Principles of Flight

[nigelisom]

Hi to you all, I am hoping someone out there can put me out of my misery on this question which came up on yesterday's CPL PoF exam. I have spent considerable time trying to fathom it out and even spoken to a PoF ground training instructor and other than the general thought that it is to do with the lift equation Lift = Cl1/2rho(Vsquared)S and the answer must be a reduction I have got nowhere.

The wording may not be exact but the gist of the question is:

An aircraft is traveling at 2xVs and encounters a gust which causes a load factor of 2. If that aircraft had only been traveling at 1.3xVs when it encountered that gust, what would the load factor have been?

answers given were:
(a) 2
(b) 2. (something I don't remember the figure precisely say 2.3)
(c) 2. (something more as above say 2.6)
(d) 1.69

I gave the answer 1.69 on the basis of the logic above but can someone please help with a clear explanation of how to solve it.

Thanks

Nigel

[12Watt Tim]

At anything less than 1.41Vs you would have stalled before hitting a load factor of 2.

The lift at a given angle of attack is proportional to the square of the speed. Stall occurs at stall AoA. At Vs and 1g the AoA is stalling AoA, and lift = weight.

So if you are flying at 1.41 Vs then at the stalling AoA your lift = weight * 1.41^2 so lift = 2* weight at the stall so you can just maintain aerodynamic flight at 2g.

However if you are flying at 1.3 * Vs then the lift at stalling AoA is only 1.3^2 * weight. 1.3^2 is 1.69, so as the aircraft pulls through 1.69g it stalls, and never exceeds that load factor.

Have you ever seen the limitations in the AFM that above a certain speed you must not use full deflection of the controls? The reason is that above that speed it is possible to exceed the g limitations. The speed is actually your stall speed at the limiting load factor for the aircraft (typically 3.8, 4.4 or 6g for light aircraft depending on category). Below that speed it is not aerodynamically possible to over-stress the aircraft*, as you will stall first. Note that speed, Va or manoeuvre speed, actually reduces with reduced all-up-weight (i.e. if light you have to be more careful) as you will not stall until a lower speed at a given load factor, including the maximum certified load factor or g limit.

* Not quite true. Most will overstress earlier if there is significant aileron input, but high g while actually rolling is rarely encountered unless attempting aerobatics.

[nigelisom]

Tim

Thanks for your reply.
I am well aware of the principles involved here and partly based my answer on the limits you mention in the AFM of the Arrow i fly. However what i am looking for is a clear and unambiguous explanation of the method and principles required to answer that examination question.
Once again thank you for taking the trouble to post a reply but if your explanation does fully answer my question then I am afraid I don't fully follow it and would you be good enough to rephrase your explanation so I can have another crack at understanding it.

Meanwhile anyone else care to have a go?

Am I just being thick?

Nigel

[jcbmack]

Cl1/2rho(Vsquared)S... nigelisom, here is the "ATPL Theory Summary."

They show and illustrate better than I can, but "n" load factor= 1/cos times the bankangle. The squrae root of the load factor= Vstall increasing factor.

http://www.freelancepilot.nl/ATPL%20summary.pdf


Essentially it is just setting up the rigth equation the right function and plugging in the values.

Mario Asselin has a great book from 1997 titled:
An introduction to aircraft performance

On page 270 on Google books too, you may find a more detailed treatment of load factors with different velocity, wind gusts:

ngust= Lgust/W= 1/2 rho (V+-u)^2 SCl/W considers an horizontal gust.

For a full treatment, purchase this inexpensive book, or go on to Google Books and read page 270, (start on page 269, which begins the topic of flying in adverse weather) among other pages... happy trails! :ok:

[126.9]

Yes, you're just being thick. Or, possibly (forgive me if after 31 years at this I'm a cynic) trying to show us what a smartarse you think you are. :ok:

[jcbmack]

Read and review your materials. This is just simple algebra. Almost forgot: Pilot's Handbook of Aerounautical Knowledge from the FAA is available on Google for free, and is the 2008 edition: Pilot's Handbook of Aeronautical Knowledge (http://www.faa.gov/Library/manuals/aviation/pilot_handbook/)

[nigelisom]

Jcbmack
Thanks for the ATPL summary (very useful) and the further references, I will indeed follow them up.
126.9
Pot. Kettle. Black.

Nigel

[Keith.Williams.]

Consider two conditions.
Condition 1 is straight and level flight in still air.
Let CL = CL1 and V = V1

Lift 1= CL1 1/2ρ V1squared S

In straight and level flight Lift = weight so we can say that
Weight = CL1 1/2ρ V1squared S

Rearranging gives
S = Weight / CL1 1/2ρ V1squared……………………Equation 1

Condition 2 is in a sudden vertical gust.
Let CL CL2 and V = V2

Lift 2 = CL2 1/2ρ V2squared S

Rearranging this gives
S = Lift 2/ CL2 1/2ρ V2squared …………………….Equation 2

S is the wing area which, for the same aircraft is the same in both cases. So we can combine equations 1 and 2 to give.

Lift 2/ CL2 1/2ρ V2squared = Weight / CL1 1/2ρ V1squared

Multiplying both sides by 1/2ρ gives
Lift 2/ CL2 V2squared = Weight / CL1 V1squared

Rearranging gives
Lift 2/ Weight = CL2 V2squared / CL1 V1squared

But Lift2 / Weight = new load factor so
New load factor = CL2 V2squared / CL1 V1squared

If we assume that V1 is VS then we have
New load factor = CL2 V2squared / CLmax Vs squared

If we also assume that the aircraft stalls in the gust then we have
New load factor = CLmax V2squared / CLmax Vs squared

Cancelling out Clmax from the top and bottom of the right side gives
New load factor = V2squared / Vs squared

Taking the figures Vs = 1 and V2 = 1.3 Vs = 1.3 gives
New load factor = 1.3 squared / 1 squared = 1.69
So the load factor in the gust is 1.69

BUT WE HAVE ASSUMED THAT BOTH AIRCRAFT STALLED.

If one or both of them did not stall then we cannot assume that both were at CLmax and so we cannot give a definite value for load factor. We can however say that the gust cannot (theoretically) produce a load factor greater than 1.69 when flying at 1.3vs.

[nigelisom]

Keith

Thanks that is much appreciated. I will give all that further thought this evening.
I still can't help thinking that this is all a bit convoluted for a 1 point question in a 45 minute exam. There must be a shortcut to work this out, unless all they were after was that the load factor reduced and rely on there only being 1 answere that fits.
Who can know the mindset of the CAA!
Nigel

[jcbmack]

Every point matters when you are in the sky! Just use the mauals and see the equations for vertical and horizontal gust.:ok:

[Keith.Williams.]

Nigelisom

Yes there is an easier way for the exam, but you you did say

but can someone please help with a clear explanation of how to solve it.

For the exam just remember the final bit of the process.

New load factor = V2squared / Vs squared

But as I said, the question is defective anyway.

[nigelisom]

Keith

I have just had time to sit and work through your explanation and yes that fully answers my question and I now understand how to address the problem.

Once again I thank you for taking the time and trouble to set that all out and I walk away a (slightly) wiser man. I am also relieved that my intuitive feel of the situation was correct (at least I got that one correct). I am much happier now that I can put the numbers in place for the problem as well, as it always worries me not knowing how to go about solving a problem.

Thanks again also to everyone else who took the trouble to try to help.

Now back to the long wait to find out how many of the rest of the paper I got right!

Nigel

[jcbmack]

:DRead your advisory circulars and the Pilot's Handbook of Aeronautical Knowledge.

[Keith.Williams.]

It is of course possible that the examiner is being really devious….

All gust load calculations questions have previously been concerned with vertical gusts. This is why my earlier explanation considered only the vertical gust scenario.

But it is possible that this new question is concerned with horizontal gusts.

If so the solution takes the following form.

Horizontal gusts will not change angle of attack or CL, but they will change the dynamic pressure and lift. Because the angle of attack remains constant the wing will not stall.

At 2Vs the gust caused load factor to double.

This means that V squared increased by a factor of 1.41 from 2Vs to 2.82Vs.

So the gust speed was 0.82 Vs

At 1.3 Vs adding 0.82 gives a new speed of 2.12 Vs

New load factor = New V squared / Old V squared

So new load factor = 2.12 squared / 1.3 squared = 2.66

So the new load factor is 2.66

If this was the examiner’s intention then it really was a devious question because most candidates, being familiar with previous questions would have assumed that it was a vertical gust.


Hmmmmmmm.......The examiner -Instructor arms race moves on

[nigelisom]

Gee thanks Keith, just when I was feeling happy that I had cracked it!

The trouble with these exams is that you will never know which ones you got wrong so lose the learning opportunity that would give. It would be really nice to get a resume of the errors for future reference.

Looking again at the problem I bet your second thought is correct as for the vertical gust you don't need to know the load factor of the 2xVs situation. That doesn't stop them including it as a red herring of course!

Nigel

[Alex Whittingham]

At the risk of putting the cat amongst the pigeons I believe the question that was issued by the JAA was:

Q. An aeroplane maintains straight and level flight at a speed of 2 * VS. If a vertical gust causes a load factor of 2, the load factor n caused by the same gust at a speed of 1.3 VS would be:

(A) n = 1.65.
(B) n = 1.69.
(C) n = 4.
(D) n = 1.3.

With (A) being marked as the correct answer. I have seen an explanation of why the answer 'is' 1.65 rather than 1.69 but it was quite lengthy and certainly too much for a one mark question. What may have happened here is that the CAA received complaints about the original question then one of their resident 'experts' decided to tart it up and modified the answers. Which only goes to show, you can't polish a t*rd.

[nigelisom]

Alex

I will defer to you on the precise wording of the question but the answers were definately one at l/f 2 two of them at greater than l/f 2 and the last one at l/f 1.69

I hope your version of the wording of the question (including vertical gust) is correct!

nigel

[Keith.Williams.]

The question

Q. An aeroplane maintains straight and level flight at a speed of 2 * VS. If a vertical gust causes a load factor of 2, the load factor n caused by the same gust at a speed of 1.3 VS would be:

(A) n = 1.65.
(B) n = 1.69.
(C) n = 4.
(D) n = 1.3.

Was appealled by Oxford in June 2007 and put on hold.

In the ensuing debate several instructors put in various arguments, but all agreed that the question was unsafe. The CAA eventually decided to allow the appeal and put the question on hold to allow the SET to look at it again.

As Alex has said, the new question is probably an "improved" version of the old one.

But the numbers appear to have changed and one of the new options is correct for a horizontal gust. This raises the question of whether their "improvement action" has actually radically changed the situation.

[Alex Whittingham]

This dates from, I think, a March 09 issue of the CQB but the original question dates back to 2003. Because the question is still in the CQB in 2009, apparently unchanged, I would suspect that the CAA said it was 'on hold' in 2007, put it on local hold, didn't process the query back through the SET and then modified the question locally in some wierd way. Dreadful.

What is even worse is that the CAA will no longer allow FTOs to appeal questions in the way that Keith describes. They will only accept appeals from candidates.

[nigelisom]

Don't you just love bureaucracies that hold a monopoly.

Nigel

[jcbmack]

hitherto: "On page 270 on Google books too, you may find a more detailed treatment of load factors with different velocity, wind gusts:

ngust= Lgust/W= 1/2 rho (V+-u)^2 SCl/W considers an horizontal gust."

Keep up the discussion...:8

[nigelisom]

jcbmack

I can find reference to An introduction to aircraft performance by Mario Asselin on google books but it wont let me read the section you suggest. I am not familiar with the google books site is there something I need to do to be able to download this?

Nigel

[jcbmack]

nigelisom,
unfortunately you cannot download the book, but you can sign up for Google books library and save the given book too. You can also scroll down to the pertinent chapter and you will find page 269 which begins flight in weather. If you scroll down fast, you will not be able to load the pages well, if at all, so scroll down slow.

Also if you google on scholar and google books, principles of flight, you will find many good selections, and the FAA provides many publications online for free. The pilot's handbook of aeronatutical knowledge link I gave you does work and it is also free to download each chapter.

John Tullamarine also has great suggested websites as does checkboard among others, please see these links via tech log.
http://www.pprune.org/tech-log/66205-useful-website-document-references.html

[nigelisom]

So the long and short of it is if you want to read it you got to buy it.
I don't have a problem with that, however I am not sure that I wish to spend 65 dollars getting a further explanation on an exam I have already done. Unless I have failed it of course and need to do a resit!
Thanks again to you all for your imput and lets hope I don't need to buy the book.
Nigel

[jcbmack]

It is free to read most of the book on Google books!!! Page 269, 270 and thereafter are all available for free on Google Books.:bored:, Not sure how you read into my post that you had to purchase it to read that information at all; if I miscommunicated to you, I apologize... the links I gave you for all the information from PPRUNE are free and the handbook is free too. You do not have to pay to see the references fromm google books I gave you.:ugh:

[jcbmack]

All of the information you need to for this aforementioned test and future tests are available online for free or via mail order for around 12 bucks.:eek: Amazon.com, Payhalf.com, Ebay, Craig's list have examples of such materials for sale. However, flying is expensive business which can end very fast with a stall, a crash onto the runway (like with windshear, or all engines out, if one is not prepared; even some who are prepared) or a deep spiral dive. If you are truly training to become a pilot, then you know there is nevere too much you can know or know how to do regarding your aircraft.:ooh:
Leave nothing to chance, my young friend. We are not just discussing one exam, but rather, we are discussing your lifetime process of assimilating and accomodating knowledge/skill sets, so that you do not end up pitch down into a @*$%^&! sand dune.:ouch:

http://www.pprune.org/tech-log/66205-useful-website-document-references.html

http://www.pprune.org/private-flying/387435-gusty-conditions-approach.html

[Pugilistic Animus]

just to add a little,... it is important to remember a few circumscribing facts, since it is possible to encounter conditions outside of the part 25 gust envelope because
the theoretical model of the 'gust' considered is an alleviated sharp-edged gust modeled on a bell-shaped curve
it assumes that the gust steadily increases to a maximum then dies out likewise---however if a real sharp edged gust is encountered [severe CAT ] then a much higher load factor than computed will ensue possible leading to ultimate loading from the instantaneous increase in AoA without alleviation
and the value of the bell-shaped gust likewise decreases with with increased speed
going from Vb [max gust instensity] Vc [design cruise] Vd [design dive]
lastly, the the TAS value of the gust is rightly decreased with altitude [thinner air] but don't get a false sense of security from this fact either

so although far 25 offers a great deal of protections it does have its limitations the does not preclude the real possibility of structural failure if real life conditions are encountered beyonded the certificated envelope as is a very real possibility in real life even at the VTP/VRA

so always respect turbulence and slow down!

[Pugilistic Animus]

this may be considered controversial:ouch: but one should slow to the computed Va if severe gusts are really encountered ---don't worry about the stall you wont exceed design limit loading and if equipped/necessary you'll have stick pusher protection or the stall would be a better option than structural failure: so if really caught out; [B]slow way way down and remember that since maximal wing loading i.e. weight to surface area loading occurs at the stall
Va will thus be dependent on Vs [as previously described by Keith Williams]
and Vs is a function of weight the Higher the Vs the Higher the Va will be hence you will have a Higher Va at a Heavier weights,...FAR 25 is comprehensive but there are several large Gaps that can kill those caught unaware of the limitations of the design envelope

Actually, the whole picture is quite complex:\

PA:)

[Dick Whittingham]

PA

Quite complex? More like very complex. Would you please elaborate on "maximal wing loading i.e. weight to surface area loading occurs at the stall"

Dick

[Pugilistic Animus]

sorry DW I could have said that in a simpler manner meaning that that maximum weight to be carried by the wing[mainly] is the weight that the wing carries at the stall i.e the ratio of W/S is increased to a maximum; this gives rise to the fact that a stall at 1Vs loads the wing with a maximum 1 'g' however at 2Vs an accelerated stall g of 4 g based on the relation ship Vsn = Vs[n [load factor]^1/2

Va is computed similarly except that n [any load factor] is replaced by the design limit load N therefore Va represents the speed that if a stall occurs the wing loading will not exceed design limit loads,...this is a mathematical certainty at odds a bit with the somewhat artificial/ statistical world of design standards [as JT always says 'a line in the sand'] in both cases the Change in Load factor DeltaN i= q*delta AoA but....

in FAR 25. [340???] the worst gust assumed [Uref] to impact the airframe are alleviated i.e statistically assumed to build up gradually reach maximal intensity then decay gradually but in reality in extreme turbulence the gust may be sharpedged and result in an[I] instantaneous increases in AOA this will result in higher than assumed load factors ---hence Vra/Tp becomes very very artificial and only speeds near Va can protect you,...in reality for Extreme turbulence it may just be better to stall

and in my opinion the original question is very poorly worded and should remain off of the exam

I hope I didn't mess anything up:\

[jcbmack]

Thank you for such an enlightening treatment of the subject.

[nigelisom]

Just on the remote chance that anyone has the slightest interest, I am happy to say despite my lack of knowledge of this area I managed to pass my PoF exam along with AGK and OP.
So just 6 to go, back to the books for me.
Nigel

[jcbmack]

Nigel, congrats man!!!:ok: Keep up the good work, and never stop learning.

[Air1980]

I really wish the JAA would quit trying to have everybody find the square root of things, rather than just applying common sense, which is - slow down in turbulence. Plain and simple. I too passed PoF, but not without a great deal of eye-rolling and mumbled cursing.....

[Pugilistic Animus]

Oh I forgot to write---

you must add 1g to the Nz because your already in sustained 1g flight:
for example if you compute delta N to be 50000lbs and the plane weighs 25000lbs then the load factor would be 2+1g =3g

PA

[manucordier]

Keith,

Do you think we could use the same reasoning to answer the following question:

Is the Gust load increasing or decreasing when altitude increases (IAS and all other factors of importance constant) ?

I assume vertical gust.

Altitude 1 < Altitude 2
IAS1 = IAS2

Using your argumentation I get this formula :

L2/W = gust load = Rho2 (TAS2)² / Rho1 (TAS1)²

If IAS constant, when altitude increases TAS increases too. However air density decreases much more thus gust load decreases.

Could that be a good explication ?

Thanks for your answer Keith.

Have a good day,
Emmanuel Cordier.

[Keith.Williams.]

In order to produce the Indicated Airspeed (IAS) our Airspeed Indicator measures the dynamic pressure, then produces an indication that is determined by the value of that dynamic pressure.

So if we are climbing at constant IAS then we must be climbing at constant dynamic pressure.

This means that as we climb 1/2Rho2 (TAS2)² must be equal to = 1/2Rho1 (TAS1)²

This in turn means that if we are to have constant lift to match our (assumed to be) constant weight, then our angle of attack must also be constant.

If we hit an upward vertical gust this will increase our angle of attack, which will in turn increase our lift and our load factor.

The increased load factor in the gust is proportional to the amount by which the gust increases the angle of attack.

The increase in angle of attack is determined by the relative magnitudes of the TAS and the vertical speed of the gust.

If we climb at constant IAS we will have a gradually increasing TAS.

If we assume that we meet a series of gusts of a constant vertical upward TAS while climbing at constant IAS, then in each case we will have a constant upward TAS (the gust) being added to an increasing horizontal TAS.

This means that the relative magnitudes of the Gust and the aircraft TAS will gradually decrease. This will cause the change in angle of attack to gradually decrease. This in turn will cause the gust load factor to decrease.

So the gradual decrease in gust load factor as altitude increases at constant IAS, is caused by the gradual reduction in the relative magnitudes of the (constant) upward TAS of the gust, and the (increasing) forward TAS of the aeroplane.

The only part in all of this that is played by the reducing air density is that this causes the aircraft TAS to increase in our constant IAS climb.

All of the above is of course a simplification of the situation, because the addition of the gust to the aeroplane TAS will also change the dynamic pressure acting on the aeroplane.

[manucordier]

Thanks again Kieth for your very complete and logical explanation, as always.

But I do have a problem,... following your argumentation, it leads me to think that the fastest you fly, the longest is the aircraft TAS vector in comparison to the vertical gust vector, then the least sensitive to gust would be the aircraft. However we know that it is not the case since we always have to slow down to Vb (outside yellow arc for C152) while flying through turbulent air.

How can you explain this contradiction ?

Thanks again for your help Kieth,
Emmanuel Cordier.

[manucordier]

Have a look at that question:

The manoeuvre stability of a large jet transport aeroplane is 280 N/g. What stick force is required, if the aeroplane is pulled to the limit manoeuvring load factor from a trimmed horizontal straight and steady flight? (cruise configuration)

I suppose that the limit manoeuvering load factor that wee need is 2,5.
Well at least with that load factor I get the right answer which is : 420 N

Could someone give us all the limit load factor we need to know for small and light aircraft, and for large transport jet that we need to know for the JAA ATPL exam ?

Thanks a lot
Emmanuel Cordier.

[Keith.Williams.]

I think that you are mixing up two very different situations.

Situation 1 Increasing IAS at constant altitude.

As we go faster the dynamic pressure increases with the square of TAS so the angle of attack and CL both decrease to maintain constant lift for level flight.

Because the CL and angle of attack are decreasing, the sudden increase in angle of caused by an upward gust will represent a greater proportional incease in CL, lift and load factor. So if we go fast enough a gust that was no problem at low speed (when the angle of attack and CL were high) will tear the aircraft apart.

So acceleration at constant altitude increases gust response, so we must not go too fast in gusty conditions.


Situation 2 Increasing altitude at constant IAS.

As we go higher at constant IAS the dynamic pressure, angle of attack and CL are constant, but our TAS increases. So any given upward gust velocity produces a smaller increase in angle of attack CL and load factor.

So climbing at constant IAS decreases gust load factor.

[Keith.Williams.]

The trick here is to note that in trimmed level flight the load factor is one but the stick force is zero. So the first 1g is free in terms of stick force.

Limiting load factor for a large transport aircraft in the clean condition is 2.5g.

So to go from 1g straight and level to 2.5g we require an increase of 1.5g.

Each 1g reuqires a 280N stick force, so an increase of 1.5 g from 1g to 2.5g requires a 420 N stick force.

The only other limit load factors that appear in the JAR ATPL exams sare:

2.0g for large transport aircraft with flaps down.

4.4g for a light utility category aircraft.

[manucordier]

Ok, that's clear now !

Thanks and
Good night.

[violingineer]

I know this topic/question is 4-5 years old, but in coming across it today, as an engineer, I tried to work it, and kept coming out with a different answer than what was explained by those that replied to the original poster. The algebra does not work out, and the replies, while getting the published known answer, got the actual problem (_as posed_) wrong.

The original poster's problem stated that 2Vs gives a load factor of 2. If you solve for Lf2 with v1=2Vs, Lf1=2, and v2=1.3Vs, taking weight, surface area, air density, and drag coefficients to be all constant for the purposes of this problem (they don't change with respect to the difference in velocities): then, load factor is just a function of velocity (Lf1=f(v1^2)): So we compare the ratios:
Lf1/Lf2 = v1^2 / v2^2. so, substituting known values:
2/Lf2 = (2Vs)^2 / (1.3Vs)^2. Vs cancels, and solve for Lf2 = 0.845.

[In fact, at 2Vs, the load factor should be 4, not 2 as posed!! If you work it with putting Lf1=4 above, then you get the correct answer of Lf2=1.69 for 1.3Vs]

Stated better:
Any aeroplane flying at a multiplicand of Vs and at the angle of attack to attain the maximum lift will experience a load factor equal to the square of the multiplicand as a g force, e.g 1.3Vs creates 1.69g.
from Principles of Flight for Pilots by Peter Swatton
Principles of Flight for Pilots - Peter J. Swatton - Google Books (http://books.google.com/books?id=VPEgZ49tAFYC&pg=PT389&lpg=PT389&dq=2Vs+1.3Vs+load+factor&source=bl&ots=mTT2rD-Ghx&sig=tZd8p90pB3dBADhTXGzuLOGIHn8&hl=en&sa=X&ei=6-ONU8fEFNKPqgb23oLoCQ&ved=0CDsQ6AEwAg#v=onepage&q=2Vs%201.3Vs%20load%20factor&f=false)