You can next see a 3d snap shot of a harder landing. To make the graph less complex we have just visualized longitude and vertical accelerations which take most of the energy of a landing bump. We will soon come up with graphs how the plane rotated during a hard landing, that will give you information about front wheel landings as well. We hope to come to a relyable statement about such incidents.
You want to go for a better understanding of the graph ? Here is how:
The green graph represents the acceleration vertically which takes the majority of the bump.
Positive is the direction "acceleration to earth", negative is up into the air. The latter is our direction of an hard landing bump as we are getting pushed back upwards during a hard landing to reduce falling speed to zero or even push us back upwards.
So consequently the first 200ms of our green graph before it turns positive represents our bump, all the rest is sweeping out. In a very rough estimation we have averagely 2g negative during the first 200ms.
That gives us a difference in Speed = 2g*200ms = 20m/(s*s) *200ms = 4m / s = 14 km/h. Our plane actually lost as much energy as is contained in a slow down of 14,4km/h which is 9mph.
You could also express that as an equivelent of dropping altitude by expressing it as potential rather than a speed energy. To find out you would set equal
Energy = m*v*v/2 == m*g*altitude. Reordering the formula gives us
Altitude = v*v/2g .
Putting numbers in results in
Altitude = (4*4 m*m*2) /(2*10m s *s) = 0,8m.
We can roughly estimate the energy contained in the blue horizontal graph, which follows the same formula to 30% i.e. 0,25m and the hidden transversal vectors will be good for annother 0,05m so we are in total talking about a dropping altitude of more than 1m or 3 ft. You can imagine that is a pretty hard landing.
And it was, the graph is a real one of an incident in Bavaria Germany, - the landing gear was hiddenly damaged, but detected by the fleet owner supported by charterware.