If the Columbia was brought down because critical components were heated to failure due to a breach in the Thermal Protection System (TPS), it is then important to determine what the ultimate temperature imparted to these components was.  Since the temperature sensors monitoring these components did not register any temperatures high enough to cause damage, it must then be determined what these temperatures were by using heat transfer calculations and engineering methodology.  The three most important factors affecting the final temperature reached by specific components of the shuttle are,

On Orbit Heat Transfer

On orbit Heating Vs. Cooling:

The shuttle orbits the earth upside down and backwards about once every 90 min. with the exact orbit period depending on its altitude.  The only mode of heat transfer to and from a spacecraft in orbit is through radiation.  When the shuttle is in direct sunlight the black surface on the belly of the shuttle absorbs solar energy while the white surface on the top of the shuttle reflects infrared energy coming from the earths atmosphere.  When the shuttle is in the earths shadow all of the shuttles surfaces emit thermal radiation cooling the shuttles tiles and eventually its aluminum skin.  It can be assumed that the shuttle typically spends half its time heating and the other half cooling, (45 min. / 45 min.).  The shuttle surfaces may not absorb and emit thermal radiation at exactly the same rate so it will have to be determined by calculating the radiation rates for the shuttles surfaces whether or not the shuttle cools completely to absolute 0K before it begins heating again.  This analysis will be done for the black tiles on the orbiters belly because that is the area of concern.

Reentry Heat Transfer

Heating of suspect areas:

A few specific areas of the Space Shuttle have been the subject of extensive analysis and experimentation during launch, ascent and reentry throughout the shuttle program.  These locations are typically the site of thermal or aerodynamic anomalies.  NASA has an extensive library of technical papers using data taken from these areas of the shuttle during the OEX program, (see Technical Article TA-G1 on Data Recorders).  This data allowed engineers to determine if the shuttle was staying within the design envelope for thermal and aerodynamic stresses on the airframe and flight control surfaces.  The locations for data collection were chosen for different reasons such as where shockwave impingement might occur, the possible existence of vortexes or some other extreme thermal or aerodynamic condition.  The data was used to fine tune the shuttle design as well as the ascent and reentry flight paths.  The sensors collecting this data along with their required hardware such as multiplexers, data recorders etc. were kept completely separate from other flight critical hardware.

Fig. D1 shows not only how the shuttle's wing was sectioned for data collection but also the location of radiometers which sensed heat on the inside of the left hand RCC panels.  The small dots located next to the wing leading edge are the radiometer locations.  A sensor at the 55% location also happens to fall on RCC panel 9.  This is the location of a double shock region which severely exacerbates the heating problems and coincidently is also the exact area that the official investigation concluded had the breach from the foam debris impact.  This 55% location as well as the entire section WS134 will be the focus of this discussion since it was also the focus of the official investigation.

Fig. D1

Fig. D2 is the thermal energy seen by the left wing location WS134 during reentry.  This data was taken on Columbia during one of the first five missions and was recorded by the OEX data recorder from the various OI sensors as described above.  After the shuttle landed the data was retrieved from the OEX while the shuttle was still on the runway.  The OEX recorder and its tapes always remained on the shuttle and the data was transferred to an external device that was rolled up to the orbiter after landing.

Fig. D2

Underside of wings and fuselage:
The shuttles surface temperature, (the temperature the thermal tiles are exposed to), during reentry varies not only with time but also depends upon the location on the shuttle itself.  The underbelly of the shuttle heats up far less than the leading edge of the wings or the shuttle nose.

The following graphs in Fig. D3 show temperature variation over the course of reentry.  The information was taken from thermocouples attached to the belly of STS-96, (OV 103 Discovery), and the experiment is detailed in the following document,

AIAA_2001-0352.pdf;  (Infrared Sensing Aeroheating Flight Experiment).

Fig. D3

It appears that the belly of the shuttle heats almost uniformly during reentry.  The temperature of these tiles almost never exceeds 1700°F.  If the black tiles  are in place and functioning properly the shuttles skin temperature will almost never exceed 160°F and is specified to not exceed 350°F any where on the orbiter.

Wing leading edge and nose:

The leading edge of the wings and the nose of the shuttle see the most heat by far of any other part of the orbiter.  These areas are at or near the stagnation points of the shockwaves created by the orbiter and are subject to stagnation heating.  The temperatures seen here are well over 2500°F for much of the reentry period.  The Thermal Protection System (TPS) is considerably more robust in these areas as well.  A location along the leading edge designated the 55% semispan location sees the highest temperatures due to an unusual crossing of shock waves from different parts of the orbiter, (a double shock region).  The absolutely highest temperature at the leading edge occurs 5 inches below the midline of the wing at that point due to the shuttles 40° angle of attack as pointed out on Page C, "The Effects of Hypersonic Flow During Reentry of the Space Shuttle". 

Skin temperature:

Fig. D9 closely follows Fig. D3 and is Time Vs. Temperature plot from document, NASA_TM-1987-88286.pdf;  (Thermal Stress Analysis of Space Shuttle Orbiter Subjected to Reentry Aerodynamic Heating).  The figure shows the temperatures reached at the wing section WS134 based on both calculated and measured data.  It can easily be noted that at the point on the chart where Columbia broke up, 900 seconds, the skin temperature of the orbiter has only reached 10 or 20°F, (still bellow freezing for water).  Even when the TPS is degraded by 20% the effect on the temperature of the skin is minimal.  At the location Bay 1 Wheel Well, the increase is only about 10°F.  If the TPS is in tact and working properly the orbiters skin on the wings and fuselage should stay well within the critical 350°F limit.  The underlying structure of the orbiter will not retain heat as does the thermal tiles because of heat conduction by the shuttles 0.160" thick 6061-T6 aluminum skin and the extensive array of wing spars and ribs that support it.  Thermal energy that reaches the underlying structure of the orbiter is conducted away so fast that there is virtually no chance for any one point to see excessive heating.

Fig. D9

If the skin temperature needed to be calculated for other values of TPS effectiveness besides 100% and 80% it's possible that a simple conduction equation could be used for deviations from those values.  The calculated data in Fig. D9 was obtained using a finite element heat transfer analysis and the input data for the TPS thickness was multiplied by a factor of 0.8 to calculate the skin temperature at 80% TPS thickness.  If the assumption is made that a linear heat transfer relationship exists between the effectiveness of the TPS and the temperature of the aluminum skin, then the highest temperature reached at the location Bay 1 (Wheel Well), at the 900 second point would be about 60 to 80°F.  This is again due to the massive conduction of thermal energy throughout the structure of the orbiter.  If this is true then a missing tile or several missing tiles should make little or no difference anywhere on the orbiter.

The Shuttle Airframe:

One straight forward way to determine if the RCC panel breach scenario could lead to the aluminum structure under the wing reaching melting temperature or not is to simply model it in an Finite Element Analysis program.  After modeling all of the spars and the skin, apply a heat load at the location of the breach with an area about the size of the estimated hole.  The model should be run using conduction alone to see what the results are.  If the program returns a value that is close to failure the analysis done in the NASA technical reports concluded that both internal convection and radiation made a big difference in how heat was conducted throughout the wing.

The skin temperature continues to rise even after the shuttle is well passed the peak heating period of reentry and in some cases rises even after touchdown.  This is because the TPS is a thermal barrier for heat attempting to leave the space shuttle as well as heat trying to enter it.  After the shuttle comes to a stop on the runway, the vent doors may be left open for several hours to dissipate the heat in the structure of the orbiter.  In addition to passive cooling after landing, tanker trucks pull up to the orbiter and circulate coolant through fluid jackets within the structure of the orbiter to keep excess heat from damaging the shuttles tiles.