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An aeroplane maintains straight and level flight at a speed of 2 VS. If, at this speed, a vertical gust causes a load factor of 3, the load factor n caused by the same gust at a speed of 1.9 VS would be:
• A
n = 3.61.
• B
n = 2.90.
• C
not greater than 2.90, because the aeroplane is stalled with a higher load factor at 1.9 VS.
• D
n = 2.85.
Refer to figures.
A gust is a localized sudden and rapid change to the speed of the air in the atmosphere that can be either horizontal or vertical. The horizontal gust is of little importance because it causes a change to an airplane’s dynamic pressure that results in an insignificant change to the load factor. The vertical gusts are far more important because they change the effective angle of attack, total lift, and the load factor.
The gust load is the extra load imparted to the airplane by vertical gusts or turbulence. Its magnitude is unaffected by increased altitude but is increased with increased aspect ratio and/or decreased mass.
The load factor for any given angle of attack can be derived from the basic load factor for the normal cruise angle of attack because it is increased by the same percentage as the increase of angle of attack.

To solve this exercise, consider figure 2:
An aircraft travelling at a certain speed (Vold, in black) encounters a vertical gust which increases its load factor (nold) to a certain amount.
The objective is to compare the effect of the same gust on an aircraft travelling at a different speed (Vnew, in blue) and assessing the resultant load factor (nnew).
Vold = 2VS
nold = 3g
Vnew = 1.9VS
nnew =?

The first thing we should do is check if in the first situation the aircraft is stalled by comparing the two VS0:
VS1 = VS0 ∗ √(nold)
VS1 = √3 ∗ VS0 = 1.73VS0
1.73VS0 < 2VS0

Therefore, the aircraft is not stalled!
As the aircraft does not stall in the first situation, we can calculate de load factor resulting from the same gust on an aircraft travelling at Vnew using a direct proportion:
Vold ∗ (nnew−1) = Vnew ∗ (nold−1)
nnew = ((Vnew ∗ (nold−1)) / Vold) +1

nnew = ((1.9VS ∗ (3−1)) / 2VS) +1

nnew = 2.90g

Encountering the same gust with a speed of 1.9VS the load factor will be 2.90g.

The last step of the exercise is to assess the limiting load factor at which the aircraft would stall and conclude if the new load factor calculated would be reached or the aircraft would stall before that.
To do this, let us compare Vnew with the stall speed (VS) and load factor in straight and level flight (n1g):
Vnew = VS * √(n1g)

From here results that our limiting load factor is:
n1g = V2new
n1g = 3.61g

As our limiting load factor is higher than the new. In this case encountering the gust the aircraft would have its load factor increased to 2.90g without stalling.

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• Poland
• United Kingdom