Longitudinal static stability (LSS)

[jason.bourne]

how is aspect ratio of a wing related to longitudinal static stability (LSS)?
like, if we increase the aspect ratio, is it going to increase or decrease the longitudinal static stability (LSS)?

suppose we have an aircraft whose centre of gravity is fixed at a particular location, if the propeller is mounted on the nose of the fuselage instead at the wing, what's its effect on LSS ?

 

[Cyrus]

how is aspect ratio of a wing related to longitudinal static stability (LSS)?
like, if we increase the aspect ratio, is it going to increase or decrease the longitudinal static stability (LSS)?

suppose we have an aircraft whose centre of gravity is fixed at a particular location, if the propeller is mounted on the nose of the fuselage instead at the wing, what's its effect on LSS ?

I know of no relations on longitudinal static stability explicitly in terms of aspect ratio, but I will make some general comments.

For longitudinal stability you are primarily concerned with the pitch stiffness of the airplane. This is the slope of the Cm vs alpha curve, and should be negative. What you can do, is calculate the 3D pitching moment of the wing for the various aspect ratios you are considering. This curve will be added to the pitch moment curve of the rest of the airframe. Because the airframe does not change, the primary thing to see is: which wing creates a larger destabilizing pitching curve. This will tell you what you are after, and it is something you can roughly compute using theory, or references like Jan Roskam.

Edit: Did you just say 'like'?

 

[jason.bourne]

does it vary from aircraft to aircraft?

doesnt it has any generic variation?

something like you know, aircraft with high wing config has more longitudinal static stability at higher angle of attack than compared with low wing config at higher AOA.

 

[Cyrus]

Does it vary from aircraft to aircraft?

Of course it does.

Does'nt it have any generic variation?

It's possible, but I am not aware of any such variation. I'll look more into it though.

Something [STRIKE]like [/STRIKE]you know, aircraft with high wing config. has more longitudinal static stability at higher angle of attack than compared with low wing config at higher AOA.

The stability has to do with the stability derivatives, which generally don't change significantly unless in post stall flight, so this sentence doesn't make much sense.

I hope your next post is typed properly, or I won't provide any more help.

 

[jason.bourne]

"I hope your next post is typed properly, or I won't provide any more help"

well when i post here, i try my best english with least mistakes.
its bit difficult because m from non english speaking country, people here do speak english but barely with any grammar. m sorry. i'll try my best.

 

[Cyrus]

"I hope your next post is typed properly, or I won't provide any more help"

well when i post here, i try my best english with least mistakes.
its bit difficult because m from non english speaking country, people here do speak english but barely with any grammar. m sorry. i'll try my best.

No worries.

 

[jason.bourne]

aircraft with high wing config. has more longitudinal static stability at higher angle of attack than compared with low wing config at higher AOA

The stability has to do with the stability derivatives, which generally don't change significantly unless in post stall flight, so this sentence doesn't make much sense.

i found out this from a textbook.
i don't have it now but i'll post the details in a day or two.
he mentions it clearly about this with a graph of Cm vs Cl for aircrafts with high-mid-low wing configs. unfortunately he didnt mention the reason for this, but i don't think there's some obvious reason for this. m trying to find out more on this.

 

[Cyrus]

i found out this from a textbook.
i don't have it now but i'll post the details in a day or two.
he mentions it clearly about this with a graph of Cm vs Cl for aircrafts with high-mid-low wing configs. unfortunately he didnt mention the reason for this, but i don't think there's some obvious reason for this. m trying to find out more on this.

As stated previously, the stability derivative is the point of tangency of Cm vs alpha graph. So it is not the data points on the curve that matter, but their local slopes.

 

[Brian_C]

I found an article which describes wind tunnel tests on wings with a NACA 0012 profile. They didn't calculate any stability derivatives, but they did tabulate the Cm variation with angle of attack for three different aspect ratios. It would be pretty straightforward to calculate the derivatives using a polynomial fit.

Here is the link:
http://www.scipub.org/fulltext/ajas/ajas22545-549.pdf

 

[Cyrus]

I found an article which describes wind tunnel tests on wings with a NACA 0012 profile. They didn't calculate any stability derivatives, but they did tabulate the Cm variation with angle of attack for three different aspect ratios. It would be pretty straightforward to calculate the derivatives using a polynomial fit.

Here is the link:
http://www.scipub.org/fulltext/ajas/ajas22545-549.pdf

Thanks for the link to that paper Brian.

 

[jason.bourne]

Thank you for that paper.

But the data didn't quite help me.

When i calculate the slope of -Cm vs AOA values for different Aspect Ratios, I don't see a definite pattern of increasing or decreasing slope.

Can you guys help me further on this?

 

[Cyrus]

Thank you for that paper.

But the data didn't quite help me.

When i calculate the slope of -Cm vs AOA values for different Aspect Ratios, I don't see a definite pattern of increasing or decreasing slope.

Can you guys help me further on this?

There should be a very clear slope that is either positive or negative.

 

[jason.bourne]

Yes, the slopes that i found are negetive. so its stabilizing moment.

But the slope for AR = 1.9474 is greater than compared to AR = 2.761
and the slope of AR = 3.0198 is almost similar to AR = 1.9474, which is more than AR = 2.761.

I just don't get it.

 

[Cyrus]

Yes, the slopes that i found are negetive. so its stabilizing moment.

But the slope for AR = 1.9474 is greater than compared to AR = 2.761
and the slope of AR = 3.0198 is almost similar to AR = 1.9474, which is more than AR = 2.761.

I just don't get it.

Without seeing your work or what you did, I have no way of knowing if this is right or wrong.

 

[mugaliens]

how is aspect ratio of a wing related to longitudinal static stability (LSS)?
like, if we increase the aspect ratio, is it going to increase or decrease the longitudinal static stability (LSS)?

suppose we have an aircraft whose centre of gravity is fixed at a particular location, if the propeller is mounted on the nose of the fuselage instead at the wing, what's its effect on LSS ?

Hi, Jason. Aspect ratio affects the the angle of attack required by a wing to generate lift. Put simply, wings with a high aspect ratio (square of wingspan divided by wing area) are very sensitive to changes in lift as a function of the AOA, while low aspect ratio wings are less sensitive.

It terms of longitudinal stability, this effect requires a larger tail surface for higher aspect ratio wings in order to provide greater longitudinal precision along the pitch axis. Wings of lower aspect ratio require less tail surfaces all the way down to delta wings, which require no tail surfaces at all, except in the form of elevons at the trailing edge of the delta planform.

Thus, it's not just the aspect ratio which determines overall longitudinal stability, but the combination of wing and horizontal stabilizer planforms which work together as a system.

 

[Cyrus]

Hi, Jason. Aspect ratio affects the the angle of attack required by a wing to generate lift. Put simply, wings with a high aspect ratio (square of wingspan divided by wing area) are very sensitive to changes in lift as a function of the AOA, while low aspect ratio wings are less sensitive.

It terms of longitudinal stability, this effect requires a larger tail surface for higher aspect ratio wings in order to provide greater longitudinal precision along the pitch axis. Wings of lower aspect ratio require less tail surfaces all the way down to delta wings, which require no tail surfaces at all, except in the form of elevons at the trailing edge of the delta planform.

Thus, it's not just the aspect ratio which determines overall longitudinal stability, but the combination of wing and horizontal stabilizer planforms which work together as a system.

Again, be careful. Deltas have to have the trailing edge curved upward to induce pitch stability in the longitudinal axis. They are not inherently stable on their own.

 

[mugaliens]

Again, be careful. Deltas have to have the trailing edge curved upward to induce pitch stability in the longitudinal axis. They are not inherently stable on their own.

Hence the replacement of such measures in modern, dynamically unstable aircraft with computer sensors and controls.

Douglas noted this in the F4 Skyray. When they designed the Skyhawk (a nearly simultaneous design), they corrected for this by using a horizontal stab. By decoupling the moment arm, they dramatically reduced the negative lift aspect of the Skyray. As a result, the A-4 was a remarkably agile 1950's era fighter that remains in service to this day.

 

[Cyrus]

Hence the replacement of such measures in modern, dynamically unstable aircraft with computer sensors and controls.

Douglas noted this in the F4 Skyray. When they designed the Skyhawk (a nearly simultaneous design), they corrected for this by using a horizontal stab. By decoupling the moment arm, they dramatically reduced the negative lift aspect of the Skyray. As a result, the A-4 was a remarkably agile 1950's era fighter that remains in service to this day.

What do you mean by decoupling the moment arm? Without a moment arm, a tail doesn't do its job. It has to produce a pitch down moment.

 

[mugaliens]

What do you mean by decoupling the moment arm? Without a moment arm, a tail doesn't do its job. It has to produce a pitch down moment.

My choice of words was poor. I should have said, "lengthened the moment arm." The longer moment arm meant less downward force was required.

 

[Brian_C]

Hi, Jason. Aspect ratio affects the the angle of attack required by a wing to generate lift. Put simply, wings with a high aspect ratio (square of wingspan divided by wing area) are very sensitive to changes in lift as a function of the AOA, while low aspect ratio wings are less sensitive.

It terms of longitudinal stability, this effect requires a larger tail surface for higher aspect ratio wings in order to provide greater longitudinal precision along the pitch axis. Wings of lower aspect ratio require less tail surfaces all the way down to delta wings, which require no tail surfaces at all, except in the form of elevons at the trailing edge of the delta planform.

Thus, it's not just the aspect ratio which determines overall longitudinal stability, but the combination of wing and horizontal stabilizer planforms which work together as a system.

This isn't entirely true. The zero-lift angle of attack doesn't really change with aspect ratio. Anderson's book on aerodynamics (page 380) actually has a graph which shows the Cl variation with alpha for different aspect ratios. Also, the original poster was interested in the pitch stability of the wings. Control surfaces and horizontal stabilizers have nothing to do with this discussion.

 

[FredGarvin]

I really have to get a copy of Anderson's book...

 

[mugaliens]

This isn't entirely true. The zero-lift angle of attack doesn't really change with aspect ratio.

Correct. I made no claim to the contrary. Again, aspect ratio affects pitch sensitivity (how lift as a function of AOA).

Also, the original poster was interested in the pitch stability of the wings. Control surfaces and horizontal stabilizers have nothing to do with this discussion.

Let's take another look at what he was after:

how is aspect ratio of a wing related to longitudinal static stability (LSS)?
like, if we increase the aspect ratio, is it going to increase or decrease the longitudinal static stability (LSS)?

Looks pretty straightforward to me, and if you don't think the horizontal stab has anything to do with the discussion, try flying an airplane without them and see what that does to your longitudinal stability!

By the way, the horizontal stab isn't a control surface. It's a stabilizer. The elevator is the control surface.

 

[jason.bourne]

It terms of longitudinal stability, this effect requires a larger tail surface for higher aspect ratio wings in order to provide greater longitudinal precision along the pitch axis. Wings of lower aspect ratio require less tail surfaces all the way down to delta wings, which require no tail surfaces at all, except in the form of elevons at the trailing edge of the delta planform.

Yes, I quite agree with you.

Thank you guys for discussing on this topic.

I have attached a pdf version of a research memorandum by John A Axelson and J Conard Crown.
I request you to check it out.

From their experimental investigation, they found out, as the Mach Number increases towards the Drag Divergence at higher Mach Number, the stabilizing action of the horizontal tail decreases with the increasing Mach Number.

The reduction becomes more pronounced as the wing Aspect Ratio is reduced.

This was the variation with the Mach Number.

But from this paper can we say in general that longitudinal static stability decreases as the wing Aspect Ratio is decreased, even if the Mach Number variation is ignored?

My opinion is yes. If we consider a fixed Mach Number, increasing the Aspect Ratio will decrease the downwash effect (this effect is basically due to the wing tip vortices) so the longitudinal static stability will improve.

 

[Cyrus]

Yes, i quite agree with you.

Thank you guys for discussing on this topic.

I have attached a pdf version of a research memorandum by John A Axelson and J Conard Crown.
I request you to check it out.

From their experimental investigation, they found out, as the Mach Number increases towards the Drag Divergence at higher Mach Number, the stabilizing action of the horizontal tail decreases with the increasing Mach Number.

The reduction becomes more pronounced as the wing Aspect Ratio is reduced.

This was the variation with the Mach Number.

But from this paper can we say in general that longitudinal static stability decreases as the wing Aspect Ratio is decreased, even if the Mach Number variation is ignored?

My opinion is yes. If we consider a fixed Mach Number, increasing the Aspect Ratio will decrease the downwash effect (this effect is basically due to the wing tip vortices) so the longitudinal static stability will improve.

The tail of an airplane has nothing to do with the answer to your question. This is also not a question of your opinion. I gave you the answer earlier. Please go back and look it over.

 

[jason.bourne]

The tail of an airplane has nothing to do with the answer to your question

.

Yes. I agree.

I need to be more specific.

suppose if we consider aircrafts with tail, instead of tailless aircraft, will the above point hold?

 

[Cyrus]

.

Yes. I agree.

I need to be more specific.

suppose if we consider aircrafts with tail, instead of tailless aircraft, will the above point hold?

As I already stated - the pitch stability of the airplane is a function of the slope of the pitch moment curve. If the rest of the airframe remains invariant, the wing which has the more negative pitch stiff is better.

 

[Cyrus]

Correct. I made no claim to the contrary. Again, aspect ratio affects pitch sensitivity (how lift as a function of AOA).

Pitch sensitivity is not a function of lift, its a function of moment.

 

[mugaliens]

Pitch sensitivity is not a function of lift, its a function of moment.

"Four forces affect the overall pitch of the aircraft: the airfoil pitching moment (Cm), the lift produced by the wing, the lift force produced by the horizontal stabilizer, and drag. Lift only affects pitch when the CG is not located at the AC of the wing." http://ciurpita.tripod.com/rc/rcsd/lowSpeedStability/lowSpeedStability.html"

 

[Cyrus]

"Four forces affect the overall pitch of the aircraft: the airfoil pitching moment (Cm), the lift produced by the wing, the lift force produced by the horizontal stabilizer, and drag. Lift only affects pitch when the CG is not located at the AC of the wing." http://ciurpita.tripod.com/rc/rcsd/lowSpeedStability/lowSpeedStability.html"

You are correct that the lift of the wing will contribute a pitch moment when it is offset from the aircraft CG - but this is now looking at the airplane as a whole. But again, it is the slope of the pitch curve vs AoA that is defined as pitch stiffness. The effect of the lift offset from the cg is included in this measurement when one tests an airplane in aggregate.

Here is a good analogy to demonstrate the effect. Think of a bowl. If the bowl is right side up, a marble will always roll back to the bottom of the bowl - a stable equilibrium point.

If the bowl is inverted, any where you place the marble it will roll off the bowl - this is an unstable situation.

If the marble is exactly at the top of the inverted bowl, it is at a metastable equilibrium point. Any slight perturbation and it rolls off.

The first case corresponds to negative slope of pitch moment vs AoA.

The last two cases correspond to positive slope of the pitch moment of AoA.