Effects of CG on Performance: Fat Kids and Teeter-Totters
In the commercial pilot curriculum, the FAA introduces concepts about the impact of various CG locations on stability and on performance. The location of the plane's CG can actually impact its cruise speed!
To illustrate this, we'll need a playground, a teeter-totter, a fat kid, a strong dude, and an assortment of kids of various sizes.
Teeter-totters and Fat KidsWe take our playground teeter-totter, one that's 8 ft long, and put a fat kid on one end of the teeter-totter, not quite at the end, but just 1ft to the left of center. Since there's nothing to balance him out, the teeter totter will slump to the left.
We want to balance that teeter-totter, so imagine we have a collection of kids of various sizes, some fat, some skinny, that we can place on the right side of the teeter totter, but we can only place the "balance kid" at the very end.
Now, if we have that 100lb fat kid 1ft to the left of center, we put a small, 25lb "balance kid" on the right edge, and the teeter-totter balances.
What if we move the 100lb fat kid further to the left, so that he's now 2ft left of center (halfway along the left side). The teeter-totter will slump to the left again. No problem, we kick off the 25lb balance kid, and put up a 50lb balance kid. Now, with our 100lb fat kid halfway along the left side, and our 50lb balance kid on the right edge, we're in balance again.
The further to the left we move the fat kid, the heavier a "balance kid" we need on the right edge to balance him. Worst case, if we put the fat kid on the left edge, we'll need a 100lb "balance kid" on the right edge to balance him, and that's the heaviest balance kid we have. If the fat kid on the left edge eats another twinkie, he'll be 101lbs, and now we don't have a balance kid heavy enough to balance him, the teeter-totter will slump to the left, and we won't be able to stop it.
Now, take all the kids off the teeter-totter, and put the fat kid right in the middle again. Now shove him a few inches to the _right_. The teeter-totter will slump to the right. Well, putting a balance kid on the right edge won't help any, so we'll get one of our balance kids to grab the right edge and lift. We're back in balance again. But as we move the fat kid further and further to the right, our "balance kid" has to lift more and more on his side to keep things in balance. At some point we'll move the fat kid so far to the right, that our balance kid runs out of strength, and can't hold his edge any more, and the teeter-totter slumps to the right.
Now, for our last trick, imagine that we get a strong dude to grab the teeter-totter in the middle, and pick the whole thing up over his head. If we imagine the teeter-totter itself is fairly light, then he's pretty much just lifting the weight of the kids. If we have a 100lb fat kid on the left edge, and need a 100lb balance kid on the right edge, then our strong dude is holding up 200lbs. If we had our 100lb fat kid halfway along the left edge, then we only need a 50lb balance kid on the right edge to balance him out. Now, our strong dude is only holding up 150lbs. If we put our fat kid right in the middle, then we wouldn't need a balance kid at all, and our strong dude would only need to lift the weight of the fat kid, or 100lbs. So the further out to the edge we put our fat kid, the heavier a balance kid we need, and the more total weight our strong dude needs to lift.
Okay, so let's get back to airplanes.
Keeping Our BalanceIf we have a forward CG, that's like putting the fat kid further to the left on our teeter-totter. Our "balance kid" is our elevator, which is a wing, and which can apply a downward force to balance out the CG. But as the CG moves more and more forward, we need a stronger and stronger downward force on the tail to balance it (a heavier balance kid).
At some point, our tail is producing the maximum downward force it can, and it stalls. When this happens, the downward force on the tail disappears, and the plane noses over. When the plane noses over, it descends and picks up speed, and as the airspeed over the tail increases, its effectiveness goes up, until it can create enough downward lift to balance again. So having a forward CG is dangerous, particularly at slow speeds, but in flight it has something of a stabilizing effect, because a lack of lift at the tail results in an increase in airspeed, which increases tail effectiveness.
What can happen if our CG is too far forward? Well, on the takeoff roll, we might not have the elevator effectiveness to even rotate the nose into a climb position. Alternately, on landing, if we run out of elevator effectiveness, then as we slow we run the risk of our nose dropping, possibly damaging the nosegear on landing.
On the other hand, if you move the CG backwards to the point where the tail can no longer balance it with an upwards force, the plane will be nose-high, and will stall, and the tail may not have the effectiveness needed to bring the nose back down. This is an unstable situation, and fairly dangerous. Clearly, the "what can happen" is much worse for a rear CG.
StabilityFor regular old "in flight stability", with a forward CG, our tail is producing a downwards force to balance the nose. If a little wind shear or turbulence bumps the nose up a bit, the plane climbs and slows, the reduction in air flow over the tail means it loses some downwards lift causing the nose to drop back down again, restoring the original attitude. Alternately, if some turbulence bumped the plane's nose downwards a touch, the reverse effect would occur. The nose-down attitude would cause a rise in airspeed, increasing the downwards lift at the tail, which would cause the nose to be pulled back up again.
With the tail producing a downwards lift force, any perturbation of the plane's pitch attitude results in a change of the lift generated by the tail that encourages a "correction" back towards the original pitch attitude. This is positive stability. The plane "fixes itself" in response to small variations of pitch attitude, making the plane easier to fly for the pilot.
If you move the CG rearwards enough, such that it falls behind our center of lift from the wings, the tail then needs to generate "upwards" lift to keep the nose from pitching up. Now, with the tail needing to generate upwards lift, if the nose attitude bumps up a bit (turbulence, whatever), the plane slows, causing the tail to lose some _upwards_ lift, which results in the nose rising even more. The plane then slows some more, the tail loses even more lift, etc.
With the tail producing an upwards lift force, any perturbation of the plane's pitch attitude results in a change of the lift generated by the tail that encourages further pitching. The plane now displays "negative" stability. For every twitch of the plane's attitude, instead of fixing itself, the plane tends to make the excursion worse, requiring the pilot to provide inputs at the controls to correct the excursion, and keep things under control. This lack of stability makes for a lot more work for the pilot.
Of course, if the CG is so far back that the plane is demonstrating negative stability in pitch, that would certainly be outside the acceptable CG envelope as specified in the POH, for any conventional GA aircraft.
Impact on Cruise SpeedNow, consider our "strong dude". When the CG is right in the center (right below the center of lift), the tail doesn't need to exert any up or down force, so that our wings only need to generate enough lift to hold up the weight of the plane. This is like putting our fat kid right in the middle of our teeter-totter. Our strong dude only has to hold up the weight of the fat kid, because no "balance kid" was necessary. But when the CG is way forward, the tail has to exert a strong downward force to balance it, and the wings need to generate enough lift to carry both the weight of the plane, _plus_ provide additional "support" to counter that downward force on the tail. This is like putting the 100lb fat kid all the way to the left of the teeter-totter, so that we need to put a 100lb balance kid all the way on the right. Now our strong dude has to hold up 200lbs over his head.
The greater the lift the wings have to generate, the more induced drag the plane will experience, so with a forward CG the plane flies less efficiently, and you lose a few knots of airspeed. With the CG nearer the rear-ward limits, the tail has to generate less downwards force to balance it, the wing needs to generate less extra lift to compensate for the extra downwards lift of the tail, so there's less induced drag, and the plane flies a little more efficiently, gaining a knot or two.
Harry Mantakos / firstname.lastname@example.org