I recall in the ST:TNG episode The Schzoid Man that they perform a warp-transport-warp transport. Counselor Troi notes that it felt like she was in the wall for a minute, which Worf replies: "That's because you were". Why would this happen though?
2 Answers
From Memory Alpha's Transporter Page:
Using transporters when a ship was at warp speed was very dangerous because warp fields created severe spatial distortions. (TNG: "The Schizoid Man") Therefore, transport at warp generally violated safety regulations. However, at-warp transport was attempted a handful of times, usually under high-stakes combat conditions (TNG: "The Best of Both Worlds", "The Emissary"), by making a few adjustments.
Simply put, the Warp Field that contains a ship travelling at warp distorts the transporter signal, making it very difficult to perform a transport (to say nothing of the extreme velocity).
However, it has been attempted (and sometimes performed successfully) a number of times.
If both ships maintained exact velocity (that is, the warp field on both vessels must have the same integral value/factor) transport at warp speed was possible. Failure to maintain the same velocities would result in severe loss of the annular confinement beam (ACB) and pattern integrity.
If the ship was traveling at warp speed and the object to be beamed was stationary, transport was possible by synchronizing the ACB with the warp core frequency. This would cause difficulties in obtaining a good pattern lock. The Maquis were known to have used this method. (VOY: "Maneuvers")
Sometime before 2387, Montgomery Scott discovered the necessary formulas enabling transwarp beaming. These were passed on to his alternate reality counterpart, but using these to beam onto the USS Enterprise caused him to be stuck in a water pipe leading to a turbine. (Star Trek)
In short, warp fields create a distortion that can be compensated for, but the success rate for this is very, very low.
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In ST:XI (Into Darkness, I believe) doesn't Spock give Scotty the formula for inter-warp beaming? And it has something to do with considering space as the moving item?– DanielCommented Nov 15, 2015 at 23:30
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@Daniel That would be the first J.J. Abrams "Star Trek" movie (the one without a subtitle) and Scotty did make a comment in that vein, but without having the context for it we can't be sure what was actually preventing warp-transport. Unfortunately, I can't find a transcript for it, but they may have been referring to a different problem (transport to a ship not using Warp, but using the Impulse drive, IE, transporting to a rapidly-moving object).– ZibbobzCommented Nov 16, 2015 at 13:02
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Well, I do know that after Scotty was given the formula, he and Kirk beamed up to the Enterprise while traveling at Warp speed. But like you said, not that much context.– DanielCommented Nov 16, 2015 at 14:15
Lacking a canon quote from someone on the production team, I felt that this could be read one of two ways;
1) The affects of transporting at speed means that the transporter needs to compensate for some kind of distortion. Her "beam" was literally going to materialise inside the wall unless the transporter had made the appropriate corrections.
2) On several occasions we see O'Brien working on transporter components that are built into the the walls and floor of the transporter. Worf may have been alluding to the fact that there was a slight chance that her pattern would have been stuck inside the "pattern buffers" or something similar.
My personal impression was that the former is more likely.