Principles of Flight Questions

[Crosswind Limits]

I have a couple of Qs I am unsure about and would be grateful for some feedback:

1. What happens to the gust load at a given IAS?

i) Increases with an increase in altitude
ii) Decreases with an increase in weight

a) both are correct
b) i) is correct ii) is incorrect
c) i) is incorrect ii) is correct
d) both are incorrect


2. What happens to the gust load (all other factors remaining the same):

i) increases with an increase in aspect ratio
ii) increases with an increase in altitude

a) both are correct
b) i) is correct ii) is incorrect
c) i) is incorrect ii) is correct
d) both are incorrect

Any help much appreciated.

CL

[ 19 January 2002: Message edited by: Crosswind Limits ]</p>

[Paul Hickley]

For technical questions on specifically JAA-type matters, I suggest you post them on Oxford's new free website, which is available to non-Oxford students (but don't expect an answer now until Monday!)

Post them in the 'Groundschool' section of @SK OXFORD FORUMS on

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which is
<a href="http://www.oxfordaviation.net/forum" target="_blank">http://www.oxfordaviation.net/forum</a>

Paul

[Keith.Williams.]

Crosswind Limits,

QUESTION 1.
To understand the effect of increasing altitude we need to remember that the principal effect of gusts is to increase and decrease angle of attack. This in turn varies CL and load factor.

The important thing to note is that it is the TAS rather than the CAS that determines response to gusts. In a vertical gust the change in angle of attack is proportional to the ratio of TAS : vertical gust velocity. (The tangent of the angle of attack change is equal to the vertical gust velocity divided by the TAS.

As altitude increases the TAS at any given CAS increases, so the effect of a vertical gust decreases. At 40000 ft ISA for example, the TAS at any given CAS is about twice its sea level value, so the effect of a vertical gust is reduced accordingly.

This is similar to the way aerodynamic (usually simply termed roll) damping reduces with increasing altitude. So as altitude increases the gust load for any given combination of CAS and gust velocity decreases. Statement (i) is therefore incorrect.

The effect of increasing weight is a little more problematic, so we need to consider it from two points of view.

The first factor is that increasing weight reduces the rate at which an aircraft will accelerate upwards or downwards in a vertical gust. If an aircraft hits an upward gust and the extra lift causes it to accelerate upwards, this will partly offset the increase in angle of attack. A light aircraft will accelerate more quickly and so will experience a lower increase in angle of attack.

The second thing we need to consider is the degree to which any given gust will alter Cl and hence load factor, if we ignore the vertical acceleration of the aircraft.

Let's consider 2 identical aircraft, one at 10000 Kg and the other at 20000 Kg. If they are both flying at the same altitude and IAS, then the angle of attack and Cl of the light aircraft will be half that of the heavy one. Let's suppose the angles of attack are 3 degrees and 6 degrees respectively. In straight and level flight they will bot be at 1g.

Now assume both aircraft hit the same gust and it increases their angles of attack by 3 degrees. The light aircraft will experience a doubling of its angle of attack, Cl and load factor. But the heavy aircraft will experience only a 50% increase. So the heavy aircraft will experience 2g while the light one experiences only 1.5g. So increasing weight decreased the gust load, which means that statement (ii) is true.

If we look more closely at the first factor of vertical motion, we can see that the greater aceleration of the lighter aircraft is a direct result of the greater change in load factor.
The fact that light aircraft jump about more in turbulence is due to the greater changes in load factor they experience.

So option c is correct.



QUESTION 2.
The important thing here is that a high aspect ratio wing has a steeper CL : alpha curve than a low aspect ratio wing. So for any given gust induced increase or decrease in alpha, the change in CL will be greater for a high aspect ratio than for a low aspect ratio. So gust load increases with increasing aspect ratio.

You can demonstrate this simply by drawing a steep and a shallow CL :alpha curve on a piece of paper. Now apply the same change in alpha to both curves and see how the CL varies.

The effect of altitude is discussed above.

So option b is correct.

[ 19 January 2002: Message edited by: Keith Williams. ]</p>

[CAT3C AUTOLAND]

Keith Williams IS the king of POF!

Only experienced his expert teaching on PPL ground school, but my word this guy is good!

[Keith.Williams.]

Cat3 Autoland,

Thanks for the plug, but if my teaching was so good why did you look so puzzled?

. .Crosswind Limits.

Here are my answrers to the questions above.

1. b.. .Sweeping back the wings decreases aspect ratio. Decreasing aspect ratio decreases the gradient of the CL:Alpha curve. So for any given gust induced change in alpha, the CL change will be smaller for a swept wing than for a straight one. So increasing sweep back angle decreases gust load in any given gust.

. .2. b.. .The CL: alpha slope is a straight line up to the stall, so doubling the intensity of the upward gust would double the increase in CL. A gust causing a 1 degree increase in angle of attack increased CL by 0.15 from 0.55 to 0.7. A gust of twice this intensity would therefore increase CL by twice as much which is an increase of 0.3.

. .3. b.. .The CL : Alpha curve is a straight line up to the stalling angle, so within this range, if a 1 degree increase in alpha produces an increase of 0.06 in CL, then a 5 degree increase in alpha will produce an increase of ( 5 x 0.06 = 0.3) in CL.

Load factor = lift / weight and in straight and level flight this equals 1. So assuming the aircraft was in straight and level flight prior to the gust, its load factor would have been 1. Although the weight of the aircraft is not given, its load factor of 1 can be expressed as a ratio of CL to some figure representing weight, provided the ratio of the two is equal to 1. That is to say the load factor before the gust equals 1 which can be expressed as 0.44 / 0.44.

. .On this basis the load factor in the gust is equal to the new CL / 0.44 which is = (0.44 + 0.3) / 0.44.

The new load factor is therefore 0.74 / 0.44 which is 1.68.