CG and "Static Margin"

 

In the last article in this series, we showed that each aircraft configuration has a "neutral point" (NP), and discussed ways of finding it using a CG calculator.  If the model's CG is forward of the NP location, the model will be stable in pitch.  If it's behind the NP, the model will be unstable.

We also noted that CG calculators ask the user for something called "static margin" before finding the acceptable CG range.

So what's static margin?  Simple - it's the distance between the CG and NP, expressed as a percentage of the wing mean aerodynamic chord (MAC).  For example, if your model has a 5" wing MAC, a static margin of 10% puts your CG 0.5" (half an inch) in front of the NP location.

Static margin is important because it's a measure of relative stability - planes with similar static margins will have similar amounts of pitch stability.  Put another way, knowing your CG is ahead of the NP lets you know your model will be stable - but knowing your static margin gives you an idea of HOW MUCH stability you have.

How much static margin do you need?  This depends on the type of model, the desired flight characteristics, and to some extent on personal preference.  In the full-scale aircraft world, transport category airplanes and civil light aircraft tend to have fairly large static margins, up to about 25% of wing MAC.  Airplanes designed for aerobatic competition often have much lower static margins, maybe as low as 5%.  Modern fighter aircraft with full-time automatic stabilization may have "negative" static margins (CG behind the NP), i.e. be unstable.

We can apply the same principle to models.  If your plane is a trainer, or a steady Sunday flyer, you may want to go with a substantial static margin.  This can also be important if you have an unconventional aerodynamic configuration that might have reduced tail efficiency (like a stab very close to the wing), or a very wide fuselage that might contribute substantially to lift.  In such cases it's better to start with a safe forward CG than take your chances.

However, there are downsides to excessively forward CGs.  The model will have a greater tendency to nose over on takeoff and landing, especially if the gear is too near the CG.  Since pitch stability is really resistance to changes in angle of attack (AoA), you may find the model wants to cling to one AoA and it takes a lot of elevator pressure to fly faster or slower than your trim speed.  In such cases the model will tend to climb under power and descend when throttled back.  Since the model wants to fly at one speed, it may also be susceptible to "porpoising" or "roller coastering" - a series of climbs and dives as it trades altitude for speed and vice versa.  Finally, it will require quite a bit of up elevator pressure to flare the model for landing, which leads to carrying excessive speed and flipping over on touchdown.

For an aerobatic model, many prefer to have a smaller static margin.  The plane will still be stable, but there is less tendency to stay on speed and climb under power.  However, there is also less stall resistance, and you will have to fly the model all the time rather than relaxing and letting it fly itself.

Let's apply this to the author's Carl Goldberg Bucker Jungmann:

First, the inputs needed for the cgCalc spreadsheet.  This seems like a lot, but using a straightedge and yardstick I was able to pick all the numbers off the plans in about fifteen minutes.

Since the Jungmann is a biplane, there are two sets of wing dimensions.  "Stagger" is just the distance the leading edge of the bottom wing is behind the leading edge of the top wing, measured at the root chord.

Because the Jungmann is an aerobatic plane, I selected a static margin of 5 - 10% MAC for my CG range.  That should be large enough to allow for any errors in tail efficiency, but small enough to avoid an overly nose heavy plane for first flight.

Now let's see what the result looks like:

This shows a surprisingly rearward CG, near the aft limit shown on the plans.  One reason is the sweep in the wings, which pulls the MAC locations (blue lines) aft relative to the root chord.  Another is the wing stagger.  Recall that a biplane's wing AC will be between the AC of the top wing and the bottom wing - about halfway between if the wings are of equal area and similar shape.

Marking this on the model, the suggested CG is just about even with the rear cabane strut attachment bolt.  The plan CG range is pretty broad, going about an inch forward of this point.  So as long as the model balances on the bolt or forward, I shouldn't have to add any ballast to have a safe CG location for first flight.  If the plane is too nervous feeling I can always add ballast (or move the battery pack forward); if it's too stiff I can do the opposite.

Jump in and give a CG calculator a try, especially if you have a model with no known CG range.  You may be surprised how far off your CG location is, and corrections may give you a better flying model.

Next time, I'll discuss some common myths about CG location, and see how some classic "rules of thumb" compare to engineering methods.