[L109] Various analyses were performed in support of the investigation of the STS 51-L incident. Included in this appendix are the following analysis summaries:

A. Structural Analyses of SRM Segments, Field joints, and Seals

B. SRM Temperatures, Prelaunch and Launch

C. Assessment of joint Leakage from Near Ignition to 58 Seconds

D. Flow and Thermal Analyses

Section C considers the events between the near-ignition time frame when the smoke puff was observed, and the observed hot plume after 58 seconds.

A. Structural Analyses for SRM Segment, Field joints, and Seals

1. Organization/Responsibilities

This appendix deals with all analyses relative to the SRM field joint and seals in terms of structural capability, mating characteristics, O-ring seal gap opening, O-ring response, and fracture mechanics. Additional loads and analyses are presented in the Systems Working Group Final Report.

Various MSFC and contractor personnel contributed to the successful completion of Appendix B. The overloads reconstruction tasks were conducted by MSFC, JSC, and Rockwell Space Division and are reported in the Systems Working Group Final Report.

Marshall Space Flight Center

ED21/Structural Dynamics Division

Tulon Bullock

Larry Kiefling

Dr. Carlton Moore

Dr. John Townsend

Wayne Holland

David McGhee

EP41/Structural Division

Carmelo Bianca

Dick Brolliar

Rod Stallworth

Larry Craig

Greg Swanson

Tim Kelley

Bobby Elkins

Morton Thiokol

Arnie Thompson

Dr. Ron Webster

Bill Macbeth

Keith Sperry

Lockheed

Mike Foley

Johnson Space Flight Center

Rockwell International Space Division

Rocketdyne

USBI

Teledyne Brown

The structural analysis lead was Robert S. Ryan in support to the SRM group.

2. Method of Investigation

The method followed for these analyses was: (1) determine all events important to joint/seal analysis, (2) determine or acquire natural and induced environments for these events, (3) develop appropriate structural models to characterize the hardware for the event, (4) perform static, dynamic, and capability analysis using models and event environments, and (5) evaluate results in terms of findings and conclusions. Figure B.1 is a list of the events analyzed starting with SRM segment mating and ending with the max Q flight event. Figure B.2 breaks down further the overall approach while Figure B.3 depicts the overall flow including special 51-L geometric dimensions. The SRM joint Deflection Reference Test (MTI 103) was used to fine tune and verify the various models. Because of the complexity of the structural configuration and the stringent prediction accuracy requirements, several different models, parameter effects, etc., were required in order to meet the objectives of the investigation. Figure B.4 is a listing of the major models developed and used.

The environments were determined from telemetered data, flight event reconstruction, special analyses, and measured natural environments. The flight event reconstruction determines all external loads environments and is discussed in the Systems Working Group Final Report.

Simplification of the overall analysis was achieved by four special studies which allowed reducing the model and approach to a quasi-static or static analysis, using simplified pin/hole constraints, and propellant as mass only. These analyses were: (1) dynamic effects of bending and shell modes on field joint response, (2) effect of elastic propellant on field joint response, (3) nonlinear iteration of joint, pin boundary to check the simplified pin/hole constraint assumptions, and (4) O-ring response analysis. The results of these analyses will be discussed along with the overall field joint analysis results.

3. Terms and Acronyms

The terms and acronyms used in this appendix are identified in the main body of the report.

4. Narrative Description

This section of the report will discuss the assumptions, results, and findings that contribute to the field joint response. Special studies conducted to verify assumptions and determine unique effects will each be discussed. Next, the basic joint response will be formulated and the combined behavior will be determined. Special capability studies will also be discussed. Finally, the findings and conclusions will be stated.

4.1 Dynamic Effect of Bending and Shell Modes on Field Joint Opening

Bending and shell modes were developed for the 360° one-diameter forward and aft segment models including models of the clevis, tang, and pins. Figure B.5 shows the finite element models for the clevis, tang, aft ET attach ring and the forward and aft one-diameter length segments. Approximately 150 modes were calculated for a frequency range of 7 Hz thru 7,000 Hz. The dynamic response was run for the SRM ignition time portion of the lift-off transient and compared to a time point static analysis. The difference in shell deflection and field joint gap deflection between the static and dynamic analyses was negligible. As a result of these analyses it was concluded that a quasi-static analysis was adequate for determining gap opening as a function of time to the various induced and internal loads acting on the SRM case and joints.

4.2 The Effect of Elastic Propellant on Field joint Response

(a) Model Description

The SRB aft field joint was modeled using EAUSPAR finite element code. The math model defines a total of 220 nodes in a symmetric 4° segment of the motor. The propellant grain is [L110] modeled with 80 Solid elements while the steel motor case is represented by 19 quadrilateral plate elements. The model includes 116 inches of the motor length such that the effects of the end boundary conditions are not significant near the field joint. Figure B.6 gives a graphic representation of the propellant/case model. Note in particular joint 91, where the MACRO and plate elements join. The model is used to determine the static and dynamic effects of the elastic propellant on field joint response.

(b) Applied Loading

The pressure time history function used in the present analysis is shown in Figure B.7. The maximum pressure is 768 psi at t = 0.652 seconds. The pressure time trace defines the internal pressure applied to the inside bore of the propellant grain. This pressure function was reconstructed from hoop strain gage data (TWR 13852 and TWR 14914) taking into account the propellant radial stiffness effects and ballistic model results. For the purpose of understanding the influence of the propellant elasticity and damping characteristics of field joint response, a second analysis was performed using the same pressure function applied directly to the steel motor case model without the propellant. The math model is only capable of predicting the response to zero harmonic loading; therefore, no strut loads were considered. Previous analysis has shown that the case response is dominated by the internal pressure in the motor.

(c) Propellant Damping

Propellant damping is nonlinear; the function is dependent upon temperature, strain, and frequency. Figure B.8 shows the propellant damping properties as a function of temperature and frequency. The data points are given in terms of equivalent linear damping where percent damping equals one-half of the loss modulus/storage modulus ratio. Notice, as temperature drops percent damping decreases with less dependency on frequency. In general, propellant damping is high, greater than 20 percent for all cases. For the analysis reported herein, 30 percent damping is assumed for the propellant and 1 percent damping for the structural shell. The effects of propellant structural damping on field joint response are clearly depicted in Figures B.9 through B.11. Acceleration, velocity, and displacement responses of Joint 91 are plotted with and without propellant. Joint 91 response is typical of all positions along the case shell. As evidenced from these plots, propellant damping filters out much of the high frequency noise in the velocity and acceleration response, but has virtually no effect on the displacement response (amplitude or time).

(d) Static and Dynamic Response Calculations

Dynamic response analysis of the field joint was performed using the method of modal superposition. A total of 250 vibration modes were used in the summation, and response quantities were computed at several locations on the motor case. Figure B.11 shows the time history for the radial component of displacement for Joint 91 on the shell. The maximum value of the shell displacement for this analysis was 0.357 inch. When the same value for the maximum pressure was applied statically, the radial deflection was also 0.357 inch. Similar results were found for other response quantities. Thus for this particular model and load time history, no real difference was noted between the dynamic and static response when the dynamic load was applied quasi-statically.

Four different model configurations were analyzed for a static pressure load of 768 psi. The results of these cases are summarized below in Table B.1. Notice, propellant elasticity (assumed to be constant at 800 psi) has minimal effect on shell radial growth and primary gap opening. Compare Case 1 to 2, and Case 3 to 4.

(e) Findings

The findings apparent from this investigation related to the structural behavior of the SRM aft field joint are:

(1) The elasticity and damping effects of the solid propellant on the field joint response are small. The structural behavior of the SRM is dominated by the steel motor case.

(2) The dynamics of the problem do not yield results that differ from a quasi-static analysis using dynamic loads. The displacement response virtually tracks the applied load, with almost no time lag.

4.3 Nonlinear Iteration of joint, Pin, etc.

Using ANSYS, Thiokol built a finite element model of the web, pin, tang, and a length of the membrane. ANSYS allows the assumption of gaps between the pin and holes, introduction of friction forces, allowing the elements to contact and move or lock as a function of the applied loads. The analysis was run for the ignition pressure buildup case allowing the model to iterate at each step and acquire a position of the pin relative to the hole elements. This case was compared to an analysis where the pin was frozen (locked) in the tang and clevis and ran as a linear analysis. Figure B.12 shows the model and the radial deflection for the linear run. Also shown is the displacement as various colors. Displacements are shown overall and locally in the clevis/tang. Figure B.13 shows the force vectors and displacements acting on the pin with the clevis contact shown at the top and the tang at the bottom. Internal displacement amplitude distribution is shown by the various colors. The color sequence from minimum to maximum displacement is given as dark blue, light blue, green, yellow, and red. Figure B.14 and Figure B.15 are the same plots for the nonlinear analysis. The pin hole contact locked at 200 psia internal pressure. The position and resulting forces and stress field are very close to those assumed for the linear case. This verifies that the engineering assumption made to arrive at gap openings was reasonable and adequate.

In addition, the gap opening was compared to the results obtained by the MSFC analysis. Overall gap opening was 0.034 inch MSFC vs. 0. 031 inch Thiokol. The MSFC model used 3D solid elements while the Thiokol model was axisymmetric. The split between axial force and pressure force (radial) was 15 percent and 85 percent respectively for both models. The nonlinear model untuned gave a gap of 0.040 inch and a 10 to 90 percent split between axial and pressure forces. As a result of this study, a linear locket pin model was used for all gap response analysis. Errors introduced by this assumption should not exceed two mils at maximum gap opening.

[L111] 4.4 O-Ring Response Analysis

An O-ring type sea] has two mechanisms for sealing in an application like the SRM field joints where joint rotation (gap opening) occurs as pressure increases: (1) the resiliency of the seal is sufficient to allow the seal to expand and track the gap opening maintaining a sealing surface, (2) free-floating seal translated into a sealing position by pressure forces in particular flow across the seal through the gap. In practice it is highly desirable to depend on the resiliency and not the free-floating pressure actuated approach. This section will analyze both cases.

(a) Model Assumptions

The O-ring seal was modeled with wedged-shaped solid elements using the finite element code SPAR. The model is limited to a 0.1 segment of the 6-foot-radius O-ring with the proper axisymmetric boundary conditions, and the seal material is characterized as linear elastic. Actually, the Viton seal material is highly nonlinear and has a large time dependency. Typical O-ring relaxation and resiliency data are plotted in Figure B.16. Nonlinear stiffness due to large strains and corresponding deflections and nonlinear material behavior are not defined in the present seal model. An axisymmetric model will not allow various sectional seal initial states on circumferential cross talk. By its nature this approach assumes the same behavior for the total 360° of the seal. Although linear elastic analysis has major limitations for the analysis of the highly nonlinear O-ring, an important understanding of the seal dynamic response is obtained from the results.

(b) Enforced Displacements

A two-dimensional slice of the O-ring cross section positioned inside of the O-ring groove is shown in Figure B.17. The O-ring displacement shapes for three different states of compression are also given. A nominal diameter O-ring (0. 280 inch) is compressed in a maximum depth groove (0.216 inch). A tang-clevis contact boundary, causes a steel-to-steel compression of the O-ring of 0.064 inch, and the O-ring seals on the sides of the O-ring groove. In the fully compressed state, flow around the O-ring is restricted. As the gap opens during the SRM ignition transient, O-ring resiliency and the tang-clevis/O-ring flow boundary characterize the seal response.

(c) Response of Fully Compressed O-Ring

The transient response of the seal after steel-to-steel compression of the tang and clevis was investigated using an uncoupled linear analysis scheme employing superposition of vibration mode shapes. Thirty modes of the O-ring cross section were used from 2,000 to 8,000 Hz. Pressure was applied to the O-ring cross section along the top 180 degrees. The sides of the O-ring were considered sealed. A linear representation of the response is presented in Figure B.18 for release of the fully compressed O-ring. The response plot with a pressure of 936 psi shows that the pressure drives the seal farther into the groove locking the O-ring in this position. For this case, tang-clevis gap sealing cannot occur. The linear assumptions show the seal being driven through the bottom of the groove while in fact this is not possible. The important and correct result is that the seal does not respond to any gap opening and is compressed into the groove by pressure. Additional response plots for the initial steel-to-steel compression of the O-ring are presented for pressures of 468 and 374 psi. The overall trend is to force the seal into the groove. These plots show a slight initial tendency to respond up. This is due to the natural tendency for the top enforced flat on the O-ring to return to a circular configuration. The exact transition pressure between holding the seal in and allowing the sides to unseal is hard to obtain realistically from this analysis. A pressure less than the transition pressure would allow pressure to get under the seal to allow it to respond as the pressure increases. The exact determination of the transition pressure requires a detailed nonlinear analysis taking into account nonlinear properties which vary with time and temperature. The O-ring steel-to-steel compression response plots have a constant pressure load over the top 1800, which would not be the case the instant the seal sides unseal. The plots shown in Figure B.18 investigate the tendency of the 0ring to lock in the groove. Note, seal damping is assumed to be equal for all pressure states given at 2 percent.

(d) Response of O-ring Compressed 0.046 Inch

As in the previous response investigation, linear elastic uncoupled modal transient analysis techniques were used. The initially compressed 0.046-inch seal was modeled with model superposition. This study assumes the tang-clevis combination to instantaneously be separated by 0.048 inch (Figure B.19). Sonic conditions at 400 psi were assumed at the top of the O-ring and the pressure distribution around the O-ring was calculated from area ratios. The downstream side of the O-ring was assumed to have separated flow, and the middle bottom of the O-ring was assumed sealed on the bottom of the groove. The flow velocity between the tang and clevis was 1,038 ft/sec and the velocity over the 0ring top was 2,481 ft/sec. The one-dimensional flow analysis assumed has limitations that have not been test verified. The degree that the Bernoulli induced forces are present for this application are not known. Tests indicate strongly that pressure can actuate seals if initial seal compression is not too large. These test results do not, however, quantitatively verify assumptions made. The first response plot, Figure B.20, shows the linear elastic response of the 0.046-inch compressed O-ring without pressure. Figure B.21 shows the O-ring response of the pressure loading defined by the 0.048-inch tang-clevis separation. This pressure loading state speeds up the response. Although the linear elastic analysis shows very fast response, the nature of the material suggests this is not the case. These plots demonstrate that the dynamic inertia forces are very small.

If in fact the material is slow to restore to its original undeformed shape, it becomes necessary to depend on other sealing phenomenon for quick reaction. An analysis was then done allowing the seal to be free floating to see if it would translate into a sealed position. This was done using the mode shapes of a free O-ring cross section. The first free cross section mode was 4,000 Hz. The response plot given in Figure B.22 shows that the 0ring is capable of free floating into position at a faster rate than the tang/clevis gap opens. Note that this type of pressure sealing is independent of flow material response.

(e) Seal Groove Tolerance Effects

The analyses performed in subsections (c) and (d) showed the criticality of three factors: (1) groove dimensions, (2) seal dimensions, and (3) initial gap size (O-ring initial compression) on O-ring sealing capability at low resiliency. This section analyzes the various gap and O-ring dimensional variations arriving at initial minimum gap characteristics where seal touches groove sides. This position in combination with low resiliency (low temperature) greatly retards the ability to reach a sealing position.

Figure B.23 is the result of combining a nominal O-ring diameter with an average groove assuming 2.5 angle on sides. At a gap of 0.004 inch the seal touches that groove sides. Figure B.24 shows the condition for a maximum O-ring diameter and a minimum groove. In this case the seal touches the groove sides for a gap of 0.032 inch. If the combination of a nominal C-ring and maximum groove is assumed, the O-ring will never touch the groove sides (Figure B.25).

Taking the measured groove dimensions for the right. SRM aft field joint primary (0.2105 depth, 0.307 width, side angle 1), secondary (0. 2 101 depth, 0. 306 width, side angle 1) and the range of O-ring variations possible (not measured) leads to the following results:

Measurements of the other field joint gaps showed them to be within ± 0.003 inch of the above groove dimensions. The expected gap at which wall-to-wall contact is made would therefore range [L112] from 0 to 0.025 inch. The critical dimensions determining whether a seal is in an undesirable initial condition are: (1) O-ring diameter, and (2) initial gap characteristics (O-ring squeeze).

(f) Findings

(1) Initial forces necessary to compress O-ring steel-to-steel (0,064 inch).

Note: The temperature/modulus relationship is based on early test data. (Fluoroelastomer = Viton-E/fluorile)

(2) Steel-to-steel compression of the O-ring results in contact and sealing on the sides of the 0-ring groove. This side groove sealing can couple with pressure forces to hold the seal in a fully compressed state making pressure sealing impossible.

(3) If the seal is not sealed on the sides of the groove (as in the steel-to-steel case), the Bernoulli induced flow forces are sufficient (based on one-dimensional flow assumptions of this analysis) to rigid body translate the O-ring to the sealed position faster than the gap opening transient. This rigid body translation of the seal to a sealing position is known as a free-floating seal. It should be noted that according to the Parker Seal Handbook, it is not recommended that free-floating seals be used for pressures over 200 psi. Obviously, a free-floating actuated seal is highly susceptible to flow induced oscillations.

(4) Although linear elastic theory predicts a very fast snapback of the seal from the compressed state, the extreme time dependency of the Viton material makes response from a highly compressed state too slow to follow the gap opening transient. The seal must depend on a free-floating translation for quick sealing of large gaps which is not the most desirable and reliable approach.

4.5 SRM Field Gap Response for Various Flight Events

The SRM field gap opening as a function of internal and external forces has been analyzed for all flight events in terms of delta gap opening (gap change from any initial state). As stated previously, several finite element models were developed and analyzed because of the complexity of the problem. In generally they generically match the tang and clevis portion shown previously on Figure B.5. The resulting analysis using these models can be classified in two broad categories: (1) static analysis of a narrow width 2 to 4 model of the clevis tang, pin, and segment membrane of 50-inch to 70-inch length depending on the individual choice, and (2) quasi-static analysis using the 360, and one-diameter length segment models with and without the ET attachment ring. The static analysis model, Category 1, is capable of line load and internal pressure only, while the quasi-static model, Category 2, can handle simultaneously pressure, line, and external forces. The quasi-static analysis serves as the base model since external forces can be applied.

(a) Static Analysis of Gap Response

As stated, several static models have been developed. The models were adjusted slightly so that they match the 103 joint Deflection Test conducted at Thiokol. All adjustments were within the variation expected for materials, properties, etc. Figure B.26 is a plot of the strain data versus pressure for various gage locations used for correlating model simulated strains. Figure B.27 shows the gap opening measured at the midpoint of the ridge between the primary and secondary O-ring measured circumferential. Figure B.28 shows gap opening for several pressures versus linear voltage displacement transducer (LVDT) locations or tang/clevis/pin location. Agreement between model and test was achieved within 2 mils at maximum pressure (gap opening) using the ignition pressure buildup at lift-off. A static analysis of the primary and secondary seal aft field joint was run assuming the primary seal does seal, then assuming it does not seal and pressure gets between the primary and secondary seal. Finally, the effect of the alignment gap was analyzed. Table B.2 summarizes the results presented in Figures B.29 through B.34.

The effective peak pressure on the aft field joint of 7 70 psi was used in this analysis. Strut loads were not considered in this simplified model. Observations indicate that the basic model matches the test results well. That is, if the primary seal leaks the gap opening increases due to pressure on the secondary seal and the larger clevis tang area, and the area around the alignment slot has an increased gap opening of at least 2 or 3 mils.

(b) Quasi-Static Gap Opening Analysis for Flight Events

The model used for this analysis was shown in Figure B.5 and has the capability of handling external and internal loads as a function of time. These loads were reconstructed using the procedure shown on Figures B.35 and B.36 developing a time-dependent set of functions. Figure B.37 is a time response of two of these reconstructed loads of the aft field joint. Shown in this figure are the key lift-off events: the axial load and the pitch plane bending moment. The major load is the internal pressure of the SRM. Clearly evident is the structural elastic body ring out when the SSME buildup introduced energy is released.

Table B.3 lists the design limit load and the results of the 51-L loads reconstruction for all field joints. Since all field joints are designed to the highest axial load (forward field joint) and the gap opening is a function of this axial load in conjunction with the equivalent internal pressure and external loads, the forward field joint should experience the highest load and field joint seal gap opening. Effects of all of these combined loads will be evident in the data that follows.

Figures B.40 through B.52 are the delta gap response plots for all the flight events/SRM for-ward and aft field joints for 51 -L. For reference, the SRB attach member (strut) identification and the Shuttle Coordinate System shown in Figures B.38 and B.39, respectively. Both a time response for the maximum circumferential is shown in conjunction with the peak plotted for the total 360° around the joint. The highest delta gap opening occurs for the forward field joint primary seal (37 mils) at lift-off while the aft joint peaks near 28 mils. All joint delta gap openings peak at lift-off. The primary seal delta gap opening is approximately a factor two higher than the secondary seal gap. The mid-field joint gap (not shown) is slightly lower than the forward field joint.

The aft field joint, because of the external loads applied through the struts, shows smaller dynamic activity (Figure B.40). Here the approximately 3 Hz vehicle mode produces a small delta gap opening of ± 2 mills. A max/min for any aft joint location is plotted on Figure B.41 and shows about a 3-mil variation circumferential. Max Q gap openings are approximately 30 percent less than lift-off; however, the external loads influence is greater.

The aft field joint was also used to check the effect of installation alignment slots on the seal gap opening. Figures B.33 through B.55 show this effect. Approximately 2-mil gap opening increase is observed. A blowup of this area is shown in Figure B.54 with the increase and the influence of the alignment slots on gap opening. The gap opening at the alignment slots is also apparent in the MTI 103 joint Deflection Test data (Figure B.55).

Delta field gap opening is a very dynamic phenomenon at SRB ignition with a total travel of 20 to 30 mils within 600 milliseconds. All other transient gap conditions occur at a much slower rate.

4.6 SRM Structural Capability

In this section, the structural capability of the SRM is assessed in terms of: (a) mating loads and resulting stresses on the [L113] aft field joint. (b) effect of partial joint failure, and (c) effect of local membrane holes.

(a) Mating Analysis

The analysis to assess the stresses and deflections during mating -if the aft center segment to aft segment is scheduled to be completed by April 13. As part of this analysis we have:

(1) Determined the point load required to deflect the suspended segment the width of the chamfer on the tang (0.2 inch).

(2) Set the tang on the inner leg of the clevis at one point and allowed the segment to rotate until the tang on the opposite side 180 degrees away was almost resting on the outer leg of the clevis.

(3) Determined the loads required to mate on ovalized tang and clevis.

(4) Determined the maximum bending stress that resulted from use of the SRB circumference alignment tool during mating of :he right aft center segment of 51-L.

The radial load required to deflect the suspended segment 0.2 inch as in (1) above is only a low 75 pounds because the overhead crane cable is over 640 inches long. The axial load applied to the clevis inner leg by the loading in item (2) above is 8,000 pounds. The loading required to mate an ovalized tang and clevis is currently in progress. Initial indicators are that the peak radial force per circumferential inch required to mate the two segments is less than 100 pounds per inch. The maximum load applied radially inward using the alignment tool was 4,000 pounds. Calculations using Flexible Circular Ring Analysis resulted in a bending stress of 59,656 psi. Safety factors for the bending stress are 3.02 on yield and 3.2 7 on ultimate. The analysis is conservative because the stiffness of the propellant is not considered. The mating scenario has also been analyzed from a fracture mechanics viewpoint (Section 4.7). The conclusion reached from the stress and fracture mechanics analysis is that the mating loads caused no damage to the joint.

(b) Effect of Partial joint Failure

As a part of the investigation, the length of the aft field joint failure around the circumference that could be failed without an overall joint failure was determined for various loadings and temperatures of the unfailed joint.

In Figure B.56 the circumferential opening (W) is the sum of all joint lengths around the circumference of the field joint. In this figure the maximum failed joint length is 315 inches with .he unfailed joint at room temperature. The example shows this failed length decreases to 273 inches when the temperature is raised 800°F. In Figures B.57 and B.58 the failed joint length is continuous. Figure B.57 considers both the axial load and the vehicle bending moment in determining the allowable failed joint length. The length is 158 inches with the remainder of the joint at room temperature. Figure B.58 considers the axial load and the internal pressure-induced bending moment. For this condition, the maximum failed length is 131.9 inches with the remainder of the joint at room temperature. Both Figures B.57 and B.58 show the failed joint length as a function of the temperature of the remainder of the joint.

(c) Effect of Local Membrane Holes

As a part of the failure investigation, various membrane failures were examined. A round hole was examined with a case internal pressure of 600 psi. For this hole and pressure the stress at the hole edge is 240 ksi which is 23 percent above the D6AC design strength and overall failure of the shell wall would result. At 600 psi internal pressure, elliptical holes with the dimensions shown in Figure B.59 would survive and at 975 psi the elliptical hole shown in Figure B.60 would survive. If the elliptical hole grows in the circumferential direction to a ratio of the major to minor axis of an ellipse (B/A) of 8.0 as shown in Figure B.61, the maximum allowable internal pressure is 227 psi. The analyses support the conclusion that the anomaly was not associated with a burn through in the SRM case membrane.

4.7. Fracture Mechanics

The fracture mechanics analysis that has been completed to date assesses the stresses and deflections during mating of the aft center segment to aft segment. The O-ring groove area has been analyzed to determine the criticality of a flaw in the highest stressed area.

If the clevis was damaged by the mating forces, the weakest location, which would be damaged first, is at the secondary O-ring groove. A fracture mechanics analysis was performed using a conservative 1,000 pound radial load shown in Figure B.62 combined with an 8,000 pound axial load shown in Figure B.63 and the 936 psi internal pressure shown in Figure B.64. The stresses at the O-ring groove for each of these loadings is also shown in Figures B.62 through B.64. Figure B.65 shows the O-ring groove model along with the stress variation for the internal pressure loading case. The load history used for the fracture mechanics analysis is shown in Table B.4. Table B.5 shows the initial flaw size and the final size after 100 launch cycles for two flaw shapes. The flaw size analyzed was larger than that typically found by Magnetic Particle Inspection. The flaw growth is less than 2 percent in 100 launch cycles. The conclusion reached from the fracture mechanics analysis is that mating loads caused no damage to the joint, and that the failure was not the result of growth of an undetected flaw.

4.8. SRM Case Pressure Rounding Discussion

Twelve-foot-diameter shells one-half-inch thick containing propellant weighing over 300,000 pounds are assembled using a tang/clevis joint arrangement. The axial loads are transferred through 177 pins in double shear. The joint has some assembly clearance which is reduced after assembly by installing shims. Some radial clearance remains after shimming. Because of the weight of the motor segment and the high ratio of diameter to shell thickness (D/t) ratio, the assembled joint clearances can vary form one side of the clevis to the other. This clearance was 0.020 inch for the STS 51 -L right SRM aft flight joint. If both parts (tang/clevis) were round and concentric, then a radial clearance of 0.004 inch would be predicted. The pin/hole stop is sufficient to allow this configuration to vary to both sides of the clevis, even though they are on a 2-degree angle.

The aft segment is supported on the four posts on the MLP. The posts are in a rectangular configuration. This nonaxisymmetric loading influence appears to show up on the aft segment clevis field joint as an out-of-round condition. The aft center segment is also out-of-round due to the two-point lifting which causes a water bucket effect.

For the STS 51-L right SRM aft field joint a condition of zero gap (metal-to-metal) minimum to a maximum of 0.020 inch is assumed to exist between the sealing diameters. This represents the maximum and minimum sealing gap at stacking conditions. Some gap equalization will occur due to O-ring compressive forces. This analysis is forthcoming.

The aft center segment tang is lowered into the clevis of the aft segment. The joint is pinned as pin holes line up. Finally, the total load is transferred from the crane to the pins. It is estimated that the line loads are sufficient to create friction loads that will hold the tang/clevis in the as assembled position. The radial loads are estimated to be relatively low so that no repositioning of tang/clevis occurs during the remainder of the stacking.

The SSME firing prior to ignition of the SRM relieves the compression pin load so that some opportunity does exist that will allow adjustment of the sealing gap. Considerable gap adjustment will again occur as pressure builds up in the SRM case after ignition. The out-of- round joint and case membrane tends toward a round condition as this represents a minimum energy condition. Some simple estimates indicate that this may happen at about 200 psi. There are, however, no tendencies to cause the cases to be concentric. STS 51-L right SRM aft field joint would have an annulus of 0.004 inch assuming a round and concentric condition. Therefore, 0.008 inch would be estimated if the case is against one side (metal-to- metal) and the full, nonconcentric gap on the other side (180). The time for this readjustment to occur is very fast; friction is overcome. A snap-action, maybe on the order of 0.008 seconds, occurs. This means that the initial [L114] gap of zero will suddenly become 0. 008 inch. The seal gap of 0. 020 inch could suddenly become 0.008 inch for a change of 0.012 inch.

In the meantime, the SRM pressurization will continue to open the seal gap according to the linear function shown in Figure B.66. These data were determined from the Test MTI 103 which showed a gap opening of 0.034 inch at 1,004 psi. This measurement was taken at the midpoint of the land between the O-ring load. Analysis to transfer this measurement to the primary sealing gap and the secondary sealing gives 0.035 inch and 0.022 inch, respectively. The pressure time function of the joint is shown in Figure B.67.

The effective O-ring squeeze is established as follows:

Table B.1 has been developed based on an initial gap of 0. 020 inch. It is assumed that when the chamber pressure reaches 200 psi that the compressive pin loads are relieved so that they can assume a new position. The loads that are involved in joint mating are different than those at launch. Therefore, the tang/clevis relative changes can occur during changeover from compression prior to SRM ignition to tension which is developed by pressure blowoff loads. This changeover is estimated to occur at about 200 psi. With these assumptions, Table B.6 was developed for total gap opening and O-ring squeeze at various time steps. Table B.7 was developed with similar assumptions, except that an initial seal gap of zero or (metal - to- metal) was assumed.

Figure B.68 shows the gap results as a function of time for the primary and secondary O-rings. Initial assumption of zero gap and 0.020 inch are shown. The O-ring resiliency response is aggravated by the sudden increase of gap of 0.008 inch due to rounding. At 25°F, the O-ring could not follow the case movement due to pressure, let alone the sudden jump. The case rounding starting at the max gap of 0.020 inch helps to reduce gap opening motion when the 0.020-inch initial gap goes to 0.008 inch. This could cause the seal to open and then recontact the sealing surface so that if pressure were to arrive at the O-ring it could seal.

4.9 Total Gap Opening Versus Flight Time

This section of the report combines the various analysis results to produce an overall SRM field gap opening versus time (flight events designated) for 51-L. (Figures B.69 through B.75 for all field joints right and left SRMs.) Figures B.69 and B.73 are the overall gaps for right and left SRMs while the other figures give a more detailed view of the transient, rounding, and roll maneuver areas. The approach taken has been to add the delta gap to the geometric gap and gap change due to rounding. Indicated on the graph for the lift-off peak and max Q peak are the gap opening range for the design limit load envelope. The rounding effect assumes that the 20-mil worst gap opening is combined with a metal-to-metal condition. When the case rounds the two become essentially equal. Other cases are possible; however, the data presented should be representative.

The principal gap occurs during the first 600 milliseconds of SRM burn going to a peak between 36 and 45 mils. Only the aft field joint gap responds at any significant level to the dynamics. This response is mainly due to strut loads. The bending moment effect is present but not as pronounced. The roll maneuver adds approximately 2 mils. At approximately 20 seconds the gap starts reducing due to internal SRB pressure reduction. Since pressure dominates the SRM loads and gap opening the dynamics (mainly rigid body motion) adds only about 3 mils opening to the pressure and line load-induced opening. These dynamics are due to the wind shear and gust-induced vehicle response. These results match the joint rotation test data differing only by the external loads influence and tolerance stack ups.

Combining the results of the gap opening data with the seal response data indicates strongly that the critical gap opening and seal blowby time occurs within the first 600 milliseconds of SRM burn with some delta motion occurring through the first two seconds. If the O-ring seals normally at lift-off there is no additional situation occurring which should cause the seal to leak since the internal pressure reduces, therefore the gap reduces during max Q. If the seal is degraded or if the joint gets heated, then the gust-induced response could possibly start a leak. In particular, heating the joint would lead to amplification of the gap opening due to dynamics. If the seal was cold (low resiliency) and a metal-to-metal condition existed (seal pressed against groove), it is unlikely that the seal would have pressure actuated and sealed early. The forward and midfield joints have 6 to 10 mils more opening of the primary seal gap at lift-off and max Q. All things being equal these joints should leak first.

In conclusion, the gap openings presented for the primary and secondary O-rings are representative of the situation that occurred on 51-L. The accuracy of the results should be well within ± 10 percent and should be adequate.

5. Findings and Conclusions

a. SRM field joint seal gap opening is primarily due to internal pressure. This pressure bulges the case (radial) and lengthens the case longitudinally (line load). Thrust also adds to line load. Approximately 85 percent of the gap opening is due to the radial bulging for the case where no external forces are applied.

b. External loads and dynamics have a small effect on seal gap opening.

c. The forward field joint has the highest load and seal gap opening with the aft field joint the lowest.

d. The majority of the field joint seal gap opening occurs the first 600 milliseconds after SRM ignition due to the fast buildup of internal ballistics pressure.

e. The largest field joint seal gap opening occurs during the lift-off transients. The roll maneuver has a comparable value.

f. Stackup tolerances and case loading can add up to 8 mils to the dynamic seal gap opening that occurs from pressure and loads.

g. There is a vehicle structural dynamic oscillation during the lift-off transient of approximately 3 Hz. This oscillation adds ± 2 mils to the seal gap opening.

h. Modeling the solid propellant elasticity and damping effects had a small influence on seal gap opening (less than 2 mils maximum).

i. SRM lateral bending and shell modes had negligible effect on seal gap opening predictions.

j. Steel-to-steel compression of the O-ring results in contact and sealing on the sides of the O-ring groove. This side groove sealing can couple with pressure forces to hold the seal in a fully compressed state making pressure sealing improbable.

k. If the O-ring is not sealed on the groove sides, the Bernoulli induced flow forces can rigid body translate the O-ring to the sealed position faster than the gap opening transient.

1. Although linear elastic theory predicts a very fast snapback of the seal from the compressed state, the extreme time temperature dependency of the Viton material makes response from a highly compressed state too slow to follow the gap opening transient. In this state the seal must depend on a free-floating translation for quick sealing of large gaps.

m. The mating and fracture mechanics analysis results show the mating loads and resulting stresses during assembly of the aft center segment to the aft segment were low, causing no damage to the joint.

n. Motor case structure integrity is maintained for a family of membrane burn through cases that result in elliptical hole [L115] formation. if the elliptical hole grows in the circumferential direction to a B/A of 8.0, where B/A is the ratio of major to minor axis of ellipse the maximum allowable internal pressure is 227 psi.

o. The max Q region of flight had active response due to wind gust. The Q was slightly outside the flight experience envelope as was the SRB gimbal duty cycle.

p. If the seal is degraded or if the joint gets heated, then the gust-induced response could possibly start a leak. In particular, heating the joint would lead to amplification of the gap opening due to dynamics.

B. SRM Temperatures

The STS 51-L vehicle experienced the coldest ambient temperatures at launch of any of the Space Shuttle launches to date. Since many of the SRM failure scenarios relate to cold temperatures at least in part, and because some abnormally low infrared temperature measurements were made on the right-hand SRM aft segment prior to launch, there has been a significant effort to assess the pre-launch thermal environments.

The SRM case temperatures are normally predicted to be within a few degrees ( ± 5) of the local ambient temperature except when ambient conditions are changing rapidly or when the motor case is exposed to sunlight. The infrared measurements made on the right SRM were 15° to 17°F below the ambient temperature and were clearly thought to be indicative of an anomalous condition, such as a cryogenic leak, unless the measurements could be found to be in error.

Several studies and tests were conducted to assess the infrared instrument used to take the measurements. In addition an analysis was performed to assess the possibility that normal launch pad or vehicle systems could locally depress the ambient temperature near the SRM enough to be consistent with the infrared measurements. Pre-launch film coverage and other on-pad observations were also reviewed to assess any possibility of cryogenic leaks.

It was concluded from this effort that the infrared measurements were in fact in error, that the local environment on the pad in the vicinity of the SRM was somewhat colder than the ground level ambient temperature, but that there was no indication from these data to suggest a cryogenic leak or anomalous venting on the pad. It was further concluded that the best estimate for the right SRM aft field joint temperature at the coldest location at the time of launch was 28°F with an uncertainty of ± 5°F and that the minimum temperature on the other five joints was approximately the same within 3°F.

1. Ambient Environment

The ground level temperature was falling throughout the preceding night with a value of 30'F at midnight (00:00 E.S.T.) and a minimum of 24°F just before dawn at 07:00 E.S.T. After dawn the ground level ambient temperature increased to 36°F at the time of launch (11:38 E.S.T.). The winds were generally out of the northwest (azimuth of 260° to 310°) at 5 to 9 knots throughout the launch operations. The relative humidity was from 45 to 65 percent with a corresponding dew-point temperature of 16°F to 18°F during the preceding night, and had fallen to 30 percent with a dew-point temperature of 11°F at the time of launch. These data are summarized in Table B.8.

The ambient temperature measurement for the Launch Pad 39B is a ground level measurement located at camera site 3, approximately 1,000 feet from the pad. The ambient temperature on the launch pad is not measured, however it can be inferred from surrounding meteorological tower data. At the time of launch the surrounding towers showed a significant temperature stratification versus altitude with the air temperature at the SRM aft joint elevation (120-foot level) about 5°F colder than the ground level ambient. This is shown in Figure B.76, and summarized in Table B.9.

2. Observations and Measurements

Data pertaining to conditions on the launch pad consist of reported observations from the Ice/Frost Team inspections, infrared measurements of the vehicle and launch pad, and photographic and video coverage of pre-launch operations. These data were reviewed in an attempt to obtain a consistent evaluation of the pad environmental conditions, and to assess the possibility of any anomalous cryogenic systems which could affect the local temperatures.

The Ice/Frost Team observations are well documented by KSC in reports and photographic files which are available upon request. The following is a summary and an assessment of the SRM environment reports.

a. Water Trough Observations

During the night ice had formed in the overpressure water troughs which are located at the base of each of the SRBs. The troughs had been filled with an antifreeze mixture which should have protected against freezing down to temperatures of 16°F. Since the measured ambient temperature was near 24°F, there was some concern that the freezing in the troughs was an indication of additional cooling of the local ambient on the pad. The reports concerning the ice in the troughs read as follows:

During the first assessment made by the Ice/Frost Team at 01:30 E.S.T., "the secondary overpressure water troughs were found to have sheet ice estimated to be 1/2-inch thick. Eight left-hand troughs and 12 right-hand troughs had ice. The ice density was approximately 25 pounds per cubic foot No ice was observed in the primary water troughs until the T-3 hour subsequent inspection was made."

During the subsequent T-3 hour assessment which began at 07:00 E.S.T., the Ice/Frost Team observed "Ice in the troughs had thickened and was found to be solid. All secondary troughs except the northern most one now had ice. The two inboard primary hole troughs were also forming ice. An attempt to use a waterjet from a Firex hose to break up the ice was unsuccessful. . . . Approximately 95 percent of the ice was removed. . . ."

A final assessment was made between 10:30 and 10:55 E.S.T. and the observations from this inspection were "the water troughs were checked and found to be forming ice, which was again removed. . . . During the third inspection. only the two south primary troughs remained ice free."

The first inspection was conducted after a stop flow of the ET cryogenic loading operations. At the time of the inspection there was little or no propellant in the ET, although the pad and Orbiter systems had been cooled down, as well as the ET aft LH₂ dome. At this time the Ice/Frost Team estimated that there was 1/2 inch of ice in some of the troughs. Calculations indicate the.....

[L166]....ice could easily be forming in these troughs due to cooling from the night sky alone. The troughs are recessed somewhat below pad level and are thus protected from wind-driven convection. Because of the horizontal orientation, the water/anti-freeze mixture will experience maximum radiative cooling to the night sky. The underside of the troughs is also protected from convection because of the position high in the Mobile Launch Platform (MLP) exhaust hole.

Calculations of the heat balance for the water troughs was performed for ambient temperatures beginning on the previous evening. These calculations predict the equilibrium temperature that the mixture would reach if allowed to completely freeze and come to steady state, as well as the freezing rate in inches per hour if held at the 16°F freezing temperature reported for the mixture. A summary of these calculations is presented in Table B.10 and shows that the mixture could have begun to freeze as early as 07:00 p.m. the previous evening. This probably did not occur, however, since the troughs were being filled with the antifreeze mixture near that time. Note that the "equilibrium mixture temperature" is a calculated lower limit and not the expected mixture temperature.

The freezing rates shown would predict about 0.3 inch of 25 lb ft² density ice at the time of the first inspection which is considered to be within range of the observations. Additional cooling due to the evaporation, or a higher than expected freezing temperature of the mixture could explain the difference between the calculation and the observed 0.5-inch thickness. (Tests at KSC indicate that the water-antifreeze solution may have stratified and that the top layer could have been freezing at temperatures between 18°F and 22°F.)

b. Left SRB Icing Observations

An additional observation made by the Ice/Frost Team which relates to the SRM environment was that the left SRB aft skirt and aft motor segment had formed patches of sheet ice due to water spray from the Fixed Service Structure (FSS). The occurrence of ice on the left SRB is used to explain the infrared measurements made at this location. The spray of water from the FSS and subsequent freezing on the SRM surface would provide a 32°F surface temperature as viewed by the infrared instrument, even though the pad ambient temperature was near 22°F.

c. Infrared Measurements

The Ice/Frost Team routinely use an infrared pyrometer to aid in the assessment of icing conditions on the ET. This instrument provides for remote sensing of the tank surface temperature based on the infrared energy omitted from the surface. Measurements are also made of selected SRB and Orbiter surfaces as well as the launch pad structure. During the STS 51-L inspection an Omega Scope 2000A infrared gun was used to make the measurements. The gun had been in use for the previous two inspections including the STS 51-L abort and STS 61-C.

The initial readings obtained during the STS 51-L inspection revealed several measurements which were abnormally low, including a 7°F reading of the right SRB skirt, and a 9°F reading on the right aft motor segment. At the time of these readings, the ambient temperature was at 22°F at pad level and had been gradually falling several hours as shown in Figure B.76. Exposure to the cold night sky and the cold ET surface could cause the SRM case to be somewhat below ambient in this transient, but not as low as the 9°F obtained from the infrared measurement.

d. Infrared Pyrometer Testing

Testing of the infrared pyrometer used by KSC, and testing of the same type (model) but of a different unit, were performed by both MSFC and JSC. All three investigations revealed a substantial transient error or bias in the instrument when it is exposed to a change in temperature similar to the transition from room temperature to the 22°F ambient as experienced for STS 51-L. The transient error for the instrument tested by KSC is shown in Figure B.77. A similar but slightly higher error (-18°F) was observed on the instrument tested by MSFC, and the tests at JSC show an even greater error on their instrument especially when exposed to wind at the lower temperature. All three tests showed good measurement accuracy once the instrument had stabilized at the exposed environment.

In addition to the transient bias of the instrument discussed above, an error due to surface emissivity was also identified, both analytically and by test. The error occurs because the instrument is set for a surface emissivity of 1.0 whereas the actual SRM surface emissivity is from 0.87 to 0.95 depending on surface contamination. The right SRM is especially susceptible to the error since the reflected background radiation is primarily from the night sky, which emits little radiation in the wavelength at which the instrument operates. The estimated corrections to the right SRM for emissivity is + 3°F with an uncertainty of + 2.0°F. Surfaces which are wetted, or which have ice or frost formations would have little error expected because both ice and water have an emissivity near 1.0 which eliminates the error. The ET, the water troughs, and the areas of the left SRM which had ice formations are in this category.

e. Corrected Infrared Measurements

The infrared measurements were corrected based on the transient error reproduced by the NASA-KSC tests on the actual instrument and on the timeline of observations made by the Ice/Frost Team. The additional errors due to emissivity and general instrument inaccuracy were also added and the uncertainties in each were root sum squared (RSS) to obtain an overall uncertainty. The error budget for the right and left SRM measurement locations is presented in Table B.11 below.

The left and right SRM measurements were corrected based on the total error shown in Table B.11 and compared to our predicted temperature for the same location (Table B.12). Also included in Table B.12 are three other selected measurements made on the MLP level and corrected in the same manner. The range accounts for the uncertainty in both the corrected measurement and the analysis.

[L167] The right SRM shows as good agreement as is normally expected between measured and predicted data. The left SRM prediction does not account for the water and ice buildup observed which would explain the corrected measurements. The two ET measurements agree well with predictions, and the water trough measurements agree with the reported antifreeze freezing temperature of 16°F. The low value of the water trough prediction is for a transient cool-down of a frozen mixture, whereas the high value is for a partially frozen mixture and was thus set at the reported mixture freezing temperature.

f. Photographic and Video Analysis

Both photographic and video coverage of pre-launch operations were reviewed to assess the possible transport of the SSME seal drain vapors toward the right SRM as well as detect any indication of a cryogenic leak or venting on the pad. The vapors from the engine drain lines were observed to be blowing toward the right SRM at times, and were generally consistent with a launch pad flow analysis discussed later. No other anomalous vapors were noted.

3. Analysis of Local Ambient Temperature Depression

The thermal analysis which is performed to predict the pre-launch SRM temperatures normally does not include any depression of local ambient temperature due to the effect of pad or vehicle cryogenic or subcooled venting, or due to convective cooling from the ET. (Radiation to the cold ET surface, however, is included.) In view of the low infrared measurements made on the right SRM and the ET (uncorrected) a study was initiated to quantify the possible depression of the ambient temperature on the launch pad.

a. Pad and Vehicle System Purges and Vents

Cryogenic or subcooled gases are routinely vented in the vicinity of the Shuttle vehicle including the oxygen vent at the top of the fixed surface structure, the SSME seal drains which vent at the base of the Orbiter, and several inerting purges which vent at various locations. The vehicle and ground purges were reviewed and none were found to be of a magnitude or in a position to affect the environment near the right SRM. The oxygen venting at the top of the fixed surface structure similarly is not in a position to affect the right SRM although it could influence the ET upper surface temperatures. The SSME drain seals, however, do provide a large flow rate (approximately 1.1 lbm/sec of 250°F gas from each of the three engines). They are in a location where southwest winds may provide a transport of gas to the vicinity of the right SRM. This was selected for further study.

b. ET Convective Cooling

Convective cooling from the ET surface as it affects the SRM temperatures is normally assumed to be minor since the ET insulation system provides very good insulating capability and thus limits the heat loss to the surrounding air. In addition, any natural or forced thermal boundary layer which may form on the tank surface would tend to mix and rapidly dissipate in the continually changing wind conditions before interacting with the SRM surface. Conditions which would be favorable to maintaining a cold local environment around the SRM would be little or no wind, which would also limit the effect on the SRM. In view of the low measurements on the right SRM, however, the potential for convective cooling from the ET was selected for further study in an effort to at least establish bounds on the possible effect.

Two efforts were initiated by MSFC to further study the potential for a local ambient temperature depression. The first was a three-dimensional flow and heat transfer analysis of the Shuttle and Launch complex to assess the interactions of the wind with the pad structure and vehicle, convective cooling from the ET, and the possible transport of the SSME drain seal gases to the SRM. This was performed by CHAM of North America Incorporated. The second effort was part of a general independent SRM thermal analysis performed by SRS Technologies which was intended as an audit of the MSFC analysis. The SRS effort assessed the potential effect of ET convective cooling on the SRM in the absence of any wind.

(1) Launch Pad Flow and Thermal Analysis

The three-dimensional thermal and flow numerical model included the launch pad (mound), the MLP, the support structures, and the Shuttle vehicle. These features were modeled in an attempt to determine the wind flow around the vehicle, and also to assess any wind induced vertical flow either through the SSME exhaust duct or near the Shuttle vehicle. The wind conditions in the launch area during the STS 51-L launch operations were used, with the wind directions of 260°and 300° considered. The analysis has shown that the maximum cooling near the right SRM is about 4.5°F for the 260° wind direction, and about 3°F for the 300° wind direction.

(2) ET Natural Convection Analysis

The purpose of this analysis was to determine the temperature and velocity in a boundary layer that could possibly have developed on the ET and intersected the SRM. The boundary layer analysis performed considered the flow to be initially laminar and then transitioning to turbulent flow with a simultaneous heat balance solution at the ET surface. The results of the analysis predicted that at the SRM surface, 12 inches from the ET, the velocity would be 1.73 ft/sec and the temperature 5.5°F below ambient. This is at the station of maximum boundary layer thickness which occurs at the base of the ET near the SRB attach point.

The boundary layer was allowed to grow over the entire height of the hydrogen tank undisturbed by wind, thus producing the maximum thickness, velocity, and cooling at the SRM surface, which should be considered a worst-case bounding of the problem. The occurrence of this type of boundary layer would also result in colder than normal ET surface temperatures, calculated to be below -25°F at the point of maximum boundary layer thickness. There was no indication that this had occurred either from the infrared measurements or from observations, such as excessive frost buildup.

c. Summary of Local Temperature Depression

The three-dimensional thermal and flow analysis and the ET natural convection analysis indicate that an ambient temperature depression on the order of 3°F to 5°F could be possible in the vicinity of the right SRM for the conditions which existed during STS 51-L. These results were subsequently used to adjust the depressions in the aft field joint predicted temperatures discussed in subsection C-5.e.

4. SRM Thermal Analysis

a. SRM Thermal Model Description

Thermal analysis of the SRM case is performed using a two-dimensional model of a SRM segment which can be configured to represent either the left or right aft or mid-segments. The model includes the motor case, insulation, and propellant and is constructed in eight circumferential nodes (around the case) and nine radial nodes from the steel case inward through the propellant. The external environment simulation includes convection based on an average wind speed, solar radiation, and radiation to the ambient, the ET, the Orbiter, and the sky. Sky temperature is calculated from ambient temperature using a simplified algorithm, and solar radiation is simulated by an al