When I went through Air Force instructor pilot school I was told: "Never let the student exceed your limits." I was flying the Boeing 707 out of Hawaii where we didn't have a formal IP course so they sent me to the closest one nearby, the KC-135A instructor school house at Castle AFB, near Merced California. That is also where they taught new KC-135A pilots and copilots. A few months after I was there they crashed an airplane after what we were told was a case of the instructor letting the student take it too far. Upon reflection, I don't think it was a case of the instructor letting the student exceed his limits. I think it was more likely the instructor allowing the student the full breadth of his, the instructor's limits. The student was ill-prepared to do that. So now I think of my IP duties thusly:
"Narrow your limits with consideration of the student's."
As we shall see, that KC-135A instructor pilot was given an impossible task. Thankfully, many of us have very good simulators to handle those impossible tasks. Many, but not all. So it behooves us to study those cases where things didn't work out well. That way we will be able to understand just how narrow our new limits have become.
NOTE: This is a work in progress.
Everything here is from the references shown below, with a few comments in an alternate color.
The old KC-135A tanker was a handful. It didn't have a yaw damper and it really needed one. The airplane had a negative lateral stability. In English: if you took your hands off the controls, it had a natural tendency to rock its wings in an ever increasing Dutch roll. There is an art to killing a Dutch roll manually but it takes time and practice to learn the art. The only way to learn that art is in the airplane very low to the ground. This is a case of a very good instructor pilot letting a very inexperienced copilot take it too far. There are lessons for us all.
More about this accident: Case Study: KC-135A 59-1443
I've made my share of instructor pilot mistakes and if there was a recurring theme to them, it would be assuming the student was more capable or knowledgeable than he or she was. The way to prevent that mistake and better understand the student's ability and knowledge is to conduct a thorough prebrief and mini briefs during the flight. This is a case study of where I assumed too much and almost got burnt. (As is true with most of my life, I got lucky.)
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