FINDING THE RIGHT CG LOCATION. HISTORY, DEFINITION, AND USE
By Michael Oser
Editor's Note: The following article represents the views of the author and does note imply an endorsement of the AMA.
This paper has been a long time coming. I have been looking for a definitive way to establish a good CG location for most any airplane for quite some time. I have found what I was looking for and it turned out to be both very simple and very effective. This method can tell you exactly where to set the CG -- as opposed to the not very useful 5 to 15% MAC that is typical up to now. I will go over the history of how this method came about, as it may be helpful for the reader to more fully understand and appreciate how this new method works and why it is so simple and useful compared to anything else. This method
was developed primarily for RC airplanes of tailless and canard designs which I had been working on. But it can be used successfully for anything from a hand-launched balsa glider to a real C5 galaxy. For those not familiar with conventional aerodynamic terms like NP, MAC, SM, etc., I’ll provide definitions in the appendix.
Note that there is very little math here, so don’t expect to get intimidated by traditional aerodynamic papers. If you can multiply and divide a few numbers you have all you need to follow this.
Many years ago, I got interested in learning the intimacy of aircraft stability. I’ve always been an airplane enthusiast and amateur aerodynamicist, but I wanted to go beyond what I already knew. Rather than just go by the old %MAC (which I had concerns about and which has failed in several instances) I wanted something exact for any airplane configuration – if such a thing even existed (spoiler alert – it does now). So, I studied many papers from simple amateurs to professional aeronautical engineers. What I learned was very disappointing – ALL such papers, from simple to very complex, accomplished the same thing – determining the location of the aircraft Neutral Point (NP), and only stating that for stability the CG must be in front of the NP – which we all know. No paper or any other source has ever provided a mathematical way of determining an accurate CG location beyond the simple 5 to 15% ahead of the NP which, by the way, only works for a very conventional airplane, and even then, doesn’t give you any real starting point. Let me explain…
First, you have to understand that the MAC is nothing more than a reference dimension that has no fundamental basis in aircraft stability (some of you are cringing right now – bear with me). From what I can tell, it basically came about because it scales with airplane size and because almost all airplanes were very similar in configuration back in the day. It was and is still used a useful dimension for measuring along a distance that is defined by the wing geometry to locate the CG. Note that real airplane CG locations are determined by wind tunnel and other in-house calculating or testing means, not by just choosing a MAC location between 5% and 15% and hoping it works. As it turns out, there is no need whatsoever for the MAC with this new method of locating the CG. Even though all airplane manufacturers use %MAC to define the CG location, it is literally meaningless by itself. What I will call the Stability Margin (also called the “Static Margin”) is the real measure of stability, and it should be relatable to any airplane configuration.
There have been others I know of that agree with me that simply using a %MAC is not the way to calculate a good and appropriate CG location. One is Jo Ivens, who wrote a paper on airplane stability without using the MAC at all. He calls his method the “Proper Method” to locate the CG. This was my primary inspiration to move forward with my own theories. However, even though I agreed with much of what Ivens stated, I disagreed with the final method, thinking that it could possibly get one in a bit of trouble. In Ivens’ method the CG is simply located as a percentage of the distance between all the lifting surfaces (those ahead of the NP) and all the stabilizing surfaces (those behind the NP). Very simple, but there is no account, that I can see, for the relative size of those surfaces. So, the CG for an airplane with a small stabilizer would be the same as the CG for the same airplane but with a much larger stabilizer, although the NP does change. Also, with his method, the SM gets larger with the spacing between wing and tail, and I was not sure this should be the case. However, as shown by his many examples, his method does work for many models. Ivens method is what I call “parametric” rather than analytical, meaning that Ivens uses some existing geometry and applies some rules and it just works (more or less). I still thought something was missing, that being the fundamental reason why the CG needs to be in a specific location. The other paper that suggested part of what I am proposing is by J Lamar and W Alford. I’ll go into that once I resent my method.
BACKGROUND
Once I started looking closely at how much “stability” an airplane needed and why, I evaluated a lot of possible methods to resolve this issue. I initially looked at “moments” as generated by stabilizing forces and trim forces (note that this was also suggested as a possible method by Jo Ivens). So, I spent a lot of time trying to see if what is called “moment of inertia” for structural members might be appropriate to relate all the moments generated by the wings and stabilizers. I tried setting up a “second moments of inertia” method, which ultimately did not scale or carry across to various airplane configurations. I then tried “first moments of inertia” which I thought was the answer. But, again, I could not get this to be consistent with scale or configuration. And, there were many other attempts to find a real mathematical relationship between the flying surfaces and the CG – without success – although I did learn a lot about aircraft trim which will be very useful as well.
The resolution I found was to separate Stability from Controllability to establish the CG, then put them back together again later.
As a mechanical engineer I have many times reverted to first principles to analyze and calculate structural stress, buckling, etc. in my work, and I thought it was time to do so for airplane stability. This indeed was the answer as it directed me away from the “normal” stability and trim methods. I mentioned that the MAC has nothing to do with stability in and of itself, then there are also the “tail volume” calculations typically used to size the vertical and horizontal stabilizers. The horizontal tail volume is based on the MAC, which again has nothing to do with the tail moment, and more interestingly, the vertical tail volume is usually based on the wing span, which in my mind is almost ridiculous. What you have to keep in mind is that, in these calculations, the MAC and wing span are simply “reference” dimensions that are only appropriate when comparing aircraft of very similar size and configuration. So, if the tail volume of a Spitfire works for it, then it should work for P-51s and FW 190s because they are actually very similar. All of the tail volume calculations require consulting tables of “coefficients” to adjust the calculation for a specific type/size airplane. But these calculations cannot be relied upon for deltas, flying wings, canards, or tandems, or other non-standard configurations, or even for things like sailplanes that have long, skinny wings even though they are conventional configurations. By the way, the long and slender wings of sailplanes and also biplanes caused me more grief than unconventional designs while evaluating other methods.
FIRST PRINCIPLES
Now let’s throw out all conventional aerodynamics and start over from scratch. This at first sounds like a daunting task, but actually makes things simple as heck and clear as a bell. We have to first define what is “stability” in a fundamental sense for airplanes. Well, as shown in figure 1 below, I define it as just the distance the CG is in front of the total lift force, nothing more or less. This is the only thing that defines the effect of gravity, which simply generates a “moment” to pull the nose down. Hint: the moment arm A is the stability or static margin (SM), which should be the same for a given amount of weight and lift for a constant amount of stability across all airplane sizes and types. This is the key concept.
This concept alone, however, defines essentially just an arrow that will fall straight down. If we want to fly horizontally, we have to provide another “moment” to raise the nose and keep it horizontal. A “downforce” at the tail now balances the entire force and moment diagram and fully defines the basis for stability and trim (figure 2).
With the arrangement shown, any airplane with almost any dimensions of A and B can be made perfectly stable and flyable given a proper sized tailplane. All that is required is that the CG (at A) be in front of the lift, and a downforce is available at B behind the lift to balance the downward moment of the CG. Or, for a canard an up-force can be placed in front (to the left in the diagram) of the CG for balance as well. For now, let’s just stick with a tailplane to keep things simple.
Here is the fundamental key to this method -- other than the Weight plus A and B, there are no other airplane dimensions that control stability. And, in fact, this is all that can in any case. The Weight defines how much lift is needed, and the distances A and B define how much tailplane is needed. The only practical limits on A and B are to obtain an efficient design with good handling qualities -- and there are no fundamental or calculatable values for A and B that will just work. So, we have to find a way to get those values for any airplane size, shape, or configuration.
As an aside, note that the tailplane volume (or, in reality, tailplane moment) is just the tailplane force (T) times B (or A+B as some prefer). All this tells you is that you can have a small tailplane at a large B, or a larger tailplane at a small B and get the same result. This is commonly referred to as the “Tail Volume Ratio”, but this is calculated differently in conventional aerodynamics compared to what we want here. The tailplane force (T), which is relatable to its size, is then found simply from
T x B = W x A
so, T = W x A / B
Also note that the total lift must be equal to W + T, so the larger the tailplane downforce the more lift is needed to carry a given weight. This suggest that the distance B should be as large as possible – which minimizes T, but there are obviously practical limits.
NEW METHOD
As you can see, there is no MAC (or other common reference dimension) in any part of the fundamental stability of an airplane. So, how do we define how much stability is good, and how do we find the CG location that provides good stability without the MAC?
This approach means that wing size or shape, or how many wings does not matter. But we do need to establish some reference numbers that we can relate to the airplane dimensions (just not MAC). We start by noting that the lift acts at the neutral point (NP) and the lift can be related to the wing area. The wing area is also a good starting point because it can define the usable vehicle weight. Unfortunately, the wing area varies with the square of the airplane size, so it would not be consistent as you scale up or down. However, the squareroot of the wing area is scalable and consistent, and is independent of the shape or quantity of wings. Now we are getting somewhere.
Long after determining that the above method was the way forward, I found a paper by J. Lamar and W. Alford, titled, “Aerodynamic-Center Considerations of Wings and Wing-Body Combinations”. Here is an excerpt from that paper (S is the wing area):
This, of course, justified the path I was on.
So √S (wing area) is directly relatable to the “size” of the airplane and the potential lift. What I did next is simply set the stability margin (SM), the distance of the CG in front the neutral, point as:
SM = C x √S
Where C is some arbitrary constant
Note that SM is equal to A in figure 2. And that is it – we just have to find a reasonable value of C. Some may be thinking: that can’t be all there is to it and what about the tailplane? Well, yes it can. And the tailplane only affects trim, as outside of contributing to the NP location, it has nothing to do with basic stability. And remember the tailplane is just defined by T = W x A / B. So, once we have W and A (or SM) and we know B, we quickly get what T needs to be to trim the plane. Now let me tell how this is used in a simple and effective way to define the CG location of any airplane.
All we need now is to find or define an airplane design that flies well with a given wing area (S), and known Neutral Point (NP) and CG location. We will call this the “Nominal” airplane and define it as shown below. This is a classic, simple, conventional airplane that is very close to quite a few airplanes I have flown.
I “tweaked” this design a bit so that it has a nominal 10% stability margin based on the MAC (just to make things easy). The only point for this being that these type planes fly very well with this CG location. Now we can find a good value for C.
The NP is located at 4.633 inches behind the wing leading edge.
The CG is located at 3.53 inches behing the wing leading edge.
The wing Area is 660 sq. inches.
SM (or A) is CG – NP = 4.633-3.53 = 1.103 inches. And the square root of the Area is 25.69 inches. This means that:
C = SM / √S = 1.103 / 25.69 = 0.0429
(when units are inches).
Therefore, to find the CG location (in front of the NP) – for any airplane -- just multiply the square root of the wing area by what we will call C10 = .0429. So what we are really doing is setting the CG of any another airplane to an effectively similar position to the nominal airplane that we know flies well. I call this concept: the “Nominal 10 Stability Method”.
Here is an example to show how well this works. I designed a delta canard airplane and initially set the CG to a 10% based on the MAC (before I developed this method).
It flew well, but was obviously a bit nose heavy. Over time I moved the CG back quite a bit and it just flew better and better. I stopped before I got in trouble with too far aft a CG because I did not know how far back I could go. For grins I checked the CG location and found that it was now at 6.5% MAC ahead of the NP. OK, so I then used the new method to calculate where the Nominal 10 CG location would be:
Wing Area = 963.18, sq. root = 31.035
NP = -5.972 behing wing leading edge
CG = -4.640 behing wing leading edge
Actual SM = 5.972-4.640 = 1.332
Nomial 10 SM = C x √S = 0.04293 x 31.035 = 1.332 !!
Isn’t that amazing, the Nominal 10 method showed me exactly where I should have started in the first place! The reason the basic %MAC method did not work well is because the MAC is rather long on a delta, meaning that a 10% margin is just too far forward. With this new method there is no guessing as to whether to go with somewhere between 5% to 15% MAC (the normal method). For your information, with Nominal 10 we are actually setting the CG to 4.3% ahead of the square root of the wing area, which will be the same CG location for any wing planform or multiple wings if the total area is the same for all. This will always work as long as you know where the neutral point (NP) is (more on this later).
Finally, to expand the method a bit, I note that some flyers may like a more forward CG and others like it a bit more aft for aggressive flying. To cater to such preferences let’s calculate the C value for both 12% and 8% MAC nominal equivalents:
C12 = C10 x 1.2 = .04293 x 1.2 = 0.0515
C8 = C10 x 0.8 = .04293 x 0.8 = 0.0343
In inch units
A flyer might consider a forward CG (C12) for scale airplanes, but only if they are already a bit sensitive on elevator or to limit elevator power because scale planes often stall early. For gliders and sailplanes an aft CG (C8) might be better to improve glide efficiency. In ALL cases, however, C10 is an excellent place to start. Note that I would never go less than C6(0.0257) as this would be a marginally stable condition for any airplane, used only perhaps for high performance sailplanes or pattern planes. Keep in mind that we have thrown out all existing methods and notions of CG location so you really cannot compare the Nominal 10 result to other methods.
Comments have came up about tandem wings. One commenter suggested that the CG should be well forward (a % of the distance between the wings) because of the large spacing between the wings. Another commented that even with tandem wings the CG should be just a %MAC on the largest wing and all will be OK. Well, both are totally opposite ideas and both are totally wrong (IMO) and both can get you into trouble. The CG for a tandem is the same C10 x √S as any other type airplane. Note, however, that tandem wings have a tremendous trimming capacity, so the CG range can be relatively large *but* it is most efficient at the Nominal 10 location regardless of the number of wings or the spacing between the wings. Again, with this method there is no need for guessing or assumptions, or opinions based on hearsay, for a plane to fly well.
The only other thing to check is whether or not the stabilizer/elevator is large enough to effectively trim the airplane with the given CG (which is usually the case for most airplanes). We can do this in two ways, use the Nominal 10 standard airplane as a relative reference as we did for CG, or use actual aerodynamic formulations to calculate. The latter is quite complex, so let’s further develop the Nominal 10 airplane concept for tail size.
TAIL SIZE
First let’s define what we mean by “Tail”: it is whatever generates the downward force T in the basic moment diagram of Figure 2. Again, we’ll ignore canards for now, but actually they work the same, but with minor additional considerations. For a conventional airplane we typically have a “horizontal stabilizer” which may have part of it used as an “elevator”. Stabilizers without elevators are called “stabilators”. As before, we will start with first principles with basic forces and moments and use the Nominal 10 airplane to calculate an effective tail size. For the moment we will assume the entire tail is effective for basic stability. The actual “elevator” size may have to be considered for control power (later).
As stipulated above, T = W x A / B. We can re-arrange things so that the actual weight does not matter. Note that W requires a certain amount of LIFT, and that the LIFT is generated by a certain amount of wing area. “S” is usually used to denote Surface areas. So now we can translate the weight W and the tail force T to effective areas:
Stail = Swing x (A / B) x Ktail
I added a K factor to account for the relative effectiveness of the tail. For the Nominal 10 airplane:
Swing = 660 sq. inches
A = 1.103 inches (this is the Stability Margin SM)
B = 25.38 inches (from the NP to the aerodynamic center AC of the tail)
K = 1 (for now)
So, putting in the numbers gives us that Stail = 28.68 sq. inches, assuming the tail is as efficient as the main wing(s). This is only 4.4% of the wing area, which is way lower than you would expect, however, this is all that is truly needed to hold up the nose in level flight at 1 G. But for effective maneuverability significantly more area is necessary. There are other issues affecting tailplane size as well like slow speed control power, and even pitch damping. Let’s therefore let’s skip all the aerodynamic calculations and just relate the tailplane to the Nominal 10 airplane.
The actual Nominal 10 airplane stabilizer is 120 sq. inches, which is 18% of the wing area. This is very close to what I’ve seen for many, many airplanes. In fact, the common conception is that the tail area should be between 15% and 20%+ of the wing area. I’ve witnessed that my planes that have larger tails (18%+) simply fly smoother with more precise control, so the 18% is a good reference point, particularly for RC airplanes. This means that the K factor should be:
Ktail = 120 / 28.68 = 4.18 for a typical airplane.
Note that this K factor is analogous to the “Tail Volume Ratio” of conventional aerodynamics.
We now have the entire Nominal 10 Method in a nutshell:
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Fundamental CG location (using C10)
SM (CG distance in front of the NP) = 0.0429 x √Swing inches [Eq.1]
Guidelines for tail sizing
Stail (tailplane size, includes elevator) = Swing x (SM / B) x 4.18 sq. inches [Eq.2]
Selevator (elevator size) = Recommend 25% of Stail minimum,
~50% for acrobatic planes, up to 100%
For aggressive flying. Nominal 10 uses 50%.
Selevon (elevon size for tailless planes) * = Swing x (SM / Belevon ) * 1.304 sq. inches [Eq.3]
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* See “Plain Delta or Flying Wing” below
Remember that A = SM, and that as B gets larger the required tail surface area will decrease and vice versa. All of these calculations relate the CG and tailplane size of any airplane to that of the Nominal 10 airplane. You can, of course, also use the C12 and C8 factors for a bit more or less stability. Note that “more” stability is rarely a good thing. If your plane is too pitch sensitive then reduce elevator throw rather than move the CG forward. Once a plane flies well, more stability makes a plane less controllable, land faster, and be more susceptible to wind gust.
Here are some recommendations to utilize this method to best fit various configurations, which affects how to calculate the effective wing area needed for this method.
- Canard, whether or not the canard is used for control. Canards must have a more forward CG than conventional airplanes especially if the canard is close to the wing. Either use the C12 factor with the main wing area (S), or use the combined wing and canard area with C10. Check both and start with the largest SM between the two options. The tail sizing formulas will also work for canard elevators – but be warned, canards can be tricky to predict and are heavily influenced by close proximity to the wing. In any case you must know the effective neutral point (NP) of the total airplane.
Note that canards close to the wing are in the wing’s upwash and this will be destabilizing. This causes two things: a requirement for a more forward CG, and possibly early stall of the canard limiting its control power. I actually placed a small canard slightly overlapping the wing and with a “negative” (!) incidence on my delta. This, I have been told by everyone, just won’t work, but this was intentional and the airplane flies extraordinarily well. In fact, the canard with negative incidence was used to improve takeoff and turn performance and enhance inverted flight – it worked. - Biplane / Triplane. The problem with Biplanes is knowing the effective wing area – which is typically not the sum of the areas. This is a similar problem as with the standard %MAC method as you have to find the effective MAC of all the wings. Two options are available. (1) use the projected outline area of all of the wings based on a top view. In this case, the largest influence is the stagger of the wings. I’ve seen this done in several cases and it seems to work. (2) Use an efficiency factor. Multiplanes are somewhat inefficient due to interference between the wings, with the effective wing area being only about 70% of the total. Use this adjusted total wing area with C10.
- Sailplane. With long skinny wings the wing area is relatively large even though the chord is small. Because of the short chord, the CG may be farther forward than you might expect compared to the standard %MAC method. The C10 CG is still very correct (i.e. it will not be nose heavy), but C8 (or even a bit less) should result in slightly better glide ratio.
- Tandem, any number of wings. Just use C10 as normal with the total combined wing area as long as the wings areas do not overlap. For tandems C12 also works well, because of the large trimming capacity. If the elevators are on either of the wings, use the following for tailless planes to size the elevators.
- Plain Delta or Flying Wing (tailless). Use C10 based on the total wing area including control surfaces like elevons. The normal tailplane sizing calculation doesn’t apply for tailless airplanes because elevons actually affect the rear of the wing which increases their effective area. But we can define the elevator/elevon size using a similar method as done for CG. We will use my delta airplane mentioned above as a nominal reference. My delta flies extremely well, but I think the elevons are a bit oversized, so I’ll use 90% of the elevon area for this calculation. Note that “elevon” can be replaced with “elevator” in the equations below if separate ailerons and elevators are used. Belevon is defined from the NP to the centroid of the elevon/elevator.
Selevon = Swing x (A / Belevon) * Kelevon sq. inches (remember A=SM)
For my delta (latest version), Swing = 936.27, A = 1.339, Belevon = 15.72,
Selevon (90%) = 104. Solving for K:
K = Selevon / [Swing x (A / Belevon)] = 1.304
Therefore, use the equation [3] above with Kelevon = 1.304 to solve for an effective elevon/elevator size.
As for the Ktail established previously, the Kelevon is also analogous to a “Tail Volume Ratio”, however, whereas the Ktail relates to both stability and control, the Kelevon only relates to control. It is the reflexed airfoil profile (or other means) that provides the necessary stability, not just the elevons, that’s why the Kelevon is much less than Ktail and also because elevons tend to be significantly larger than normal elevators.
NOMINAL 10 METHOD SUMMARY
Hopefully this paper accomplished two things for the benefit of the reader. The most important is a very simple calculation to find a good CG location using equation [1]. The second, which most benefits plane designers, is a simple method to appropriately size the tailplane (or foreplane) along with elevators and elevons using equations [2] and [3]. The latter can also be used to check the tailplane properties of an existing design.
One last comment: things like Leading Edge Extensions (LEX), very large/wide or oddball fuselage shapes, etc., can dramatically affect the airplane’s stability – but they affect ONLY the neutral point (NP). If one can find the NP with extreme shapes then the Nominal 10 Method will still work just fine. As an example, because of the large fuselage and small wings on an F-104, the CG can actually be ahead of the wing leading edge.
NEUTRAL POINT (NP)
What is the Neutral Point? It is the point where all the lift surface forces, including the fuselage, are balanced. Theoretically, if the CG is located at the NP the airplane will literally be neutrally stable, where it will stay at whatever angle of attack it is at unless a control is input. To obtain some level of stability, the CG must be ahead of the NP so that the plane always tries to point into the relative wind.
This new method is extremely simple, but is dependent on the Neutral Point parameter which is not so simple to find. Fortunately, many people have solved this and provided calculation software or on-line tools to obtain it. Many of these are available on various internet sites for RC airplanes. The best I’ve found is an Excel spreadsheet created by [email protected] (the only contact I have). His spreadsheet, the latest which is called:
CGCalc_1.05.xls
You can find this on RC Groups and RC Universe web sites. You input the geometry of your airplane and it calculates a LOT of aerodynamic parameters – including of course the Neutral Point. Since all you need is dimensions, this spreadsheet is actually easy to use. You can use this spreadsheet as per original form and hand calculate the Nominal 10 CG (which is easy), but I have edited dpross’ spreadsheet to include the Nominal 10 method and call it:
CGCalc_1.05A (Nom 10 – Sweep Adj).xlsm
As seen in the name above, this spreadsheet also includes an optional correction for highly swept wings, which tend to have a more aft NP than straight wings.
I will upload this modified spreadsheet to RC Groups and RC Universe for anyone to use. Let’s go over the basic use and results. I won’t go into all of the details of how to use, but just give some suggestions and the new addition of the Nominal 10 calculation.
After inputting the dimensions of the wings, stabilizers, and fuselage you get the following plot:
This is for my delta canard design. My suggestion for all flying surfaces is to continue all surfaces straight (meaning horizontally per figure 3) across the fuselage, and do not check the “Remove Intersecting Wing Area” box on the fuselage input and press the “Run Calculations” button:
Some of the key calculated results will appear on the Top View above, but the full results are shown like this (yes, a bit intimidating):
In spite of all the information shown, you only need a couple things. First, the NP is provided in the top left corner, and the Nominal 10 CG location is calculated and provided in the light blue cells at lower right, with and without considerations for sweep affects (light red cells). Consider the swept CG mainly for highly swept narrow wings (like F-100 or F-8) rather than deltas. The second useful thing is the top right button “Static Margin Wizard”. With this you select a desire static margin (I chose 6.5% for this case) and run the wizard – which will calculate the CG that provides that Static Margin based on conventional %MAC. This may be useful to compare the %MAC method to the Nominal 10 Method.
The Stabilizer and Elevon moment ratios are also calculated at the lower left corner. If you have a tailless airplane then the Stab Moment Ratio is irrelevant, and you must then manually enter the Elevon area and moment arm in the yellow boxes.
CONCLUSION:
That is all there is to it. Using SM = .0429 x √Swing, combined with the above spreadsheet to get the NP, you find the CG as NP – SM, where CG is in front of the NP. Or just see the light blue cells where the actual Nominal 10 CG is calculated for you. Note that you can change from C10 to C8 or C12 (or anything else) just by typing 8 or 12 or other number in the yellow Nominal 10 cell. If the yellow cell is blank then C10 is the default. Caution: on most any spreadsheet NEVER type a space to blank out a cell – instead delete the cell contents.
I have provided contact information below if anyone would like more information.
Current Contact Address:
Michael Oser
1231 Kiowa Dr E, Lake Kiowa, Tx 76240
[email protected]
APPENDIX
Definitions:
Stability Margin or Static Margin – the distance from the CG to the NP. The primary measure of airplane stability.
CG – Center of gravity, the effective point where all the mass is concentrated.
MAC – Mean Aerodynamic Cord. The effective chord of the wing at its centroid. This is the original dimension used to “size” an airplane’s wing for reference purposes.
%MAC – Percent of MAC for the CG location. This is often measured from the leading edge (at the MAC) backward, but that is not the proper method. It should be measured from the NP forward to the CG. Note that when measured from the wing leading edge, this is only a “location” and it is not the Static Margin.
NP – Neutral Point. The point where all aerodynamic forces and moments are balanced. An aircraft has zero stability if the CG is located at the NP.
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