I've seen them maneuver. They definitely can go backwards. How fast can they go in reverse? Is warp speed possible, or is reverse limited to impulse power? If it is limited to impulse power, can they travel backwards under impulse power as fast as they travel forwards under impulse power?
Most Federation ships are not designed to maneuver much under thruster-based power. As far as their schematics go, Federation ships are very limited on what they show for control surfaces for thrust. Given the design limitations, I would give them no more than 1/8 to 1/4 impulse at a full out reverse thrust reaching 5 to 10 percent the speed of light. (and sufficient enough to escape Earth's gravity...)
- Why do I think it is so slow? Because there are no specifications for any Galaxy class ship which places a complete and fully functioning impulse engine facing forward for maneuvering control.
- I base this on the lack of thrusters shown on their schematics (I am certain this was an oversight/design flaw). See image below:
- Could they use some exotic force field arrangement or the deflector array? Perhaps, but that certain seems more complicated than its worth. To be fair, this is not the first time this question has been asked (and unsatisfactorily answered by all involved.) See: Ex Astris Scientia - Sublight Propulsion
Since I didn't like their answer entirely, I decided to try my own.
Mobility and Maneuverability
Most ships have a main dorsal impulse engine and a main hull impulse engine. We assume these engines have a limited capacity to turn, at least a bit, allowing main engines to promote some maneuverability. These engines are the most power non-warp engines on the ship.
Given how nimble most Federation ships, even the Galaxy-class ship, able to make a 180 degree rotation in under three seconds, it makes sense there would not be a major need for a powerful reverse thrust capacity. But even the ability to change direction so quickly requires some kind of attitude adjustment capacity and a very powerful one at that.
One that distributes thrust evenly and across all the surfaces of the ship avoiding shearing stress (though with structural integrity intact, that should be less of a problem)
There are three kinds of maneuvering on any Federation starship.
Warp power: This is the most effective energy to movement power. As far as we know, a ship may change its orientation while in warp without affecting the warp bubble or changing the ships direction. However, we have never seen a ship go to warp without first being aligned in the standard flight configuration.
Impulse Power: This is thrust delivered by the powerful reactor impulse engines. These engines max out at .75c and are used for inner star system, non-emergency flight.
Maneuvering Thrusters: used to navigate the ship at very slow speeds with high degrees of precision. Used in docking maneuvers with space stations, other ships or space docks for repairs. This can be a slow as meters per second or up to hundreds of meters per second (clearing a docking area). These maneuvering thrusters are not prominent on any design specifications but we can make the assumption they are there and are part of the basic hull design.
So where did they hide them?
My theory? In the surface of the ship. Consider such thrusters to be on the flat surfaces of the ship capable of being swiveled and rotated giving directional capacity but remaining flush with the surface of the ship.
Think of them like the tiny fans you see in your overhead when you are onboard a plane. Rotate them to change the direction and intensity of the wind from them. These could be built into the ship as comparatively tiny things linked to the ship's subspace field, becoming more active as the field is intensified.
The subspace field reduces inertial drag, giving the thrusters less ship to move. This removes the issue of why we don't see individual thrusters, they could instead be "thruster clusters" all over the surface of the ship allowing for maximum control with minimum profile.
In the Real World
Using my experience in the US Navy, since Roddenberry was fond of naval ships, perhaps his goal was to consider Federation ships in a similar fashion. Most Navy ships are capable of reverse thrust, used to get into and out of port but this is a very limited capacity. These speeds tended to top out at 1/8 to 1/4 of the ship's maximum forward thrust.
These commands would sound like: "All back full." "All back 1/2" "Back 1/4" indicating how much thrust would be expected to be expended on reversing power. In most cases, this would amount to about 2 - 8 knots top speed (a man could run faster).
Given that most of the design specifications barely seem to consider adding thruster mechanisms of any kind, it would appear obvious thrusters were not considered by the show's designers, who wanted to create visibly elegant ships that were as far away from our bulky rocket-engine-driven designs of ships as possible.
Just a speculation as i haven't seen this issue addressed in any episode,
- impulse thrusters on federation ships are always directed to push ship forward, with most hull designs having these thrusters on main hull, so there is no hint how it could propel ship backwards, Voyager had them on nacelle pylons, there it would be easy, but may be reverse is done by some complicated system of force fields deployed in thruster exhaust to push ship backwards
- maneuvering thrusters can push ship in any direction
- warp field is generated around entire ship but hull geometry is binding factor and also the deflector dish is facing forward, if reverse is possible its most likely very limited because deflector cannot project to aft as easily as forward
For Galaxy class reverse on maneuvering thrusters - definitely, impulse thrusters on engineering section are bit outside so some system of reverse thrust quite likely, on saucer are on other hand bit hidden so may be, may be not.
We have a few examples from on-screen evidence where both Riker and Picard ordered the ship to go in reverse at full impulse (most notably with the Cytherian probe that chased the Enterprise-D).
But, from what we saw, ships can't go to warp in reverse.
And their maneuverability at sublight is actually quite high because all ships seem to employ subspace fields to lower their mass, making even huge ships as nimble as fighters, and able to achieve high sublight velocities (0.25 to 0.75c without relativistic effects since subspace manipulation would be used).
I'm pretty sure the science of warp speed is that the starship isn't moving at all. Space is being "warped" around the ship, essentially bending matter and giving the ship the appearance of movement when in reality it's the space that's moving, not the ship. So in theory there is no real reason to have thrusters since as soon as the warp field is collapsed space will return to normal and the ship will slip out and arrive at its destination.