THE CRATER MODEL

0.0195(L/d)0.45(d)(ρP)0.27(V-V*)2/3 p= (ST)1/4(ρT)1/6

¶p = penetration depth L = length of foam projectile d = diameter of foam projectile ρP = density of foam V = component of foam velocity at right angle to foam V* = velocity required to break through the tile coating ST = compressive strength of tile ρT = density of tile 0.0195 = empirical constant

¶In 1966, during the Apollo program, engineers developed an equation to assess impact damage, or "cra- tering," by micrometeoroids.44 The equation was modified between 1979 and 1985 to enable the analysis of impacts to "acreage" tiles that cover the lower surface of the Orbiter.45 The modified equation, now known as Crater, predicts possible damage from sources such as foam, ice, and launch site debris, and is most often used in the day-of-launch analysis of ice debris falling off the External Tank.46

¶When used within its validated limits, Crater provides conservative predictions (that is, Crater predictions are larger than actual damage). When used outside its validated limits, Craterʼs precision is unknown.

¶Crater has been correlated to actual impact data using results from several tests. Preliminary ice drop tests were performed in 1978,47 and additional tests using sprayed-on foam insulation projectiles were conducted in 1979 and 1999.48 However, the test projectiles were relatively small (maximum volume of 3 cubic inches), and targeted only single tiles, not groups of tiles as actually installed on the Orbiter. No tests were performed with larger debris objects because it was not believed such debris could ever impact the Orbiter. This resulted in a very limited set of conditions under which Craterʼs results were empirically validated.

¶During 1984, tests were conducted using ice projectiles against the Reinforced Carbon-Carbon used on the Orbitersʼ wing leading edges.49 These tests used an 0.875-inch diameter, 3.75-inch long ice projectile to validate an algorithm that was similar to Crater. Unlike Crater, which was designed to predict damage during a flight, the RCC predictions were intended to determine the thickness of RCC required to withstand ice impacts as an aid to design engineers. Like Crater, however, the limited set of test data significantly restricts the potential application of the model.

¶Other damage assessment methods available today, such as hydrodynamic structural codes, like Dyna, are able to analyze a larger set of projectile sizes and materials than Crater. Boeing and NASA did not currently sanction these finite element codes because of the time required to correlate their results in order to use the models effectively.

¶Although Crater was designed, and certified, for a very limited set of impact events, the results from Crater simulations can be generated quickly. During STS-107, this led to Crater being used to model an event that was well outside the parameters against which it had been empirically validated. As the accompanying table shows, many of the STS-107 debris characteristics were orders of magnitude outside the validated envelope. For instance, while Crater had been designed and validated for projectiles up to 3 cubic inches in volume, the initial STS-107 analysis estimated the piece of debris at 1,200 cubic inches – 400 times larger.

¶Crater parameters used during development of experimental test data versus STS-107 analysis:

¶Test Parameter Test Value STS-107 Analysis

¶Volume Up to 3 cu.in 10" x 6" x 20" = 1200 cu.in. *

¶Length Up to 1 inch ~ 20 inches *

¶Cylinder Dimensions <= 3/8" dia x 3" 6" dia x 20"

¶Projectile Block Dimensions <= 3"x 1"x 1" 6" x 10" x 20" *

¶Tile Material LI-900 "acreage" tile LI-2200 * and LI-900

¶Projectile Shape Cylinder Block * Outside experimental test limits

145

¶Crater equation parameter limits:

¶Crater Equation Parameter Applicable Range STS-107 Analysis

¶L/d 1 – 20 3.3

¶L n/a ~ 20 inches

¶ρd 1 – 3 pounds per cu.ft. 2.4 pounds per cu.ft.

¶d 0.4 – 2.0 inches 6 inches *

¶V up to 810 fps ~ 700 fps

Outside validated limits

¶Over the weekend, an engineer certified by Boeing to use Crater entered the two estimated debris dimensions, the estimated debris velocity, and the estimated angle of impact. The engineer had received formal training on Crater from senior Houston-based Boeing engineering staff, but he had only used the program twice before, and had reservations about using it to model the piece of foam debris that struck Columbia. The engineer did not consult with more experienced engineers from Boeingʼs Huntington Beach, California, facility, who up until the time of STS-107 had performed or overseen Crater analysis. (Boeing completed the transfer of responsibilities for Crater analysis from its Huntington Beach engineers to its Houston office in January 2003. STS-107 was the first mission that the Huntington Beach engineers were not directly involved with.)

¶For the Thermal Protection System tile, Crater predicted damage deeper than the actual tile thickness. This seemingly alarming result suggested that the debris that struck Columbia would have exposed the Orbiterʼs underlying aluminum airframe to extreme temperatures, resulting in a possible burn-through during re-entry. Debris Assessment Team engineers discounted the possibility of burn through for two reasons. First, the results of calibration tests with small projectiles showed that Crater predicted a deeper penetration than would actually occur. Second, the Crater equation does not take into account the increased density of a tileʼs lower "densified" layer, which is much stronger than tileʼs fragile outer layer. Therefore, engineers judged that the actual damage from the large piece of foam lost on STS-107 would not be as severe as Crater predicted, and assumed that the debris did not penetrate the Orbiterʼs skin. This uncertainty, however, meant that determining the precise location of the impact was paramount for an accurate damage estimate. Some areas on the Orbiterʼs lower surface, such as the seals around the landing gear doors, are more vulnerable than others. Only by knowing precisely where the debris struck could the analysts more accurately determine if the Orbiter had been damaged.

¶To determine potential RCC damage, analysts used a Crater-like algorithm that was calibrated in 1984 by impact data from ice projectiles. At the time the algorithm was empirically tested, ice was considered the only realistic threat to RCC integrity. (See Appendix E.4, RCC Impact Analysis.) The Debris Assessment Team analysis indicated that impact angles greater than 15 degrees would result in RCC penetration. A separate "transport" analysis, which attempts to determine the path the debris took, identified 15 strike regions and angles of impact. Twelve transport scenarios predicted an impact in regions of Shuttle tile. Only one scenario predicted an impact on the RCC leading edge, at a 21-degree angle. Because the foam that struck Columbia was less dense than ice, Debris Assessment Team analysts used a qualitative extrapolation of the test data and engineering judgment to conclude that a foam impact angle up to 21 degrees would not penetrate the RCC. Although some engineers were uncomfortable with this extrapolation, no other analyses were performed to assess RCC damage. The Debris Assessment Team focused on analyzing the impact at locations other than the RCC leading edge. This may have been due, at least in part, to the transport analysis presentation and the long-standing belief that foam was not a threat to RCC panels. The assumptions and uncertainty embedded in this analysis were never fully presented to the Mission Evaluation Room or the Mission Management Team.