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Old Jul 02, 2006, 12:21 AM
turn, turn, turn.
Athol, Massachusetts
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Question
Does long tail moment affect speed?

From what basic understanding I have of sailboats, if you take two boats of equal size, the boat with the longest length at the water line is fastest.
Since air and water can both be treated as fluids...could this be true with sailplanes as well?
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Old Jul 02, 2006, 02:25 AM
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Quote:
Originally Posted by kkens4
From what basic understanding I have of sailboats, if you take two boats of equal size, the boat with the longest length at the water line is fastest.
Since air and water can both be treated as fluids...could this be true with sailplanes as well?
It is not the length, but the aerodynamic shape (hydrodynamic with boats).

If you have a long tail arm, you can reduce the sizes of fin and stab, reducing drag.

Jürgen
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Old Jul 02, 2006, 06:02 AM
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I agree with Jurgen.

The long tail arm increses fuselage drag but the tail reducing drag is over comes the fuselage drag.

Also, if the the tail arm is too long and it makes the fuselage too flexable, you might loose control at high speed.

I quote Don Stackhouse:
"The flight of a model sailplane is a complex phenomenon, each portion of the model seeing its own unique set of conditions at any given time, yet still having an influence on all of the other parts of the model at the same time."
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Old Jul 02, 2006, 07:36 AM
Lift is cheap - Drag sucks
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kkens4,

The 'Length at Water Line' calculation is a rule of thumb that equates wave patterns for hulls of different size. In the days before computers, it allowed performance scaling between hull models and their full sized equivalents. Boats operate in the interface between two fluids. Airplanes do not.

Your question is whether a long sailplane will go faster than a short one. If you only had a fuselage (hull) to contend with, that might be true. It would have a better fineness ratio and a higher Reynolds number. But, the large surfaces sticking out at the front and back are more of a problem than the 'hull'.
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Old Jul 02, 2006, 08:56 AM
turn, turn, turn.
Athol, Massachusetts
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Thanks to all.
It was just an idea I had while driving.
Apparently...not a good idea.
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Old Jul 02, 2006, 11:04 AM
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Quote:
Originally Posted by kkens4
From what basic understanding I have of sailboats, if you take two boats of equal size, the boat with the longest length at the water line is fastest.
Since air and water can both be treated as fluids...could this be true with sailplanes as well?
Long tail moments for sailplanes are generally (within reason) a good idea, but not for the reasons you're suggesting.

One of the biggest drag issues for a boat is "wave drag". The hull makes waves as it travels along the surface of the water. The speed at which the waves travel is proportional to their wavelength, i.e.: the distance between wave crests.

As the boat goes faster, the waves its hull makes have to get further and further apart in order to keep up with it. Eventually they get far enough apart that one is at the bow and the next is at the stern. Unfortunately they can't get much further apart than that! From that point on, any additional power applied to the boat to try to make it go faster ends up just making the bow and stern waves bigger. The boat is literally trapped between two hills in the water that are of its own making, and any attempt to escape just makes the hills bigger!

The way out of this trap is to use a "planing" type hull (as opposed to the "displacement" type), which can lift up partially out of the water, allowing it to climb up and sit on top of its own bow wave. No longer constrained by the wavelength of its bow and stern waves forced to being equal to its waterline length, it can now go quite a bit faster. However, getting enough power into a sailboat to accomplish this "getting on the step" is a pretty tough proposition that entails some other compromises, which is why we don't see really extensive use of planing hulls on sailboats. There is some, but not to nearly the extent that we see in powerboats.

The key difference between a sailboat and a sailplane in this case is the surface. Both move through fluid mediums, but the sailboat has to move along a "free surface" in that fluid, and therefore has to deal with wave action in that free surface. An aircraft does not. In that regard, it is more analogous to a submarine, not a surface vessel.

However, a long tail moment on a sailplane will generally result in smoother handling, which can often translate into better speed, among other things.

There are two kinds of stability we need to consider in the handling qualities of a model: static, and dynamic.

Static stability simply means that if you disturb the airplane (for example, pull the nose up a few degrees and then let the stick go back to neutral), it will try to return to the attitude and angle of attack it had before it was disturbed.

Dynamic stability is the ability to damp out oscillations. For example, in the example above, odds are that the model will drop its nose when the control stick is released, it will pitch over into a shallow dive in an attempt to return to its original airspeed (something it needs to do in order to get back to steady flight at the original angle of attack), but it will probably not be able to pull out of that dive before it gains a little too much speed (unless it's a Chrysalis 2-meter), so it will have to pitch up again to bleed off the excess speed, but will overshoot again and end up pitching down again, etc., resuting in a series of up-and-down oscillations.

If the oscillations get bigger and bigger, it is "statically stable" (because it keeps trying to come back to the original angle of attack and airspeed), but "dynamically unstable", because the oscillations get bigger and bigger. If the oscillations continue indefinitely, neither getting bigger nor smaller, then it has "neutral dynamic stability". If the oscillations gradually get smaller and smaller till they die out completely, then it has "positive dynamic stability".

Now, within the realm of positive dynamic stability, there are planes that overshoot and then go through these oscillations till the oscillations die out ("underdamped"), ones that when disturbed come slowly back to the original angle of attack and airspeed (the "setpoint") without any overshoot or oscillations at all (i.e.: "overdamped"), and ones that come back to the setpoint exactly as quickly as possible without any overshoot (i.e.: "critically damped").

Most models are underdamped, typically needing about two and a half cycles to damp out a moderate disturbance. The Chrysalis is slightly overdamped. In terms of being easy to handle, dynamic stability (in my experience) is actually more important than static stability. I have tested deliberately setting the C/G far aft enough on a Chrysalis 2-meter that the plane became slightly statically unstable (i.e.: pull the nose up and release the stick, and the plane wants to pull its nose up even more) and then let a first-time beginner fly it. Because the plane was so well damped, she was able to mentally stay ahead of it without trouble, despite the static instability.

So, what does this have to do with tail moment?

Static stability is linearly proportional to tail surface area, and to tail moment arm. It's also dependent on C/G location.

Dynamic stability is not so much a function of C/G, but it is linearly related to tail area. However, it's proportional to the SQUARE of the tail moment arm.

Doubling the tail area gives you twice the static stability and twice the dynamic stability. Doubling the tail moment arm gives you twice the static stability, but FOUR TIMES the dynamic stability.

Or, with a pod-and-boom fuselage construction, which aproaches the case of the extra weight and skin friction of the tail section of the fuselage being nearly negligible, doubling the tail moment and at the same time cutting the tail area in half results in essentially the same static stability, twice the dynamic stability, and slightly more than half the tail assembly's skin-friction drag.

There are tradeoffs, so it is possible to make the tail assembly too long (one of our old Monarch HLG's competitors fell into that trap, and ended up with great dynamic stability, but was about as maneuverable as a schoolbus), particularly if the rest of the design isn't properly tuned to work effectively with all that dynamic stability (which is how we avoid that problem with the 2-meter Chrysalis). However, properly managed and integrated into the overall design, a long tail can have very significant benefits.

Don
(former sailboat racer and sailboat designer, among other things)
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Old Jul 02, 2006, 11:31 AM
turn, turn, turn.
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So I guess it's not a stupid thought experiement?
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Old Jul 02, 2006, 02:17 PM
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Quote:
Originally Posted by kkens4
So I guess it's not a stupid thought experiment?
Not at all. Your "what?" was on the mark, but the "how?" and the "why?" needed a little work.

Of course, thoroughly understanding the "how?", and especially the "why?" is the real secret to successful engineering.
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Old Jul 02, 2006, 03:52 PM
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Don, Thanks for your laymans explainations. Enjoyed your long post very much!

Here's a related question for you (or others) about tail moment I've been curious about for some time. You explained the relationship of dynamic and static stabilty to tail moment--does the same relationship apply to roll stability? No doubt other aerodynamic factors play a bigger factor in roll stability, but does a longer tail or more tail surface area contribute to self righting qualities at all? I'm especially curious about three channel gliders or trainers in which use a side slip to produce a roll.

Thanks! I hope it's not too far off the thread starters question. -Steve
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Old Jul 02, 2006, 04:02 PM
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The Lockheed T-33 was found to be faster than its parent, the P-80.. with the same wing and motor. The difference was in the fuselage length, the T-33 having a section added in for the second cockpit.
I liked the explanation of bow waves,... and why a model,totally immersed in air can't use that property.
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Old Jul 02, 2006, 11:21 PM
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The 'Wack, BC, Canada
Joined Oct 2002
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Actually there IS a connection but not a model related one. Do a Google on "area rule fuselage" for info on the coke bottle shape that was developed for some of the early supersonic aircraft. It's not directly hull speed related but it is sort of the airplane version of it.

PS: Pauls note about the two seater T33 being faster may be part of this as well.
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Old Jul 02, 2006, 11:47 PM
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The longer fuselage, or "fineness ratio" has been used a few times.
For some reason, the exact opposite idea was promoted by Lockheed and Boeing. A -shorter- fuselage was proposed as more efficient. Lockheed's L-1011-500, and Boing's 747SP were the result.
Only Pan Am bought the SP.. Just before they went under.
There's several -500s flying, some with the RAF.
The "area rule" only works for marginally powered planes that just inch past Mach 1. It's a way to get a smooth transition in total aircraft cross section from front to rear.
Overpowered planes don't bother with it.
Craig Breedlove had a Lockheed Flight Test Engineer design one of his land speed record cars using the area rule. ???? There weren't any wings whose cross-section needed to be considered for the real area rule.
I -almost- asked the FTE why he'd done it that way, as it had no purpose.. but native fear kept me quiet.
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Old Jul 03, 2006, 05:09 AM
Needs brain lubrication
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Aachen, very western Germany
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Quote:
Originally Posted by Don Stackhouse
Static stability is linearly proportional to tail surface area, and to tail moment arm. It's also dependent on C/G location.
I can't see a direct connection between static stability and tail surface area or tail moment arm.
That is because there is no tail needed for static stability.
In my eyes, only the CG as giving the actual static margin is determining the static stability.
That being said, I would of course admit, that adding a tail (or changing its place and size) will shift the planes' NP and with the CG held constant, the static margin would actually change.

biber
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Old Jul 03, 2006, 02:16 PM
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Quote:
Originally Posted by biber
I can't see a direct connection between static stability and tail surface area or tail moment arm.
That is because there is no tail needed for static stability.
Not true. Read on...

Quote:
In my eyes, only the CG as giving the actual static margin is determining the static stability.
That being said, I would of course admit, that adding a tail (or changing its place and size) will shift the planes' NP and with the CG held constant, the static margin would actually change.
Well, you've sort of answered your own question.

A tail is needed to get static stability, which is not the same thing as static equilibrium.

It's possible to find a location of the C/G that will put all of the various forces and moments in balance. An airplane (even a bare wing with a conventional positive-cambered airfoil) in this condition will continue to fly in a steady flight path as long as it is not disturbed. This is static equilibrium.

However, the moment that you disturb it, the plane will diverge and not try to recover unless it posesses positive static stability. For positive static stability, you have to have something that gives it a net recovering moment, so that a pitch-up results in a desire to pitch down, and vice-versa. This generally requires a tail of some sort, even in the case of a flying wing.

In a plank-type flying wing, you could consider the reflexed portion of the trailing edge to be the horizontal tail. In that sense, a plank is just a conventional-tailed aircraft where the tail moment arm is so short that the leading edge of the tail coincides with the trailing edge of the wing. You can even use the theory of tail volume coefficients to predict how much reflexed portion you need.

In the case of a swept flying wing with washout, the wing tips act as the horizontal tail.

As you implied, the neutral point ("NP", the location of the C/G that results in exactly neutral static stability, with no tendency to either recover or diverge further if the plane's attitude is disturbed, i.e.: the plane goes exactly where you point it) is dependent on both the wing and the tail, including both the tail moment arm and the tail area.

The difference between the resulting NP location and the C/G location (typically expressed as a percent of the wing's Mean Aerodynamic Chord) is the "static margin", the standard measurement of static pitch stability. If the C/G is ahead of the NP, then the plane will have positive static stability, and the more static margin it has, the stronger it's static stability.

Of course if the C/G is behind the NP, then the plane is statically unstable, and the greater this distance is, the more negative its static margin and the more strongly unstable the plane becomes.

There are some other factors that come into play, but in general, the NP will be at about the same location as the aerodynamic center of the complete aircraft (basically the wing plus the tail, inflenced somewhat by their airfoils and relative aspect ratios, with usually minor contributions from the fuselage, possibly significant ones from propellers, and further influences from any other appendages that interact with the airflow). Generally for models the wing and the tail are the main ones, and the others are usually fairly minor. If you find the aerodynamic center of the wing, the aerodynamic center of the tail, then use the ratio of their areas to find the approximate aerodynamic center of the two together, you'll probably be in the ball park.

Note, there is a static margin and NP for yaw, just as there is for pitch, and the two are not necessarily the same. In the case of the yaw NP, it's the interactions between any side-lifting areas that matter.

For example, in the performance measurements that Mississippi State did on the Horten H-IV flying wing sailplane, they tried to "improve" it by installing a fairing over the nose skid. This added side area ahead of the C/G, and they had to fly with a much more forward C/G in order to avoid yaw instability. Running the C/G that far forward forced them to carry bunches of up elevator (or elevons in this case) to keep the plane in static equilibrium ("pitch trim") at the desired flight speeds, which totally screwed up the plane's spanwise lift distribution, which then caused a big penalty in induced drag. This was one of the factors (there were a number of others, many also related to ill-advised "meddling" with the original design) that caused their measurements to fall short of the measured performance the plane displayed during flight tests back in Germany during its original flight tests in Germany.

Yet another classic example of how a seemingly minor change in an airplane's design can have significant "ripple effects" throughout the rest of the design!
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Old Jul 03, 2006, 02:30 PM
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Quote:
Originally Posted by Griffin
...You explained the relationship of dynamic and static stabilty to tail moment--does the same relationship apply to roll stability? No doubt other aerodynamic factors play a bigger factor in roll stability, but does a longer tail or more tail surface area contribute to self righting qualities at all? I'm especially curious about three channel gliders or trainers in which use a side slip to produce a roll. ...
Yes and no.

There isn't a direct connection between tail moment arm and static or dynamic roll stability.

However, there is a relationship between dihedral and yaw stability. If you have too much dihedral and not enough vertical tail effect, the plane will be prone to "dutch roll". Conversely, too much vertical tail effect and not enough dihedral effect will give the plane negative "spiral stability"; in other words, in a turn it will want to steepen up the bank all by itself, into a "graveyard spiral".

The mass distribution is also a factor. There is a sort of "sweet spot" in the combinations of dihedral and vertical tail in between having a dutch roll problem and a spiral stability problem. In general, the more mass you have out at the extremities, the nose, the tail and especially the wing tips, the smaller that sweet spot will be. In extreme cases, the sweet spot could actually become negative, meaning that there is no combination of vertical tail and wing dihedral that doesn't result in either dutch roll, spiral instability, or both!

This is one reason why having a longer nose to reduce the amount of ballast required to get the correct C/G is not necessarily always a good idea. Besides adding projected side area (yaw) and projected horizontal area (pitch) ahead of the C/G (which then requires more tail area and tail mass), it also moves the weight further forward of the C/G, which then makes this balance of vertical tail and wing dihedral more critical.

Isn't airplane design fun??!! Just no end of new parameters to keep track of, and new details to think about!
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