We asked Boeing to advise the recorded 'G' figure that would represent a Hard Landing. They responded to say that the Flight Recorder takes instantaneous values at a sampling rate of 16 times per second. This means that the recorded 'G' value does not necessarily co-incide with the maximum value that occured. There is therefore no way to co-relate a Hard Landing to a recorded 'G' value. They went on to define a Hard Landing as a landing which, in the opinion of the crew, was a Hard Landing.
In an airliner you would expect to see obvious signs such as baggage bins breaking open, oxygen masks deployed and so on. One aircraft reached the stand with the fuselage buckled just forward of the wing leading edge. The crew hadn't noted a hard landing in the log and, upon being shown the damage, they then entered it into the Technical Log as a 'Firm Touchdown' We don't know what the passengers thought...