How to choose tail A/R ? - RC Groups
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Nov 11, 2008, 07:27 PM
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rdeis's Avatar

How to choose tail A/R ?

I'm futsing about with my Spirit-V (with a new wing and tail is it still a Spirit?) and wondered how to choose a correct aspect ratio for the tail?

I know the area and angle I want, but I'm not certain what to use for the root and tip chords.

Have been reading from here:
And from Don Stackhouse.

How do I balance the effectiveness of a higher aspect ratio against the better reynolds number of a lower one?
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Nov 12, 2008, 08:26 AM
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Resurgam's Avatar
I doubt it makes a huge difference to the flight performance. I would simply copy another design. 2m Chrysalis might be good.
Nov 12, 2008, 11:39 AM
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rdeis's Avatar
If it makes no difference, then I'll more likely make my own based on asthetics.
Nov 12, 2008, 06:32 PM
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What I would do:

Once you have determined what area you need for your desired control responsiveness and margin of stability, and the root airfoil section, figure out how much load will be exerted at full deflection at the anticipated Vne.

Using this assumption, you can figure the bending moment at various aspect ratios.

At those aspect ratios, you can figure the root chord and the section thickness. Based upon the spar material you intend to use, you can then extrapolate how much material you must use in your spar caps to achieve the appropriate bending strength. If it's prohibitive, a larger chord is in order.

Otherwise, go with aesthetics.

Nov 13, 2008, 12:12 AM
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I think if you make the airfoil correctly, then I think the structural issue will be your limit. When you make the tail's aspect ratio higher, it provides more stability for a given area.
Nov 13, 2008, 01:19 AM
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Originally Posted by lincoln
I think if you make the airfoil correctly, then I think the structural issue will be your limit.
No concern for Re number, then?

When you make the tail's aspect ratio higher, it provides more stability for a given area.
Right- unless Re number falls far enough to be a problem.

With the short tail moment on this one, though, it needs an awful lot of area, so I could see structural limits coming in to play before the chord gets small enough to cause Re problems.

Nov 13, 2008, 07:01 PM
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I did say, with the right airfoil. Look how high the aspect ratio is on the tail on some of the Apogees. I actually asked Mark Drela the same question and he said that if the airfoil was right, then the structure became the limit. Will maybe check out on Profili when I get that running again.
Nov 13, 2008, 09:42 PM
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Don Stackhouse's Avatar
As the others have noted, there's a whole list of factors. One thing in particular is the lift curve slope, or "dCl/d-alpha" (dee-see-ell-dee-al-fah). This is how much the lift coefficient (of the entire flying surface in this case) changes for a given change in its angle of attack.

Higher aspect ratio surfaces generally have a higher lift curve slope, so they generate a stronger stabilizing force for a given sized disturbance. However, Reynolds number also can have an influence, particularly at the Re's where we operate. Also, at lower Re's there can be more problems with things like aerodynamic hysteresis.

The "optimum" answer (if there is one) will be different for each different design, and will depend on aerodynamic factors, structural factors, and the relative importance the designer attaches to each. In general, a longer tail moment arm will probably favor a lower tail aspect ratio, and a higher aspect ratio for shorter tail moments.

The good news is that for reasonably conventional layouts, if you can't or don't want to go through an elaborate optimization, just basing it on aesthetic considerations is probably not really that bad. What looks good to us is largely a matter of what we're used to seeing. The effects of "natural selection" in airplane designs has over the decades pushed designs towards what seems to work reasonably well most of the time. As a result, "TLAR" (That Looks About Right") might not get you an absolutely optimum world-beater, but as long as your plane's arrangement isn't too unconventional, it will probably work OK.
Last edited by Don Stackhouse; Nov 13, 2008 at 09:48 PM.
Nov 14, 2008, 05:03 AM
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About 30 years ago, I used higher aspect ratio stabs but had some flutter problems. I have since gone back to aspect ratios less than 6 and have had no structural flutter problems. The high aspect ratio stabs had to be statically balanced about the pivot to control stab flutter during rotation after launch.
Nov 15, 2008, 12:52 AM
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I just ran Profili on the HT08. At Re=60k, Cd is around 0.012 to 0.013. At 30 k, .018 to .019 or so.
Nov 15, 2008, 01:01 AM
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Don Stackhouse's Avatar
However, what happens if you re-optimize the tail airfoil for the lower Re?

Also, is your tail area dictated by stability, or by control authority concerns? If stability is the issue, and not tail stalling, the the higher aspect ratio and the higher lift curve slope that goes with it may allow a smaller tail area that offsets the increase in Cd.

OTOH, if tail area is determined by control authority issues, such as having enough tail lift force to overcome the pitching moment from large wing flaps, then you're stuck, unless you can use a cambered tail airfoil to increase the tail's Clmax enough to deal with that.

Like I said before, a whole shopping list of issues, and no single or simple answer.
Nov 15, 2008, 02:07 PM
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However, what happens if you re-optimize the tail airfoil for the lower Re?
Any airfoil with fully attached laminar flow, like the HT08, has very simple and predictable drag and lift behavior vs Reynolds number:
Clmax = constant
dCl/da = constant
Cd = constant/sqrt(Re)

The stabilizing power of a stab of some area S and aspect ratio AR is
dL/da = q S dCL/da = q S dCl/da / (1 + 2/AR)
and the drag is
D = q S Cd

We can now determine the AR,S combination which gives minimum drag at some fixed required stabilizing power. The dL/da equation gives the necessary S versus AR such that the stabilizing power is kept the same:
S = constant * (1 + 2/AR)
where the value of the "constant" is not important -- it will turn out that only the proportionalities matter.
The average chord is
c = sqrt(S/AR)
so that the drag is
D = constant * S / sqrt[ sqrt(S/AR) ] = constant * S^0.75 * AR^0.25
Again, the value of the "constant" doesn't matter.

Substituting for S from the stabilizing-power constraint we get a D vs AR relation:
D = constant * (1 + 2/AR)^0.75 * AR^0.25
It's a Calculus-101 exercise to find that the minimum D occurs at AR=4. So from a profile drag viewpoint, any strictly-laminar tail should have AR=4.

However, the optimum is extremely flat as the attached plot of D(AR) shows. If any of the following occurs:
* There is some turbulent flow (launch, large control inputs, imperfect airfoil)
* The stab carries some upload or download, so there's also induced drag
* Weight is also an issue
then the real optimum will shift towards the larger AR in each case. Any because of the flatness of the curve, the shift can easily be considerable. For these reasons I normally try to make the tail AR as big as is practical. The SG2 tail has a stab with AR=5.1, which theoretically is only a 0.5% stab drag penalty (the airplane drag penalty is perhaps 0.02% -- negligible). But it's surely better than a AR=4 stab when the other considerations are factored in.

Update: I added a second plot which also shows the chord and area of the "optimum stab", versus AR.
Last edited by markdrela; Nov 15, 2008 at 02:26 PM.
Nov 18, 2008, 05:02 AM
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Neil Stainton's Avatar
Superb, you are a great teacher. Thank you.

Nov 18, 2008, 07:55 AM
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Resurgam's Avatar
Thank you for the analysis, Dr. Drela. It's always nice to have theoretical confirmation of an intuitive feeling
Nov 18, 2008, 10:27 AM
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Neil Stainton's Avatar
BTW Mark, does this analysis hold for fins too?



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