Refer to figure.
The annex depicts an aircraft in a constant bank angle left turn. If the crew (1) _____ airspeed, they are at risk of collision with the other traffic. If they (2) _____ airspeed they are at risk of collision with terrain.
Refer to figure.
Note: We have created this question from limited feedback and are unsure as to how exactly the question annex appears. We would be grateful for any further feedback on this. Thank you!
There are only two variables that determine the turning radius of an aircraft. As in the figure, lift is inclined into the turn according to the bank angle (φ). This acts as the centripetal force ⇒ the force acting towards the inside of the turn, which leads to the turning motion. The force required to maintain a turn of a certain radius is:
- Fcent = mV2 / R
From the figure, we see that: Fcent = L sin(φ)
The mass of the aircraft, m, is equal to its weight (W) divided by the acceleration due to gravity (g). This gives us:
- L sin(φ) = WV2/ gR
In the turn, we also have W = L cos(φ). From trigonometry, we know that sin(φ) / cos(φ) = tan(φ). This leaves us with:
- L sin(φ) = L cos(φ) V2/ gR
- tan(φ) = V2 / gR
We can now re-arrange the terms to find the relationship for the turn radius, R.
- R = V2 / g tan(φ)
Where V is the TAS
- g is the constant acceleration due to gravity
- φ is the bank angle
The question asks about how a change of speed will effect our turn radius while maintaining a constant bank angle. If we increase our speed, the turn radius will become larger - and we at greater risk of colliding with the crossing traffic. If we decrease TAS, the turn radius decreases, and we are at risk of colliding with the mountain.
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This question has appeared on the real examination, you can find the related countries below.
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Switzerland2
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Greece1
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Portugal1
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