December 7, 2018, ©. Leeham News: Last week we looked at the pitch stability of an aircraft wing with fuselage. We could see the combination was unstable. Now we add a rear wing called a horizontal stabilizer to get the whole aircraft stable in pitch.
We use the DC9 as our example of a pitch stable airliner (Figure 1) as it has some interesting pitch stability problems outside the normal flying envelope. This we will discuss in coming Corners.
Figure 2 shows the pitch moment curve we discussed in the previous Corner. It shows the pitch moment around a point at 40% of the wing’s chord (actually the graph shows the Pitch moment coefficient curve over Angle of Attack (AoA). See the comment section of the last Corner for good explanations of the difference). The moment curve is measured in a wind tunnel on a model of what eventually became the DC9.
The combination is unstable, the pitching moment nose up increases with AoA for the reason we discussed in the last Corner.
Now we add an aerodynamic surface behind the center of gravity, which is the point around which an aircraft moves. This surface is called a horizontal stabilizer. This surface, sitting well back from the center of gravity, will add stability to the pitch moment curve by adding a nose up or down moment depending on what is needed to control the pitch moment of the aircraft.
A horizontal stabilizer is placed as far back on the aircraft as possible, by it increasing the moment arm from the center of gravity for the stabilizing forces. The combination of the long moment arm and the force from the tailplane turns the curve to a stable pitch moment curve between 0° and 17° ° Angle of Attack (AoA), Figure 3.
Normal flight with a clean aircraft (no slats or flaps) is flown between 2-4° at cruise and up to 6-8° in a turn or when waiting for landing at moderate speed in a circling pattern. There is, therefore, ample margins to the area of the curve where the pitch stability is turning neutral (the curve is horizontal) at 18° AoA. Above 18° the curve has a positive gradient, the aircraft is unstable in pitch. Then it turns stable until 23° and then unstable again.
We will discuss this undulating part of the curve in a following Corner. Now we focus on the normal flying range, the curve below 17°.
If we sum all parts of the aircraft producing lift into one point, this is called the Center of Lift, Figure 4. The figure shows the probable location of the center of lift for a DC9 type of aircraft. Its location is a bit behind the aircraft’s Center of Gravity.
A good way to estimate where an aircraft’s center of gravity is, is to look where the main wheels are placed. The center of gravity is placed just ahead of the main wheels to not have the aircraft tip on its tail when loaded. The center of gravity cannot be placed too far from the main wheels, however. Then a very large force is required from the horizontal stabilizer’s elevator to rotate the nose up when taking off.
The Center of Gravity being ahead of the Center of lift means the aircraft’s horizontal stabilizer is angeled against the airflow until it produces a pitch moment to balance the nose down moment created by the Center of Gravity being ahead of the Center of Lift. In this case the pitch moment is nose up.
This enables the aircraft to fly straight ahead at cruise. The position of the tail to create this moment equilibrium is called the trim position. The aircraft is in trim, flying at a constant altitude, with a constant pitch angle.
Any disturbance like a gust increasing the AoA on the wing will increase lift on the wing but also on the stabilizer. This will produce less pitch up moment from the stabilizer and the aircraft will turn nose down to return to stable flight. The aircraft is stable.
The equilibrium of pitch moment around the aircraft’s center of gravity will change as we change the aircraft’s speed. How and why we will discuss in the next Corner.