B 737-500 Depressurization Incident

Date:         22 Feb 99 03:30:16 
From:         Puranjai Dass <PJ@CAAF.ORG.FJ>
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This question is directed towards experts in Aircraft Performance &
Airframe Pressurization  (sorry for sending such a long email):-

I work for a regulatory authority and I am helping senior investigators
who are writing a report on a  depressurization incident  involving a
B737-500. They requested me to graph the variation of both the actual
aircraft altitude and the cabin pressure altitude with time by
extracting data from  the ATC transcript. I need some help on this

The details of the incident are as follows:-

" The aircraft was cleared by Approach Control to descend from FL 370 to
FL 350 then re-cleared  to descend to 10,000 ft. At FL 360 the F/O
called "one to go". Just below FL 360 the Master Warning sounded and the
Left Bleed Trip-Off light came on. The F/O  reached for the QRH. 15 to
20 seconds later the Right Bleed Trip-Off Light illuminated. The F/O
operated the Trip Reset button, then turned to the Captain who was
putting on his oxygen mask. The F/O donned his mask. The cabin altitude
warning (an intermittent horn) sounded at 10,000 cabin altitude and this
was silenced by the F/O operating the horn cutout. He then armed the
passenger oxygen switch. The aircraft cabin altitude continued to climb.
Approaching a cabin altitude of 14,000 ft the Captain ordered manual
deployment of the passenger oxygen masks.

At about FL340 in the descent both bleed lights extinguished and the
duct pressures returned to a normal reading. An emergency descent was
initiated. The F/O selected manual mode of the pressure controller and
manually operated the outflow valves to the closed position. A duct
overheat illuminated at about the halfway point during the descent. This
was extinguished after reference to the checklist.

The aircraft was leveled out at 5,000 ft. The descent from cruise level
to this altitude lasted approximately 15 minutes. The cabin outflow
valve was opened at 5,000 ft. The aircraft was now 100 nm from the
destination and continued to descend for a visual approach and landing."

As a result  of this incident a passenger suffered permanent ear damage.
The senior investigators believe that the pressure differential was
maintained at  8.65 psi (by the safety relief valves) some time after
the F/O manually closed the outflow valve (passing 34,000 ft) until the
a/c reached the 5,000 ft altitude when the outflow valve was re-opened.
If we assume the pressure differential reached 8.65 psi when the a/c was
at say 31,000 ft then the cabin altitude would be 4,000 ft (using
standard atmosphere calculations).

My problem is - how do you express negative cabin pressure altitudes
since the cabin pressure was definitely below sea level when the a/c
reached 5,000 ft. As far as I know all the pressure equations are based
on altitudes of sea level and above. Negative altitudes are not a
reality of life, are they?

I would be very grateful if the experts could help me out.