level flight: IAS doubled, then CL?
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Maybe I'm reading the original question wrong, but isn't coefficient of lift purely a function of angle of attack? You can't change the coefficient of lift, unless you change the shape of the wing (e.g with flaps), but you can change the angle of attack to that corresponding to the appropriate lower CL.
Sorry to be pedantic!
Sorry to be pedantic!
Last edited by Jetdriver; 6th Nov 2013 at 11:54.
Maybe I'm reading the original question wrong,
An aeroplane maintains straight and level flight while the IAS is doubled.
Doubling IAS without changing CL will produce 4 times as much lift. This will make the aircraft climb. So to maintain the left flight condition of the question the pilot must reduce angle of attack in order to reduce CL to 1/4 of its initial value.
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Maybe t'internets diminshes the tongue in cheek element of my post, but the physicist within is forcing me to be incredibly pedantic here.
Yes, I do understand the question. Physically, we all know that if you shove on the power (i.e. increase speed) you'll have to push the nose down (reduce the AoA) to avoid climbing. Equally I understand it mathematically and I agree with the answers above; you are keeping the LHS of the lift equation constant whilst changing terms on the RHS, so:
ro * cl(old) * v(old) ^ 2 = ro * cl(new) * v(new) ^ 2
since ro is constant (level flight), you can rearrange to get:
cl(new) = cl(old) x v(old)^2 / v(new)^2
since v(new) = 2*v(old)
cl(new) = cl(old) * (1^2 / 2^2), i.e. cl(new) = 0.25 cl(old)
(pause for standing ovation).
Now back to my point. I argue the question implies we have a CL level in the cockpit - I don't in mine. We don't alter the CL as this set by the aerofoil designer - we change the AoA to that corresponding to appropriate CL. Yes, we all get the meaning of the question, but the authority/question bank asking this should be precise - there is no reason not to be! So after all that, all I am saying is the question should be asking something along the lines of
"An aeroplane maintains straight and level flight while the IAS is doubled. The angle of attack must be altered to that corresponding to a lift coefficient that is: ..."
Semantic? Pendantic? Certainly - but why cut corners and dumb everything down?
Yes, I do understand the question. Physically, we all know that if you shove on the power (i.e. increase speed) you'll have to push the nose down (reduce the AoA) to avoid climbing. Equally I understand it mathematically and I agree with the answers above; you are keeping the LHS of the lift equation constant whilst changing terms on the RHS, so:
ro * cl(old) * v(old) ^ 2 = ro * cl(new) * v(new) ^ 2
since ro is constant (level flight), you can rearrange to get:
cl(new) = cl(old) x v(old)^2 / v(new)^2
since v(new) = 2*v(old)
cl(new) = cl(old) * (1^2 / 2^2), i.e. cl(new) = 0.25 cl(old)
(pause for standing ovation).
Now back to my point. I argue the question implies we have a CL level in the cockpit - I don't in mine. We don't alter the CL as this set by the aerofoil designer - we change the AoA to that corresponding to appropriate CL. Yes, we all get the meaning of the question, but the authority/question bank asking this should be precise - there is no reason not to be! So after all that, all I am saying is the question should be asking something along the lines of
"An aeroplane maintains straight and level flight while the IAS is doubled. The angle of attack must be altered to that corresponding to a lift coefficient that is: ..."
Semantic? Pendantic? Certainly - but why cut corners and dumb everything down?
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.
... 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.
The NASA TN reiterates the appropriate solution to Euler's equation, presented in NACA Rep. 837, taking account of the isentropic change in state variables along a streamline as air is brought to rest at the head of the pitot probe. The total pressure at the head of the probe is certainly not given by summing the freestream pressure with the dynamic pressure but rather it is the sum of the freestream and impact pressures; neglecting measurement problems.
While it is true that a four-fold increase in dynamic pressure is associated to a two-fold increase in TAS, it is necessary to impose standard atmosphere sea level conditions for the statement to be similarly true about the change in CAS (IAS).
gfunc,
... isn't coefficient of lift purely a function of angle of attack? You can't change the coefficient of lift, unless you change the shape of the wing (e.g with flaps), but you can change the angle of attack to that corresponding to the appropriate lower CL.
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Thanks for the detail Selfin - so in the context of this question, given the air mass remains the same (i.e. same pressure temperature) am I correct in saying that ro, csound and viscosity are constant (as are the airframe terms) so that CL is only a function of alpha?
If the answers which we give to questions in these threads are to be of any value to the questioners, it is essential that we consider the context of the question. If we ignore this need we will be wasting our time and theirs.
The original post was
The following facts can be deduced from the post:
a. The author of the post is on some kind of course.
b. The author understands very little about the basic relationships
between airspeed, dynamic pressure and lift.
c. The author's grasp of fairly basic maths is not very good.
What may be less clear to some readers is the fact that the question has been taken from the Principles Of Flight section of the JAR/EASA ATPL question bank.
Any useful response to the OP must be pitched at a level that is appropriate for both the level of the JAR/EASA ATPL syllabus and also the level of knowledge of the author.
gfunc
Yes we could of course launch into a debate about poor quality of the question. But this would serve no useful purpose. We could argue about whether or not the syllabus has been dumbed down to an unacceptable level. But again this would serve no useful purpose. Any useful response must concentrate on the thought processes employed by the examiner in constructing the exam question and how these led to the required answer.
selfin
Yes, we could construct an explanation dealing with every apsect of the subjects that you have raised. We could, if we wished, go to even higher levels of detail and complexity. But given the apparent state of knowledge of the original poster, he/she is unlikely to gain anything useful from reading it. His/her response is far more likely to be "Oh sod it, this is far too complicated, I'll just rememeber the answer". You may be surprised at how many ATPL students do exactly that.
The original post was
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?
"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?
a. The author of the post is on some kind of course.
b. The author understands very little about the basic relationships
between airspeed, dynamic pressure and lift.
c. The author's grasp of fairly basic maths is not very good.
What may be less clear to some readers is the fact that the question has been taken from the Principles Of Flight section of the JAR/EASA ATPL question bank.
Any useful response to the OP must be pitched at a level that is appropriate for both the level of the JAR/EASA ATPL syllabus and also the level of knowledge of the author.
gfunc
Yes we could of course launch into a debate about poor quality of the question. But this would serve no useful purpose. We could argue about whether or not the syllabus has been dumbed down to an unacceptable level. But again this would serve no useful purpose. Any useful response must concentrate on the thought processes employed by the examiner in constructing the exam question and how these led to the required answer.
selfin
Yes, we could construct an explanation dealing with every apsect of the subjects that you have raised. We could, if we wished, go to even higher levels of detail and complexity. But given the apparent state of knowledge of the original poster, he/she is unlikely to gain anything useful from reading it. His/her response is far more likely to be "Oh sod it, this is far too complicated, I'll just rememeber the answer". You may be surprised at how many ATPL students do exactly that.
Last edited by keith williams; 7th Nov 2013 at 10:26.
CCCP,
As Keith says, you are probably on a course.
Therefore I suggest you ask your instructor.
If he cannot answer that very simple question the CHANGE SCHOOL !
BTW, please don't PM me.
As Keith says, you are probably on a course.
Therefore I suggest you ask your instructor.
If he cannot answer that very simple question the CHANGE SCHOOL !
BTW, please don't PM me.
Thanks for the detail Selfin - so in the context of this question, given the air mass remains the same (i.e. same pressure temperature) am I correct in saying that ro, csound and viscosity are constant (as are the airframe terms) so that CL is only a function of alpha?
In the original question the examiner appears to be content losing distinction between IAS and EAS, which is good to first order but fails to deliver satisfactory results at higher speeds and altitudes. It follows that the examiner probably does not want Mach and Reynolds numbers effects to be considered which is fine, so long as you appreciate the unstated assumption and the validity of any conclusions.
Here below I've reproduced an aircraft manufacturer's graph showing the relationship between the body alpha and the lift coefficient, at various Mach numbers, for a modern transport aeroplane. The lift coefficients in this example are linear functions of alpha while the slope parameters are close to a quadratic function in Mach number.
In summary there are two ways of viewing the practical problem of understanding the relationship between the angle of attack and the lift coefficient. For low speed aeroplanes, not operated at very high altitudes, the lift coefficient can be well modelled as a function of the angle of attack only. In all other cases that function should be expanded to include the effect of the Mach number, and the Reynolds number if necessary.
