# Vertical tail volume coefficients - what am I missing?

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#### Grimace

##### Well-Known Member
I am trying to do some preliminary sizing of a vertical tail for an ultralight glider. I have the following -

Swing: 143sqft
b: 41.5'
Lvt: 10'
Cvt: .04 (per Raymer)

And it says I need about 24sqft of surface area for the vertical tail. That is ridiculously huge. I looked at other comparable aircraft as best I could and it looks like I'm about twice the size that I would expect. Using the TLAR method, the tail is 1/3rd the size it should be. With the "Well, just make it a smidge smaller than comically huge" method, I am still drastically undersized by about half.

What am I missing? I realize that a 10' Lvt is pretty short, but the vertical tail is 16% of the wing area? Bear in mind, these numbers are approximate. I'm just trying to see if I am in the ballpark... And apparently I am not.

I think I must be off with my maths. Either that, or there must be some trick I'm missing or there's better data for ultralight aircraft and my assumptions based on heavier gliders and aircraft are off. Any thoughts?

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##### Well-Known Member
You have the math right. You have a long (for an ultralight) wing span and a short tail arm, both of which are driving a larger area for the tail.

The target vertical tail volume coefficient may be off, though. Other sailplanes have smaller tails, with coefficients around .02, which sounds like would yield a size closer to what you are expecting from a TLAR perspective. You'll need to make sure you're using an appropriate value, based on the aircraft type.

Thomas' Fundamentals of Sailplane Design has historical data on sailplane geometries, which may be of use to you in setting a starting value. (He includes procedures for sizing, also, if you want to get more detailed from there.)

#### Grimace

##### Well-Known Member
My mother taught me to never abandon your common sense. So when something looks off, I question it. TLAR isn't in any textbook that I am aware of, but it is probably the most powerful tool us humans have in solving problems that have already been solved by somebody smarter than us.

I will reevaluate the coefficient. Thank you. And I am not familiar with Thomas' work. I will check it out. Thanks.

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#### Speedboat100

##### Banned
I agree my granny also said that each time your hear something impossible don't believe it.

Ad little bit tail fuselage area to it.

#### wsimpso1

##### Super Moderator
Staff member
Short tail arm ends up doing some other undesireable things:

The tail down force is bigger with a shorter arm which comes with its own induced and form drags. Make the arm longer and the tail area and its drag decreases;

The tail down force is added to the weight of the craft, which the wing must lift. Longer tail arms reduce this effect, allowing smaller wing or lower stall speed and less drag;

Pitch damping goes with tail arm squared. If you have too little pitch damping, any control change or bit of turbulence will overshoot and oscillate until it settles. We tend to prefer deadbeat response where it does not overshoot and oscillate. Longer tail arms make for nicer flying airplanes.

If your design looks like it has short tail arm, that is probably because most designers go with longer arms, smaller tails, less drag, and better manners.

Billski

#### TFF

##### Well-Known Member
I have built some RC planes with short fuselages with long wings and they are just about unflyable
Although calculations will give you numbers, there is a crossover point where you really have a flying wing with an extended trailing edge. What you don’t have is all the stability tricks a flying wing has.

#### Lendo

##### Well-Known Member
Grimace, a good starting point is to look at 3 times the Wing Cord from CG to 25% Mac HT or preliminary design 25% Mac wing to 25% Mac HT, anything less it's short coupled and it doesn't hurt to add a bit of length as well. Sweep in the Wing, HT and VT reduces efficiency and drives up more area.
Raymer's 0.04 coefficient is correct for Light Aircraft, I'm surprised that Sailplanes have half that coefficient, although I must say I have never looked at that in Sailplanes before and I can't understand why that might be.

#### Topaz

##### Super Moderator
Staff member
... Raymer's 0.04 coefficient is correct for Light Aircraft, I'm surprised that Sailplanes have half that coefficient, although I must say I have never looked at that in Sailplanes before and I can't understand why that might be.

Sailplanes tend to have very long tail arms, which makes for good yaw damping, and T-tails, which increase the effectiveness of the vertical tail through the end-plate effect. Together with the overwhelming desire for drag-reduction, it makes for tails that are smaller in area than you might otherwise see in a shorter-tailed airplane.

#### Grimace

##### Well-Known Member
Grimace, a good starting point is to look at 3 times the Wing Cord from CG to 25% Mac HT or preliminary design 25% Mac wing to 25% Mac HT, anything less it's short coupled and it doesn't hurt to add a bit of length as well.

It's for an ultralight, so I can't go too crazy on the tail length. I already decided to lengthen it from 8' to 10 because of the sizing problem. But the wing chord is a little less than 3.5' so I am already close to 3x. And if I can convince myself that .02 is the correct Cvt for this plane, I may very well go back to 8 feet to save space.

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#### Grimace

##### Well-Known Member
Short tail arm ends up doing some other undesireable things:

The tail down force is added to the weight of the craft, which the wing must lift. Longer tail arms reduce this effect, allowing smaller wing or lower stall speed and less drag;
...
If your design looks like it has short tail arm, that is probably because most designers go with longer arms, smaller tails, less drag, and better manners.

I love the way you're able to put things into simple terms. Always a pleasure to hear from you (and Topaz too). But my chord is 3.5' so the 10' tail is just about spot on. But the effects of the HT on aircraft weight is something fun to ponder and consider. It might lead to a new iteration. Thanks for that.

Although calculations will give you numbers, there is a crossover point where you really have a flying wing with an extended trailing edge. What you don’t have is all the stability tricks a flying wing has.

Thank you. That's a very neat insight. I probably spent a half hour today thinking about this and mentally playing with edge-cases to consider how this comparison would look in real life. (You are the second person I responded to saying "It's not short-coupled! And you might think it bothers me and that I am being facetious when I said I pondered this for 30 minutes, but I'm being serious. It was a fun thought exercise that I wouldn't have had otherwise. And I do seriously get delight in you and others voluntarily chiming in with anything you see that might be heading towards a trap for newbs. I try to do the same and I am NOT an expert in this, so I will never object to anyone who eagerly wants to volunteer solid knowledge, gratis.). But again, I don't think this is very short coupled with a 10' tail and a 3.5' chord.

Still, all this talk about short-coupled tails has given me some really cool insights and I'm not complaining about that in the slightest - I honestly enjoy it. However, I was actually more expecting someone to notice the span and the wing area and chime in cautioning me about Reynolds numbers than a short-coupled tail (and that conversation would totally be welcome because I think I have come to a decision on this matter, but there are also serious gaps in both my knowledge and in the available information on this topic).

Does anybody else have some sources for me to snag measurements off a few sailplanes? Maybe you have some dimensioned 3-view drawings handy of light gliders? Or a collection of tail surface areas and tail lengths for gliders? Yeah.... I know that's probably asking too much.

Also, Topaz and anyone else who cares to chime in - one thing I was considering was a slab-sided rear fuselage for lightness and simplicity. I have mostly decided to shelve this idea, but if it helps with stability, maybe it's worth reexamining? Are there any examples you know of of fuselages that are thin with flat sides - let's say 4 inches wide and a foot tall or something similar? I know that primary gliders have a flat tail, but what about filling it in for extra stability? This idea is too obvious and so, too, must be the reason you don't see it done. I just can't spot it yet. But I was thinking that for an ultralight with something like a 90mph Vne (or likely a fair bit less), maybe the idea at least deserves a few minutes of reconsideration, given modern materials like CF. Perhaps there is a use case worth considering out here in the fringe world of 3-axis UL gliders with a design that maybe hasn't been reconsidered since the age of spruce sticks, Irish linen, and resorcinol.

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#### Grimace

##### Well-Known Member
Sailplanes tend to have very long tail arms, which makes for good yaw damping, and T-tails, which increase the effectiveness of the vertical tail through the end-plate effect. Together with the overwhelming desire for drag-reduction, it makes for tails that are smaller in area than you might otherwise see in a shorter-tailed airplane.

But the tail length is already factored into the equation, so it just further begs the question - why do all the other gliders get to have cute little bunny tails while my drawing is stuck over here looking like Roseanne's posterior? LOL. It sounds like some wise minds already spotted the issue with the Cvt and they are probably right. Now it's just a matter of determining a better value. Though yeah, maybe I will have to be careful about the inclusion of T-tails as well. Or at least be wary of how they might skew the data.

I suspect that with a stall speed hovering somewhere in the 18-25 range, I won't be able to trust results from larger heavier gliders and will have to be more selective of which ones I include in this "study". Maybe I'll have to cap the empty weight at 250lbs or something for my sample set... And closely consider the experience of the designer, absent any pireps on the handling characteristics. The suspected upcoming lack of data and the relatively low numbers of examples built in the class makes me concerned that there may be some potentially disastrous data points out there. Hopefully if I miss one or two of them the averages will balance them out.

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#### wsimpso1

##### Super Moderator
Staff member
Note than many of the 3 views reveal tails much further aft of the wing than 3xMAC. Oh, and you measure from 1/4c of the wing to 1/4c of the tail.

#### TFF

##### Well-Known Member
Just looking in general at a sailplane, the proportion of the fuselage length is close to the same as one wing panel. There are versions that are not, but they do not make the majority of one percent of the total. If you are going to be different than the rest, yours will not look like the rest.

#### BBerson

##### Light Plane Philosopher
The vertical tail size must considered with the dihedral, the vertical CG, if low wing or high wing, the wing span and the type of stability desired and the destabilizing area ahead of the CG and if additional fuselage area is behind the CG.
Old free flight models had very tiny vertical tails with huge dihedral to eliminate spiral dives.
Manned aircraft have large vertical tails and minimal dihedral for improved directional stability and less air sickness. Glider pilots are forced to use the rudder constantly and get by with less area.
Then there is prop destabilizing, area for spin recovery and is the tail in bad air? ......

#### Lendo

##### Well-Known Member
Someone said to me once (no names mentioned to protest the guilty), that the extra area needed in the extended tail is less that the are saved in the HT and VT, so there is savings in weight and parasite drag with the extended tail, and why I assume Gliders have long slender tails.
Things to consider!
George

#### Grimace

##### Well-Known Member
I appreciate all the feedback and insights. Thank you all.

The glider is an ultralight. It has about 6 feet of fuselage ahead of the front spar (the spar runs below and forward of the pilot's shoulders, somewhere around the mid-spine, so the pilot doesn't have a great effect on CG, but the pilot can be semi-reclined so the fuselage can be smaller than if the seat were hanging down vertically from the spar, as you see in many ultralights). And the VT and the forward fuse have about a 50/50 share of the area from the side view, but the CP for the tail is about 8 feet farther back than the fore fuselage. Although you are only swinging 350lbs around the CG at full gross, flight at near-stall is going to pretty clearly be the defining factor in sizing the tail. When I get deeper into it, that will be more closely considered. But maybe some additional examination now may be illuminating, regardless of what preliminary sizing might suggest.

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#### lr27

##### Well-Known Member
You might want to recalibrate your sense of TLAR by looking at the vertical stabs on the Carbon Dragon and the ULF-1. Plus I've seen at least one other short fuselage ultralight glider with a big vertical stab.

Damping from the vertical stab, all else being equal, is proportional to the distance between the cg and the ac of that stab. So, if damping is important, you'd expect the stab on a short boom to be quite large. Another important factor in damping, or lack of damping, is the moment of inertia in yaw related to the weight of the aircraft as flown. This means that lighter wingtips and heavier pilots allow you to get by with less area in the vertical stab, or a slightly shorter tail boom. The pertinent figure of merit is the radius of gyration. On an existing aircraft, this is easily measured by suspending the aircraft two wires, giving it a wiggle, and timing the wiggles with a stopwatch. Timing ten wiggles is probably easier. Do a search on yaw radius of gyration drela and you will find a nice note on doing this. Don't forget to include the weight of the pilot.

#### wsimpso1

##### Super Moderator
Staff member
As I have gotten it from Lednicer and Roncz, yaw and pitch damping are a function of tail area and arm length squared, or put another way, tail volume times arm length. If you hold tail volume constant, then longer tail arms damp much better than shorter ones, even as tail area drops.

#### Grimace

##### Well-Known Member
You might want to recalibrate your sense of TLAR by looking at the vertical stabs on the Carbon Dragon and the ULF-1.

I've done that. And I agree. It really got me reconsidering things when I did and caused me to pose this question. Adding 2' to the tail and using .02 as a Cvt lets me get closer to expected results. Otherwise, I get bigger than Carbon Dragon or ULF type results. They're valid data points nevertheless.