First I reserve the right to reuse this title for a Sandoval story.
In the middle of the night, last night in fact, dog number two woke us up by barking downstairs. Middle of the night I stumble down the stairs to where we keep downstair and figure he's looking out the window and barking at a cat or barking at someone on the street or one of the local raccoons.
Nope. He's standing in the middle of the living room barking at ... nothing I can see. I'm a fairly rational guy but this gave me a momentary chill so I checked the front door, and behind the shower curtain.
Acceleration compensators make me feel that way. THere's almost certainly nothing wrong but it doesn't feel that way.
Acceleration compensators are a necessary piece of (usually) handwavium technology in any story where the spaceship is only there to get you to the story (fast!) While the ftl dingus keeps trips between stars from taking decades or centuries the acceleration compensator let's your ship accelerate rapidly allowing you to speed about like a bejeebus without turning your characters into dramatically unappealing pancakes salsa or film depending on your engine of choice.
As an offside, one gee of acceleration will feel like you never left Terra and get you to Pluto in two weeks! Acceleration compensators are for the truly impatient who have to get to Pluto NOW!
Anyway if your ship is pulling 2-4 gees you could probably squeak by with powered exoskeletons, high tech water beds, and meds. Any higher than that and you probably need to invent a way to freeze the humans solid and defrost them after the really hard maneuvers are done. This probably is not an optimum solution for fighter pilots and some others.
In most science fiction acceleration compensators are assumed, especially if the spacecraft is laid out like a boat. While artificial gravity holds you to the deck, acc-comp keeps you from slamming into a wall when you put it in drive. Some drives, like the Alcubierre Warp Drive, do not actually accelerate the ship and don't need acceleration compensators for the long range journeys. They might still need rockets to enter orbit and land but this sort of thing is handled by mere humans even now without compensators.
But say you want to blow all your delta vee at once? If you have a ship that has 500 kps delta vee you could blow it all to get to say the moon in 12.8 minutes (double the time if you want to slow down). Unfortunately the human body only can take 2-3 gees for any length of time. Accelerating to 250 kps at three gees would take over two hours and deceleration equal time and making the trip at 1 gee would take 4 hours. So acceleration compensators really don't start looking good till we have space opera style drives operating at least at tens of gees with very high maximum velocities.
What could be some limits of compensators? Limits make characters act all inventive by sticking problems in their way.
No Compensators -No Gravity
The drive affects the entire ship somehow keeping everything in free fall. This has its own set of problems as astronauts discover everyday. Some ships spin some section of their ships to create a gravity effect.
Compensators operate over a very limited area, say one (very expensive) compensator will affect about 3-4 cubic meters. In this case we have something like the stasis tubes in Forbidden Planet that protect the occupants from some kind of deceleration on exiting ftl flight. The rest of the time they make due with strapping in and using a gentle gee acceleration.
Acceleration compensators are aligned with the thrust of the ship. Gees from lateral thrust will be fully felt and fast maneuvers to evade danger might throw people about.
You Can't Butter Toast on Both Sides
Due to power configurations or whatever fancy double talk you invent you can have acceleration compensators or artificial gravity on but not both at once. If you're screaming along at five gees then you're in free fall.
Acceleration dampers don't reduce the effects of acceleration by a fixed number of gees but a percentage. A fifty percent compensator will make two gees feel like 1 gee. A ship with this sort of compensator will be laid out like a building with decks at a right angle to the axis of thrust.
The effects of the compensator quickly fall off the further you are from the compensator. Designing a ship is a delicate balance of sticking components as far from the compensator as they can stand. Moving against the axis of acceleration might be quite nauseating or result in unconsciousness at higher accelerations (like combat conditions). The bridge and living areas might be built on top of the compensators or fuel tanks if sloshing fuel is a concern. These ships will probably be built with decks at right angles to the direction of thrust.
Compensators vary just a little in their effects and it's enough to cause nausea in people especially when making hard maneuvers.