Other commitments have taken me away from this project for the last month. I don't yet have the program harness working. Programming is my field, and I understand the problem, but don't have a solution yet.
Meanwhile I've been trying to get some useful information out of the simulator. Bear in mind that the simulator results are all that's available, but they can only be considered an approximation. I covered the fact that knife-edge flying is not possible at 160 knots. Two other questions are answerable by hand-flying: What are the behavior characteristics of an Electra banking right under full left rudder, and what attitude would result in a five degree descent slope.
Several pilots have agreed that the rudder must have been hard left. This would be an instinctive response, it would have an immediate effect, and they would have maintained it until they regained level flight. So we have an airspeed of about 160 knots and hard left rudder in a right bank. The first issue is to determine what this does to the turn radius. All my illustrations are based on balanced turns, because no one could estimate what the rudder inputs would do to the radius.
We have evidence that the bank angle at impact was near 34 degrees, so I used that angle when collecting a representative radius value, but I'm not saying this radius calc is itself evidence for a 34 degree bank. A balanced turn at 160 knots and 34 degrees gives a turn radius of 3370 feet. A 35 degree bank at 160 knots and hard left rudder in the simulator gives a turn radius of 5275 feet. I'll be running more trials to get an average, but it's in this ballpark. The left-rudder turn radius is around 1.5 times that of a balanced 35 degree turn, give or take.
In my illustration on page 20 of the 160602 document, I said that the red-dotted path was the most extreme possible, but that was based on a balanced turn. That path would have resulted in an impact bank angle of about 22 degrees, which made it unrealistic. Given the new unbalanced turn radius estimate, that path becomes much more reasonable. The plane could have reached the 271 heading with considerably more bank than 22 degrees. So the initial emergency probably started with a higher bank farther southeast than I had thought.
The second question is: What attitude would result in a 5 degree descent slope. At 160 knots a 90 degree bank results in free-fall, as discussed earlier. When this project showed me that they weren't in a 90 degree bank as reported, I wondered why they didn't climb. The simulator says at a 34 degree bank and 160 knots with hard left rudder it's easy to climb. So I'm looking for a bank angle extreme enough that the plane has insufficient lift to stay up, but not yet stalling.
As the bank increases, the elevator angle has less and less effect vertically, and starts to serve only to tighten the turn. Meanwhile the rudder has more responsibility for keeping the nose up, but it's going too slow to do that. N137US weighed 93,000 lbs and would have stalled at about 63 degrees in a balanced turn at 160 knots. My numbers are rough, but it appears that the simulator is giving stall warnings just above 55 degrees. Pulling back on the yoke increases the stall likelihood by lifting the nose, while not pulling back keeps the plane descending.
The exact rate of descent is highly sensitive to airspeed and bank angle, but a descent of 1400 to 2000 feet per minute seems within reach. The 5 degree slope Lockheed estimated would be 1400 feet per minute. The simulator run suggests they were at the stall boundary and unable to stop descending. My latest report characterizes their effort as just trying to manage an unstoppable descent, but seeing the stall warning makes it clearer.
This view, rough as the numbers are, is the best evidence I've seen that my 34 degree impact bank angle estimate is too low. This gives about a 20 degree gap between the simulator's result of a maximum 55 degree bank in flight and physical evidence of a mid-30 bank at impact. I can see a couple possibilities. One is that the flight bank and impact bank are both somewhere in the middle, and computation errors in the simulator are showing a steeper bank than they actually could have had.
The other is that in the last two or three seconds the bank angle was changing, perhaps as the aileron boost unit was returning to neutral. If the second one is the case, then the turn radius was decreasing and the elevators would have been able to pull the nose up. In other words, it's possible the impact was actually a flare that they were unable to initiate until too late.
The idea that the bank was changing rapidly in the last couple seconds feels conceptually awkward, a bit too close to magical thinking. I'm inclined to think the first possibility is the better one.
The rate-of-descent data is very rough because I have a really tight window to get into position and collect data, and I'm no pilot. I wasn't able to collect turn radius data at this extreme bank. If I can get the harness working it will give better numbers.
Meanwhile, I'm always interested in feedback.