LATERAL-DIRECTIONAL TRIM SOLUTIONS

The lateral-directional equilibrium equations are those involving Y-force, rolling moment, and yawing moment—the Y, R, and N equations. The aircraft

components that are significant in these equations are the main rotor, tail rotor, vertical stabilizer, and the fuselage.

Hover

In hover, the airframe aerodynamic effects may be neglected so that only the two rotors enter into the equations. For example, Figure 8.28 shows the relationships that result in the equilibrium equations:

TJls + TT=-G. W. Ф

(dRM ^ dbx

N QM — 1тТт — 0

These equations yield some interesting results for special cases as presented in Table 8.9 and illustrated by Figure 8.29.

The example helicopter has the pertinent parameters given in Table 8.10 These values, used in the equations for bx and Ф, give:

bls = —.027 rad = —1.5 deg ф =—0.050 rad =—2.9 deg

Besides the roll angle and the lateral flapping, the tail rotor pitch and its corresponding pedal position required to maintain heading in hover can be calculated from the conditions that satisfy the yawing moment equilibrium equation:

Qm ~ Ir^r ~ 0

TABLE 8.9 Special Cases of Trim in Hover Helicopter Parameters Results Lai. C. G. offset, yM Rotor Type Height of Tail Rotor, hT Ф b, 4 0 Teetering Ь}Л 0 —TT/G. W. 0 Any 0 -Tj/G. W. 0 Any Very rigid Any -Tt/G. W. 0

TABLE 8.10 Example Helicopter Parameters Physical Dimensions Trim Forces in Hover (OGE) Dimension Symbol Units Value Force Symbol Units Value Main rotor lat. offset Ум ft 0 Gross weight G. W. lb 20,000 Main rotor vert, offset ft 7.5 Main rotor thrust Tm lb 20,840 Main rotor stiffness dPyJdby^ ft lb 200,940 Tail rotor thrust Tt lb 1,540 rad Tail rotor vert, offset h2* ft 6

Before one does a numerical calculation, an interesting relationship can be obtained by rewriting the equation in terms of nondimensionalized coefficients, which gives:

Ст/&T _ (ПК)м Rm CQ/oM~ AiT (ClR)2T (lT-lM)

Thus for a given helicopter, this ratio is constant and independent of altitude. If the small effects of compressibility are ignored, the constancy of this ratio also defines another ratio that is independent of altitude: Q0t/Ct/cm, since with this assumption and for given rotor geometries, CT/cT is only a function of 0Ot and CQ/oM is only a function of CT/cM. The practical application of this is that the tail rotor pitch as a function of main rotor thrust/sohdity coefficient need only be calculated for sea-level, standard conditions and then used for other altitudes simply by accounting for the effect of density ratio on CT/cM. For the example helicopter, the work was done as an intermediate step while preparing Figure 4.30 of Chapter 4. Figure 8.30 shows the result, which can be used to guide the

CjkTM

FIGURE 8.30 Tail Rotor Pitch Required in Hover

designers in choosing the maximum tail rotor pitch travel. For the example helicopter at its design gross weight of 20,000 lb, Figure 4.35 gives standard day hover ceilings of 12,400 ft out of ground effect and 15,000 ft in ground effect. Using Figure 8.30, it may be determined that, in each case, a tail rotor pitch of 22.2 degrees is required to hover. A prudent designer would, of course, allow some margin for maneuvering.