In order to inject the probe into an intercept trajectory it needs some form of propulsion system. As discussed in Section 4 for a launch-on-demand probe the available launch systems are mainly designed to place a payload into low Earth orbit (LEO). The injection propulsion system must therefore provide the required delta-V to go from LEO to an escape trajectory with V_hyp sufficient to intercept a target at a distance of 0.05 AU within a timescale of at most a few weeks. This requires that V_hyp be at least 2 km/s and preferably higher to minimize mission duration.

Three main propulsion systems are available: solid, liquid and hybrid. All have advantages and disadvantages, as summarized below. Note that propellant efficiencies are compared in terms of specific impulse I_sp, the thrust per unit weight of fuel consumed per second.

• Solid Propellant systems are simple, consisting of a metal or composite case holding a solid charge. Once ignited the charge burns to provide a single impulse. Solid motors are reliable and moderately efficient, with typical I_sp of 290s. They provide a large thrust in a short time, which is advantageous in terms of providing an efficient impulsive burn but means that they can impose large structural loads and accelerations on spacecraft, especially low-mass ones.
• Liquid Propellant systems come in two varieties: monopropellant and bipropellant. Monopropellant systems use a fuel such as hydrazine (N₂H₄) or hydrogen peroxide (H₂O₂) that decomposes in the presence of a catalyst to give hot exhaust. Bipropellant systems burn separate fuel and oxidizer; they are more complex than monopropellant systems but are also more efficient. Monopropellant hydrazine has an I_sp of about 220s whereas hydrazine combined with nitrogen tetroxide (N₂O₄) oxidizer has an I_sp of approximately 300s. Higher-performance combinations are available (e.g. hydrogen/oxygen) but involve the use of cryogenic propellants. All liquid propulsion systems are more complex than solid-based ones, but are much more controllable and the thrust level can be selected by sizing the engine as required.
• Hybrid Propellant systems combine attributes of solid and liquid rockets. They usually use a liquid oxidizer such as liquid oxygen or hydrogen peroxide flowing over a solid fuel element. Unlike conventional solid motors they can be stopped and started again, but they are simpler than bipropellant liquid systems. I_sp is comparable to that of solid rockets, but as yet hybrid rockets are still at the research phase.

The performance of a propulsion system can be obtained from its I_sp (multiplied by standard gravitational acceleration g₀), its fuelled mass M_f, its empty or 'dry' mass M₀ and the payload mass M_p. From the rocket equation delta-V can be found:

(10-1)

For injection from LEO the resulting V_hyp for a given delta-V can be found from Fig 7-2.

Propulsion System Selection. All three types of propulsion system were potentially suitable for injecting to probe into its intercept trajectory. However hybrid systems, whilst very promising and the subject of research for just such applications by the University of Surrey small satellite programme [Sellers95], have not yet been space proven and as such it was not felt appropriate to specify them for such an experimental mission.

Injection via Solid Motor. Solid rocket motors have been built in sizes from a few grams to hundreds of tonnes. For this project though motors in the range 100-1000 kg offered appropriate performance. Several widely-used solid motors are produced in this size range, notably the Thiokol 'STAR' series. To evaluate their use a spreadsheet was set up to calculate the final V_hyp after boost from LEO for payload masses from 50 to 250 kg for a range of candidate rocket motors (Fig 10.1).

The rocket motors evaluated ranged in fuelled mass from 141 kg (a cluster of 3 STAR 13B motors) to 1149 kg (STAR 37FM). Data on motor I_sp and dry and empty mass was obtained from a range of sources [Larson92, Fortescue95, Jane's]. Although propulsion modelling was done at an early stage of the project, well before the final probe configuration had been arrived at, early estimates suggested that the injected probe mass was unlikely to be less than 100 kg, particularly as this must include attachment and separation fittings between the probe and motor. Examination of potential launch vehicles (Section 4) also indicated that mass in LEO should probably not exceed 1 tonne. Together with the requirement that V_hyp exceed 2 km/s these constraints eliminated most of the candidate motors as being too heavy or of insufficient performance. Four motors (MAGE 1S and 2, and STAR 30C and 30E) gave the required performance. So as to maximize probe design margins the STAR 30E was selected as the highest-performance of these motors. The characteristics of the STAR 30E are listed at Table 10.1.

The use of the STAR 30E allows a probe mass (inc fittings) of up to 230 kg, for which the total LEO mass is approx 900 kg. A probe mass of 140 kg would allow a V_hyp of 5 km/s, and 100 kg a V_hyp of 6 km/s. However, the high thrust of this motor would make its use with very low-mass probes problematical due to the high accelerations involved. On the worst-case assumption that motor peak thrust is at burnout a 100 kg probe would experience a peak acceleration of 292 m/s², or almost 30g. A 140 kg probe would experience 23g and a 230 kg probe 15.5g. Although these figures sound high they are low compared to those experienced by many missile systems and are not far beyond the accelerations associated with all-solid propellant launchers such as Scout [Jane's]. As a compromise 140 kg was chosen as a target probe mass, giving a V_hyp of 5 km/s, sufficient to reach 0.05 AU in 2½ weeks.

Injection via Liquid Motor. Although a wide range of liquid propellants have been used for space applications, either hydrazine (monopropellant) or hyrdrazine/N₂O₄ (bipropellant) tend to be the main choice. They are non-cryogenic and fairly dense (allowing small, light tankage) and a range of space-qualified motors exist that use them. They have the disadvantages of being toxic and awkward to handle, but safer propellant combinations such as hydrogen peroxide/kerosene have little recent space heritage.

An advantage of liquid propulsion systems is that they can easily be sized to meet the propulsion requirements. We can thus directly calculate the size of liquid-propellant boost stage needed to give the delta-V required. From Fig 7.2 the delta-Vs required from LEO for V_hyp of 2 km/s and 5 km/s are 3.4 km/s and 4.3 km/s respectively. The total mass ratio for a given delta-V is found by rearranging Eqn 10-1:

(10-2)

The ratio of upper stage mass to payload mass M_s/M_p is then found from

(10-3)

where f_f is the stage's fuel fraction, i.e. the fraction of its total mass that is propellant. For most rocket stages f_f is typically about 0.9 [Jane's]; assuming this we can calculate M_s/M_p for both hydrazine (I_sp = 220s) and hydrazine/N₂O₄ I_sp = 300s) as in Table 10.2.

The total mass in LEO is M_p(1+ M_s/M_p). For this not to exceed 1000 kg means that for a monopropellant hydrazine boost stage the payload mass would be limited to 40 kg for V_hyp = 5 km/s and 119 kg for V_hyp = 2 km/s. A bipropellant boost stage offers much better performance, allowing 168 kg to be accelerated to V_hyp = 5 km/s and 240 kg to V_hyp = 2 km/s. A bipropellant system, whilst more complex than one using monopropellant hydrazine, thus offers much better performance.

Hydrazine/N₂O₄ rocket motors are available in a range of sizes [Jane's] with 400N being a widely-used thrust (e.g. in communications satellite apogee motors) appropriate for this mission. Using a 140 kg probe and V_hyp = 5 km/s to allow comparison with the solid-propellant option gives an upper stage with a fuelled mass of 693 kg and a dry mass of 69 kg. With a 400N motor this results in a peak acceleration of 1.91 m/s² or only 0.2g. This clearly involves much less dynamic stress than the solid-motor burn and so would allow the probe's structural mass to be reduced. Unfortunately low accelerations also imply long burn times and mean that orbit manoeuvres can no longer be assumed to be impulsive. The propellant mass flow rate for a motor of thrust F is

(10-4)

i.e. 1.33 kg/s for a 400 N hydrazine/N₂O₄ rocket motor. The total burn time for a propellant mass of 624 kg is thus 468 s or almost 8 minutes. If necessary though this could be broken down into two shorter burns; the first would place the probe and boost stage into an elliptical orbit whilst the second, at perigee, would inject the probe into the required trajectory.

Choice of Injection Propulsion System. Both solid propellant and liquid bipropellant boost stages offer acceptable performance and mass for the probe mission. A liquid bipropellant stage has a low peak acceleration and is by nature accurately controllable. However it would have to be specially developed, poses extra safety and handling problems and may require a multiple-burn injection strategy for optimal performance. A solid-propellant stage is less accurately controllable than a liquid-propellant one and imposes much higher accelerations on the probe. However it is safer to handle, allows single-burn injection and is available in space-proven form.

Based on these factors it was decided to use a Thiokol STAR 30E solid propellant rocket motor as the boost stage for the probe. This simplified overall mission design but constrained probe mass to a maximum of 230 kg (with a target of 140 kg) and required that the probe be built to withstand a peak acceleration in excess of 20g.

Delta-V Error. One issue raised by the choice of a solid propellant motor is the delta-V error associated with it. Whereas the burn of a liquid propellant motor can be terminated once the required delta-V has been attained a solid motor will burn its entire propellant loading on one go.

Propulsion error figures for solid motors are hard to come by but the STAR-48 motor (larger than but of similar design to the STAR 30) is quoted as having a 1000 km 3-sigma error in injected apogee altitude when used as a perigee boost motor to inject satellites into geostationary transfer orbit [Jane's]. Assuming that this is from a 300 km parking orbit this equates to an error of about 17 m/s in the required delta-V of 2425 m/s, or a 3-sigma error of about 0.6%. For the purposes of this model it is assumed that this percentage error is constant for varying motor delta-V.

A non-nominal boost motor delta-V will have two effects. The direct effect will be a change in V_hyp; this change can be larger than the error in delta-V as a small change in velocity causes a large change in specific energy. The second effect is an indirect one in that a change in V_hyp will cause a change in the hyperbolic departure asymptote. This will result in an angular error between the actual trajectory direction and the intended one. The hyperbolic departure asymptote _hyp is the angle between the point of injection and the trajectory asymptote, as measured from the centre of the Earth. It is related to V_hyp by

(10-5)

where is the gravitational parameter of the parent body (i.e. Earth) and r is the radius at which injection takes place, which is that of the parking orbit.

For injection from a 200 km parking orbit to V_hyp = 5 km/s requires a delta-V of 4300 m/s. Fig 10.2a and b shows the effect of errors up to 0.6% (i.e. 26 m/s) in this delta-V on V_hyp and _hyp.

It can be seen that the error in V_hyp is about 3 times the error in delta-V and that for the 3-sigma error this produces a trajectory direction error of some 0.5° in addition to a V_hyp error of some 75 m/s. The combined effect of these errors would put the probe some 65,000 km wide and 115,000 km short or long of the intercept point at 0.05 AU. The magnitude of the velocity correction required at this point is approximately 85 m/s. The probe's on-board propulsion system must therefore be able to supply this trim delta-V.