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Old Jan 19, 2012, 08:25 AM
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Spiral Stability for Free Flight

I was looking at the Blaine Rawden calculation for Spiral Stability which came up in this post...

B = EDA x (ver_tail_arm/span) / CL


I thought I'd have a look at a couple of free flight rubber models to see how it worked for them but found the B value incredibly high - like 25-30!

Obviously these models have a lot of dihedral but I was suprised by the high values. Is this because the formula takes no account of actual tail volume? The Vertical tail volume on the models was quite high (like 0.08) The models I looked at don't suffer from any partiular dutch roll so I'm guessing the high Vv is playing a part...

Is it neccesary to add some kind of correction for Vertical tail area or do I just start building up a list of typical B values for free flight to set some rough parameters?


Jon
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Old Jan 19, 2012, 02:39 PM
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Jon, I suspect you made a typo since Dutch roll comes from too small a vertical tail volume or too much dihedral to go with it.

If you look around at all the more successful designs you'll likely find that the ones that win all the contests tended to have relatively small tail volumes. By polyhedral RC glider standards almost all FF contest models have disgustingly small tail volumes.

I believe that with a near Dutch Roll size tail volume the yaw stability seems to be a little relaxed. This seems to allow the models to be re-directed by local air conditions so that they tend to turn into thermals more easily on their own. Now this is based more on just observing my and other flyers' models in flight. Some of the old timers with bigger tail volumes don't seem to be able to hunt out and ride the lift as regularly as the designs that are on the edge of dutch roll.
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Old Jan 19, 2012, 05:38 PM
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Quote:
Originally Posted by BMatthews View Post
Jon, I suspect you made a typo since Dutch roll comes from too small a vertical tail volume or too much dihedral to go with it.
Bruce, no typo but perhaps I didn't put it very well.

What I meant was that with such high 'B values' (excess Spiral Stability) I would expect to see some dutch roll... but the models also have large tail volumes which will (as you say) reduce the dutch roll tendency.

In other words the Blaine Rawdon formula shows very high spiral stability but the large tail volume reduces the actual spiral stability.

So the formula is only useful when comparing models of similar Vv.


By the way the two models I looked at were basic FF sport models:

Keil Kraft Playboy...... B= 28.5(!).....Vv=0.092
Frog Redwing........... B=23.1..........Vv=0.082

I will analyze a few more when I get round to it... I'd like to get to a point where I could establish a sensible minimum B value for free flight scale models.

The Playboy is the one of the two that has better spiral stability (in fact its close to dutch roll) so the formula 'works' but it would be nice to find a way to integrate the Vv into the formula for a straight comparison? Any ideas how you might do it?
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Old Jan 19, 2012, 11:46 PM
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Jon,

I believe that formula is applicable to sailplanes. With that big destabilizing prop up front, more fuselage side area than a sailplane, and the wheels ahead of the CG, it may need modification for a rubber model.

Kevin
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Old Jan 20, 2012, 03:07 PM
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Yep, what Kevin said.

I also think that we're into another terms misunderstanding.

Vt becomes higher when the fin area is increased. Similarly the Vt becomes higher when the tail length is increased.

A Vt which is too high will produce a higher degree of "spiral stability". Note that I quoted that since what happens if it becomes too high is that the model actually wants to wind in tighter if the Vt is too high. In other words to my thinking it becomes spirally UNstable since the tendency to tighten into a non self recovering spiral dive takes over. On the other hand a smaller Vt actually promotes spiral stability up to the point where it no longer can keep the nose pointed forward in a proper manner. At that point it's marginally stable or in an extreme case unstable in yaw but spirally highly stable. It may go into Dutch roll with a minor case and maybe fall into a flat spin in an extreme case but at least it won't fall into a spiral death dive...

As Kevin says Blaine's equation really is specific to RC sailplanes. It avoids a lot of factors such as side area that are small enough that they are insignificant on a "broom handle" like RC saiplane. So it really doesn't fit well with something like the Redwing. To make it work better you'd have to do some manner of calculation of the fuselage side area and prop effect and existing fin to come up with an "equivalent vertical fin area" that would plug into the equation.
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Old Jan 22, 2012, 12:20 PM
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Thanks Kevin, they aren't very clean aerodymically ... I'm not sure whether you could learn enough from just a new set of parameters or whether I ought to start adding other factors into a formula.

Steve 'Jet Plane Flyer' Bage did some stuff on this for small free flight models a while back here. Including a simple correction for high wing/low wing position.


Quote:
Originally Posted by BMatthews View Post
I also think that we're into another terms misunderstanding.
I think so but not sure exactly where we're crossin wires Bruce just terminology maybe? The way I understand it is that a model with low Spiral Stability (and low B values) would be more likely to spiral dive. Or at least the bank angle where this happens is reduced.


I agree with all you have said except:
Quote:
Originally Posted by BMatthews View Post
A Vt which is too high will produce a higher degree of "spiral stability".
I would have said that a Vertical Tail Volume that was too high would reduce spiral stabilty. In other words increase the 'death spiral' tendency.


My original point was simply that the Blaine Rawdon formula only compares models of similar Vvt.

If two models have the same B value, then the one with a larger tail area will have less spiral stability even though ostensibly they should have the same.
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Old Jan 22, 2012, 03:58 PM
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Quote:
Originally Posted by Yak 52 View Post
I was looking at the Blaine Rawden calculation for Spiral Stability which came up in this post...

B = EDA x (ver_tail_arm/span) / CL


I thought I'd have a look at a couple of free flight rubber models to see how it worked for them but found the B value incredibly high - like 25-30!

Obviously these models have a lot of dihedral but I was suprised by the high values. Is this because the formula takes no account of actual tail volume? The Vertical tail volume on the models was quite high (like 0.08) The models I looked at don't suffer from any partiular dutch roll so I'm guessing the high Vv is playing a part...
Is it neccesary to add some kind of correction for Vertical tail area or do I just start building up a list of typical B values for free flight to set some rough parameters?
"Spiral instability" mean different things to RC'ers and FF'ers. The B parameter applies to the RC definition. For FF, "spiral instability" is a really a pitch instability, which is initiated or aggravated by excessive yaw stability. Looky here:
http://www.rcgroups.com/forums/showthread.php?t=731709
Post #20
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Old Jan 22, 2012, 04:26 PM
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Excellent! Thank you Mark I knew I was missing something but didn't know what.
Now to digest that thread...

Many thanks
Jon
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Old Jan 22, 2012, 04:31 PM
agnotology
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I should have known Mark had already posted the solution to this long ago. Sometimes I forget to do a search for "markdrela" and the question under discussion. The answer comes up about 99.98% of the time.

Thanks again Mark!

Kevin (following your latest design work from the snippets that make the news)
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Old Jan 22, 2012, 07:34 PM
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Ok I'm getting somewhere... hopefully.

I've taken the liberty of quoting from Dr Drela from that thread (rather than resurrecting it) in order to continue the discussion here.

From post #28
Quote:
Originally Posted by markdrela View Post
...Spiral stability depends on the ratio yaw_damping/yaw_stability . Ignoring constants of proportionality, these two quantities are given by the following products:

yaw_damping = VT_area * tail_arm^2
yaw_stability = VT_area * tail_arm

So the ratio is proportional to...

yaw_damping/yaw_stability = tail_arm

i.e. the VT area cancels out, and one factor of tail_arm remains. This is precisely why Blaine Rawdon's criterion has the tail_arm factor.

If there are other aerodynamic surfaces which significantly influence yaw damping and yaw stability, the VT area and other areas will not cancel, and this simplified analysis doesn't hold. One example is a small forward fin, like those used on compass-guided FF gliders, or just a deep forward fuselage. Such forward fin area will increase yaw damping but decrease yaw stability. So the ratio
yaw_damping/yaw_stability
will strongly increase, and spiral stability will increase as well. This is why old-timers saw improved spiral stability from deep forward fuselages. The "center of lateral area" theory was an effort to explain this, but didn't address the real mechanism.

In any case, one could add a forward fin to an RC glider to improve its spiral stability and any overbanking tendency. However, if the forward VT doesn't have a moving rudder, it will reduce the rear rudder's authority (and look goofy besides ). Increasing the dihedral is a better fix.
So the influence of VT area is represented in the B parameter, just that it cancels out in the case of gliders where yaw damping is provided solely by the VT.

But in the case of my free flight rubber models, the forward fuselage area, big prop, wheels etc are increasing the ratio of yaw damping/yaw stability. So to make the B parameter 'work' for me, I would need to somehow work out the actual contributions of the forward fuselage, prop etc to get the correct ratio of yaw_damping/yaw_stability and put that in place of the simplified 'tail arm' value?

And I'm concluding from this that the conventional wisdom that 'reducing the VT area increases Spiral stability' is true in the case of these models but only because by reducing VT area you are increasing the proportional influence of the fuse, prop et al (the damping but destablizing components.)



From this thread :
Quote:
Originally Posted by markdrela View Post
For FF, "spiral instability" is a really a pitch instability, which is initiated or aggravated by excessive yaw stability.
And from post #20
Quote:
Originally Posted by markdrela View Post
Aha. Here's the main source of contention. The "spiral death dive" often referred to by free-flighters is really a combination of spiral instability and pitch instability (or "tuck-in" in RC jargon). Calling is simply "spiral instability" is not correct, at least as defined by any classical book on airplane stability (Etkin, Nelson, etc). If you look up spiral stability in any of these texts, there is no mention of CG position, simply because it's largely immaterial there.
Could you elaborate on this a little?

I'm not quite sure if that is what I meant when I referred to spiral dive. What I'm trying to avoid is typical spiral divergence from a steady turn at min_sink (ish) speeds. For these models there is no clear transition from climb to glide as in HLG or CLG models.

I was under the impression that this was spiral stability in the classic sense. In other words a tendency to roll back upright when disturbed. As a result of the correct level of lateral and directional stability.


The Redwing model above is pretty conventional and I had thought pretty stable in pitch, presumably with a download on the tail:
Horizontal tail volume: 0.59
CG: 36% mean chord
Static Margin: 10%


Thanks for the input... And Mark may I just say: I've been going through some of the MIT OpenCourseWare Aerodynamics section and it is tremendously cool to have all that info freely available. I love the 'muddy points' (although I'm up to my eyes in the stuff ) Massively appreciated!


Thanks
Jonathan
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Old Jan 22, 2012, 07:59 PM
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The cancelling out of the Vt area and having the yaw damping aspect come down to the tail arm certainly explains why the electric fusleage I built to use with a set of 2 meter wings and stab flies so much more nicely than the short pure glider version. I made the tail boom about 2 inches longer on the electric version and reduced the Vt area proportionatley to maintain the same Vt volume. But the longer electric version is BOTH so much more responsive AND stable at the same time that it was amazing.

What's needed is a procedure to determine and correctly add all the areas together using their "quarter chord" points and distances from the CG location to find the equivalent vertical tail area at the location of the existing fin. At least that's how I'd see it.
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Old Jan 22, 2012, 08:31 PM
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Quote:
Originally Posted by BMatthews View Post
What's needed is a procedure to determine and correctly add all the areas together using their "quarter chord" points and distances from the CG location to find the equivalent vertical tail area at the location of the existing fin. At least that's how I'd see it.
I don't think it's quite that simple... the fuselage is a streamlined body rather than a flying surface so it's effect is different. We're back in CLA theory territory again
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Old Jan 23, 2012, 03:42 PM
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With the various fuselage cross sections it certainly makes it more difficult. But not impossible.

But to me it makes it enough more difficult that it becomes easier to rely on "TLAR" and then make changes by replacement or modification of the fin after the initial design gets test flown.
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Old Jan 24, 2012, 04:49 PM
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Old Jan 24, 2012, 05:07 PM
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Bruce, et al: been thinking about this a bit...

My perspective is a little different as I want to assess spiral stability for free flight scale. That is to say the layout is set out already and an increase/decrease in fin area isn't all that easy to achieve. It's possible to scale VT area up or down by a few percent maybe, or even add a 'stick free' floppy rudder. But adding dihedral is likely to be the fix of choice.

For me the problem arises when trying to model scale aircraft that were intentionally spirally unstable at full size and then trying to trim them for a steady turn with some reserve in the spiral mode as a model.

What I'm really after is some method of assessing the potential for spiral problems of a model when it's in the design stage, so that I can get away with the minimum dihedral required for scale looks and still be able to trim the thing.

In the absence of full analysis I'm interested in increasing my understanding of how these changes affect spiral stability in general - so at least I will have some kind of idea of how much trouble a model will be. Of course making changes after the plan is drawn and model built is a pain so the better I can estimate, the better the model. I just don't want to spoil the looks by adding a bunch of dihedral 'for safety's sake' when it may be unneccesary.


So what I have so far is factors increasing spiral stability for FF scale:

1) Increase equivalent dihedral angle.

2) Increase the ratio of yaw damping/yaw stability (or dynamic/static yaw stability if you prefer.)
So that would mean:
- Smaller vertical tail (on aircraft with other destabilising factors)
- Bigger prop or more thrust.
- Increased fuselage area, wheels, struts forward of the CG.
- Lengthen tail moment arm

3)Trim for higher speed, lower CL

I'm not quite sure on all these points.... so correct me if I'm wrong!

But from this I should be able to work out what's going on with the model, in the design stage and also in flight. For instance: as the rubber motor run ends and the prop makes less/no thrust, I end up with slightly less spiral stability in the glide? Potential trimming problem if it's marginal to start with.


I'm also drawing a Bostonian version of the Bede BD-5 pusher. It has a pretty short tail moment arm, so low yaw damping from the vert tail. But it's a pusher (more yaw stability) and it has a large forward fuselage (more yaw damping) I'd really like to know to what extent the factors cancel out so I can get away with a minimum of dihedral. I know someone who did a Peanut version commented that it was suprisingly stable for the amount of dihedral they'd added...


Jon
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