# How exactly do “commanded delta-v burns” work in practice? (e.g. OSIRIS-REx)

Reading this answer to Could the uncertain mass of the OSIRIS-REx sample affect the trajectory of the return capsule? I infer that traditionally deep space spacecraft are sent timed commands for burns of engines or thrusters for delta-v maneuvers. These might be milliseconds to hours depending.

The burn commands to OSIRIS-ReX are commanded delta V rather than timed burns.

which is a substantial advantage over a timed burn command which requires a "best guess" estimate of the spacecraft mass, propellant flow are and engine ISP during a given burn.

But if we examine it closely, what do we see? Hopefully answers will address the following:

1. Does the command contain a set point for engine cut-off based on integrating one accelerometer, or three, or something else?
2. Does the command include a direction in an inertial frame, or the spacecraft's frame?
3. How would this technique be compared and contrasted to the famous "burn scene" in the movie Apollo 13?

Related:

Well Huston we’ve got one. If we can keep the Earth in the window flying manually, the (??) crosshairs right on its terminator, all I need to know is how long I need to burn the engine.

• I am not the downvoter, but I suspect that that downvote was due to the inclusion of the one overly dramatic sequence from Apollo 13 that most likely represented the worst departure from reality in the movie. – David Hammen Oct 27 at 12:38
• @DavidHammen people use voting for all sorts of reasons, luckily it averages out over geologic time scales :-) I know what you mean, but it's still a reference point that may ring a bell with some readers, and though it's Hollywood, the maneuver itself was real and has a connection to the question. I think that one historically-minded answer might even cite a better summary of it. – uhoh Oct 27 at 12:41
• The Apollo 13 flight computers and navigation sensors were shut down to conserve power. They could not use a commanded ΔV, so they had to resort to the backup of a timed burn. – David Hammen Oct 27 at 12:49
• @DavidHammen I wonder if I've got it wrong and commanded $\Delta V$ is more common than I'd thought? Also fyi I've just asked What was the normal function of the (coax?) crosshairs used during the Apollo 13 famous manual burn? – uhoh Oct 27 at 12:59

But if we examine it closely, what do we see? Hopefully answers will address the following:

1. Does the command contain a set point for engine cut-off based on integrating one accelerometer, or three, or something else?
2. Does the command include a direction in an inertial frame, or the spacecraft's frame?
3. How would this technique be compared and contrasted to the famous "burn scene" in the movie Apollo 13?

The answers to the first two questions are "it depends". It depends on a lot of things, and it varies from spacecraft to spacecraft. The answer to the third question is that Apollo 13 shut down its flight computers and its sensors to conserve power. The better alternative of a commanded ΔV was not available, so they had to revert to a timed burn as the only alternative.

Since "it depends" is a key part of the answer, it helps to look at the question raised in the title: How exactly do “commanded delta-v burns” work in practice? (e.g. OSIRIS-REx)

The closest reference I could find on OSIRIS-REx is the eoPortal page on the vehicle, which says regarding a trajectory correction maneuver that

This trajectory correction maneuver was the first to use the spacecraft’s ACS (Attitude Control System) thrusters in a turn-burn-turn sequence. In this type of sequence, OSIRIS-REx’s momentum wheels turn the spacecraft to point the ACS thrusters toward the desired direction for the burn, and the thrusters fire. After the burn, the momentum wheels turn the spacecraft back to its previous orientation. The total thrust is monitored by an on-board accelerometer that will stop the maneuver once the desired thrust is achieved.

Some parts of this are incorrect. Accelerometers are somewhat dumb sensors. They sense non-gravitational acceleration. While they do accumulate sensed acceleration over short periods of time so as to smooth out randomness, they do not accumulate delta V over long periods of time. A small fraction of a second counts as a "long" period of time with regard to accelerometers. Moreover, accelerometers do not command thrusters. It is the spacecraft's on-board guidance, navigation, and control software that starts the burn, that monitors accelerometer output, and that stops the burn when the accumulated delta V reaches the commanded delta V.

From that brief and somewhat incorrect description, I suspect that what OSIRIS-REx does is that prior to a burn it transitions from barbecue attitude mode to inertial hold attitude mode. At the commanded time, it sets a variable typically called dvtogo (or some variant thereof) with the commanded ΔV and initiates a burn in a fixed inertial direction. At each time step, the GN&C software decrements dvtogo with either $$(\vec a \cdot \hat d) \Delta t$$, where $$\hat d$$ is the unit vector in the desired direction, or with $$||\vec a||\Delta t$$. Which approach is taken is not clear from the quoted paragraph; different spacecraft use different approaches. Either way, once dvtogo becomes close to zero or negative, the GN&C flight software commands the thruster to shut down.

The above approach is not quite optimal. A more optimal approach with regard to fuel consumption is to change the direction as the burn progresses so as to reduce gravity losses. This added complexity ("perfect is the enemy of good enough") is probably not worthwhile for a mission such as OSIRIS-REx. For a moon lander, the added complexity of approximating a gravity turn may well be worthwhile.

• Very nice, thanks! For the short vs long period of time part, is this something along the lines of the accelerometer having some upper frequency cut-off and it needing to be sampled at a few times the associated time-constant? – uhoh Oct 27 at 14:57
• @uhoh Modern accelerometers have a good deal of built-in firmware. They typically sample internally at a rather high rate, apply some kind of filter / multiple kinds of filters, and are sampled externally at a significantly lower rate. It's important to keep in mind that the only fundamental difference between a modern vibration sensor and a modern accelerometer is whether the device filters out low frequency or high frequency components. – David Hammen Oct 27 at 15:16