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we had the student note that the nose moved toward the down wing, that movement they saw was called yaw and in that instance was produced by aileron.
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That yaw is the secondary effect of roll. It happens because at 30 degrees angle of bank the aircraft will slip and the resultant change in the direction of the relative airflow
on the fin/rudder causes Yaw.
If you were flying an aircraft which was simply a wing and rolled the aircraft with the ailerons (elevons!!) to 30 degrees AOB and the C of G was exactly central etc then the aircraft would again slip but there would be no yaw because there would be no fin/rudder and no keel surface aft of the C of G etc.
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Can someone explain to me why the private pilot license was taught in thirty hours in the 1950's and on tail wheel airplanes and today the average is around 75 to 100 hours on very basic simple to fly nose wheel trainers?
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In the UK is it still possible to obtain a licence with as little as 15 hours training.
The answer to your question however lies more in the situation of society ( and insurance companies as well as authorities) being more risk adverse and no longer accepting the loss rate / accident rate / injury rate that was associated with aviation in the 1950's. Not to mention the fact that we have learned from our mistakes!!.
The effect of high(er) terrain is covered during the operation at linimum level part of the PPL course because at 500ft MSD, even quite small hills disrupt the true horizontal.
It is not just terrain that causes problems. Over flat terrain the horizon is clear, flat and true and some 75nm away at 5000ft ASFC.
If the visibility is 9600m the visible surface ends some 4nm ahead of the aircraft when on the surface and less than this at 5000ft.
Take a student up into the clear sky over a 8/8 stratus overcast. Note well the attitude for S+L then take them back down into the 5k below and ask them to select the exact same attitude and see what happens. The aircraft now descends because they have put their "horizon" (the limit of visibility) on the same spot. This is an issue when operating in reduced visibiity as the pilot will often tend towards descending by following a false horizon.
This makes the altimeter scan quite important so ensure that the desired altitude is being maintained.
It also makes the basic technique for selecting an attitude come into focus;
Select - select the attitude
Hold - hold the attitude steady
Adjust - if the aircraft is not doing what is desired then Select a better attitude and repeat the process.
The same applies in a turn a quick glance at the altimeter and then back outside tells the pilot if the aircraft is maintaining altitude.
Having said all that for turning in a valley a few things should be remembered;
1. A climbing or descending turn will use up less horizontal ground space than a level turn.
2. As in other cases, a partially full water bottle provides a horizon reference when straight and level and in balance. Use the bottle to determine some reference features on the opposite side that are at the same level.
3. Strat the turn on the downwind side of the valley and turn into wind. This also decreases the size of the turn.
In other words - get onto the downwind side of the valley. Select a few features for reference on the other side and start the turn. If you start descending then this helps so long as a safe level above the hard bits is being acheived.
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172_driver,
The difference is simply a teaching method.
one is more trial and error than the other.
trial and error in a controlled environment can work. However, it requires a very attentive instructor and can have problems with "primacy" i.e. the students first method that achieves the aim is very hard to change becuase their brain associates that method with the successful outcome even if it is worng in your eyes.
The european system lends itself to a building block teaching style where early exercises are short and relatively simple and the length / complexity of exercises increases with experience. Early diagnosis of learning rate and progress as well as bringing a very disciplined approach to flying. (don't confuse disciplined with lack of fun!!).
The US system uses a less disciplined approach which can work with the right students but has problems in that the student can become overloaded as well as making determination of progress difficult except at ket stage points.
Thus the origin of the European system in the military with it's associated chop points compared to the US civil system where the student is more left to spend their cash for as they choose as long as they are having a good time even if they never make progress.