For the probe to carry out its mission it is essential that it be able to point itself accurately. Numerous phases of the mission, from the trajectory correction manoeuvres to the flyby and data downlink to Earth involve the probe orienting itself to a new attitude and maintaining it to a fraction of a degree. Indeed, if the encounter requires a slew manoeuvre then the probe must accurately be able to control a steady attitude rate. The probe's attitude control system must also be able to carry out the trajectory correction manoeuvres required to ensure an accurate flyby of the target.

An attitude control system consists of a feedback loop with 3 elements; a sensor (to determine attitude error), a control system to determine the required response to any error and an actuator to implement the response. The control system is provided by the spacecraft computer (see Section 13) so we must consider sensors and actuators.

Sensors. For a spacecraft in deep space the usual attitude sensors are star trackers. These track a star, or for more modern trackers a pattern of stars, and from the position of the image(s) determine the orientation of the spacecraft [Piscane94]. Modern star trackers use sensitive CCD arrays to image many stars simultaneously and can provide very accurate pointing data. The star sensors on Clementine, together with special star-pattern matching software, allowed it to determine its attitude to within 0.03° within 100 ms [Wertz96]. Two such star trackers - one facing along the probe's axis and one radially outward - would provide the necessary attitude control data, with a combined mass of 0.6 kg. The star trackers would have to cope with the thermal-control roll during cruise flight, but for the roll rate envisaged (circa 0.5 rad/s) this would take the form of a slow image rotation for the axially-pointing tracker and should be acceptable.

Other sensors often used on spacecraft include Sun sensors and rate gyrometers. The use of these would add redundancy to the attitude control system and would also allow easier measurement and control of quantities such as slew rate. For this initial design though it was assumed that star trackers would suffice for general attitude monitoring whist the main imaging payload would be used as an additional sensor during the encounter phase.

Actuators. Two principle types of actuator are available for spacecraft in deep space: reaction wheels and thrusters. A spacecraft using one or more reaction wheels requires the use of thrusters anyway to perform off-loading, but the use of reaction wheels makes fine attitude control easier and, if they are run as momentum wheels (i.e. with a non-zero nominal speed) they provide dynamic rigidity via momentum bias.

For this mission it was decided that in accordance with the policy of avoiding mechanisms wherever possible reaction or momentum wheels would not be used. The mission's short duration means, though, that fuel supply is not a major issue.

The attitude control requirements of the probe's mission can be broken down into the following tasks:

• Despin, repoint and spin up to cruise spin after boost motor separation.
• Despin, point for trajectory correction manoeuvre, repoint and spin up, repeated for each TCM.
• Despin and repoint prior to flyby.
• Slew control during the flyby.
• Repoint and spin up with antenna Earth-pointing for data download.

An initial estimate of the mass moment of inertia of the probe, based on a rough mass budget and the approximate structural design, was 20 kgm². As regards manoeuvres, the following assumptions were made:

• Spin during boost motor firing would be 60 rpm (typical for apogee boost motor firings on communications satellites).
• Cruise spin would be 5 rpm, or approx 0.5 rad/s. This figure is fairly arbitrary but should provide for reasonably even thermal control.
• Repointings for TCMs are at most 2 rad and are carried out in about 100s.
• The mass moment of inertia I used for all repointing calculations would be that around the spin axis, as this will be the largest I for the probe.
• The slew comprises a slew up to the peak slew rate and then down again. For a 20 km/s flyby at a range of 100 km this will be 0.2 rad/s. In fact the peak rate will be less than this as the probe does not track the target all the way to closest approach so this is an over-estimate.

The torque increment delta-T for changing the angular speed of an object of mass moment of inertia I by delta-omega rad/s is

(11-1)

whilst the torque required to repoint the same object by angle theta in time t is

(11-2)

For the manoeuvres described above the torque increments are as in Table 11.1.

It was estimated in Section 7 that 5 TCMs would be required. Each TCM requires a spin down from and then up to 5 rpm and a repointing manoeuvre for a combined delta-T of 20.016 Nms. The delta-T budget can thus be calculated as per Table 11.2, giving a total of 248.816 Nms.

The amount of fuel that this will require can be calculated from the impulse requirements to achieve this torque. The radius of the final configuration of the probe was 0.5 m, so a total impulse of 493.632 Ns is required for attitude control tasks. Impulse is simply the product of fuel mass and specific impulse, so the fuel masses required to achieve this for the 2 main liquid propellant thruster types are:

• Monopropellant hydrazine (I_sp = 220 s): 2.24 kg
• Hydrazine / N₂O₄ (I_sp = 300 s): 1.65 kg

To this must be added the fuel required for trajectory correction. In Section 7 a total delta-V requirement of 170 m/s was estimated. Eqn 10.2 gives the propellant to dry mass ratio required for a given delta-V; for the maximum probe mass of 140 kg the resulting propellant requirements are:

• Monopropellant hydrazine: 10.90 kg
• Hydrazine / N₂O₄: 8.08 kg

Adding these together gives a total thruster fuel budget as follows:

• Monopropellant hydrazine: 13.14 kg
• Hydrazine / N₂O₄: 9.73 kg

Reaction Control System Design. The thrusters, propellant tanks and associated lines and ancillary equipment form the reaction control system (RCS). In order mainly to estimate its contribution to the probe's mass budget a basic design for the probes RCS was carried out. This covered propellant selection, overall system design and mass budgeting.

Propellant Selection. Both monopropellant and bipropellant systems have their advantages and disadvantages. As was seen earlier, a bipropellant system, because of its higher I_sp, requires a smaller propellant mass. However it also requires additional propellant lines and valves whilst the differing masses of hydrazine and N₂O₄ required make it more awkward to maintain the position of the centre of mass of the RCS. A study by the University of Surrey into propulsion systems for small satellites concluded that the advantages of bipropellant systems outweighed their problems even for small spacecraft [Wertz96]. For this mission study though, where design simplicity was a major concern, the lower performance of a monopropellant hydrazine system was accepted to allow the use of a less complex RCS.

RCS Configuration. For full attitude control the RCS must provide for positive and negative sense thrusters in all three axes, for a total of 12 thrusters. In theory opposed thruster pairs could be used for TCMs but given the large size of these manoeuvres it was decided to use a separate TCM thruster. A number of monopropellant hydrazine thrusters are available with 20 N nominal thrust [Larson92, Jane's]; such a thruster could complete the worst-case initial TCM of 85 m/s in under 10 minutes. The attitude control thrusters would be smaller, e.g. 0.5 N. Two such thrusters mounted on the probe's circumference, i.e. 0.5 m from the axis of rotation, would take 2 minutes of continuous operation to despin the probe from 60 rpm, or longer if used in pulsed mode for more accuracy.

For the sake of redundancy two separate attitude thruster strings should be provided. It was decided not to provide a redundant TCM thruster as if necessary pairs of attitude control thrusters could be used in this role, although as mentioned above this should only be a fallback measure. A baseline design for the RCS meeting these requirements is shown at Fig 11.1. Note that 2 cross-connected tanks are used so as to allow the position of the centre of mass of the system to be maintained without having to keep a single fuel tank centrally-located.

This configuration follows the safety guidelines quoted by the University of Surrey study and provides for redundancy for each thruster and string of thrusters.

Mass Budgeting. The mass of the fuel tanks can be calculated from their volume and wall thickness, the latter being driven by the operating pressure. As this is a direct blowdown system the tank pressure will be the operating thruster pressure; this is typically 6-20 bar [Larson92].

The fuel requirement calculated earlier was 13.14 kg of hydrazine. Although this calculation was itself quite conservative it was decided to add a further margin of around 20% and carry 16 kg of fuel, i.e. 8 kg per tank. In order to avoid too much fuel thruster performance variation it was also decided to keep the tank pressure variation to no more than a factor of 3, which required an initial gas pressurant volume equal to the half the fuel volume. Hydrazine has a density of 1.0 kg/m³ so each tank has a volume of 12 litres. For spherical tanks this gives a diameter of 28.5 cm. The mass of 4 litres of nitrogen pressurant at a nominal temperature of 275K can be found from the gas law:

(11-3)

where R is the gas constant for nitrogen, 296.8 J/kgK. This gives a nitrogen mass of 98 g per tank, of 196 g in total.

The tank wall thickness is limited by the stress imposed by the internal pressure. For a spherical tank of radius r and thickness t with internal pressure p the stress sigma is given by

(11-4)

For an aluminium tank designed such that is kept 100% below the tensile strength limit the wall thickness is found to be 0.61 mm, giving a mass of 0.467 kg per tank. Allowing for tank fittings and supports a tank dry mass of 1 kg was thus assumed.

The total mass budget for the RCS is given at Table 11.3. Masses for components such as valves are taken from the University of Surrey study, whilst thruster masses are based on commercially available units [Jane's].

Summary and Design Issues. The attitude control system as presented here uses star trackers and, during the flyby, the payload imaging system as sensors and a monopropellant hydrazine reaction control system as actuator. The RCS is a dual-string system with a separate 20 N thruster for trajectory correction. It provides 170 m/s delta-V and the attitude control requirements for the mission.

This particular attitude control configuration has sufficient propellant budget and control authority to carry out the attitude control tasks required of it. However, a more detailed design study should involve modelling of the dynamics of the system (an area which has been neglected in this analysis) to ensure that such manoeuvres can be carried out with the required degree of accuracy. In particular there are two issues which such further work should consider:

Sensors. As mentioned, the attitude control system specified uses star trackers and the main imaging sensor to provide attitude data. As an important part of the mission profile (the target encounter slew) involves accurate measurement of spacecraft angular rates further study should assess whether specific rate sensors such as gyroscopes should be used. A number of compact solid-state gyroscope systems (e.g. ring laser gyros) have been developed that are potentially suitable for use on small spacecraft [Fortescue95].

Actuators. The encounter slew in particular also requires very fine attitude and angle rate control. There is a risk in using thrusters that successive impulses may result in the probe's attitude 'hunting' around the required slew. Although the RCS contains ample fuel to allow for this such behaviour would be undesirable and could compromise imaging. As such a more detailed study should address the dynamics of fine attitude control. One approach could be to use extremely small thrusters operating on cold gas. These can operate down to thrust levels of circa 10^-2 N [Fortescue95] and would have the added advantage of avoiding possible sensor contamination at the critical phase of the mission. Given the short duration of the encounter slew the required gas supply could be provided from the main RCS pressurant. An alternative approach would be to evaluate fully the use of a reaction wheel. Although not considered in this study because of the desire to avoid mechanisms where possible such a system may prove attractive on further analysis for providing fine slew control.