This was a good explanation of how math, charts, and diagrams can help pilots get a general idea of what to expect from their aircraft in high density altitude situations. Its limitation is that is only offers avoidance and offers little technique on how to handle high density altitude situations.
He is a FAA accident investigator. To understand his order of priorities we need to read, "Safer Skies: An Accident Investigator on Why Planes Crash and the State of Aviation Safety." Priority One: Make the FAA look good. Secondary Objective: Assign blame with operator, pilot, instructor, mechanic or a combination of them. Finally the Stepchild Objective: Aviation Safety and actually trying to figure out how to prevent similar accidents in the future. They generally leave this last to political damage control.
Why did it not occur to him to lower the nose in the turn. The charts show only level turns. The charts are screaming, "I'm sorry Captain, we just don't have the power." Why not use free natural energy like gravity thrust of altitude. In mountain and canyon situations we generally have more vertical space than horizontal space for turning safely. If we are going too fast, pull up wings level to slow down and trade airspeed for altitude. Turn at whatever bank, whatever bank, is necessary to get the nose going down to the safe target, the bottom of the canyon or drainage. Don't pull back. Allow the nose to go down as it was designed to do in any turn. This will trade that altitude back for airspeed. Level the wings before pulling up, wings level. This will trade the extra airspeed of the dive for altitude to return us to near the same altitude and airspeed as we started with. Using this energy management, no load factor, turn will prevent a diameter of turn that will put us into the opposite canyon wall or lee winds. Using this energy management, no load factor turn, will prevent load factor. We can turn sixty degrees of bank at 1g not 2g. 2g is a level turn. If we don't pull back on the stick, the nose will go down as designed and there will be no load factor in the turn. We will stay at 1g. There will be load factor in the pull up, wings level, before the turn and in the pull up, wings level, after the turn. We don't pull back on the stick in the turn.
The soft field takeoff is the safest takeoff in any situation and especially at high density altitude. No, we don't want to drag the tail tie down. We want the weight off the nose with the wheel just off or rolling without weight on it. We want the mains off as soon as possible and immediately lower the nose to stay in low (six inches to three feet) ground effect, the lower the better. Acceleration is much faster in low ground effect than on any surface, any surface. Six inches rather than three feet might make the difference at a high density altitude airport.
Whatever the math, charts, and diagrams say, if the airplane isn't climbing very well with the nose up, try lowering the nose a bit. If that doesn't help, go slow in updrafts and fast through downdrafts. Look for ridge lift. If nothing works, energy management turn to the middle of the drainage going down hill. Never quit controlling the airplane. We do not have to die just because that is the school solution.
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