Let's Talk About CG Placement

 Most modelers know that getting the center of gravity (CG) in the right place is important.  Too far forward and the model will be heavy on the elevator controls, hard to flare for landing, and will nose over easily while taxiing.  Too far back and it will be oversensitive or even unflyable.  So moving things around or even ballasting until the model balances in the indicated range is a really good idea, especially before the first flight of a new model.

But what if the CG range isn’t given in the manual (or marked on the plans)?  Or what about a used plane with no documentation?  What if other fliers tell you that the recommended CG is wrong?  Is there a way to figure out where it should be placed?

To answer these questions, let’s  take a look at the science behind CG location and pitch stability.

This figure shows a wing section flying at a certain angle of attack (AoA).  Let’s suppose the CG is located as shown by the usual symbol.  If the aircraft is in trim, the four forces of flight (lift, weight, thrust, and drag) can be shown as by the red arrows.  These form equal and opposite pairs, so there is no resulting “moment” (torque) around the CG.  We call this an “equilibrium condition”; nothing is making the airplane pitch up or down.

Now let’s suppose the model hits an updraft, increasing the AoA.  The Greek letter Δ (delta) is used to indicate a small change, here ΔAoA.  This will cause a small change in lift, ΔL.

OK, so what?

Well, back about the time of WWI, a couple of smart German guys named Prandtl and Munk were able to show mathematically that a thin airfoil section has something called an “aerodynamic center”.  This is not the same as the “center of pressure” or “center of lift”; it’s the point where a CHANGE in lift will be located due to a CHANGE in AoA.  Their theory predicts it will be located at 25% of the section chord length – and wind tunnel testing confirms this is a very good approximation.  So good that engineers still use it for much practical work today.

So, for our wing section the AC is shown by the target symbol, with the change in lift ΔL acting at that point.  With the CG position shown, the distance between the CG and AC acts as a lever arm – and the change in lift will obviously generate a nose-down pitching moment.  This tends to reduce the AoA, putting the model back in the trimmed condition.  This is what “longitudinal” (or pitch) stability is all about.

We can draw some important conclusions from this:

-         If the CG is located in front of the AC, the model will be stable

-         If the CG is located behind the AC, the model will be unstable (change in lift will further increase AoA)

-         The further forward the CG is, the more stable it will be

We can apply this directly to flying wings.  For stability, the CG of a flying wing must be somewhere ahead of the quarter chord – more specifically the “mean aerodynamic chord” if the wing is anything but a straight “plank”.

But what if there is more than one lifting surface?  We’ll talk about that next time.