A few years ago, Serge Krauss mentioned that a more meaningful version of the Tail Volume Coefficient formula is:
Tail Moment measured in MACs * Ratio of Tail Area to Wing AreaThe above is, of course, the exact algebraic equivalent to the more widely published version – which looks like gibberish (to me, anyway).
One advantage of this version is you don’t need to memorize it or look it up. It is simply the familiar (to most every modeler) ratio of tail area to wing area with a simple tail moment leverage factor. We can immediately see, for example, that a ballpark TVC using average chord instead of MAC won’t be too far off the mark.
We can see immediately see TVC is scalable, as the tail moment is in wing chords, not inches or centimeters. We can see it is a dimensionless number as both factors are ratios.
The above format of the TVC formula gives us a pretty clear picture of what TVC does and does not describe about an aircraft. I think we should sh*tcan the other version.
Stability vs DampingDo most people associate TVC with stability? However, isn’t it really damping? Or more like damping? The difference is not just nit-picky semantics, my opinion.
Let’s do grade school level stability and damping descriptions (that is, describe them at my understanding level).
Stable: A marble at the bottom of a bowl, if moved and released, will eventually come to rest again at the bottom of the bowl.
Unstable: Turn the bowl upside down, and displace the marble. It will move even further away from the center of the bowl.
Neutral Stability: Place the marble in the center of a cookie sheet, and displace the marble. It does not have a tendency to move back towards the center or away from the center.
Damped Motion: Pour syrup over each of the above
Suppose model
Ding has a TVC of .35 and the CG is ½” in front of the wing 25% MAC point. We build a clone of the model,
Dong, with 1” longer tail moment, but put the CG ½” behind the wing 25% MAC point.
Dong also has a TVC of .35.
Ding and
Dong have equal TVCs. Do
Ding and
Dong have equal pitch stability?
In the first
Ding Dong example, we calculated tail moment (in wing chords) from the CG. Some prefer using the 25% MAC as the wing end of the tail moment measurement. If we build a new
Ding and a new
Dong with a lead ball mounted on an adjustable jackscrew, we can do the same mind experiment and reach the same conclusion – TVC is not a predictor of pitch stability, whichever TVC calculation you use.
At the magazine-article-level-of-aeronautical-knowledge level, TVC is a descriptor akin to syrup viscosity in the marble-in-a-bowl example. Using TVC as a stand alone descriptor (not as a coefficient), TVC is useful only as a comparative number. Knowing the TVC of one airplane doesn’t tell us much – we need TVCs of several airplanes, and how they fly, to make much practical use of TVC. Knowing the actual viscosity of our syrup is less important than knowing how much thinner or thicker it is than other syrups.
I don’t see any clues in the raw TVC calculations as to what sorts of amplitudes or frequencies it might be better at damping. It probably dampens flutters better that phugoids, because syrup does.
Does TVC tell us anything about potential maneuverability? Maybe, if we massage it a little. Whaddya think?
Include CL in TVC?Using the above formula, there is a mathematical assumption built in – that the relative lifting potential of both the wing and the tailplane are the same per square unit of area. Yet they have different C
Ls typically.
In the “neutral point” formula this oversight is corrected with a second multiplier – the ratio of horizontal tailplane and wing lift curves. I’ve never seen a stunt ship where the tail was a miniaturized wing, so on the surface it seems a sensible correction. (There are also Reynolds number differences also – No, let’s not go there).
We could easily modify TVC for our use by including the C
L in the numerator and denominator of the area ratios. We immediately run into a problem – we need to assume some AoA(s) to put in the “correct” C
L . The whole calculation gets more and more speculative, and less and less real world.
Let’s say we wanted to look at maneuver entries and exits using this approach. The calculation gets pretty wild at low AoAs, as the C
L of any airfoil at a very small AoA is very small. At one degree AoA, all airfoils are pretty much equal. Dividing one small number by another small number gives absurd ratios at times. (If we do that, it is no longer TVC, and we need a new name for the function.)
For now, I’m treating this as a dead end approach. Has anyone done anything similar?
Will the Real TVC Please Stand Up?Another TVC question – should the tail moment be measured from the CG or the wing 25% MAC? My answer is “
Yes ”. Here’s why:
I like to think of the CG TVC as the “trimmed” TVC. In flight, any aircraft rotates around the honest-to-gosh CG, not some theoretical point on a drawing. If we add nose weight, we always increase TVC (by lengthening the tail moment). All of us have read Ted Fancher’s explanation(s) of how and why models with larger TVCs and more rearward CGs do better in gusty conditions.
The more theoretical TVC, calculated from the wing 25% MAC is useful in a different way. Let’s call that MAC TVC. (We can never have too many acronyms). We can compare TVC values among various designs without the “corruption” of trimming preferences the designer has incorporated into the CG location. MAC TVC “levels the playing field” in making design comparisons. MAC TVC gives a truer picture of the differences among Classic era ships, and a truer picture of how the Classics differ from more modern designs.
Having both TVCs in our tool kit makes it easy to understand some things – such as Ted Fancher’s explanation of why modern ships fly easier in gusty winds mentioned above. A model with CG TVC = MAC TVC is a windy weather airplane.
Rather than debate which is the “real” TVC, I vote for using both CG TVC and MAC TVC – but knowing the difference. I prefer MAC TVC in forum posts since it is the more unbiased comparator of the two.
A Rose, by Any Other Name, . . .The Volume of what? When someone says “tail volume”, I picture dunking the tail in water then measuring (preferably calculating) what volume of water is displaced. In one version of the formula, we multiply wing area by average wing chord, which hints of three dimensions, or at least a power of three cousin of sorts. But, as we (or any high school freshman) can see, that is only because of a clumsy way of writing the formula. The version at the start of this post doesn’t look cubic or anything other than planar. It is a planar
leverage dimension times an area, pure and simple.
Suppose we read a comic strip and measure a panel, getting the area of the panel. We measure the distance of our eye to the comic strip and multiply that times the area. We now have the
Comic Strip Volume Coefficient. Truth is, we are doing a leverage calculation. We don’t know the forces we are levering, so we use tailplane and wing areas as stand-ins for the forces. The areas are only there because they are roughly proportional to the forces.
TVC can be calculated from a silhouette of a model – two dimensional to the core. An
Impact with a 12% airfoil and ¼” sheet stab and elevator would have the same TVC as the more popular versions flying today. A silhouette is a two dimensional representation of a three dimensional object. We cannot “add back in” a third dimension using only planar measurements taken on the same plane as the others.
Ah well, engineers aren’t judged by their mastery of naming things, but by their skill at doing things. However, we shouldn’t be misled by the name into thinking we are calculating something we are not.
Larry Fulwider