Extreme Ground Effect Characterization Testing for Human-Powered Helicopter Application

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1 Extreme Ground Effect Characterization Testing for Human-Powered Helicopter Application Matthew Misiorowski B.S.E. Aerospace Engineering Benjamin Rothacker Undergraduate Department of Aerospace Engineering University of Michigan, Ann Arbor, MI, 4809 Carlos E. S. Cesnik Professor ABSTRACT An improved empirical model for ground effect of rotor blades is necessary for human-powered helicopter (HPH) applications. To establish such a model, sub-scale rotor blades were tested on a dedicated hover stand with a customdesigned movable ground plane mechanism. This movable ground plane allowed use of established measurement equipment, improving results and simplifying testing. Methods are presented for design and testing using an established rotor test stand and movable ground plane, as well as results for extreme ground effect in previously little-tested regimes very near the ground. NOTATION c rotor blade chord P C P coefficient of power, ρπr (ΩR) 3 T C T coefficient of thrust, ρπr (ΩR) C lα lift curve slope D rotor diameter F c centripetal force HPH human-powered helicopter IGE in ground effect N number of blades per rotor OGE out of ground effect P power supplied to rotor P theo normalized power IGE, theoretical P meas normalized power IGE, tested Q torque required by rotor R rotor radius T thrust created by rotor T ad j normalized thrust IGE after power correction T meas normalized ratio of measured thrust IGE v rotor induced velocity V helicopter velocity W weight of rotor blade and attachment z corr corrected rotor height z set rotor height setting on ground plane z/r normalized rotor height above ground plane α rotor plane angle of attack v λ i induced inflow, ΩR µ rotor advance ratio, V cos(α) ΩR ρ atmospheric density Presented at the AHS 69th Annual Forum, Phoenix, Arizona, May 3, 03. Copyright c 03 by the American Helicopter Society International, Inc. All rights reserved. σ Ω corr Ω exp rotor solidity, πr Nc theoretical rotor rotational speed after correction physical rotor rotational speed during testing INTRODUCTION Ground effect in helicopters occurs when the usual air flowing down from the rotor blades is impeded by the ground, as shown in Figure. This impediment spreads the vortices formed by the rotating blade tips, increasing the thrust created by the rotor for given input power and resulting in a more efficient aircraft. Previous literature (Ref. ) suggests that the closer the helicopter is to the ground, the greater this effect will become. However, since little or no data exists for extreme ground effect below 50% z/r, the trend of increasing thrust was previously difficult to verify in this regime. A more complete understanding of power input and thrust output of rotorcraft in extreme ground effect will have significant effects in both the design process and piloting strategy for human-powered helicopters (Ref. ). Most human-powered helicopter configurations employ a quad-rotor design and it may not be cost- or time-effective to use computational fluid dynamics (CFD) to accurately predict the ground effect interactions on the vehicle. Currently, only extrapolated models predict the thrust increase of a rotor in extreme ground effect; Stonier (Ref. 3) calls for expanded understanding of these models as is required for human-powered helicopter design. Current human-powered helicopters often use existing ground effect models that apply to conventional rotorcraft such as that due to Cheeseman and Bennett (Ref. 4), as shown in Figure. The difficulty in collecting accurate measurements of rotor thrust below 50% z/r combined with most rotorcraft s inability to operate in extreme ground effect have yielded

2 Less Wake Spreading Without Ground Effect Airflow Rotor Blade With Ground Effect Airflow Ground Greater Wake Spreading Fig.. A conceptual visualization of the flow a rotor blade encounters in ground effect Hover Test Stand was utilized in conjunction with a simulated ground plane. This ground plane is attached to a custom mechanism allowing precision measurement and incremental change of the ground plane by ±0.% z/r. The JR3 sensor in the test stand provides the thrust and power measurements and both are normalized by their freestream values. The test stand was mounted with modified commercially available helicopter rotor blades. Though conventional setup of the hover stand requires the blades be oriented with a positive angle of attack, the experiment required the blades to produce thrust downwards due to the ground plane s orientation. With the blades properly mounted, the ground plane mechanism was constructed around the hover stand. This mechanism is crucial to the success of the experiment as it will allow the simulated ground plane to accurately traverse from 0% down to nearly 0% z/r. At each height setting of the ground plane, the data in Table 3 in the appendix were gathered. Fig.. Selected previously existing normalized thrust vs. normalized height research (Ref. 4); note lack of data and applicable models below z/r = 0.5 mainly theoretical and extrapolated models in this regime. The premise of this experiment was to test rotor blades at a constant rotational speed while varying the distance between the simulated ground plane and the rotor blades. The thrust measurement at each instance is normalized by the thrust observed in freestream. The current work confirms the Cheeseman and Bennett model in its regime of applicability, shown in Figure, but also extends thrust and power measurements for a rotor below 50% z/r. Measurements of the thrust ratio were taken initially between 50% and 0% z/r and compared to the Cheeseman and Bennett model. Once verifying that the experimental results agreed with the predicted values of the established model, experimentation continued into the previously littletested regime. EXPERIMENTAL METHODS To accurately test the effects of extreme ground effect on thrust and power, the A SRL (Active Aeroelasticity and Structures Research Laboratory) UMICH/MIT Helicopter Hover Stand The UMICH/MIT hover stand, shown with ground plane in Figure 3, was a critical component of the experiment. The stand is powered by a kw (50 HP) electric motor; the desired maximum rotation speed of 00 RPM was well within the capability of the stand. The most crucial component of the hover stand is its JR3 sensor. This sensor can measure between. to 8.9 kn (-500 and 000 lbf.) of thrust and 00 to 70 N-m (-800 to 00 ft.-lbf.) of moment at the blade root in the rotating frame. The expected loads on the blades tested fell well within the measurable range. The hub is for a two-blade articulated rotor, with the distance from the central rotation axis and blade attachment point location given in Table. Ground Plane Design Rationale The most novel component of this experiment was the design and construction of the ground plane mechanism. Designing the experiment around a fixed rotor and adjusting the ground plane provided several advantages in the experiment. First, this allowed the use of an established rotor hover stand; the thrust and power input results were more reliable than if a custom hover stand had been designed for this experiment. The second advantage of moving the ground plane rather than the rotor is the reduction in structural weight for the height adjusting apparatus. In similar experiments where the rotor is raised up and down in relation to a fixed ground plane, the adjusting apparatus requires a more robust structural design to account for vibrations from the rotor. This additional structure can have adverse or difficult-to-predict effects on the inflow and skew results via fluid-structure interaction. The movable ground plane was designed specifically to minimize any unintended interaction between the structure and the flow. Since the ground plane was constructed out of a low density,

3 simulated an infinite ground for the rotors while also preventing unwanted circulation. Ref. 6 explains the need to reduce unwanted circulation for the hovering assumption to be valid. A dimensioned view of the ground plane mechanism is shown in Figures 4 and 5. stiff foam and subject to minimal vibration, complexity and interference of structure was kept to a minimum in this design. Rotor and Ground Plane Sizing.44 The sizing of the ground plane and rotors were determined by several factors, out of which the size of the facility proved to be the most prominent constraint. The hover facility has a shroud surrounding the hover stand with a diameter of 3.67 m ( ft.). However, the ground plane could not be made with a 3.67 m (-ft.) diameter because the flow would then interact undesirably with the shroud. The diameter of the plane needed to be large enough to simulate an infinite ground but also small enough to leave a gap between the ground plane edge and the shroud to prevent unwanted recirculated. 3.0 Extensive CFD and optimization (specific methods described in Ref. 5) would have been required to determine the maximum size of the ground plane that met these criteria. Due to scope constraints of the experiment, these methods were not used in the ground plane design. Instead, experimental analysis was used to size the ground plane. Preliminary testing evaluated multiple points along the Cheeseman and Bennett curve that have been confirmed in previous experimentation. While holding z/r constant, the ground plane diameter was adjusted in 5.-cm (6-in.) increments. If the ground plane was too large and caused undesired circulation, it would be apparent in the post processing as a significant reduction in measured thrust. Similarly, if the ground plane was too small, the wake would not travel as expected, with similarly significant effects on the measured thrust. By sizing the ground plane where the normalized thrust measurements closely match other confirmed experimental data, a.44-m PROPRIETARY AND CONFIDENTIAL THE INFORMATION CONTAINED IN THIS (8-ft.) diameter ground plane was used with confidence that it DRAWING IS THE SOLE PROPERTY OF <INSERT COMPANY NAME HERE>. ANY REPRODUCTION IN PART OR AS A WHOLE WITHOUT THE WRITTEN PERMISSION OF <INSERT COMPANY NAME HERE> IS PROHIBITED..5 Fig. 4. The ground plane, support structure, and surrounding shroud with final dimensions in meters, side view UNLESS OTHERWISE SPECIFIED:.44 DIMENSIONS ARE IN INCHES TOLERANCES: FRACTIONAL ANGULAR: MACH BEND TWO PLACE DECIMAL THREE PLACE DECIMAL.5 INTERPRET GEOMETRIC TOLERANCING PER: MATERIAL USED ON NEXT ASSY APPLICATION 4 5 NAME DATE DRAWN TITLE: CHECKED ENG APPR. MFG APPR. Q.A. COMMENTS: 5.43 SIZE DW A s FINISH SCALE: DO NOT SCALE DRAWING R.83 3 Fig. 5. The ground plane, support structure, and surrounding shroud with final dimensions in meters, top view UNLESS OTHERWISE SPECIFIED: NAME DATE The rotors were sized to provide range and sensitivity of DRAWN DIMENSIONS ARE IN INCHES TOLERANCES: TITLE: CHECKED the hover stand measurements. A screen was installed above FRACTIONAL ANGULAR: MACH BEND ENG APPR. PLACE DECIMAL to reduce signal noise TWO for other experiments. This limited the THREE PLACE DECIMAL MFG APPR. ground plane to traversing a range between 80.8 cm (.65 ft.) Q.A. COMMENTS: to 0. cm (4 in.) above the rotor. Initial tests used a smaller SIZE DWG. NO. 405-mm (5.9-in.) blade radius, which corresponds to 5USED ON NEXT ASSY 0% z/r. These tests provided the z/r range to confirm the DO NOT SCALE DRAWING thrust APPLICATION measurements agreed with previous data comprisingscale: :96 WEIGH 4 3 the Cheeseman and Bennett model while also collecting some data in the untested region (>50% z/r). The second round of INTERPRET GEOMETRIC TOLERANCING PER: PROPRIETARY AND CONFIDENTIAL THE INFORMATION CONTAINED IN THIS DRAWING IS THE SOLE PROPERTY OF <INSERT COMPANY NAME HERE>. ANY REPRODUCTION IN PART OR AS A WHOLE WITHOUT THE WRITTEN PERMISSION OF <INSERT COMPANY NAME HERE> IS PROHIBITED. MATERIAL FINISH 5 and after Fig. 3. The ground plane mechanism before (left) (right) installation around the UMICH/MIT hover stand 3 A spin

4 testing used the larger 800-mm (3.5-in.) blades, which allowed for greater resolution. The the blades could only be tested between 8-79% z/r; but tests were limited from 8-35% z/r, where the ground plane could still be assumed infinite. Fig. 6. Blades used in this study; note similarity, which simplified matching Ground Plane Mechanism The blades were selected to ensure matching inflow characteristics as expected in full-scale human-powered helicopters. In addition to using an in-house code to evaluate the loads, XFOIL and blade element momentum theory (BEMT) codes were used to verify that the blades used would have the desired near-uniform inflow, and would behave similarly despite their different rotor radii. The inflow variation is shown in Figure 7; the spike near the blade tip is a numerical artifact and is not considered in the calculations because it is not physical. Ref. 6 discusses this effect. Designing and building the ground plane mechanism provided the first known device capable of testing rotors in such extreme ground effect at this scale (see Figure 3). The ground plane mechanism was designed to raise and lower the ground plane between approximately 0% and 0% z/r, and was comprised of a structural frame and stiff foam ground plane. The ground plane itself was made out of a.44-meter (8-ft.) diameter,.9-cm ( 34 -in.) thick circular section of insulation foam, which was fastened to the ground plane stand by plastic ties covered by smooth tape for minimal airflow disruption. Inflow The ground plane was adjusted from 0% down to just above 0% z/r, over approximately 60 steps, measuring the thrust and power output from the rotor blades at each distance. Fine adjustment of the ground plane s height above the rotor blades was accomplished with Acme precision thread stock supports on each of the four supporting legs, along with meter sticks attached to the structure. The screws allowed easier and more accurate height adjustment (within ±.59 mm (± 6 in.), or ±0.% z/r) of the ground plane. 0 Tested Rotor Blade Typical HPH Design Ideal Inflow Radius (meters) Fig. 7. Inflow comparison between HPH design and tested blades; note reasonable agreement These commercial blades use a symmetrical NACA 00 airfoil, with its structural and mass center points collocated with its aerodynamic center. This collocation provides neutral stability and minimizes torsional loading on the blade. Blade Selection To ensure uniformity in blade construction two sets of commercial model helicopter blades were modified. The characteristics of each blade are given in Table. The blades were reduced in length to remove the tapered end so that each blade would be as uniform as possible. Reducing the blade s lengths also ensured that the ground plane would remain sufficiently large for each testing regime to be assumed infinite for a given test. The shorter blades were used for higher z/r testing, where the wake could spread unpredictably before reaching the ground plane; the longer blades were used near the ground plane to achieve the lowest possible z/r. Both blades are shown in Figure 6. Furthermore, XFOIL calculations were performed to determine the coefficient of moment of the blades at the angles of attack experienced under testing conditions. Moment coefficients are zero to within XFOIL s numerical error, due to the symmetric airfoil and low angles of attack, as expected. These results are based on viscous XFOIL runs at a representative Reynolds number of 400,000, representing the 75% radius location on the blade during operation. ANALYSIS AND DATA PROCESSING The data collected during the experiment required corrections for extraneous noise, constant power input and blade coning. The following sections will detail the data processing required prior to normalizing the thrust values and determining the best fit equation. Table. Tested Commercial Blade Specifications Characteristic Mavrikk WC 550 Edge 83 CF (Blade ) (Blade ) Original Radius 550 mm 83 mm Radius as Tested 405 mm 800 mm Chord Length 6 cm (.36 in.) Geometry No twist or taper Airfoil NACA 00 Attachment Point Quarter-chord from leading edge Distance, Root to Axis.6 cm (8.5 in.) Distance, Flap 7. cm (6.77 in.) Hinge to Axis Signal Smoothing The data collected from the experiment in its raw form was subject to significant noise fluctuations. The force sensor integrated with the hover stand was designed for loads on the order of hundreds of pounds of thrust. In part because this experiment yielded thrust measurements one order of magnitude less, the sensor was subject to approximately 50% variation in thrust measurements. Before finding the average of the 4

5 thrust measurements, the data was filtered through a smoothing function that reduced the extraneous noise while preserving the shape of the thrust measurements over the time period of the experiment. This smoothing operation was applied to the freestream data and every dataset collected in ground effect. After the noise was eliminated from the function, the mean of the thrust data was calculated and normalized by the mean of the freestream thrust data after accounting for the baseline signal data, as described below. Accounting for Sensor Baseline The JR3 sensor produced a baseline signal that was accounted for with a 00 RPM spin test. At freestream and each measured ground effect instance, thrust and power measurements were taken at 00 RPM to determine the minimum signal noise of the sensor at each condition. Immediately following the baseline measurement, data was acquired at the specified RPM determined to match Reynolds numbers at the rotor tips. The thrust drifting noted in the higher RPM tests were not time synced with the baseline thrust test; so to account for the baseline, the mean of the baseline thrust and power were subtracted from the mean measured thrust and power. Examples of a baseline and signal are shown in Figure Blade, Baseline Blade, Test Constant Power Input Correction The Cheeseman and Bennett model for ground effect describes the percentage increase in thrust for a rotor in ground effect compared to the thrust produced in freestream for constant power input. To maintain constant power input, each series of tests varied the distance between the rotor and the ground plane but maintained constant rotor RPM. When testing between freestream and approximately 30% z/r, maintaining constant RPM also maintained constant power input to the rotor. However, when testing below 30% z/r, the ground plane reduced the drag at the rotor tips significantly and while maintaining a constant rotor RPM the power input to the rotor decreased as the rotor neared the ground plane, as shown in Figure 9. Power ratio, P IGE /P OGE Blade, Test Blade, Test Blade, Test Thrust (lbs) Thrust (lbs) Time (sec) Blade, Baseline Blade, Test Time (sec) Fig. 8. Measured thrust data before (top) and after (bottom) smoothing operation 5 Fig. 9. Power in ground effect normalized by power in freestream. Note that power required to hold RPM constant decreases when testing below 30% z/r The decreasing power trend was not determined or quantified until post-processing the sensor data. After establishing the decreasing power trend seen in Figure 9, one could repeat the experiment using the previous power measurements with corresponding increase in the rotor RPM so to maintain constant power as the tip drag reduces. Instead, RPM rather than power was held constant during testing due to the functionality of the test stand. Because the test stand facility is set to run at specific rotational speeds, the power data was normalized in the post processing phase. Using momentum theory and a power correction as described in Equations and, an adjusted thrust value was obtained for constant power. The ratio of power in and out of ground effect was used to solve for a simulated rotor speed shown in Equation. Once the simulated RPM was calculated, that value was substituted in Equation to solve for thrust. Had power been held constant during the experiment,

6 the rotor would have experienced a greater RPM as z/r decreased and generated additional thrust. The adjustment in Equations and simulates this physical phenomena. P meas = C pρω 3 corrπr 5 P theo C p ρω 3 expπr 5 = Ω3 corr Ω 3 Ω 3 P meas exp = Ω 3 corr () exp P theo T ad j = C tρω corrπr 4 T meas C t ρω expπr 4 = Ω corr Ω exp Ω T meas exp Ω = T ad j () corr This correction was applied universally to all data points to ensure the correction accounted for constant power at each data point tested. Blade Height Correction for Coning After correcting the thrust values to reflect constant power input, the next step was to correct the z/r for blade coning. During the experiment the ground plane was set to desired distances from the rotor with the assumption that the blades are dominated by centrifugal force, are sufficiently rigid, and the thrust generated is small enough to not generate measurable coning. However, after reviewing videos of the blades in the rotating frame, significant coning at the blade tips was observed. The height above the ground plane at the blade tips was on a similar order of magnitude as the coning itself for some lower z/r. Johnson discusses reasons for the need to account for the distance between the blade tip and ground plane in Ref. 7. A corrective function was added to the post-processing that accounts for the centrifugal forces, thrust, blade and hub weights and calculates the approximate coning angle, as demonstrated conceptually in Figure 0 and given in Equation 3. Using the blade radius, this function adds the distance originally set in the experiment to the added distance between the blade tip and ground plane due to coning, given in Equation 4. Thrust ratio, T IGE /T OGE Thrust correction due to power normalization z/r correction due to blade coning Blade, Test Blade, Test Blade, Test Fig.. Summary of effect of corrections of normalized thrust data Error Analysis The large period drift in the thrust measurements in this experiment is the largest contributor to the error in the collected data. Measured thrust was seen to oscillate up to 50% from the mean thrust value. Additionally, since the baseline mean thrust value is a near zero or negative value, when the baseline is subtracted from the measured thrust value this operation increases the thrust error on the upper limit and decreases the thrust error on the lower limit. It was assumed that no additional error was introduced for theoretical corrections such as RPM/power adjustment and the blade coning correction. These operations consist of the subtraction of the baseline and the normalization between ground effect and freestream data. Figure shows the range of normalized thrust values from multiple measurements grouped by common z/r values for 90% confidence. Height set with! ground plane!. Best Fit Line "! Weight,! Thrust! Radius! Cent. sin(")! Force! Height due to coning! Fig. 0. Effect of coning on normalized rotor height ( ) W + T W + T = F c sin(θ) sin = θ (3) F c z corr = z set + Rsin(θ) (4) Thrust ratio, T IGE /T OGE Summary of Corrections In summary, data was filtered to reduce signal noise, and shifted to account for power changes and coning during the experiment. The effects of these changes are summarized in Figure Fig.. Comparison of experimental thrust ratio best fit line with 90% confidence level variation

7 FINDINGS AND APPLICATIONS The primary result was the trend for thrust ratio between freestream and ground effect rotor blade operation. As the distance between the ground plane and rotor blades decreased, the thrust produced increased exponentially, as previously suggested. The data was evaluated by plotting the ground effect to freestream thrust ratio against the rotor height to blade radius ratio, as seen in Figure 3. Thrust ratio, T IGE /T OGE Blade, Test Blade, Test Blade, Test Previous Experimental Data Best Fit Line Cheeseman & Bennett Equation Fig. 3. Comparison of experimental results and previous data, including the Cheeseman and Bennett model (Ref. and 4) To compare the Cheeseman and Bennett model to the data collected by this experiment, the existing data was included with newly acquired data to create the new model for ground effect. The Cheeseman and Bennett model, like other previous models, breaks down below 50% z/r. In an effort to improve the new model as compared to the existing Cheeseman and Bennett model, Cheeseman and Bennett s equation was generalized with fitting constants: [ TIGE T OGE ] P=constant = ( c R) z c 3 +c c 4 (5) The fitting constants were chosen to best approximate the physical behavior of ground effect. Constant c accounts for differences in blade loading, c accounts for the effects of forward flight, c 3 accounts for the nonlinear growth of ground effect, and c 4 allows for shifting towards or away from the origin based on differences in coefficient of thrust from blade to blade. Note that certain constants used are not applicable to HPHs or in this experiment, such as c, but were retained to maximize the potential applications of these results. After performing a curve-fitting, the most appropriate fitting function for these tests was determined. This new empirical formula for ground effect in hovering flight based on these 7 experimental results is given by Equation 6. For comparison, Equation 7 shows the general Cheeseman and Bennett model. [ TIGE T OGE ] P=constant [ TIGE T OGE ] = ( P=constant +.38 ( z R ) = σc lα λ i ( 4z) R 4C ( T + µ λi ) (6) ) (7) In summary, the constants in Equation 5 determined from these experiments are given in Table. Table. Empirical Constants Constant Value c -.38 c c 3 0 (hovering state) c One intended use of these findings is improving the design of human-powered helicopters. Using the results of this experiment, HPH can be better designed to take full advantage of ground effect. In Figure 4, the five human-powered helicopters that have flown are plotted along the best fit line from Equation 6. Thrust ratio, T IGE /T OGE Best Fit Line Yuri I Gamera II Da Vinci III Atlas Upturn Largest Vehicle Allowed by Rule Fig. 4. Previously flown HPH vehicles plotted against experimental best fit line; z/r determined by vehicle specifications, hovering at 3 m (9 ft., 0 in.) (competition requirement) These results will ideally aid current and future HPH teams in selecting a vehicle configuration and in the preliminary sizing process, as utilizing the benefit of ground effect is a crucial component to winning the Sikorsky Prize. HPH vehicle configuration selection is discussed in Ref. 8 and will be supplemented by these findings.

8 However, errors still reside in this experiment. The new empirical relation offers greater insight into the extreme ground effect on a rotor blade in regions where previous research and the Cheeseman Bennett model fall short. CONCLUSIONS An improved empirical model for ground effect of rotor blades was developed for human-powered helicopter applications. To establish such a model, sub-scale rotor blades were tested on a dedicated hover stand with a custom-designed movable ground plane mechanism. Detailed description of the tests and error analysis were presented. The new general form for the ratio of thrust in and out of ground effect tested successfully against the Cheeseman and Bennett model and for z/r 0.5. This new experimental model should support conceptual HPH vehicle designs. APPENDIX A matrix of test points is shown in Table 3. Repeated z/r values were performed to increase confidence over the corresponding ranges. Table 3. Test Matrix Blade Test # RPM z/r T meas Q Blade Test # RPM z/r T meas Q ACKNOWLEDGMENTS The authors would like to thank the University of Michigan Aerospace Department and the Active Aeroelasticity and Structures Research Laboratory for their generous donation of testing time on the UMICH/MIT Helicopter Hover Stand, as well as Dr. Devesh Kumar for his indispensible contributions of time and technical expertise. We would also like to thank Eamonn Shirey, Co-Lead of the University of Michigan Phoenix Human Powered Helicopter Team, for his financial and technical support.

9 REFERENCES Johnson, W., NDARC NASA Design and Analysis of Rotorcraft, NASA Ames Research Center, Moffett Field, California, pp. 83-, June 00. Naito, A., Unknown Problems in Human-Powered Helicopter, Nihon University, Chiyoda, Tokyo, Japan, pp. -5, Stonier, J. R., Man-Powered Flight - A History and a Proposal, Canadian Aeronautics and Space Journal, Vol.., Ottawa, Canada, pp , Cheeseman, I. C., and Bennett, W. E., The Effect of the Ground on a Helicopter Rotor in Forward Flight, edited by Aeronautical Research Council Reports and Memoranda, London, pp. -, Khromov, V., and Omri, R., Ground Effect Modeling for Rotary-Wing Simulation, International Congress of the Aeronautical Sciences, Vol. 6, pp. -0, Leishman, J. Hovering Height Near the Ground, Principles of Helicopter Aerodynamics, New York, New York, pp , Johnson, W., Helicopter Theory, Princeton University Press, Princeton, NJ, 980, pp Sherwin, J. R., Unconventional Aircraft, Man-Powered Flight, Hemel Hempstead: Model and Allied Publications, London, pp , 97. 9