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Analyzing Decode-1 with XFLR5: Control Surfaces

At this point, it is also possible to estimate the effectiveness of movable control surfaces on the design for small control deflections. In general, control surfaces are sized by their span-wise and chord-wise extents: as already noted, we typically opt for ailerons that extend over the outboard 50% of the main wing with flaps over the inboard parts of the wing (although these are sometimes omitted on simpler designs). For rudders and elevators, we opt for full length surfaces (and for very slow speed flying at more extreme angles of attack, full moving elevator surfaces). For hinged control surface, we design these to extend across the rearmost 30% of the airfoil section. Hoerner [10] suggests that there is little to be gained from extending a plain flap control surface beyond this and that 20% is often a good trade-off in terms of performance, structural penalties, weight, and so on. We find for small UAVs it is generally worthwhile going as far as 30% and that this can be easily accommodated in the structural design approach we adopt.

The flap hinge moment coefficient for a control surface, defined in terms of flap area and flap mean chord, CH = H/(0.5p V2Sf cf), typically varies fairly linearly with the flap deflection and the overall lift coefficient, with dCH/d6 being -0.0075 per degree and dCH/dCL around -0.05 for 30% chord ratio flaps (both being negative because of the normal convention that a positive control surface deflection produces a negative moment). dCH/d6 decreases in magnitude (becomes less negative) as the chord ratio gets greater than this, while dCH/dCL gets

XFLR5-generated polar plot for Decode-1 airframe at 30m/s with main wing setting angle of 0°

Figure 13.26 XFLR5-generated polar plot for Decode-1 airframe at 30m/s with main wing setting angle of 0°, showing variations in center of gravity position by 100 mm, reduction in tail length by 300mm, and elevator set at an angle of 0°.

bigger in magnitude (more negative). Notice that, even when not deflected, an aileron or flap (and to a lesser extent an elevator) will have a noticeable hinge moment simply induced by the fact that the overall section is creating lift and thus there is a pressure differential on the flap itself and that this effect increases as the flap chord ratio rises. Likely maximum hinge moments should be used to select appropriate servos to control the surface, typically assuming a one-to-one mechanical advantage ratio in the linkage (this is slightly conservative since servos typically have a greater angular range than control flaps and this can be used to gain slight mechanical advantage by suitable selection of the servo arm and control horn lengths). Figure 6.9 shows how servo weights typically vary with the required torques.

XFLR5 deals with control surfaces by allowing automated edits of airfoil section shapes to approximate the behavior of deployed simple trailing edge flaps. Note, however, that no account is taken of the gaps that are inevitable around the control surface or the changes to the flows that these give rise to, nor will it deal with very large control surface deflections: it is necessary to move on to a RANS-based analysis if a more complete treatment is required. The basic calculations that XFLR5 permits are those of roll, pitch, and yaw moments at a given flight speed and AoA. These can be used to estimate steady-state roll, pitch, and yaw rates. For example, if on Decode-1, ailerons extending 50% of the span and 30% of the chord are deflected by ±5° at 2.53° AoA and 30m/s, the corresponding roll, pitch, and yaw moment coefficients are -0.0355, -0.0012, and -0.0004, respectively; note that there is very little pitch or yaw coupling as desired. When deflected in this way, assuming the previous values for the hinge moment slopes and a wing CL = 0.287, we find that the resulting hinge moment coefficient for the ailerons is CH = -0.0075 X 5 - 0.05 X 0.287 = -0.0519. Taking the aileron area to be 0.04 m2 with a mean chord of 0.1 m, the required hinge moment torque is 0.114 Nm = 16.2 oz. in. In practice a much larger deflection might occur in flight and at dive speeds, so rather higher torques should be specified; if instead of a 5° deflection a value of 30° is used with a dive speed of 45 m/s, the required hinge moment torque coefficient becomes CH = -0.0075 X 30 - 0.05 X 0.287 = -0.239, leading to a torque requirement of 0.94 Nm (133 oz.in.) at 45 m/s. Using the equation for typical servo weights given in Figure 6.9 reveals that the servo will likely weigh around 2 oz. or 56 g, a perfectly reasonable value for a wing servo on an aircraft of this size.

 
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