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Velocity and Horizontal Stabilizer Settings for Helicopters

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INTRODUCTION



As in a previous report (Isham, 2004), the emphasis of experiments conducted for this report is speed. Modern military and high-performance rotorcraft can achieve speeds upwards of 160 knots TAS. Simulating such performance with sufficient control over flight stability requires careful adjustment of .air file parameters.



In an earlier report (Isham, 2004), it was noted that higher values of Main Rotor Effectiveness #2 resulted in increased forward velocity, though the aircraft had to be pitched downward extremely in order to achieve this. Without this unwanted pitch, it is expected that the aircraft would fly more efficiently with increased forward speed. Since the purpose of the horizontal stabilizer is to reduce or eliminate unintended extremes in pitch, it is a likely surface with which to experiment.



In his “1400-1404 Technical Notes”, Steve Baugh identifies a number of parameters under “Helicopter Horizontal Stabilizer” (record #1401) which affect pitch. Adjustments to three of these—Horizontal Stabilizer Lift Coefficient (hereafter, LC), Horizontal Stabilizer Drag Coefficient (hereafter, DC), and Horizontal Stabilizer Efficiency (hereafter, H.Stab. Eff.)—were made for the experiment reported here. Since the airfoil of the horizontal stabilizer on a helicopter is “upside down”, as it were, one would expect increasing parameters affecting lift to pitch the aircraft up, resulting in more efficient forward velocity. Since drag acts perpendicularly to lift and, in particular, that the lift-to-drag ratio (L/D) determines the total reaction vector which, in turn, determines the thrust vector, one would expect increasing parameters affecting drag to slow the aircraft. A more efficient airfoil would create less turbulence near the wing’s surface and. thus, would tend to damp oscillations. Baugh observed that with Horizontal Stabilizer Efficiency set to zero, the aircraft drifted in pitch.



METHOD



The experiment for this report was divided into three parts. In the first part, forward velocity in straight and level flight was measured as a function of both LC and DC, and plotted as a three-dimensional surface. Secondly, forward velocity was measured and plotted as a function of LC and H.Stab. Eff. to give a contoured surface. Finally, forward velocity was measured and plotted as a function of DC alone, where the range of values of DC was greatly extended to magnify or, at least, capture its effect.



The test flight, test conditions, and the PC used for this experiment are the same in all respects except one, to those described in an earlier report (Isham, 2004). The difference in procedure for this experiment is that tests of torque at takeoff were not included.



Part 1: Velocity versus LC and DC. Values assigned to LC were -0.05, -0.15, -0.25, -0.35, -0.45, -0.65, -0.75, -0.85, -0.95, and -1.0. Values assigned to DC were 0.0012, 0.0024, 0.0036, 0.0048, 0.0060, 0.0072, 0.0084, 0.0096, 0.0108, and .0120. Main Rotor Effectiveness #1, and Main Rotor Effectiveness #2 (record #1402) were set to 0.95 and 5.0 respectively. In this part of the experiment, the default H.Stab. Eff. of 0.75 was used. Figure 1 shows the output.


Figure 1. Surface plot of forward velocity measured as a function of Horizontal Stabilizer Drag Coefficient (DC) and Horizontal Stabilizer Lift Coefficient (LC).




Part 2: Velocity versus LC and H.Stab. Eff. Values assigned to LC were -0.25, -0.375, -0.4375, -0.5, -0.625, -0.6875, -0.75, -0.875, -0.9375, and -1.0. Values assigned to H.Stab. Eff. Were 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0. For ease of computation, DC was set to 0.005. Main Rotor Effectiveness #s 1 and 2 remained 0.95 and 5.0 respectively. This output is shown in Figure 2.


Figure 2. Contour plot of velocity as a function of LC and HStab. Eff. Dark blue interval in northeast corner denotes region in which forward cyclic did not compensate for nose-up pitch.




Part 3: Velocity versus DC. Including the portion of Part 1 for which LC takes the value -0.35, the values of DC for this part of the experiment were 0.0012, 0.0024, 0.0036, 0.0040, 0.0048, 0.0060, 0.0072, 0.0084, 0.0096, 0.0108, 0.0120, 0.0480, 0.0920 0.1360, 0.1800, 0.2240, 0.2680, 0.3120, 0.3560, and 0.4000. Main Rotor Effectiveness #s 1 and 2 were, again, 0.95 and 5.0 respectively, and H.Stab. Eff. was 0.75. LC was set to -0.35. Figure 3 shows the plot of this part of the experiment.


Figure 3. Straight and level flight velocity measured as a function of DC alone.




RESULTS AND DISCUSSION



As can be seen in Figure 1 all contour lines and intervals are virtually straight and, in this perspective, horizontal. This result is surprising. The interpretation is that, regardless of the value of LC, DC has practically no effect on velocity of the aircraft. Seeming irregularities in the 130-131, 132-133, and 139-140 KIAS intervals could suggest stepwise changes in velocity due to DC. Abrupt changes also appear in Figure 3. However, these “steps” do not appear at identical values of DC in both plots and are likely due to experimental error. That R2 is close to, but not exactly, unity in Figure 3 supports explanation by way of experimental error. It says that less than 1.6% of change in velocity is not explainable by change in DC. In this view, where DC ranges from about one-third of its default value of 0.004, to about three times its default, it has no effect on velocity. Where the range is extended to about one hundred times its default value, the effect is marginal.



This result is surprising since drag is directly proportional to the drag coefficient, CD. Where CD is increased by a factor of three, drag would also increase by a factor of three. Where CD increases by a factor of one hundred, drag would also increase by the same proportion. If efficient flight, measured here as velocity, depends upon L/D, changes of such magnitude in DC ought to have more effect. A computation using the experimental values from Part 1 for both DC and their respective measured velocities results in the plot shown in Figure 4. Equation 1, where CD=CDp+CDi was used for the computation yielding Figure 4.


Figure 4. Computed total drag as a function of previously listed values of DC and the resulting values measured for velocity.



More meaningful from a theoretical perspective is the fact that, for a given aircraft weight, drag is a function of lift, and CL varies with velocity. In straight and level flight CDp and CDi contribute about equally to drag, and CL varies with velocity. A plot of this computation using the expression


Equation 1



where


Equation 2


is shown in Figure 5 for the simulated Bell 206B. In this expression. W is the force supported by the wing. In the case of the simulated Bell 206B, if the rotor disk, at 1/3 ft. (-4 in.) from the CoG, supports a weight of 1760 lb., the moment due to the horizontal stabilizer must equal the moment due to the CoG. Where the distance of the horizontal stabilizer is 12.18 ft. (146.2 in.) from the CoG, W=49.51 lb. On the other hand, the magnitude of DC seems to depart from what might be considered typical of an airfoil.


Figure 5. Computed total drag as a function of velocity for the simulated Bell 206B. The expression uses true airspeed as its argument.




Moreover, the expression


Equation 3




where e is the wing’s Oswald efficiency factor, and AR is its aspect ratio, gives the CD in straight and level flight. Using -0.35 as the lift coefficient, and 0.75 as the Oswald efficiency factor, this expression returns 0.05452. Clearly, other processes are at work in Flight Simulator.



Contributing significantly to forward velocity are LC and HStab. Eff. as shown in Figure 2. With some exceptions, likely due to experimental error, contour lines are oriented at about 45o, northwest to southeast. Each contributes about equally and in direct proportion to changes in velocity. Lift coefficient, dependent on angle of attack (AoA) can, itself, give a rough estimate of AoA. As AoA of the horizontal stabilizer increases in a negative sense, the aircraft is pitched at greater angle to the relative wind increasing lift. As HStab. Eff., which might be taken as the Oswald efficiency factor, increases, drag is reduced, making for more efficient flight.



CONCLUSIONS



While changes in DC produce outputs that might be expected of a drag coefficient, due to its magnitude it is unclear to what aerodynamic parameter DC refers. A CD of 0.004 is exceptionally low. It might be that DC has to be this low in order to simulate the Bell 206B’s aerodynamics realistically. However, given that many or most other inputs to the .air file are relatively true-to-life, it would seem that DC should be, if it is the CD.



More easily recognizable are LC and HStab. Eff. Though LC is unconventionally negative in sign, it appears to produce results consistent with a CL. HStab. Eff. might well be the Oswald efficiency factor. Wings of a more rectangular shape, which seems apparent for the Bell 206B horizontal stabilizer, have Oswald efficiency factors in the range of 0.7-0.8. Further study is necessary in order to more fully identify these parameters in the .air file.



REFERENCES



Isham, Matthew A., (2004), “Percent Torque at Takeoff and Cruise Velocity as Functions of Main Rotor Effectiveness Numbers One and Two for the Bell 206B in Flight Simulator 2002”, Hovercontrol (www.hovercontrol.com).






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