Don discusses in depth Center of Gravity

I just flew my Pico Stik with the tape between the wings [in other words, he sealed up the gap between the wing panels], and it certainly changed behavior... Flight characteristics are quite different; much more elevator response than before, which I cannot explain.

Cliff Lawson replies...

...Increased elevator response is often a sign that the CG has moved backwards...

From : Don Stackhouse

While I agree that it resembles in some regards an aft C/G shift, what's probably happening here is a bit more subtle. The weight of the tape Isaiah applied to his Pico Stik is certainly not enough to cause a significant shift in the plane's C/G.

However, C/G is a complex thing. For starters, we need to consider the C/G from both the point of view of the measured C/G we're all familiar with, and also from the airplane's point of view, with regard to the C/G's relationship to the aircraft's overall aerodynamic center.

Many of you are probably already familiar with the idea of the wing's aerodynamic center ("AC") being at about 25-28% of its Mean Aerodynamic Chord ("MAC"), and therefore setting the aircraft's C/G at about 20% of the MAC. The idea is that having the aerodynamic center aft of the C/G is like having the feathers on the back end of the arrow, and the result will be statically stable.

There are some problems with this approach. It doesn't help much in determining the C/G for a biplane, is even less useful for figuring the C/G of a canard, and totally fails to explain how we can set the C/G of many of our R/C sailplanes at 50% or more and still have positive static stability.

The root problem is that it focuses entirely on the wing, and ignores the contributions of the rest of the airplane, particularly the tail. Yes, we generally want to have the AC aft of the C/G for positive stability, but it's the AC of the ENTIRE AIRCRAFT that matters, not just the AC of the wing alone! For example, on that sailplane with the C/G located at 50% of the wing's mean aerodynamic chord, there is a decent-sized tail on the end of a very long tail boom. When we calculate the location of the AC for the entire aircraft including that tail, we find that it is well aft of that C/G location. The basic concept was correct, we were just using the wrong aerodynamic center for our calculations.

Armed with this new knowledge, we can use the ratio of their areas to find the combined AC of the wings of a biplane, or the overall AC of a set of wings plus a tail, or plus a canard. If we then set the C/G sufficiently ahead of that point, the plane will be stable. The distance between the plane's overall AC and its C/G location, expressed as a percentage of the wing's mean aerodynamic chord, is called the "Static Margin". If we find the static margin of a plane that has the desired static stability, and then use that same static margin for our new design, we should get a similar amount of static stability, assuming that the two designs are reasonably similar. There are some articles in the "Ask Joe and Don" section of our website that go into more detail on how to figure the combined AC of an aircraft with multiple flying surfaces.

So that's all there is to it? Well, almost. This is still a simplification of what actually happens to the airplane in flight. To understand Isaiah's observations, we need to understand the concept of "lift curve slope", or "dCl/d-alpha".

"Lift curve slope" is nothing more than how much the lift changes when we change the angle of attack. The engineering term "dCl/d-alpha" (pronounced "dee-see-ell-dee-alfah") literally translated into reasonably plain English means "the delta (or change) in Cl (the lift coefficient), per a change in alpha (the angle of attack)".

There is a dCl/d-alpha for the 2-dimensional properties of a basic airfoil (typically a change of about 0.1 in the lift coefficient for each degree of change in the angle of attack), but there is also a dCl/d-alpha for an entire wing. If the wing is not infinite span and aspect ratio (in other words just about any real-world wing outside of a wind tunnel), then the wing's dCl/d-alpha will be less than its airfoil's lift curve slope as measured in a wind tunnel. The lower the wing's aspect ratio, the lower will be its dCl/d-alpha. The lift coefficient it stalls at will be about the same as the wind tunnel performance of its airfoil, but it will take a lot more angle of attack to get to that lift coefficient. This is one reason (but not the only one!) why very low aspect ratio wings such as most delta planforms can go to such ridiculously high angles of attack without stalling. (We'll save discussion of vortex lift and other 3-d airflow effects for some other time!)

The aerodynamic center of the entire aircraft can be influenced by this. If the tail has a much lower aspect ratio than the wing, it will not have as high a dCl/d-alpha as the wing. If a gust raises the nose and increases the angle of attack of all parts of the plane by the same amount, the increase in lift at the tail will not be proportionately as much as the wing. This has the same effect as if the tail was smaller than it really is, which moves the total airplane AC forward, closer to the C/G, which reduces the static margin. If the dCl/d-alpha of the tail is significantly different from the wing's, then ideally we should weight the areas of the wing and tail by their respective dCl/d-alphas when we calculate the overall aerodynamic center of the entire aircraft.

Now we're finally ready to understand why Isaiah's Pico Stik seems to have a more sensitive elevator when the gap in the wing center section is sealed. When we pull back on the elevator, we increase the plane's angle of attack. This causes the wing's lift to increase, which accelerates the plane upwards. With the old leaky wing, we didn't get as much change in the wing lift with a given change in the angle of attack. The new wing with the sealed gap not only makes more lift, but it also has a bigger dCl/d-alpha; in other words, it sees a bigger change in lift for a given change in angle of attack. Pull back on the stick by the same amount you did before, and you now get a bigger jump from the plane in response.

Another way to look at it is that the old wing had a 1 3/4" gap in the middle that made its two wing panels act like individual wings with an aspect ratio of only about 2.59:1 each. The sealed center section wing now has an aspect ratio of about 5.44:1, more than double that of the original. No wonder it's now much more sensitive to changes in angle of attack!

Taking another approach to this analysis, since the dCl/d-alpha of the wing is now more than double, but the dCl/d-alpha of the tail is the same as it was before, the overall AC of the entire aircraft is pulled closer to the now more sensitive wing. Moving the aircraft's overall AC forward reduces the static margin and has the same effect on static stability (and elevator authority) as moving the C/G aft. If you make the wing more effective, you also increase the job the tail has to do to control that wing.

Don Stackhouse
DJ Aerotech