# Aerospace Longitudinal static stability (LSS)

1. Dec 31, 2009

### 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 ?

2. Dec 31, 2009

### Cyrus

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'???

Last edited: Dec 31, 2009
3. Dec 31, 2009

### 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.

4. Dec 31, 2009

### Cyrus

Of course it does.

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

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.

5. Dec 31, 2009

### 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.

6. Dec 31, 2009

### Cyrus

No worries.

7. Dec 31, 2009

### jason.bourne

i found out this from a textbook.
i dont 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 dont think there's some obvious reason for this. m trying to find out more on this.

8. Dec 31, 2009

### Cyrus

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.

9. Dec 31, 2009

### 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.

http://www.scipub.org/fulltext/ajas/ajas22545-549.pdf [Broken]

Last edited by a moderator: May 4, 2017
10. Dec 31, 2009

### Cyrus

Thanks for the link to that paper Brian.

Last edited by a moderator: May 4, 2017
11. Jan 2, 2010

### 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?

12. Jan 2, 2010

### Cyrus

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

13. Jan 2, 2010

### 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.

14. Jan 2, 2010

### Cyrus

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

15. Jan 6, 2010

### mugaliens

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.

16. Jan 6, 2010

### Cyrus

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.

17. Jan 6, 2010

### mugaliens

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.

18. Jan 7, 2010

### Cyrus

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.

19. Jan 7, 2010

### mugaliens

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

20. Jan 8, 2010

### Brian_C

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.