I'm a relatively new guy to this hobby (~2 years), but I have yet to see a flat-winged airplane that can maintain its altitude while flying at a zero angle of attack.

From : Don Stackhouse

That's because the zero-lift angle of attack ("alpha") of a symmetrical airfoil (of which a flat plate is just one example) is zero degrees. ANY symmetrical airfoil has to have some amount of positive alpha (relative to the chord line) to generate positive lift.

All airfoils have some specific zero-lift angle. In some engineering design work (typically when we are doing aerodynamic design of something where we have not yet specified a particular airfoil shape) we measure alpha from the airfoil's zero-lift line. All airfoils are alike when measured this way, they all have zero lift at zero alpha with alpha measured form the zero-lift line. If we assume some lift curve slope (i.e.: the slope of the lift-coefficient-vs.-angle-of-attack curve, or dCl/d-alpha, pronounced "dee-see-ell-dee-alfah"), typically about 0.1 per degree, then we can do a pretty fair prediction of the behavior of lift along a wing without yet knowing its specific airfoil characteristics. It gets a little more complex at very low Reynolds numbers ("Re") such as our slow fliers, where dCl/d-alpha can get quite a bit more variable (it tends to be almost constant at 0.1/degree regardless of airfoil at higher Re's), but we can still make a fairly good stab at the wing's characteristics without having to define the specific airfoil until later.

The point is that the case of a "flat plate" airfoil (defined quite specifically for engineering purposes as an airfoil where camber and thickness are both equal to zero) is NOT some weird animal with totally different behavior that plays by some totally different set of rules. It is an airfoil just like any other airfoil, just a single point along the continuum of possible cambers and thicknesses. It's nothing special, and plays by the same exact rules as all other airfoils.

They all keep their nose up a bit, whether by means of thrust angle, control surface reflex, or something else. I guess my point-of-view on the matter is that a pure "flat" wing is one that does not deflect the air in its neutral (absent of control input) state.

I'd like to make one more qualification to your statement. The trim of an aircraft involves a whole list of factors, and whether or not the wing's airfoil is at zero alpha when the controls are at what you refer to as "neutral state" can vary. For the purposes of this discussion I'd prefer to redefine "neutral state" as whatever set of trim factors and control inputs results in the wing airfoil's alpha being equal to its zero-lift angle. That makes a little more sense within the context of your statement.

After all, deflecting air implies the existence of an airfoil, whether visible or not, and that would defy the very assumptions assumed about flat wings. In my mind, the logic of the definition rules out the possibility of self-sustainable flight with such a wing--if one meeting that definition can even exist--in its neutral state.

Let's discuss this a little further. Say, for the sake of argument, that there was something unique about "flat" airfoils, that for some reason they do indeed "march to a different drummer", "play by a different set of rules", etc.. OK, so what exactly qualifies as a "flat" airfoil? In the theoretical world it means an airfoil with both camber and thickness equal to zero. In the real world, zero camber is certainly no problem, but obviously there can be no such thing as a physical structure with zero thickness. Even one atom thick is more than zero. So, at what point does the airfoil SUDDENLY switch from these hypothetical "flat" rules to the rules observed by all other airfoils?

5% thick? I've used airfoils thinner than that on R/C sailplanes that could thermal better than other models equipped with much thicker airfoils.

2.5%? I've used airfoils about that thick on the wingtips of pylon racers that pull 17 G's in a normal pylon turn, and I've made those thin airfoils stall at higher alphas than the 11% thick root airfoil of those same wings. A tip stall in a 17 G turn only a handful of feet above the ground is not something any sane designer wants to contemplate. Of course some folks might have questions about whether I qualify as a "sane designer".

0.2% (that would be about the thickness ratio of a 2" chord airfoil made from a sheet of ordinary bond paper)?

The answer is "none of the above". Even a truly zero thickness, zero camber airfoil follows the same basic rules of operation as all other airfoils.

The key is that an air molecule does not see the airfoil we see. It sees the path that it takes around that airfoil, not the airfoil itself. As soon as the alpha is greater than the zero-lift angle, some of the air that would have gone under the wing goes instead up around the leading edge and over the top. The flow paths over the top and the bottom are no longer identical, and the airfoil starts making lift, both from pressure increase on the bottom and from pressure decrease on the top surface. The reduced pressure on top sucks air from above the wing downwards, the higher pressure below the wing pushes air under the wing downwards as well, so air both above and below the wing gets accelerated downwards. For every action there is an equal and opposite reaction, so as the wing grabs air both above and below itself and shoves it downwards, the air reacts by shoving the wing upwards. This is the case for all wings when alpha is greater than their zero-lift angle (note, we're not discussing what happens beyond stall alpha in this discussion, that gets even more complicated), regardless of how much thickness and/or camber is or is not in their airfoils.

Obviously, others here define the properties of a flat wing in different terms. I guess it's like defining how high "up" is.

One of the ones in more common use today was established by NACA (the National Advisory Committee for Aeronautics, the forerunner of NASA). This one measures thickness in percent of chord. If you then fit a line through the exact middle of the thickness (the mathematically correct way is to fit a row of circles along the airfoil, each circle tangent to both the top and bottom surfaces at its location, then fit the line through the centers of the circles), the camber is the height of that "camber line" or "mean line" at its highest point, measured up from the chord line and expressed in percent of chord.

Airfoils in this system are normally thought of as a thickness profile (a standard symmetrical airfoil shape of some specified thickness), which is then "bent" so that its now-warped former chord line matches the shape of the desired "mean line". Typically in the NACA four-digit sections, the first digit is the height of the camber line in percent, the second digit tells where in percent the max camber point is located in tens of percent, and the last two digits give the thickness. For example, a NACA 2412 has a max camber of 2%, located at 40% back from the leading edge, with a NACA-standard 12% thickness profile wrapped around the resulting camber shape. A NACA 0009 has a max camber of 0% located at 0% back from the leading edge, with a thickness profile that is 9% thick. In other words, it's a 9% thick symmetrical airfoil. A "flat plate" would be a NACA 0000. Just another number in the system, another point along the continuum, nothing magical, mysterious or even different about it.

Some of the later numbering systems (such as the ones for laminar flow airfoils) used by NACA used a slightly different convention for the camber, such as describing the design lift coefficient and the drag bucket width instead of the geometric camber shape, but they still used the last two digits to describe the thickness.

Generally speaking, at least at higher Re's, the thickness primarily influences drag characteristics within the normal operating range of the airfoil.

For higher Re's, the dCl/d-alpha (the slope of the line on the Cl vs. alpha graph) tends to be pretty much constant at around 0.1 change in the value of the lift coefficient Cl for each degree change in angle of attack. Changing the camber just takes this curve and shifts it left or right on the chart. The graph stays the same shape, but the alpha for zero lift changes. For example, a NACA 0012 (symmetrical, 12% thick)airfoil has a zero-lift alpha of zero, while a NACA 1412 (1% camber, 12% thick) has a zero-lift alpha of about -1 degree, and a NACA 2412 (same airfoil but with 2% camber) has a zero-lift alpha of about -2 degrees. Interestingly, each of them has a maximum lift coefficient ("Clmax", pronounced "see-ell-max") of about 1.6, it just takes 2 degrees less angle to reach that value of Cl with the NACA 2412 than with the 0012. The whole curve for the 2412 is shifted to the left by 2 degrees alpha relative to the curve of the 0012.

Thickness, both the amount and how it's distributed, does have an effect on the stall characteristics and the value of Clmax. For example, a NACA 0006 (symmetrical just like the 0012, but only 6% thick) at full scale aircraft Reynolds numbers has a Clmax of only about 0.9 instead of the 0012's 1.6 value of Clmax.

The Clmax of a flat plate airfoil is reduced further still, but it is still nowhere near zero. With that sharp leading edge, the alpha can't get as high (and therefore the Clmax can't be as great) before the airflow can't quite negotiate the abrupt turn around that sharp leading edge, and instead separates from the upper surface and causes the airfoil to stall. A fatter leading edge makes it easier for the airflow to negotiate the turn, and so a fat leading edge can be pushed to higher alphas and lift coefficients before the airflow cries "uncle!" and separates.

However, the same is not necessarily true at very low Re's (below about 100K or so, right where our small electric models tend to operate), where the relationship between thickness and Clmax tends to be the opposite. Too much thickness can still help the air make it around the leading edge, but in doing so it creates other problems that show up further aft on the upper surface, causing stall at lower angles and lift coefficients than a thinner airfoil can achieve. For example, I know of cases at low Re's where a 6% thick airfoil has a higher Clmax and less drag than an 8% thick airfoil, which in turn has a much better Clmax and less drag than a 12% thick airfoil. Just another example of why an absolutely stock Clark Y is not necessarily a good airfoil for models, despite all the "common knowledge" out there favoring it. The folks who think the Clark Y is good for very small models have probably never tried a properly designed and fitted thinner airfoil in those applications.

However, at these low Re's, the shape of the airfoil becomes very critical to see the maximum benefit and achieve the best performance. Both the amount of thickness and camber, and the way they are each distributed along the airfoil become very critical. It's not good enough to have a thin airfoil, it has to be a properly designed thin airfoil.

Of course then there's the whole matter of stall characteristics (not the lift at stall, but rather how the lift characteristics behave just before, during and after the stall), their effects on handling, and also the effects of things like aerodynamic hysteresis and other oddities, but those are subjects for another discussion.

So, assuming my definition for the moment: if a flat wing by definition cannot deflect the air, how is the airplane using (or made of) that wing supposed to maintain a given altitude while in motion?

Given the information that I know thus far, my answer is that it can't, or more specifically that the wing can't assist in generating the lift necessary to sustain altitude...and in the latter case, I ask myself if such an airplane is really "flying" or if it is simply "hanging" on something else.

Don Stackhouse
DJ Aerotech