Within 0.1% of the necessary pull on the yoke? No way.
Nobody said within 0.1%. I would say that on a successfully completed steep turn, the pull is within 10% at all times, but the average is within 1% or the turn would be outside tolerance. So, if it's 10% less than necessary, they'll have to correct with more than necessary to even it out, or they'll be outside the altitude tolerance.
Typically it would be probably somewhat closer to 1.4 than 1, but only because the pilot is pulling on the yoke.
Right. But if the pilot doesn't pull on the yoke at all, the airplane itself is going to tend to both level out and increase the load factor on its own. A 1G 45º banked turn is not possible to sustain for very long, and it's not a good solution to the problem we're talking about here.
Let the nose drop, the speed comes up. How fast depends on how far you let it drop. Trying to hold exactly 1.000 would be no harder than trying to hold exactly 1.414. No one can do either.
We're not talking precision here - Between holding 1.000 ± 10% or 1.414 ± 10%, it will be much easier to get the latter, and the latter is possible to sustain indefinitely in a 45º bank, while attempting to sustain the former for more than a few seconds will result in a crash.
Think about what is supposed to be the typical cause of the stall spin accident on the turn to final - using rudder / elevator instead of increasing bank because they are told over and over that it is increasing bank that increases the stall speed. That's why not. That's why it is important to understand that it is the PULL that kills you.
I don't disagree with that at all. The problem is, that a 1G 45º bank is NOT the solution! The solution is to discuss the real issue, which is the skidding base-to-final turn and why the BEST solution *is* to keep the bank to a reasonable (IMO, 30º) limit AND not to skid AND not to pull too hard!
Keeping the bank to 30 degrees does not keep you safe. In fact, if you don't let the nose drop a little in your 30 degree bank your speed will decay and you will stall even if you don't load up much. I bet if you watched closely, your nose drops as you turn when the power is off.
As it should - If you pull too much, your speed will decay more, if you don't pull enough, your vertical speed will be too great.
And, while 30 degrees doesn't keep you safe, attempting a 45º 1g turn is LESS safe than a properly executed, coordinated (even if you overshoot) 30-degree turn.
Pull kills. Bank doesn't.
So, let's tell the students WHY pull kills, and WHY a skid kills, rather than suggesting that a steeper, unloaded bank and its associated downward acceleration is the right answer, because it's not.
I shudder to think about how many pilots don't seem to understand that it's the pulling that increases the load factor - not the bank angle. And, even if you don't increase the load factor significantly, trying to keep the nose up will cause your speed to decay. The end result is the same.
Yup.
Pull kills. Bank doesn't. Why do "we" teach to not bank? What's wrong with actually teaching people how an airplane really works?
I think it's rooted in two things:
1) There are a lot of instructors out there who either don't understand how an airplane really works themselves, or don't care enough to teach it to their students.
2) There are a lot of good instructors out there who don't want to overwhelm their students with too much information too early on. It's easier for a student to remember "don't exceed 30 degrees of bank in the pattern" than it is for them to remember all the other stuff that goes into making an airplane fly, since they're likely somewhat overwhelmed with just the physical aspects of flying.
However, instructors that haven't yet covered the "why" behind the 30-degree "rule" absolutely MUST emphasize that it's OK to overshoot the centerline, and that they MUST stay coordinated.