FALLING FATALITIES
Falls are the leading cause of
nonfatal injuries and the second leading cause of brain injuries. In the USA,
falls cost $37 billion pa compared with $49 billion for motor vehicle accidents.
The cost of stair falls each year in the USA is the same as the cost of
building new stairs each year. Huge sums are spent on researching motor vehicle
accidents, but almost nothing is spent on researching falling accidents since
people (eg lawyers and architects) tend to blame the person who fell rather
than focus on potential design or maintenance issues.
Over the last few years I have
been asked by the NSW coroner and by the NSW police to provide reports on a
number of falling fatalities, specifically regarding the physics of the fall.
There are not many lawyers or police or journalists who understand Newton's
laws in sufficient detail to even know where to start. Furthermore, there is
very little information available in the forensic literature or on web sites
concerning fatal falls. Consequently, I have provided some information below,
based on cases I have already investigated.
If a person dies as a result of
a fall from a height, say off a cliff or a tall building, then it is often very
difficult to determine whether the fall resulted from an accident or whether it
was a suicide or homicide, especially if there were no witnesses and no suicide
note or any other indications of a potential suicide. Psychologists assert that
there are many indicators of suicide such as previous suicide attempts,
depression, a history of mental disorder, a patient in a psychiatric hospital,
the leaving of possessions at a cliff top, etc. None of these factors can be
taken as proof of suicide, but together might lead a coroner to conclude that
suicide was the most likely explanation.
In terms of the physics of the
problem, some or all of the following factors may need to be considered,
depending on the particular circumstances. The calculation of the trajectory
during the fall is the easy part. It is everything else leading up to that
calculation that is difficult.
1.
The fall height.
The
height of a cliff or building is not easy to measure. It is probably best left
to police experts, but it is wise to check independently whether the
measurement seems correct eg with a laser distance finder.
2.
The horizontal distance travelled during the fall.
Again,
forensic experts can measure this. It might involve one team abseiling down a
cliff and another team taking distance and angle measurements.
3.
The vertical slope of the cliff or building.
The
deceased person may have bounced or slid to the point where they were found.
If
the fall is into water, then police or navy divers may need to assist with
measurements close to the edge of a cliff.
4.
The first and subsequent points of impact.
Forensic
experts can identify the initial impact point(s) from damage caused by the
impact(s). It should marked with paint and photographed for later examination, even
if the initial investigation points to suicide. It might later turn out to be a
homicide.
5.
Identification of potential launch points.
The
actual launch point is not necessarily the closest point to the landing spot.
There may well be several potential launch points, each of which needs to be
examined on its merits.
6.
Available runup distance to each launch point.
A
horizontal flight distance of 10 m may be easier to explain than a 5 m flight
distance if the 10 m distance has an available runup distance of 10 m and the 5
m distance has an available runup of only 0.5 m.
7.
Slope, slipperyness and nature of runup path.
A
person jumping off a steep uphill slope cannot jump at the same speed as on a
level slope. A person attempting to jump forward off a 40 degree slope might
end up jumping backward.
8.
Flight distance and launch angle.
The
horizontal flight distance through the air is given by D = VT where V is the
horizontal launch speed and T is the flight time in the air. The time in the
air depends on the initial launch angle, but the additional time resulting from
a launch angle of say 20 degrees, as opposed to say zero degrees, will be small
compared to the total time if the vertical fall is 30 m or more. Furthermore
the horizontal launch speed will be reduced if the jumper attempts a launch at
say 20 degrees rather than say 10 degrees. A jump off a cliff or tall building
is not the same as a jump on level ground. In the long jump, the jumper needs
to spend as much time in the air as possible. The launch angle is probably not
known, but should be incorporated into trajectory calculations to determine
whether a launch at say 10 degree degrees above the horizontal makes any
significant difference to a 20 degree launch. It won't if the vertical fall
distance is 30 m or more.
9.
Takeoff distance.
When
a person jumps or dives, the position of the centre of mass is in front of the
back foot at the instant of takeoff.
The flight distance is the subsequent distance travelled through the
air. The takeoff distance is the horizontal distance from the back foot to the
centre of mass, and it can add an extra 0.5 m or so to the total horizontal
distance travelled.
10.
Orientation of body on impact
At
high launch speeds, a head first landing implies a dive, and a feet first
landing implies a feet first jump. At low launch speeds, a head first landing
might result from a feet first jump followed by a somersault. In a high speed
jump, a jump speed is less than the runup speed and a head first dive speed is
less than a feet first jump speed. The launch speed also depends on the
available runup distance, which may even be as small as say 0.2 m, or it might
be as large as 20 or 30 m.
11.
Nature of injuries and cause of death.
Forensic
pathologists can usually determine the cause of death from the nature of the
injuries, and can usually tell whether the deceased landed feet first, head
first or feet first then head etc. In a fatal fall from a height, there are
usually many injuries. If the fall is into water then the injuries may all be
internal.
12.
Physical evidence, if any, left at the launch point.
It
may be possible to determine what happened purely from evidence left at the top
of a cliff or building. In one case I examined, a woman overbalanced on a
balcony and left a series of impressions on the outside of a glass panel
forming part of the balcony wall, showing exactly what had happened. See
Journal of Forensic Sciences, January 2006, for a report on this incident.
13.
Athletic ability of the deceased.
If
a person lands say 15 m out from a cliff or building, then the height of the
fall and the launch speed are obviously both large. The main question then is
whether the deceased had sufficient athletic ability to achieve the required
launch speed with the available runup distance.
14.
Strength and athletic ability of any suspect.
If
a person is suspected of pushing or throwing another person off a bulding or
cliff, then the question might be whether the suspect is physically capable of
doing so. Tests can be done by pushing or throwing volunteers into a swimming
pool.
15. Prevailing wind and effect of air
resistance.
Air
resistance is relatively small and will make only a small difference to most
human body trajectory calculations, unless a strong wind was blowing at the
time or the fall is from a very large height.
16. Presence or absence of drugs, alcohol
or sedatives.
Not
really a physics issue, but it might help explain why the deceased fell.
17.
Statements made by others before or after the event.
Was
the suspect seen near the scene of the crime? Again, not a physics issue, but
one that is obviously important, especially if the suspect was actually
somewhere else at the time.
The
jpeg image here shows the trajectory of each end of an iron bar pushed off the
top of a cliff. A person would not necessarily bounce in the same manner, but
simulation studies like this are useful in getting a good idea of what might or
might not have happened.
The movie clip here shows a mannequin pushed off
the cliff. People donŐt bounce, but they can slide
and roll at high speed when impacting the side of
a cliff. Movie taken at 300 fps.
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