Analysis Guru
OEX Recorder Impact Analysis
Columbia's OEX recorder was recovered in remarkably good condition about
7 miles from Hemphill, Texas. The connector panel was missing, but it basically
had the shape of a rectangular prism or box with dimensions 17 x 22 x 7.5 and
weighing 58 pounds. The OEX recorder is enclosed in an aluminum or aluminum
alloy case (material description requires clarity). Two large reels are stacked
on top of each other inside with the motor drive apparently beneath the reels.
The recorder was found upright at a relatively dry area embedded into soft soil
on a slope near a tree. One statement asserted the connector side of the box was
embedded about 3 deep, but I believe this description requires greater clarity.
The following preliminary analysis is pending additional information and more
elaborate and precise analytical methods:
My calculations indicate for a completely tumbling scenario the impact velocity
should have been near 167 feet per second or about 114 mph with impact energy
near 33845 Joules or about 24963 ft-lbf. My calculations also suggest that even
with a lucky, non-tumbling fall scenario the minimum impact velocity should have
been approximately 128 feet per second or about 87 mph with impact energy near
20000 Joules or about 14751 ft-lbf. This is based on running my
Trajectory Java Applet with the data. Applicable start altitudes are assumed to range between
180,000 feet and 40,000 feet, but the box would decelerate rapidly to a near
terminal velocity even with some extension of the lower altitude range.
Impact elevation is unknown, but assumed to be about 200 feet.
I also assume the recorder had a coefficient of restitution of zero meaning
perfectly inelastic collision with Earth(no bounce) since it was found embedded
three inches distance into damp soil. I tried to get a rough figure on force and
pressure experienced by the impact by using mass, enclosure dimensions, minimum
impact velocity and minimum impact energy. I used the bottom surface area (17 x
22) of the OEX for calculating pressure. Unfortunately, I dont know the
thickness specification for the enclosure. This thickness would be important to
stress calculations although neglected in this preliminary analysis.
Using Energy = (1/2) x mass x velocity x velocity = Work = force x distance,
impact force exerted on bottom of OEX (method 1)= approximately 59004 lbf with
the pressure being about 158 psi.
Alternatively, using the embed distance of 3 inches and assuming a minimum time
to cause the embed, then minimum embed time = distance / impact velocity since
the velocity would decrease as it encounters friction of the soil.
maximum acceleration = change in embed velocity / change in embed time
with change in embed velocity = impact velocity - final velocity;
setting final velocity = zero and change in embed time = minimum embed time.
Impact force exerted on bottom of OEX (method 2)= approximately 115200 lbf with
the pressure being about 308 psi.
Therefore, the following ranges are established based on rough approximations of
a non-tumbling scenario:
59004 lbf < impact force < 115200 lbf
158 psi < impact pressure < 308 psi
Note that the estimated embed depth significantly influences the precision of
calculations. Forces and pressures would be greater if actual embed depth was
less.
My preliminary conclusion is as follows:
Actual stress calculations cannot be performed at this time due to insufficient
data. However, my intuition is that more damage to the enclosure and internals
should have been more evident. I disregarded the damage to the cable
connection/appendage portions of the OEX since it probably separated at a very
high altitude and thus not affecting impact velocity much. The effect of the
structural channel attached to the OEX was neglected in the analysis since the
magnitude of error would probably be insignificant given the relative size and
weight of the OEX. The internals of the enclosure seemed to have experienced
more damage although internal damage would be expected to be more severe than
the enclosure given the geometry and material properties of the enclosure could
have tolerated stresses better. Still, internal damage seemed incredibly light
given the ranges of impact force and impact pressure. I would have expected the
plastic and thin metallic parts on the inside would have been more vulnerable,
but I would need to know more about the internal shock absorption design such as
flexible parts, springs, dampers, & etc. I had thought about the possibility
that limbs from nearby tree may have partially slowed the fall, but the report
indicated insignificant scratches to the enclosure. Since the OEX was found on a
slope, it is also possible some energy was absorbed during a slide rather than
an instantaneous embed. Unfortunately, I haven't seen the actual location where
the OEX was recovered in order to assess these mitigating factors.
References:
http://www.columbiassacrifice.com
http://www.io.com/~o_m/columbia_loss_faq_x.html(link no longer available as reference)
Rebuttals and additional assistance in refining this analysis will be
appreciated.