Spiral Stability

The use of Table 10.3 should be obvious and needs no explanation. For the Cherokee example, the “time to double” of 30.2 sec is seen to exceed all of the minimum times specified in this table.

SPINNING

When stalled an airplane has a tendency to “drop off” into a spin, particularly if the stall is asymmetrical or entered with power. A pilot can purposefully initiate a spin by kicking the rudder hard to one direction at the top of the stall.

In a spin, an airplane rotates around a vertical spin axis as it is descend­ing rapidly in a nose-down attitude. The path of its center of gravity pres­cribes a helix around the spin axis. The airplane’s motion and attitude result in a high angle of attack on the order of 45° or more.

The stall/spin is one of the major causes of light plane accidents today. In my opinion, the blame for this can be placed on pilot training instead of current airplane designs. On a landing approach, too many pilots fly too slow. Rarely is there a valid reason for dragging a light airplane in under power at a speed just above the stalling speed. Under such a condition, an unexpected gust or a maneuver on the part of the pilot can produce an asymmetrical stall. If this occurs on the approach, the altitude may be insufficient to recover from either the stall or ensuing spin, regardless of how well the airplane is designed.

FAR Part 23 requires, for the normal category, that a single-engine airplane be able to recover from a one-turn spin in not more than one additional turn, with the controls applied in the manner normally used for recovery. Normally, to recover from a spin, one uses forward stick and rudder opposite to the direction of the spin. Ailerons are generally ineffective for spin recovery, since the wing is fully stalled. FAR Part 23 also requires, for the normal category, that the positive limit maneuvering load factor and applicable airspeed limit not be exceeded in a spin. In addition, there may be no excessive back pressure (on the stick) during the spin or recovery, and it must be impossible to obtain uncontrollable spins with any use of the controls.

The analysis of spinning, in order to design for good spin-recovery characteristics, is difficult because of the nonlinear nature of the problem. However, one can understand the principal factors influencing spin recovery by reference to Figure Ю.6. A side view of the spinning airplane is shown in Figure 10.6a. As the airplane descends, the aerodynamic forces on the aft fuselage and tail, Ff and FT, tend to nose the airplane downward. However, in a nose-down attitude, because of the rotation, centrifugal forces are developed on the airplane’s mass to either side of the center of gravity. These create a pitching moment about’ the center of gravity that opposes the nose-down aerodynamic moment.

The wing is completely stalled in a spin so that its resultant force, F„, is approximately normal to the wing. In a nose-down altitude, the horizontal component of F„ points in toward the spin axis and balances the centrifugal force

while the vertical component of F„. balances the weight. If 0 is the angle of the nose up from the vertical, as shown in figure 10.6 (a), then the angular velocity about the spin axis, Д the spin radius, R,, and 0 are related by,

R, = g/П2 tan 0

For a typical light aircraft Rs, for a steep spin, is of the order of 0.2 of the wing span and decreases to.06 b for a flat spin. Corresponding 0 values equal approximately 45° and 60°.

(a)

Figure 10.6 Aerodynamic and inertia forces influencing the spin behavior of an airplane (a) Side view. (b) Top view, (c) Autorotative forces.

Normally, the angle of roll, ф, is small in a spin. Using equations 10.&d, e, and/, it can be shown that the inertia moments about the spin axis and about the airplane’sy-axis are proportional to fl2 and (1-І,). Thus, the spinning behavior of an airplane is determined as much, possibly more so, by its mass distribution as by its aerodynamic shape.

The pro-spin, autorotative forces can be produced by both the wing and the fuselage. Referring to figure 10.6 (b), consider the resultant velocities in a spin at each wing tip and at a typical fuselage section aft of the eg. Assume Rs to be small as in the case of a flat spin. The velocities at each of these locations combine vectorially with the descent velocity, VD as shown in figure 10.6 (c) to produce extremely high angles of attack for the wing sections and a nearly vertical flow from beneath the fuselage. For the wing, particularly one with a well-rounded leading edge, a net moment in the direction of rotation results from the higher

angle of attack on the left side compared to the right side. The aft fuselage, depending upon its geometry, can develop a force also in the direction of rotation.

Rudder control is the principal means of recovering from a spin. There­fore, in designing the empennage, the placement of the horizontal tail relative to the rudder is important. If the horizontal tail is too far forward, in a spin its wake will blanket the rudder, making it ineffective.

An attempt to quantify the blanketing of the vertical tail by the horizontal tail is presented in Figure 10.7 (taken from Ref. 10.1). Referring to this figure, a term called the tail damping power factor (TDPF) is defined by

TDPF mb2

Figure 10.9 Criteria for spin recovery. Inertia yawing moment parameter, Ux — !y) / mb2 X 104 Figure 10.10 Spin recovery for a light airplane with different tail configurations.

shape of this area must certainly influence the damping effectiveness of this area.

According to Reference 10.1, the TDPF for satisfactory spin recovery is a function of an airplane’s mass distribution. This is shown in Figure 10.8 (taken from Ref. 10.1). Boundaries are suggested on this figure that divide regions of satisfactory spin recovery characteristics from unsatisfactory regions. However, from the points included on the figure, it is obvious that these boundaries are not too well defined. Indeed, there are several unsatis­factory points lying well within the region denoted as being satisfactory. Similar graphs for ц values as high as 70 can be found in the reference.

The scatter and overlapping of the points in Reference 10.1 appear to rule out any valid definition of the criteria as a function of /a. Instead, the graph of Figure 10.9 is offered as representative of any /л value. In the region labeled “satisfactory,” there were no unsatisfactory points to be found in the reference. For the region labeled “possibly satisfactory,” there were ap­proximately an equal number of satisfactory and unsatisfactory points. In the region labeled “probably unsatisfactory,” the data points were predominan – tely unsatisfactory.

Despite the uncertainty associated with this figure, one point is obvious. For satisfactory spin recovery characteristics, the moments of inertia about the pitching and rolling axes should be significantly different.

Figure 10.10 is taken from Reference 10.3. Obviously, neither the shape of the curve dividing the satisfactory region from the unsatisfactory region nor the values of TDPF for satisfactory recovery agree with Figure 10.9. Tails 1,3, and 4 were found to be unsatisfactory for spin recovery with ailerons neutral. With ailerons deflected, tails 2 and 7 were also unsatisfactory. This reference concludes that TDPF cannot be used to predict spin recovery. However, it is important to provide damping to the spin and very important to provide exposed rudder area for spin recovery. In modern aircraft, the T-tail is becoming very popular. The reason for this is twofold. First, from Figure

10.10, such a tail configuration provides excellent spin recovery charac­teristics. Second, the horizontal tail is removed from the wing wake, thereby minimizing downwash effects. For the same tail effectiveness, the T-tail will allow a smaller horizontal tail, thereby saving on weight and drag.