. The apogee remains over the Northern hemisphere for more than thirty years.

Summary -- Scenario D

Scenario E

Scenario E shows the reduction of total deltaV by an increased orbital period for the inclination change. The drawback is a longer time span for re-adjusting the orbital period to 16 hours.

Initial Drift Phase

Orbit period changes start with orbit #15 (day 8). 1.5 hour burns of the arc-jet at each perigee has been assumed. With such an strategy the orbital period can be increased to 22 hours before reaching an ArgP of 325°. Figures E.1.1A and E.1.1B show this drift phase. A correction for the efficiency for the longer arc-jet burns (1.5 vs. 1.0 hours) has not yet been applied.

Major Inclination Change

The major inclination change has been moved slightly to 325° in order to allow the arc-jet to achieve the orbital period of 22 hours.
Orbit ArgP sma ecc inc HeightPer HeightApo VPer VApo deltaV
# deg km deg km km m/s m/s m/s
435 325.20 39888 0.8257 7.358 576 66444 10229 977 0
436 325.51 39888 0.8255 10.36 582 66438 10225 977 94
438 326.10 39888 0.8254 25.38 587 66433 10221 978 461
440 326.56 39888 0.8254 40.39 587 66433 10221 978 455
442 326.86 39888 0.8254 55.43 587 66433 10221 978 452
444 326.97 39888 0.8252 59.00 594 66425 10215 978 106

Total deltaV = 1568 m/s

Adjustment of orbital period

Figures E.1.2A and E.1.2B show the whole powered flight period.

Final Drift Phase

The final drift phase is shown in figures E.1.3A and E.1.3B. The apogee remains over the Northern hemisphere also in this scenario for more than thirty years.

Summary -- Scenario E

Dr. Viktor Kudielka, OE1VKW
viktor.kudielka@ieee.org