Stability question. - RC Groups
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Oct 11, 2017, 01:27 PM
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Discussion

Stability question.


Two aircraft, of significantly different weights ... otherwise identical.

Each is dynamically stable about all axes.

Each aircraft is trimmed to fly at, say, 4 degrees Angle of Attack, in straight and level flight.



The two aircraft experience an identical disturbance which causes them to enter a convergent phugoid.


Which of the two will be the first to return to straight-and-level ?




I'm asking 'cos I have absolutely no idea. My best guess would be that they would match each other, in terms of time elapsed.
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Oct 11, 2017, 02:50 PM
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Please rephrase your question: if one is heavier than the other it must either fly faster or at a different AoA for straight & level flight

As a result the "disturbance" (please define) will have a different effect on each, esp. since the Re will be different for the same AoA (different airspeed, very important for a model where Re can be significant)
Oct 11, 2017, 03:05 PM
Registered User
No need to re-phrase. You got it. One is flying faster than the other.

The nature of the disturbance is the same for each aircraft ... I dunno, a bit of rough air.

I'm trying to tease out the qualities that make an aircraft stable. .. and I see that I've introduced two variables. My bad.

This relates to a different thread, in which we are trying to determine what factors affect stability under windy conditions.

So, imagine you are flying an approach in turbulent air. Is it beneficial to fly faster? ... is it beneficial to have a higher wing-loading? ... perhaps neither ... or both.




Trying to determine what the inter-relationships are between ... speed, weight, wing-loading and stability.

Subjectively, a fast and heavy aeroplane has a "solid" feel, imo. But, what are the factors which determine that solidity, how do they act, and how do they react to disturbances?

Put another way ... if you were tasked with designing an aircraft which could track down a glideslope really easily, despite the vagaries of the weather, what would it look like?
Last edited by bogbeagle; Oct 11, 2017 at 03:56 PM.
Oct 11, 2017, 03:56 PM
B for Bruce
BMatthews's Avatar
To some extent it would depend also on how the additional weight is distributed. If it's evenly more dense that means the extremities on the heavier model would be comparatively heavier.

The aerodynamic forces attempting to restore the model to stable flight would be higher at greater speed. So if the heavier model were flying faster and at a comparable degree above the stall speed I would expect it to damp out the oscillations in roughly the same number of cycles. But if both were flying the same speed the heavier one would be closer to the stall speed and likely would not behave as neatly.

Quote:
So, imagine you are flying an approach in turbulent air. Is it beneficial to fly faster? ... is it beneficial to have a higher wing-loading? ... perhaps neither ... or both.
Ah.. .so now we see where this is going. As you've likely seen me post before I'm a big fan of "light is right and lighter is righter". Unless taken to extremes this applies to flying in windy turbulent conditions as well as it does in lighter conditions. In the rough stuff I can "power" my lighter model down the glide slope at a ground speed that is the same as a heavier model in a glide that is closer to the stall. But my lighter model is then well above the stall speed. So I have good control authority to correct any bobbles and enough speed over the stall to deal with the airspeed reduction as I pass through the ground shear effect during the last few feet.

Now this isn't so much a stability issue as it is a handling issue. I just find that a lighter sort of model handles so much better that it reduces the work load on the pilot in ALL conditions.

Now if I flew in conditions where wind and lots of turbulence near the ground was a steady thing I would shift from "light at all cost" to a more moderate middle of the road favoring the lighter side. And I'd combine this with a slippery design with a symmetrical or near symmetrical airfoil and trim the model to be really close to neutrally stable. This last factor is needed to let the slippery nature of the model and the airfoil work for us properly.

Real world examples are always a nice thing so we can see what the person is advocating. Years ago I bought and built a Quickie 500 kit to use for sport flying. In the original form it was supposed to have a hot .40 engine and a minimum overall weight of 5lbs. I built mine up with some slight changes to the tail surfaces to give more rudder and elevator and powered it with an OS .25FP. The weight came out to around 3.5 lbs or 56 oz give or take a little for the age of the memories.... In any event it was on the lighter side of things. But it was a great model in the wind. It was heavy enough to not bobble around like a super light old timer design would be yet it was light enough that I got a good share of all the good things that a lighter model provides. I could hot dog it around at low altitudes and stop it in the air yet it would be back to flying with only a little power or altitude loss. It never snapped with no provocation when flying slowly near the stall thanks to the lighter sort of wing loading and it was a dream to fly both upright and inverted. In fact a fun thing to do was to try to run an inverted landing approach and just kiss the fin in the grass then fly away. I only managed that a couple of times out of maybe 80 to 100 tries. Mostly I ended up with a glow plug full of grass But it was a FUN thing to do that worked because the model was on the lighter side of things and had no bad habits as a result.
Oct 11, 2017, 04:54 PM
Registered User
Sooooo, if "lighter is better" ... what's the problem with the Old-Timer?

What was it about the Quickie that made its handling superior in rough weather? Was it just the weight ... just the speed ... or both?

Maybe it was something completely different.

If you didn't fly the Quickie at 5lbs AUW, how do you know that it was better at 3.5lbs?


I'm thinking that aircraft of higher inertia ... when exposed to a disturbance, such as a bit of turbulence ... will experience slower rates of change. You'd experience this as the aircraft being less "skittery", if you like... because the disturbances are being damped by the mass of the aircraft.

An analogy, tho I don't know that it's valid ... if I'm out on the sea in my kayak, I'm feeling every little wave. But, to you on your big ship, that sea is flat calm. Both vessels experience the same effects of currents. A most imperfect analogy, tho I feel we might learn something from observing the ways in which model boats behave, and how that behaviour changes with scale.
Oct 11, 2017, 05:12 PM
Registered User
As posted in the other thread:

Let's consider two identical aircraft again, flying at the same AoA; but B has a higher wing loading than A. Therefore B flies at a higher airspeed.

A horizontal gust produces a change in airspeed. Load factor (G's), being lift divided by weight, is proportional to the square of the airspeed. It is easily shown that A "sees" a bigger change in load factor than B for the same gust.

A vertical gust produces a change in AoA. This change is (in radians) essentially the gust velocity divided by the airspeed. Again, A will see a bigger effect than B for the same gust.

Therefore, whatever the damping may be, the initial gust response is higher for a lighter wing loading than a heavy one.
Oct 11, 2017, 05:51 PM
B for Bruce
BMatthews's Avatar
Bob, I've not flown models of the same design at wildly different weights. But I've flown a range of models that ranged from light to heavy for their size range. Gliders and old timers being on the light wing loading end and a couple of my own along with those belonging to aspiring students on the other. So there's a little of an apples and oranges issue due to no "same design" comparison. But from that overall exposure I still stand by my posting that lighter is righter.

As for the Quickie racer I also didn't fly it with the hot racing .40 that was intended. So again this would be a bit of an apples to oranges thing. But at 5lbs it would have had a much higher stall speed. And if flown into a stall would have required more height to recover. Or more throttle applied during the recovery to aid with speed build up. On top of that the takeoff and landing runs would have both been longer. Along with all this with the power of the OS25 the stall to maximum speed range would not have been as high. And I seriously doubt that I'd have enjoyed doing the "inverted landing approaches" trying to kiss the fin in the grass as much at the flying speed and potential inverted troubles that would have occurred at 5lbs as I did at the lighter weight.

The old timers I fly so far have all mostly had engines in them. So it's a climb then glide thing to try for catching thermals. It's not that I fear for how they handle in the wind so much as it is how far I can ride the lift downwind and still get back to me. With electric power that would not be an issue of course. I could climb and soar all I want and then just throttle up and trim down to punch back to home. But I hadn't thought of that when I wrote the piece above.

Mind you the old timers in rough conditions are more of a handful due to the large amount of dihedral that they typically have. But that's something apart from light weight to heavy weight. And a heavy old timer wouldn't soar well. So "lighter is righter" applies in this case or the model fails the intended mission irregardless of any stability or heavy wind issues.

You started this thread with a question about stability. And by extension since you asked about a stall recovery about how each example is able to damp out the oscillations from a stall. But from your first reply it seems to be more about an optimized weight for windy weather flying. As such I'll grant you that it's a YMMV sort of issue. My own experience over the years from both directly flying examples of each and watching many more has led me to my viewpoint. But there's far more to reaching this viewpoint for either of us than just the effect of weight on a model during something like a simple stall.

I'm a big believer also in using small free flight gliders to test things like this. It would be highly interesting to build two identical all sheet balsa gliders at around 12 to 16 inch span. One made from light materials and the other made from heavy. Then compare how they fly in a number of respects. And then to ballast the light one with a centralized lump at the CG so it is then the same weight as the overall heavier version.
Last edited by BMatthews; Oct 11, 2017 at 06:15 PM.
Oct 11, 2017, 06:21 PM
B for Bruce
BMatthews's Avatar
Sorry for the long duration edit in my post above. If you read the long and rambling version please ignore it. I tried to condense it down better while still hitting the main points.

Hey, jruley, another factor to go along with that analysis is that the heavier model would pass through any given zone more quickly due to the higher flying speed. So that should reduce the overall energy transfer and make the difference even more apparent.

There is no doubt that a heavier model LOOKS smoother than a light one when flying in heavy wind. And I suspect that the higher flying speed and lower exposure duration to any single area of side gust has a lot to do with it. Which would be another reason why great looking and well detailed WWII scale models that tend to be overweight look so good in the air even in windy conditions.
Oct 11, 2017, 06:25 PM
Registered User
If the duration of the gust is sufficiently large (3 sec vs 0.5 sec) whether by aerodynamic and/or AS, the lighter AC should be able to more quickly align itself (definition of dynamic stability) to compensate for the gust and ameliorate the effect. And that includes auto-diving, etc.. and more quickly speeding up. Or?

The traditional Chinese idea of strength is flexibility and a lighter AC should be more dynamically stable. Another way of putting it is that the lighter AC will initially get perturbed but more quickly able to smooth and ride it out. Or?
Oct 11, 2017, 06:35 PM
B for Bruce
BMatthews's Avatar
One more thing......

Bob, that 5lb weight for the Quickie was also a MINIMUM weight called for in the rules. If someone had slipped in a .40 powered model with a fairly competitive engine but at 1.5 lbs lighter than the rest of the racers it would have left them in the dust. Top speed would have been a smidgeon higher. But the big deal would have been tighter turns or the same size turns but with far less speed loss thanks to the lighter weight. Lighter is righter also works for any sort of racing which involves turning and where the G load pushes the wings into a high drag range of operation. Even a little less weight when multiplied by the G load makes a big difference.

But of course racing and sport flying don't really compare.

I'll grant you that there's some wiggle room here. For some folks there likely is a weight for some given model where they will be more comfortable. Particularly for models flown in higher winds. The trick is to find the sweet spot that aids the model with rough conditions while not creating vicious handling in other ways.
Oct 11, 2017, 07:07 PM
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richard hanson's Avatar
I did one Quickie with a KB .40 which weighed 3 lbs
I was required to ballast it to 4 lbs to fly
It was quick.
But the most fun was flying at min weight and practicing tight close in aerobatics
You cant beat min weight and max power
argue AOA etc., on n on--- but the proof is in the pudding.

ballast is for gravity powered gliders - only
The scale builders would insist you needed a scale P51 for example, to be heavy.
This was to obtain scale like performance (?)
real problem was most of em couldn't design/build to correct weight for best and most scale like flying.
Strange, but the new all foam scale electric fliers are typically much better flyers. simply because wing loadings are far lower.
Last edited by richard hanson; Oct 11, 2017 at 07:13 PM.
Oct 11, 2017, 07:23 PM
B for Bruce
BMatthews's Avatar
Quote:
I was required to ballast it to 4 lbs to fly
It's been way too many years ago. But was the Q500 minimum 4 or 5lbs? I thought I recalled it being 5. But those old grey cells ya know.....

The old classes of racing seem to be all gone. So I can't find the old Q500 rules.
Last edited by BMatthews; Oct 11, 2017 at 07:28 PM.
Oct 11, 2017, 08:07 PM
Registered User
Quote:
Originally Posted by xlcrlee
If the duration of the gust is sufficiently large (3 sec vs 0.5 sec) whether by aerodynamic and/or AS, the lighter AC should be able to more quickly align itself (definition of dynamic stability) to compensate for the gust and ameliorate the effect. And that includes auto-diving, etc.. and more quickly speeding up. Or?
The traditional Chinese idea of strength is flexibility and a lighter AC should be more dynamically stable. Another way of putting it is that the lighter AC will initially get perturbed but more quickly able to smooth and ride it out. Or?
Again, let's talk about two identical models, trimmed to fly at the same AoA.

One has been ballasted to a significantly higher weight, resulting in a higher wing loading. The CG is unaffected, therefore static stability will be the same. Because of the higher weight, the trim airspeed will be higher.

WRT the first question: because of the higher speed, the heavier airplane will pass through the gust (which is physically limited by space, not time) more quickly. Therefore it will be less affected by the gust. For reasons given in post #6, the initial response will also be less. Therefore the heavier loaded model will fly out of the gust closer to the initial trimmed conditions than the light one.

WRT the second question: Dynamic stability is the tendency of the system once disturbed to return to initial conditions. It depends on all sorts of things depending on the mode (short-period, phugoid, roll, spiral, or Dutch roll) in question. So every case is different and there's no simple answer to the question in general. However, for the special case of an airplane that has been ballasted, we can assume that the moments of inertia will not differ much between the heavy and light airplanes. This assumes that the ballast is concentrated near the CG. With no changes to aerodynamics, and little to no change in moments of inertia, the dynamic stability (damping ratio) of the heavy and light airplanes should be about the same.

Conclusion: The heavily loaded airplane will be less initially affected by the gust, so will get less far off trim conditions during the encounter. Both airplanes will damp out the resulting motion about the same.
Oct 11, 2017, 08:13 PM
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richard hanson's Avatar
Conclusion: The heavily loaded airplane will be less initially affected by the gust, so will get less far off trim conditions during the encounter. Both airplanes will damp out the resulting motion about the same.

The heavier plane takes more power to go the same speed
so forget about anything else.
aeronautics 101
Oct 11, 2017, 08:16 PM
Registered User
Quote:
Originally Posted by richard hanson
The heavier plane takes more power to go the same speed
True, but as long as sufficient power is available, it's also irrelevant.


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