level flight: IAS doubled, then CL?
 

Hi everybody

Recently I had to answer the following exercise:

"An aeroplane maintains straight and level flight while the IAS is doubled. The change in lift coefficient will be: ..."

In my opinion the true answer would be x 0.5. Explained with the lift formula which is: L = 0.5 x rho x V^2 x CL x S.
IAS is the same as dynamic pressure, isn't it?
If this is true, then IAS would be 0.5 x rho x V^2. And if this whole term is doubled, then CL must be half the previous value to maintain same lift force.

This my thoughts. But they are wrong. It was stated, that the correct answer would be x 0.25.

Has someone an explanation for this problem?

Thank you.

Best regards,

Lift = CL 1/2Rho Vsquared S

In this equation V is the TAS

So Vsquared is TAS squared

If we double the IAS at constant altitude we double the TAS.

Doubling the TAS will quadruple the Vsquared.

So to have constant lift we must reduce the CL to a 1/4 of its previous value to compensate for the fact that the Vsquared is 4 times its previous value.

IAS is NOT the same as dynamic pressure. If we double the IAS at constant altitude we will quadruple the synamic pressure. This is because dynamic pressure is proportional to Vsquared.

This just proves how big a joke the EASA pilot training standards are.
People who can' t manipulate the simplest of formula' s just memorise question banks and pass the ridiculous tests.

At least this one is trying to understand, but I can' t help but wonder how many donkeys didn' t even bother to understand and are hauling passengers in big jets over our heads right now.

EASA motto: Ignorance is bliss.

Fly Antonov,dont you have anything better to do than just criticizing peoples knowledge on subjects?...Pfff

Fly Antonov,

I have no wish to defend the JAR/EASA pilot training system, but I think that you will add more to the level of knowledge of student pilots by answering some of their questions, instead of simply pouring ridicule on anyone who asks a question.

Most of the people who ask questions in this forum do so in an attempt to increase their knowledge and understanding.

The people who intend to simpy memorise answers are too busy banging away at their on-line databases.

Your habit of attacking everyone who asks what you consider to be a simple question, will simply discourage them from asking any questions at all. Is this really what you want to achieve?

CCCP-82060
Your difficulty in recognising the square law relationship between speed and dynamic pressure is not at all uncommon. I would estimate that at least 80% of JAR ATPL students have problems with it initially, and something like 40% never quite overcome these problems.

fly antonov

For sure you are the big king in freight business. Sorry for asking a question in "Professional Pilot TRAINING". HAHA


others

Thank you.
The root of confusion was in the OAT "principles of flight". There is stated that "0.5 x rho x V^2 = dynamic pressure (IAS)". Hence I thought that dynamic pressure is the same as indicated airspeed.

It is absolutely true that 0.5 x rho x V^2 = dynamic pressure.

But it is not true that 0.5 x rho x V^2 = IAS.

The ASI is nothing more than a differential pressure gauge. It measures the dynamic pressure and gives an airspeed indication that is proportional to that dynamic pressure.

But because dynamic pressure = 0.5 x rho x V^2, the relationship is not a linear one.

If we double the airspeed we get 4 time the dynamic pressure.
If we triple the airspeed we get nine times the dynamic pressure.
If we quadruple the airspeed we get 16 times the dynamic pressure.

But in these situations we do not want to see the speed indications increase by factors of 4, 9 and 16.

To prevent this the mechanism in the ASI carries out a process called "square law compensation" This takes out the squaring effect, so that the indication increases at the same rate as the airspeed.

Everything right until here and then you banged the big aviation schools myth that I heard too many instructors quote mistakenly (look, it' s even in the Oxfords according to CCCP) and that induces people like cccp in error.

ASI gives no airspeed indication proportional to dynamic pressure, since the relation between IAS and dynamic pressure is a P = k * V² relation.
The ASI is calibrated to show a given IAS for a given dynamic pressure, but as you say yourself, the relation is not linear, it' s a square.

The ASI needle is calibrated to show a given extension for a given pressure even though it' s not a proportional equation.

But for the interest of the question, all you need to know is that:
L = k * CL * V² = k * CL/4 * (2V)², which is elementary school math.

How fascinating..............

Some people never learn!

Fly Antonov

These three statements drawn from your post are contradictory.



If


is true, then;


and

cannot be true.


The ASI gives a speed indication that is proportional to dynamic pressure. But the proportionality is not linear, it is a square root relationship.

This does not mean that the indication is not proportional.

@CCCP-82060

Try to work with the correct units - then you can see at the first glance, that even in the educational books a '=' does not necessarily mean 'the same as' but might say 'almost perhaps approximately the same' or 'might change in the same way' or 'has nothing to do with it at all'. :bored:
It's hard work to look for the most important formulas and write them down like this:

L [N // kgm/s²] = ca [ ] x S [m²] x 0,5 x rho [kg/m³] x v² [m²/s²]

but believe me, it helps! Sometimes it even helps to see how some of the rules of thumb work.

And by the way: factor 0,25 is not correct at all, because rho changes with the altitude but (for heaven's sake) this problems is kept to more genious people than to us students... :)

Wishing you lots of fun...
;)

They are not contradictory, just read well.

The mechanism of the needle of the ASI is calibrated in such way as to reflect the following relation:

Your ASI senses dynamic pressure and the needle shows the matching IAS even though the relation between Pd and IAS is not proportional.

Proportionality implies a linear or hyperbolic (inverse-proportional) graph since Y = k * X where k is a constant real number besides 0 and not a variable like X.

The worldwide aviation school myth (flight, maintenance,..) used for the purpose of oversimplifying the explanation of the mechanism of an ASI, is that Pd = k x TAS (or IAS) which is clearly wrong.

If there is a myth needing busting it is that ASIs are calibrated according to the incompressible solution of the Euler equations. ASIs are calibrated to respond to impact pressure (St Venant's 'compressible' solution of the Euler equation).

Covered previously at:

Old Smokey's 2006-01-12 post on dynamic -v- impact pressure here: http://www.pprune.org/questions/2057...ml#post2318100

Equations are in NACA Technical Report 837 (Langley, 1946), NACA UK Mirror report description page

fly antonov .....
 

Why do you even bother to post?:rolleyes:

You provide little of value here; your motivation seems to be simply to denigrate others, or to demonstrate your own inherent superiority.:D

Over the (too many) years, I have worked as an instructor and training designer in quite a few training organisations, and I have studied in many more.

But I cannot recall a single case in which the students were told that

So your

is rather less than "worldwide".


The statement that "Dynamic pressure is proportional to IAS" is however making very liberal use of the word proportional. But the vast majority of ATPL students are totally unaware of the strict mathematical definition of the word, so there is little chance of them being misled by it.

I prefer to state that:

"Dynamic pressure = 1/2Rho Vsquared."
"The V in this equation is the TAS."
"So dynamic pressure is proportional to TAS squared".
"Provided air density does not change then IAS is proportional to TAS"
"So in these conditions we can say that dynamic pressure is proportional to IAS squared."

I then go on to use some examples to illustrate the relationship.

could some provide a reasonable explanation for the original question?

If air density remains constant, the relationship between IAS and TAS will remain constant. So if we double the IAS (in conditions of constant density) we will double the TAS.

Lift = Lift Coefficient x Wing Area x Dynamic Pressure

Dynamic pressure is proportional to the square of the trueairspeed.

So if we multiply the true airspeed by 2 we will multiply thedynamic pressure by 4.

With 4 times as much dynamic pressure and the same wing areawe need ¼ of the initial coefficient of lift to generate the same amount of lift.

but dynamic pressure = IAS = (1/2) * density * (TAS)^2

accordingly twice as much as increase in IAS would be caused by 1.414 times increase in TAS ( (1.414)^2 =2)

similarly, twice as much as increase in TAS would cause 4 times increase in IAS.
It satisfies the equation, so why is it wrong?

I'd understand if the original question stated 'if the TAS is doubled', then the answer would be (1/4)Cl, but I don't understand how TAS and IAS become linear variables vis a vis 'double the IAS, doubles the TAS'.

The above conclusion is not correct.

It is true that Dynmaic pressure = 1/2 Rho V squared

But the V in that equation is the TAS.

If we keep Rho constant and double the TAS we multiply V squared by 4.

So doubling the TAS gives us four times as much dynamic pressure.

If the ASI used Dynamic pressure = IAS, when we doubled the TAS we would see four times as much indicated airspeed. This would be totally useless to the pilot.

To overcome this problem we calibrate the ASI so that if we double the TAS, this gives us four times as much dynamic pressure, but the ASI just indicates twice as much airspeed. This is all done by a system of levers in the ASI.

Thank you Keith, it makes sense now.:ok: