Stability and Moments (Part One)

A body that rotates freely turns about its CG. In aerodynamic terms for a WSC aircraft, the mathematical value of a moment is the product of the force times the distance from the CG (moment arm) at which the force is applied.

Typical airplane wings generally pitch nose down or roll forward and follow the curvature of the upper airfoil camber creating a negative pitching moment. One of the reasons airplanes have tails is to create a downward force at the rear of the aircraft to maintain stabilized flight, as explained in greater detail in the Pilot’s Handbook of Aeronautical Knowledge.

The WSC wing is completely different and does not need a tail because of two specific design differences—a completely different airfoil design creating a more stable airfoil and lifting surfaces fore and aft of the CG, similar to the airplane canard design.

WSC Unique Airfoil and Wing Design

As shown in Figure 2-2, the WSC airfoil has the high point significantly farther forward than does the typical airplane airfoil. This makes the center of lift for the airfoil farther forward and creates a neutral or positive pitching moment for the airfoil. Most WSC airfoils have this unique design to minimize negative moments or pitch down during flight.

Additionally, the design of the complete wing is a unique feature that provides stability without a tail. To understand the WSC aircraft pitch stability and moments, examine the wing as two separate components—root chord and tip chord.

Trim—Normal Stabilized Flight

In Figure 2-25A, during normal unaccelerated flight at trim speed, the lift at the root (LR) times the arm to the root (AR) equals the lift of the tip (LT) times the arm to the tip (AT).

(L_R x A_R) + (L_T x A_T) = 0
L_R + L_T = Total Lift of the Wing (L_W)

Adding all the lift from the wing puts the center of lift of the wing (CLW) directly over the CG for stabilized flight. [Figure 2-25A] If the pilot wishes to increase the trim speed, the CG is moved forward. This is done by moving the hang point forward on the wing. Similarly, to reduce the trim speed, the hang point/CG is moved rearward on the wing.

Figure 2-25. Trim, minimum controlled airspeed, and high speed pitching moments.

High Angles of Attack

In Figure 2-25B, if the wing AOA is raised to the point of minimum controlled airspeed at which the wing begins to stall towards the center of the wing (root area), the lift in this area decreases dramatically. The CLW moves back a distance “b” creating a moment to lower the nose. Therefore, the center of lift moves behind the CG at higher angles of attack, creating a nose-down stabilizing moment. The average lift coefficient verses AOA is shown for this minimum controlled airspeed in Figure 2-26. The root area is partially stalled and the tips are still flying. The specific stall characteristics of each wing are different and this stall pattern shown here is used for example.

Figure 2-26. Example of AOA versus CL for wing at minimum controlled airspeed.

Low Angles of Attack

At very low AOA, the tip chords are near zero AOA or below, not producing any lift, as shown in Figure 2-25C. At this point, the nose area is producing all of the lift for the wing. The CLW moves forward a distance “c,” creating a positive stabilizing moment to raise the nose.

Pitch Pressures

As the pilot pushes out on the control bar, this creates a pilot input force that has a moment arm from the control bar up to the wing hang point. [Figure 2-27]

Figure 2-27. Pilot actuated pitching moment.

From this pilot-induced pitch moment, the control bar is pushed out, the nose raised, and the AOA increases an equal amount for both the root and the tip chords. However, as shown in Figures 2-26 and 2-28, the average C_L change is greater at the low AOA at the tip chords, while the amount of change of the C_L is much less at higher AOA at the root chord. Therefore, an increase in AOA for the wing results in the tips creating a greater proportion of the lift and moving the center of lift behind the CG, creating a negative pitching moment to lower the nose at high AOA.

Figure 2-28. Example AOA versus CL showing the wing increasing AOA three degrees with the tip CL increasing more than the root. — Figure 2-28. Example AOA versus C_L showing the wing increasing AOA three degrees with the tip C_L increasing more than the root.

Based on the same principle, when the wing AOA is lowered below the trim position, the tip chords’ C_L decreases more than the root chord and the center of lift for the wing moves forward creating a positive moment to raise the nose at lower AOA.

In situations where the pilot is flying in severe/extreme turbulence, wind sheer, or the pilot is exceeding the limitations of the aircraft, the WSC aircraft can get into a situation where the root chord is at a negative AOA and not producing lift. This could result in an emergency vertical dive situation, as discussed later in the Whip Stall-Tuck-Tumble section. When at very low angles or negative angles of attack, the WSC wing is designed so that the wing has positive stability or a noseup aerodynamic moment. This is accomplished by a number of different systems (washout struts, sprogs and reflex lines) further explained in chapter 3 that simply keep the trailing edge of the wing up in an emergency low/negative AOA dive situation. As shown in Figure 2-29, the root area of the wing has reflex which creates a positive pitching moment for the root chord to rotate the nose up towards a level flying attitude. At the same time, the tips are at a negative AOA producing lift in the opposite direction as usual, creating a moment to bring the nose/root chord up to a positive AOA to start producing lift and raising the nose to a normal flight condition. The negative lift or downward force as produced at the tips and root as shown provide a positive moment to raise the nose back to a normal flying attitude.

Figure 2-29. Emergency vertical dive recovery for a WSC wing.

Reflex also provides a stable pitch up moment for an airfoil when it is flying at normal flight angles of attack. The greater the reflex, the greater the nose up moment of the airfoil. This is used in some WSC airfoil designs and also for trim control as discussed in Chapter 3.

Carriage Moments

The wing design is the main contributing factor for pitch stability and moments, but the carriage design can also influence the pitching moment of the WSC aircraft. For example, at very high speeds in a dive, a streamlined carriage would have less drag and, therefore, a greater nose-up moment because of less drag. The design of the carriage parts can have an effect on aerodynamic forces on the carriage, resulting in different moments for different carriage designs.

The drag of the wing in combination with the drag of the carriage at various airspeeds provides a number of pitching moments, which are tested by the manufacturer—a reason the carriage is matched to the wing for compatibility. Each manufacturer designs the carriage to match the wing and takes into account these unique factors.

Pitch Moments Summary

Overall, the amount of sweep, twist, specific airfoil design from root to the tip, and the carriage design determine the pitching moments of the WSC aircraft. Some have small pitching moments, some have greater pitching moments. Each WSC model is different with a balance of these aerodynamic parameters to accomplish the specific mission for each unique carriage and wing combination.

Flight Literacy Recommends

Rod Machado's Private Pilot Handbook -Flight Literacy recommends Rod Machado's products because he takes what is normally dry and tedious and transforms it with his characteristic humor, helping to keep you engaged and to retain the information longer. (see all of Rod Machado's Products).