Effect of CG

On

Aircraft Efficiency

Most pilots, when asked how aircraft loading affects aircraft efficiency, correctly identify an aft center of gravity location as the most efficient loading condition.  However, understanding of the subject commonly ends there. Since an aviator’s worth is based on knowledge of the fundamentals of aerodynamics, and this subject is commonly broached on pilot employment interviews, here is a treatment of this topic in simple physical terms.

Consider Figure 1 below:  Gravity acts on an airfoil through the center of gravity toward the center of the Earth.  When a Bernoullian airfoil, such as a wing, is subjected to an airstream, lift is generated.  This lift is centered along a line that is approximately two-thirds of the chord from the leading edge.  Since the center of lift is aft of the center of gravity, torque is generated around the CG.  This creates an inherent pitch-down moment that adversely affects controllability, and helps to explain the scarcity of flying-wing aircraft designs.  The flying wings that do exist must have CG’s that are very close to their centers of lift in order to be controllable.  This compromise results in severe loading limitations in order to maintain controllability, so aircraft utility is diminished.

The most common way to solve this dilemma is to place a second airfoil, in the form of a horizontal stabilizer, at the end of a lever arm (tail boom) behind the wing.  The main purpose of the horizontal stabilizer is to generate a down load to counteract and neutralize the torque effect caused by the caused by this pitch-down phenomenon.  This arrangement is depicted schematically in Figure 2 below.

This entire assembly has a center of gravity that is allowed to vary within limits.  The forward CG limit is defined as the most nose-heavy loading condition that will allow the aircraft to be rotated on takeoff and flared upon landing.  The aft CG limit is defined as the most tail-heavy loading condition that will still allow the aircraft to be recoverable in a stall.  The utility of an aircraft is directly proportional to the length of the weight and balance envelope.

Consider an airplane loaded to the forward end of its center of gravity envelope, depicted in Figure 3 below.  This airplane is engaged in straight and level, unaccelerated flight at a constant weight.  The horsepower is distributed as follows: 50% of the available horsepower is dedicated to generating the lift necessary to maintain a constant altitude.  10% of the available horsepower must be dedicated to generate the download with the horizontal stabilizer necessary to counteract the natural nose-down pitch.  That leaves 40% of available horsepower to generate thrust and overcome drag.  (This is a simplified example to demonstrate this concept, and the numbers are not intended to reflect accurate values).

In Figure 4 below, the same airplane has been reloaded to the same weight, but the center of gravity now at the most aft allowable location.  The weight shifted aft helps to offset the effects of the pitch-down tendency, relieving the horizontal stabilizer of some of that work.  In this example, the overall weight of the airplane has not changed compared to the previous example, so 50% is the portion of available horsepower necessary to maintain level flight.  However, now the decreased workload of the horizontal stabilizer decreases its power requirement to 5% of the total horsepower available.  The other 5% has been freed up and is now available to be added to the thrust value.

Once that transformation is accomplished, the wise aviator has several options.  The same power setting can be maintained, yielding a higher cruise airspeed.  Or if a higher cruise airspeed is not the primary goal, the same cruise airspeed can be maintained at a reduced power setting, resulting in lower fuel consumption.  Thirdly, a combination of these two advantages can be exploited.

An interesting note:  An elegant solution to the pitch-down problem is to reconfigure the aircraft structure as depicted in Figure 5 below.  In this example, an airfoil known as a canard is mounted forward of the wing.  This surface counteracts the pitch-down torque by generating positive lift at the end of a lever arm.  This upload reduces the amount of lift that must be generated by the wing to maintain level flight.  The combined energy values of the upload provided by the canard and the lift provided by the wing must equal the original 50% value, allowing the remaining 50% of the energy to be reserved for thrust.

Although the canard configuration seems to be the ideal answer to this problem, there are other considerations that explain the relative scarcity of production canard designs.  Aft-mounted engines present cooling challenges that commonly require the addition of drag in the form of air intakes and other cooling apparatus.  This additional drag degrades the efficiency that is the goal of this design.  Additionally, if the canard is controllable and provides pitch control, it cannot be allowed to stall before the wing stalls.  In order to accomplish this, normally the travel of the control surface is limited.  This noticeably reduces effectiveness in the landing flare, requiring higher approach airspeeds and longer landing distances.  This also narrows the CG envelope (the forward limit is defined by the ability to rotate on takeoff and flare on landing, remember?).

Here’s a practical experiment:  Fly a light airplane equipped with groundspeed readout (GPS, DME, LORAN) in calm conditions.  Place the pilot and copilot seats as far forward as practical and trim for hands-off level flight. Allow the groundspeed to stabilize and note the reading.  Then move the seats (and their occupants) as far aft as practical.  Retrim the nose down for hands-off level flight and allow the groundspeed readout to stabilize.  The increase will impress you.