3.5.46 · D5Guidance, Navigation & Control (GNC)
Question bank — Reaction control system — thruster selection, plume impingement limits
The vocabulary assumed below — thruster, wrench , allocation matrix , couple, keep-out cone — is all defined in the parent note. If a symbol here feels unearned, that is your cue to re-read the parent before answering.
True or false — justify
A single offset thruster produces a pure torque.
False. It produces torque and net force , so the ship also drifts; you need an opposing thruster to form a torque-only couple.
Firing every thruster maximizes control authority.
False. Authority is about the net wrench ; extra jets often add unwanted force or cancel torque, so the useful net can shrink even as grows.
A thruster whose force line passes through the center of mass gives no torque.
True. Then , so ; it is a pure translation thruster.
You can reverse a thruster's push by commanding negative on-time.
False. Thrust is one-sided, — a jet can only push. To get the opposite direction you fire a different, oppositely-mounted thruster.
Halving the distance to a surface doubles the plume pressure it sees.
False. Pressure falls as , so halving quadruples the pressure — the danger grows fast up close.
An on-axis surface () always sees the harshest plume for a given distance.
True. The shape function peaks at where ; every off-axis angle gives , so on-axis is worst case.
The plume impingement constraint is a hard on/off rule, not something to optimize.
Partly false. It is enforced as a hard keep-out (inhibit thrusters that violate limits), but the remaining selection is still a minimum-propellant optimization over allowed jets.
Two thrusters forming a couple produce zero net force.
True. Equal, opposite forces cancel () while their torques add, giving pure rotation with no drift.
Plume force can act as a disturbance torque on your own maneuver.
True. Impingement on an offset surface (a panel, the ship's own belly) applies a force at a lever arm, producing a torque that fights or corrupts the commanded wrench.
A tighter plume (larger ) is more forgiving for nearby surfaces off-axis.
True in the off-axis sense. Larger makes drop faster with angle, so off-axis surfaces see less pressure — but the on-axis peak () is unchanged, so anything dead-ahead is no safer.
Spot the error
" thrusters means the allocation problem has no solution."
Error. More thrusters than DOFs makes the solution non-unique (many hit the same ), which is why we optimize — it is over-determined-free, not unsolvable. See Control Allocation & Pseudo-inverse.
"Torque equals force times mount distance, always ."
Error. Torque is , whose magnitude is where is the angle between lever arm and force. Only the perpendicular component of the lever arm matters; radial thrust gives zero. See Cross Product & Rigid-Body Torque.
"The plume vanishes at the nozzle exit because we're in vacuum."
Error. In vacuum the exhaust is under-expanded, so it keeps fanning out into a widening cone — it spreads more, not less, and reaches distant surfaces.
"Minimizing is nonlinear because thrust involves exhaust velocity squared."
Error. For a fixed , both force and propellant mass-rate scale linearly with on-time/throttle, so the objective and constraints are linear — a linear program.
"If a thruster is inhibited, the commanded wrench simply cannot be achieved."
Error. Redundancy usually lets other thrusters (e.g. off-axis pairs) reproduce the same , just at a propellant penalty — the point of an over-actuated cluster.
"Heat flux and pressure impingement give the same keep-out limit."
Error. They are separate constraints ( and ); a geometry can pass one and fail the other, so both must be checked. See Rarefied Gas Dynamics / Plume Modeling.
"A gimballed engine would always beat a fixed-thruster cluster."
Error. Gimbals are heavy, slow, and a single point of failure. A fixed cluster is redundant, fast on/off, and can torque about any axis by combining jets.
Why questions
Why must RCS thrusters come in opposing directions?
Because thrust is one-sided () — you cannot reverse a jet, so the only way to push the opposite way is to mount a second thruster aimed the opposite way.
Why does the cross product appear in the torque term?
Torque is lever-arm-times-force, and the cross product automatically extracts the perpendicular leverage and gives the rotation axis — exactly what "twist about a point" means. See Attitude Dynamics — Euler's Equations.
Why does plume density fall as rather than ?
Mass is conserved through expanding spherical shells; each shell's surface area grows as , so the same flux spread over that area thins as .
Why is plume impingement especially critical during docking?
The target vehicle can sit only a couple of metres ahead, right where makes pressure large and where an on-axis forward thruster points straight at it, so limits are easily violated. See Rendezvous and Docking.
Why does inhibiting a thruster sometimes cost extra propellant?
The optimizer loses its most efficient combination and must reproduce the wrench with a less-aligned subset, so more total thrust (fuel) is burned to hit the same — safety outranks efficiency.
Why does the shape function use with peak on the axis?
The gas is densest along the centerline and thins toward the cone edge; captures that fall-off, and tunes how tightly the plume is collimated.
Why is total thrust a poor measure of control authority?
Because torques and forces can add or cancel; two big jets in opposition contribute a lot to but produce only a couple (or nothing), so only the net wrench counts.
Edge cases
What torque does a thruster give if its mount position is exactly at the CoM ()?
Zero, since — it is a pure translation thruster no matter which way it points.
What happens to as a surface moves to the very edge of the plume cone ()?
, so the modeled impingement drops to zero — surfaces outside the cone axis region are essentially safe from that jet.
What is the impingement pressure as ?
It tends to zero like ; far-away hardware is safe, which is why keep-out cones have a finite range .
If a commanded wrench needs pure torque, what extra constraint enters the selection?
The net-force-zero condition , forcing a couple so the body rotates without translating.
What if two thrusters mounted opposite fire in the same direction instead of opposite?
Their forces add (net translation) and their torques tend to cancel — the opposite of a couple, giving drift with little or no rotation.
Can the impingement force ever help rather than hurt the maneuver?
In principle its direction could align with the command, but it is unmodeled and geometry-dependent, so control design treats it as a disturbance to bound, not a resource to exploit.
If all thrusters whose plumes clear the target are inhibited, what does the LP return?
Infeasibility — no satisfies under the constraints, signalling the maneuver must be re-planned (different geometry, timing, or attitude).
Recall One-line self-test
Is "fire more thrusters for more authority" ever correct? ::: No — authority is the net wrench ; adding jets can cancel torque or inject unwanted force, so the right subset beats the full set.