Helicopter tail rotor noise analyses

Helicopter Tail Rotor Noise Analyses Albert R. George and S.-T. Chou Sibley School of Mechanical and Aeorspace Engineering Upson and Grumman Halls Cornell University Ithaca, New York 14853 Final Technical Report Prepared for Langley Research Center under Grant NAG -1-590 Period : June 1, 1985 - January 31, 1986 Summary A study was made of helicopter tail rotor noise, particularly that due to interactions with the main rotor tip vortices, and with the fuselage separation mean wake.

The tail rotor blade - main rotor tip vortex interaction is modelled as an airfoil of infinite span cutting through a moving vortex. The vortex and the geometry information required by the analyses are obtained through a free wake geometry analysis of the main rotor. The acoustic pressure-time histories for the tail rotor blade-vortex interactions are then calculated. These acoustic results are compared to tail rotor loading and thickness noise, and are found to be significant to the overall tail rotor noise generation. Under most helicopter operating conditions, large acoustic pressure fluctuations can be generated due to a series of skewed main rotor tip vortices passing through the tail rotor disk.

This noise generation depends strongly upon the helicopter operating conditions and the location of the tail rotor relative to the main rotor.

The interaction between the tail rotor and the fuselage separation mean wake does affect the loading noise characteristics, however it does not seem to be as important as the other harmonic noise sources such as thickness noise and blade-vortex interaction noise. However, the fuselage separation wake turbulence is important to tail rotor broadband noise.

Main Rotor Tip Vortex-Tail Rotor Interaction During the forward flight of helicopters, tail rotors operate in a very complicated environment containing the main rotor wake, the fuselage wake, etc. 1 In this section, we will focus particularly on the tail rotor chopping the tip vortex convecting from the main rotor. The strong and concentrated main rotor tip vortex can generate significant velocity perturbations in the inflow field of the tail rotor. Using thin airfoil theory, these strong velocity perturbations can result in large unsteady loadings on the tail rotor blades; significant noise is therefore generated. In order to study the problem, clearly we first have to define the main rotor tip vortex trajectory around the tail rotor disk during flight conditions of interest.

Main Rotor Tip Vortex Free Wake Geometry Calculation Since the main rotor tip vortex system is generally highly distorted, classical rigid wake analysis cannot predict the accurate trajectories of the vortex. The calculation of the free wake geometry of main rotor tip vortex is very important because the trajectories of vortex directly affect the characteristics of the interaction and the noise generated. In the present study, we use the comprehensive rotorcraft aerodynamics and dynamics analyses program (CAMRAD) of Johnson 2 to calculate the main rotor tip vortex wake geometry. The CAMRAD analysis is based on a rotor - free wake goemetry calculation model of Scully 3.

In our application, we assume non-uniform inflow at the main rotor disk, but the presence of the tail rotor is assumed to have no effect on the main rotor tip vortex system, and no fuselage wake effect is included. To demonstrate the analysis procedure, the UH-ID was selected to be the model helicopter for the present study. Three cases were run, which corresponding to a UH-ID at i00, 80, and 60 knots level flight respectively. Free wake geometry results are

presented in figures 1 through 3. From these results, the

interactions between the tail rotor blade and the main rotor tip

vortex are evident.

Determining the Locations of Blade-Vortex Interactions The characteristics of a certain blade-vortex interaction are mainly determined by its location on the tail rotor blade. The normal incident velocity of the ingesting vortex relative to the tail rotor blade, the strength of the ingesting vortex element, and the skew angle between the ingesting vortex element and a line parallel to the rotor axis are the main controlling parameters for the tail rotor blade-main rotor tip vortex interaction noise. These parameters are generally not constant as a vortex sweeps through the tail rotor disk. Figures 4 through 6 present the main rotor tip vortex trajectories on the tail rotor disk, they correspond to the three cases shown in figures 1-3; the points shown are interpolated from the free wake geometry analysis results, and each point is exactly 15 degrees (main rotor rotation) apart.

Notice that the tip vortices involving in the interactions with the tail rotor are relatively "young" (less than 180 ° for all three cases considered), which implies that the ingested vortices are not fully rolled-up (Johnson 2 had suggested that a vortex is not fully rolled-up unless the vortex age is larger than 180 ° or so). Since a vortex is not fully rolled-up, the strength of the ingesting vortex should be less than the maximum bound circulation on the main rotor blade; we followed the assumption made by Scully 3, and set the strength of the tip vortex strength to 0.8 of the maximum bound circulation on the main rotor blade span.

Also the tail rotor RPM is generally not an integer multiplier of the main rotor RPM; the location of the blade-vortex interaction is different for each main rotor revolution. In the present study, both # 1 blades of the main and the tail rotors are set such that

both blades will start from _ = 0° initially. (Figure 7 shows the

definitions of azimuthal angle for both the main and the tail

rotors.) The exact locations of a series of blade-vortex

interactions can then be determined numerically. These results are

shown in tables 1-3, they provide the required input data for the

aerodynamic and acoustic analyses and are used in the following

sections. Sketch of blade-vortex interaction geometry and vortex

orientation are shown in figure 8.

Noise Generation Due to Blade-Vortex Interaction The tail rotor blade-vortex interaction is modelled as a flat plate of infinite span chopping through a moving skewed vortex using a method similar to that of Amiet 4. The acoustic pressure-time behavior is related to the airfoil lift response for certain perturbation velocity field. According to Amiet, the far field pressure-time history is given by p(t) = i" (KczP0U2/2a0 _2) x'w(kx, ky) "L(kx,ky,M) 'exp(i (kxUt+_(Mx-(;))) dk x where P0 is the density of the acoustic medium, c is the tail rotor blade chord, a 0 is the speed of sound, M = U/a0, _ = kxM/(l-M2), and L is the effective lift function; see =/x2+(l-M2) (Y2+Z2) • reference 4 for details. w is the Fourier decomposed vortex velocity field.

In the present study, the effect of a moving vortex is included numerically, so U is the vortex normal velocity relative to the blade. Also in order to be consistent with the free wake geometry analysis, a different vortex model is used. In the present analysis,

the tangential velocity for a concentrated vortex is defined by the

widely used model:

V8 = (F/2Kr).r2/(r2+rc 2)

where F is the vortex strength, r c is the vortex core radius (r c

equals to 0.0025 of the main rotor tip radius in the present study).

The vortex model Amiet used is given by

V8 = (F/2Kr) • (I+i/2_) • (l-exp (-_(r/r c) 2)

where _ = 1.25643. At large radial location, the vortex model used

in the present study decays more slowly than the model used by Amiet.

Figure 9 shows the comparison between the two vortex models. Since a

different vortex model is used, w, the Fourier decomposed vortex

velocity which is normal to the tail rotor plane, is replaced by

= i'tanSvFrckyK 1 (r c ky2+kx2/COS28v ) / ((2_) 2 ky2+kx2/COS28v )

j J

where K 1 is the modified Bessel function of the second kind, 8 v is defined in figure 8. It should be noted that _ only accounts for the effect of the tangential velocity of the vortices; the axial flow in the main rotor tip vortices is neglected in the present analysis as discussed in the conclusion.

To evaluate the effect of using the present vortex model, the acoustic pressure-time history for a given blade-vortex interaction is compared to that obtained using Amiet's original analysis. The comparison is shown in figure i0. Beside minor differences, the two different analyses show very similar pressure-time behavior.

The data defining a series of blade-vortex interactions which we

had obtained in the previous section are now used as the input for

the noise calculation. Figure ii shows the pressure-time history

results for the tail rotor blade-main rotor tip vortex interaction of

a UH-ID helicopter for I00 knots level flight (horizontal tick marks

are 0.i second apart); the far field observer is assumed to be

stationary relative to the helicopter (the helicopter is positioned

50 m above the observer , and 25 m to the right of the observer).

Notice that the pressure peaks are not separated by equal time

intervals; therefore if one Fourier analyzed the pressure-time

history, the resulting acoustic spectrum will behave more like

broadband noise with widened spectrum peaks rather than pure

harmonics. Figure 12, with a smaller time scale (horizontal tick

marks are 0.01 second apart), shows the first 0.2 seconds of figure

II, showing the detailed shapes of the pressure peaks resulting from

tail rotor blade-vortex interactions. Clearly an interaction with

large normal velocity will result in a large but relatively short

perturbation pressure peak; while an interaction characterized by

smaller normal velocity will result in a lower but longer pressure

perturbation.

Figures 13 and 14 show the similar results for a UH-ID at 80

knots level flight. Figures 15 and 16 show the acoustic results

corresponding to the 60 knots level flight cases.

Effect of Tail Rotor Location As discussed previously, the vortex trajectory on the tail rotor disk is very important to the tail rotor blade-vortex interaction noise. The tail rotor location relative to the main rotor, and the helicopter operating conditions are two primary variables that change the vortex trajectories on tail rotor disk. To study the effect of tail rotor location on the blade-vortex interaction noise, we

artificially lowered the UH-ID tail rotor by 0.5 m. This will cause

the blade-vortex interactions to occur with advancing blades, thus

enhancing the strength of the interactions.

For the I00 knots level flight case, the main rotor tip vortex

trajectory on the tail rotor disk is now shown in figure 17. Notice

that the path is higher than that shown in figure 4 due to a lowered

tail rotor. As before, the interaction locations and vortex

properties are then determined; results are shown in table 4. The

acoustic pressure-history of the tail rotor blade-vortex interaction

is shown in figure 18. There are considerable differences between

the results shown in figures I0 and 18. Since the vortex is passing

through the advancing side of the tail rotor, this results a higher

relative velocity between the tail rotor blade and the vortex

element, so generally the pressure perturbation has higher peaks.

Also the interactions are more frequent than previous cases.

Unquestionably, with this configuration (with lowered tail rotor), tail rotor noise will be higher than that from a standard tail rotor.

Figure 19 shows the first 0.2 seconds of figure 18, showing the detailed pressure peak shape.

The 80 knots flight case is also studied; the tail rotor is also lowered by 0.5 m as in the previous case. The tip vortex trajectory is shown in figure 20. The input data to the acoustic analyses are given in table 5. The acoustic results are shown in figures 21 and 22. Again the results show higher pressure peaks and more frequent interactions.

CQ_parison to Other Noise Mechanisms The tail rotor blade-vortex interaction noise is compared to other tail rotor noise sources in order to determine its relative importance to the overall helicopter noise radiation. We compare the noise generated by tail rotor blade-vortex interaction to the thickness noise and the steady loading noise. The thickness and

loading noises are calculated using program WOPWOP of Langley, the

calculations are based on the analysis of Farassat 5 Tail rotor

loading is calculated using approximate aerodynamic analysis, and the

loading is matched to balance the main rotor torque calculated in the

free wake geometry analysis.

Only one case is presented, this is for a standard tail rotor at

I00 knots level flight. Figures 23-26 plot the first four tail rotor

blade-main rotor tip vortex interaction signals (see figure Ii) along

with the calculated thickness and loading noise results. Each figure

shows the pressure-time history representing one tail rotor

revolution; the solid line shows the overall thickness and loading

noise, and the dash line shows the tail rotor blade-vortex

interaction signal.

Notice that these figures do not include some of the strongest

peaks, and they do not represent four consecutive tail rotor

revolutions. For cases such as a i00 knots UH-ID with lowered tail

rotor, the result not presented here show stronger tail rotor

blade-vortex interaction peaks. However, even in the case shown, the

importance of the tail rotor blade - main rotor tip vortex

interaction is quite evident.

Tail Rotor - Fuselage Separation Wake Interaction The effect of the fuselage separation mean wake on tail rotor noise is also studied. The separation mean wake is modelled as an axially-symmetric wake, and the wake is assumed to be steady. This will primarily affect the loading noise as the tail rotor inflow is changed. We scaled the BK-II7 fuselage separation wake results of Polz and Quentin 6 and use them to calculate the resulting loading noise. The fuselage separation mean wake for an 80 knots level flight BK-II7 is expressed by the velocity deficit Ud: U d = 0.7 U h exp(-(z+l.15)/0.8656) where U h is the helicopter flight speed, and the definition of z is shown in figure 8.

The results are shown in figures 27 and 28; figure 27 gives the acoustic pressure-time history for 180 ° of the tail rotor rotation, and figure 28 shows the acoustic pressure spectrum obtained from the pressure-time history results shown in figure 27. In figure 27, the solid line shows the overall noise, the dash line shows thickness noise, and the dotted line shows the loading noise. In figure 28, the 'o' symbols show the overall harmonic noise level, the '+' symbols represent the thickness noise, and the '*' symbols represent the loading noise. Figures 29 and 30 show similar results for the BK-II7 in 80 knots level flight except that no fuselage separation wake effect is included. Both of the two cases are for an observer fixed in space, and the BK-II7 is 50 m above the observer and 25 m to the right of the observer. Notice that the pressure-time histories shown in figures 27 and 29 are not periodic, this is due to the fact that the observer is not moving with the helicopter.

In this particular case, the loading noise is much smaller than the thickness noise, and the fuselage separation wake does not result

in any significant change to the overall tail rotor noise. Since the

presence of the fuselage separation mean wake generally does not

result in any unsteady loading fluctuation of significant amplitude

on the tail rotor blade, it will not be very significant to the tail

rotor noise. However, the fuselage separation wake turbulence will

have an important effect on the high-frequency tail rotor broadband

noise I .

i0

Conclusions Tail rotor blade-main rotor tip vortex interaction is a very important tail rotor noise mechanism. The noise generated depends strongly on the main rotor operating conditions and on the tail rotor location. Major parameters governing this blade-vortex noise generation are the ingested vortex strength, the ingested vortex skew angle relative to the blade, and the relative velocity of the ingested vortex to the tail rotor blade. The present study shows that this noise mechanism is at least of the same order of magnitude as some of the strongest tail rotor noise sources such as thickness noise. More detailed study should be devoted to the problem considering a vortex chopped by an airfoil of finite span.

The present study does not include the possibly major effect of the axial flow in the main rotor tip vortex. This can be another strong contributor to the unsteady loading fluctuation on a tail rotor blade. The result of free wake geometry analysis does indicate some evidence of the main rotor tip vortex drifting normal to the tail rotor disk. Also the strength of main rotor tip vortex is not constant, this will result in an axial pressure gradient inside the vortex, thus inducing some axial flow. These important problems should be addressed in future studies.

The fuselage separation mean wake effect does not seem to be as important as the tail rotor blade-vortex interaction noise. However, the fuselage turbulent wake, with small scale turbulent eddies, will be an important tail rotor broadband noise source when it is ingested into the tail rotor disk.

ii Reference i. George, A. R., Chou, S.-T.: A Comparative Study of Tail Rotor Noise Mechanisms. Proceedings of the American Helicopter Society 41st Annual Forum, Fort Worth, Texas, May 1985.

2. Scully, M. P.: Computation of Helicopter Rotor Wake Geometry and its Influence on Rotor Harmonic Airloads. M.I.T. ASRL Report TR 178-1, March, 1975.

3. Johnson, W.: A Comprehensive Analytical Model of Rotorcraft Aerodynamics and Dynamics, Part I, II, and III. NASA TM 81182, 81183, and 81184, 1980.

4. Schlinker, R. H., Amiet, R. K.: Rotor-Vortex Interaction Noise.

NASA CR 3744, October 1983.

5. Farassat, F., Succi, G. P.: The Prediction of Helicopter Rotor Discrete Frequency Noise. Vertica, Vol. 7, No. 4, 1983.

6. Polz, G., Quentin, J.: Separated Flow Around Helicopter Bodies.

Paper # 48, 7th European Rotorcraft and Powered Lift Aircraft Forum, September, 1981.

TABLE I. TAIL ROTOR BLADE-VORTEX INTERACTION UH-ID I00 KNOTS, STANDARD TAlL ROTOR M.R. PSI RADIUS T.R. PSI U THETAV PHIV GAMMA T.R. # 32 976 0.721 168 753 123.087 19.181 -84.670 11.855 i 102 534 1 204 345.368 207.403 19.411 -252.082 11.791 2 0 843 168.410 144.768 19.177 -84.847 11.859 2 208 537 278 145 1 083 345.151 186.263 19.381 -252.554 11.795 I I 384 161 0 964 168167 166.026 19.187 -85.039 11.863 453 756 0 961 344 880 165.075 19.352 -252.972 11.799 559 786 1 085 167 977 187.235 19.196 -85.286 11.868 11.804 i 629 359 0 840 344 544 143.791 19.323 -253.307 11.872 i 735 410 1 206 167 826 208.411 19.206 -85.570 11.807 2 804 913 0 717 344 192 122.254 19.306 -253.514 -253.576 11.811 I 980 467 0 595 343 695 100.586 19.288 11.846 2 1122 367 0 461 170 102 76.629 19.204 -84.838 19.270 -253.380 11.815 2 1156 021 0472 342 940 78 690 0.584 169 311 98 877 19193 -84.608 11.850 i 1297.897 0.234 339 286 33 904 19 238 -250.793 11.823 i 1327.379 1473.427 0.708 168 796 120 879 19 182 -84.655 11.855 2 1542.976 1.216 345.387 209 530 19 414 -252.032 11791 I 168.439 142 623 19 176 -84.832 ii 859 I 1648.978 0.831 1.095 345.175 188 395 19 384 -252 509 Ii 795 2 1718 587 168.188 163 887 19 186 -85 017 Ii 863 2 1824 602 0.952 344.910 167.212 19 355 -252 933 ii 799 i 1894 198 0.974 167.994 185.100 19 195 -85 259 II 867 i 2000 226 1.073 344.574 145.956 19325 -253 280 ii 803 2 2069 807 0.853 1.194 167.840 206.278 19205 -85 540 ii 871 2175 851 I • 0.730 344.233 124.428 19.307 -253 499 Ii 807 2245 361 0.607 343.754 102.778 19.290 -253 579 Ii 811 2420.915 0.448 170.206 74.366 19.206 -84 885 II 845 I 2562.818 343.033 80.910 19.272 -253 417 ii 815 I 2596.469 0.485 169.375 96.649 19.195 -84616 II 850 2 2738.347 0.572 Ii 822 2 0.261 340.046 39.373 19.242 -251 430 2768.376 TABLE 2. TAlL ROTOR BLADE-VORTEX INTERACTION UH-ID 80 KNOTS, STANDARD TAIL ROTOR PSI RADIUS GAMMA T.R.

M.R. T.R. PSI U THETAV PHIV 0 879 170 351 147.861 17.005 -87.191 13.130 i 33.294 100.352 0 623 334 907 100.834 17 369 -243.453 13.089 13.133 2 208.790 0 979 169 670 165.672 16 992 -87.003 I 275.577 0 519 332 906 81.472 17 330 -242.187 13.092 13.135 i 384.363 1 077 169 134 183.107 16 971 -86.833 13.095 2 450.802 0 416 329 911 61.558 17 292 -239.929 487.928 1 226 339 974 209.299 17 587 -245.345 13.073 i 559.936 1.175 168 687 200.487 16 949 -86.752 13.138 2 597 642 0 347 180 723 47.814 17 096 -94612 13.115 I 620 508 0 202 313 943 13.551 17 217 -225215 13.101 i 663 508 1 129 339 530 192.078 17 550 -245 355 13.076 13.141 i 735 509 1 273 168 310 217.828 16 927 -86.741 -91138 13.118 2 772 621 0 455 176 631 69.526 17 070 -245.284 13.078 i 839 072 1 032 338 996 174.753 17 514 -89239 13.121 i 947 600 0 564 174 115 90.367 17 044 -245.109 13.081 2 1014 572 0 933 338 328 157.152 17 480 17 025 -88177 13.124 2 1122 815 0 669 172 472 109.809 17 446 -244.776 13.083 i 1190 073 0 835 337 502 139.461 17 016 -87.563 13.127 i 1298 282 0 769 171 318 128.007 121.646 17 411 -244.223 13.086 2 1365 573 0 737 336 456 0 869 170 429 146.049 17 006 -87.215 13 130 1473 750 13 089 i 1540 833 0 633 335 072 102.763 17 373 -243.544 13 132 I 1649 236 0 969 169 729 163.913 16.994 -87.026 13 091 2 1716 058 0 529 333 143 83.443 17.334 -242.350 13 135 2 1.067 169183 181 352 16 973 -86.845 1824809 13.094 i 330.278 63 599 17 295 -240.221 1891283 0.426 340.015 211 033 17 591 -245.340 13073 1928.373 1.236 i 198 739 16 951 -86 757 13138 2000.382 1.165 168.729 181.280 45548 17 098 -95 107 13.114 2038.148 0.337 -228 331 13.100 2 2061.657 0.225 317.196 19584 17 225 -245 357 13.076 i 2103.953 1.139 339.578 193 814 17 554 16.930 -86 739 13.140 2 2175.955 1.263 168.345 216 082 17.072 -91 398 13.118 i 2213.127 0.444 176.953 67 389 17.517 -245.295 13.078 2 2279 525 1 042 339.057 176.522 17.046 -89.386 13.121 2 2388 106 0 553 174 324 88.292 158.928 17.483 -245.133 13.081 I 2455 025 0 943 338 402 107.966 17.026 -88.258 13.124 I 2563 271 0 659 172 608 141.248 17.449 -244.819 13.083 2 2630 526 0 845 337 594 126.181 17.017 -87.611 13.127 2 2738 739 0 759 171 421 123.447 17.415 -244.292 13.085 i 2806 027 0 746 336 574 TABLE 3. TAlL ROTOR BLADE-VORTEX INTERACTION UH-ID 60 KNOTS, STANDARD TAlL ROTOR M.R. PSI RADIUS T.R. PSI U THETAV PHIV GAMMA T.R. # 33 357 1 050 170.768 176 808 14.661 -88 140 14 893 I 71 558 0 439 185,614 62 689 14 881 2 14.910 -98 775 133 915 0 652 326332 104 390 15.432 -232 263 14 861 I 170 623 1 244 334 253 211 438 15.817 -236 717 14 851 2 208 873 1 123 170 099 189 981 14.633 -87 939 14 894 2 246 486 0 517 181 651 78 221 14.879 -95 330 14 882 i 309 010 0 575 324 076 89 799 15.385 -230 486 14 863 2 346 191 1 172 333 722 198 611 15.771 -236 562 14 852 i 384 434 1 196 169 527 202 953 14.606 -87 646 14 896 i 421 414 0 596 178 733 93 563 14.848 -92 930 14 884 2 484 106 0 499 321127 75,065 15.337 -228 015 14 865 i 521 721 1 099 333116 185 662 15.726 -236 377 14 853 2 559995 1 269 169,020 215 906 14.579 -87 419 14 897 2 596 656 0.672 -91 338 14 885 i 176.628 107 831 14.815 658938 0.421 316.887 59 347 15.288 -224 282 14 866 2 697.238 1.027 332.422 172 651 15.680 -236 120 14 855 i 772.020 0.746 174.988 121 646 °90 210 14 887 14.782 2 832.414 0.328 308.754 39 202 15.233 -216 802 14 868 I 872.754 0.954 331.622 159 614 15.634 -235 758 14 856 2 14 888 I 947.383 0.821 173.647 135 392 14.749 -89 380 1005.889 0.246 294.740 19 088 -203 441 14 870 2 15.178 1048.228 0.881 330.681 146,422 15.587 -235 254 14 857 i 1122.812 0.895 172.546 148.911 14.719 -88 801 14 890 2 1166.382 0.239 211.348 16.823 15.008 -122 955 14 876 i 1223.634 0.807 329.553 132.997 15.537 -234 560 14 859 2 1298.312 0.969 171.629 162.209 14.691 -88 415 14 891 I 1338.377 0.340 193.709 41.516 14.954 -106.161 14 879 2 1399.040 0.734 328.198 119.516 15.487 -233.640 14860 I 1473.811 1.042 170.841 175.473 14.663 -88.160 14893 2 14.881 i 1512.068 0 431 186 092 61.113 14.913 -99.200 -232.413 14.861 2 1574 409 0 660 326 530 105.853 15.437 334 303 15.822 -236.729 14.850 i 1611 069 1 251 212.728 188.674 14.636 -87.973 14.894 i 1649 319 1 116 170 161 181 996 76.666 14.882 -95.622 14.882 2 1686 997 0 509 0 583 324 330 91.274 15.390 -230.692 14.863 i 1749 504 1 179 333 779 199.904 15.776 -236.581 14.852 2 1786 637 169 581 201 647 14.609 -87.672 14.896 2 1824 881 1 189 92 025 14.851 -93.136 14.883 i 1861 925 0 588 178 992 15.342 -228.304 14.864 2 1924 600 0.507 321464 76 558 186 971 15730 -236.398 14.853 I 1962 173 1.107 333.181 214 602 14 581 -87.439 14.897 i 2000 442 1,262 169.068 106 435 14 818 -91.472 14.885 2 2037.123 0,664 176.813 15 294 -224.837 14.866 I 2099.595 0,431 317.508 61 354 15 684 -236.151 14.854 2 2137.690 1,034 332.496 173 963 I 0,738 175.139 120 258 14 785 -90.309 14.887 2212.487 0 337 309.775 41 247 15 239 -217.757 14.868 2273.071 I 0 961 331.708 160.928 15 639 -235.800 14.856 2313.206 TABLE 3 CONTINUED PHIV M.R. PSI RADIUS T.R. PSI U THETAV GAMMA T.R. # 2387 850 0 813 173.771 134.009 14.752 -89.453 14 888 2446 547 0 253 296 548 21.060 15.184 -205.183 14 870 2488 691 0 888 330 785 147.772 15.592 -235.314 14 857 2563 266 0 888 172 647 147.570 14.721 -88.848 14 890 2607 188 0 230 213 926 14.492 15.013 -125.449 14876 2664 097 0 815 329 676 134.351 15.542 -234.639 14859 14891 2738.765 0 961 171 715 160.871 14.694 -88.448 14.879 2779.184 0.328 194 981 38.998 14.959 -107.348 14.860 2839.503 0.741 328 346 120.877 15.492 -233.745 TABLE 4. TAlL ROTOR BLADE-VORTEX INTERACTION UH-ID I00 KNOTS, LOWERED TAIL ROTOR M.R. PSI RADIUS T.R. PSI U THETAV PHIV GAMMA T.R. # 27 565 1.088 141 595 211.687 19.179 -58.128 11.860 i 54 738 0.514 103 671 137.105 19.211 -16.784 11.835 2 77 516 0.605 35 597 145.656 19.276 54.150 11.814 I 106 904 1.293 7 534 2 243.277 19.439 86.363 11.787 203 616 1.188 143 810 227.163 2 19.188 -60.737 11.864 231 803 0.555 Iii 133 140.759 19.211 -24.635 11.837 i 254.330 0.551 42 526 140.332 19.264 46.822 11.817 2 282.956 1.192 9 339 227.257 84.013 11.791 i 19.414 379.666 1.289 145 679 -62.999 11.868 I 243174 19.197 408.868 0.605 2 117 461 145766 19.211 -31.352 11.840 431.630 0.513 49 473 137 039 19.254 39.544 11.819 I 459.111 1.094 II 425 212 171 19.388 81.323 11.794 2 585.934 0.661 122 772 152 056 19.211 -37.052 11.842 I 608.930 0.483 57 393 134 853 19.244 31.291 11.822 2 635.265 0.998 13 917 197 694 19.362 78.228 11.798 i 762.545 0.732 127 846 160 775 19.205 -42.559 11.845 2 786.230 0.464 66 146 133 630 19.234 22.206 11.824 i 811.420 0.904 16 930 183 992 19.336 74.610 11.802 2 938.945 0.812 132 233 171 451 19196 -47.398 11.849 i 963.530 0.457 75 411 133 198 19224 12.608 11.827 2 987.890 0.822 20 337 172 382 19318 70.716 11.805 I 1115.344 0.897 135 812 183 281 19.187 -51.431 11.853 2 1140.830 0.462 84 734 133 465 19214 2.953 11.829 i 1164.544 0.746 24 279 162 428 19.304 66.353 11.808 2 1291.744 0.984 138 767 196 028 19.178 -54.838 11.856 i 1317.968 0.479 94 139 134 580 19.211 -6.823 11.832 2 1341.198 0.676 29 074 153 657 19.291 61.137 11.811 I 1467.963 1.078 141 349 210 162 19.178 -57.842 11.860 2 1495.033 0.510 102 855 136 811 19.211 -15.928 11.834 i 1517.853 0.611 34 938 146 309 19.277 54.852 11.814 2 1644.013 1.178 143 604 225 578 19.187 -60.491 11.864 i 1672.099 0.551 II0 434 140 329 19.211 -23.897 11.837 2 1694.602 0.555 41 881 140 728 19.265 47.501 11.816 i 1723.344 1.202 9 148 228 806 19.417 84.265 11.791 2 1820.064 1.279 145 504 241 540 19.196 -62.784 11.867 2 1849.164 0.600 116 872 145 202 19.211 -30.724 11.839 I 0.516 48.728 137 319 19.255 40.322 11.819 2 1871.902 213 665 19.391 81.611 11.794 I 1899.498 1.104 11.199 151 368 19 211 -36.520 11.842 2 2026.229 0.655 122.279 135 026 19 245 32.164 11.821 I 2049.202 0.486 56.554 199 121 19 364 78 561 Ii 798 2 2075.653 1.008 13.644 159775 19 206 -42 018 II 845 I 2202.908 0.724 127.351 65.234 133.715 19 235 23 151 ii 824 2 2226.502 0.466 185.331 19 338 75 003 ii 801 I 2251.807 0.914 16.599 2379.307 0.804 131.831 170.319 19 197 -46 951 Ii 849 2 2403.802 0.457 74.467 133.210 19 225 13 585 Ii 826 I 2428.227 0.829 19.980 173.442 19.319 71 115 Ii 805 2 TABLE 4 - CONTINUED M.R. PSI RADIUS T.R. PSI U THETAV PHIV GAMMA T.R. # 2555.707 0.888 135.482 182.044 19.188 -51 056 II 852 i 3 914 2581.102 0.461 83.806 133.406 19.215 Ii 829 2 2604.881 0.754 23.847 163.381 19.306 66 827 ii 807 i 2732.106 0.975 138.493 194.708 19.179 -54 519 ii 856 2 2758.263 0.477 93.204 134.420 19.211 -5 849 Ii 832 I 2781.535 0.683 28.546 154.481 19.292 61 707 II 810 2 TABLE 5. TAIL ROTOR BLADE-VORTEX INTERACTION UH-ID 80 KNOTS, LOWERED TAlL ROTOR M.R. PSI RADIUS T.R. PSI U THETAV PHIV GAMMA T.R. # 28 302 1 186 145 116 220.053 16.990 -62.489 13 133 i 59 068 0 581 123 063 129.149 17 103 -36.777 13 114 2 82 624 0 388 61 452 109.593 17 232 27.528 13099 i 108 368 0 759 14 507 153.067 17 433 78.032 13084 2 204 195 1 273 146 431 234.210 16 970 -64.144 13.135 2 235 454 0 644 127 730 137.332 17 084 -41.888 13.116 i 259 907 0 380 70 367 109.103 17 212 18.290 13.101 2 284 602 0 688 17 892 142.883 17 404 74.216 13 086 I 411 841 0 710 131 545 146.498 17 066 -46.148 13 118 2 437 189 0 381 79 458 109.188 17.193 8.875 13 103 I 461 273 0 627 21 565 134.751 17.377 70.031 13.088 13.071 I 492 384 1248 2 517 229 839 17.624 92.570 588.227 0.779 134696 156 453 17.047 -49.743 13.121 I 614.421 0.392 88440 109 880 17.174 -0.433 13.104 2 i 637.944 0.570 25.998 127 480 17 350 65 085 13.090 668.336 1.163 3.832 216 002 17 590 90 838 13.073 764.578 0.851 137 350 167 153 17 029 -52 845 13.123 13.106 I 791.443 0.413 97 347 IIi 466 17 161 -9 671 13 092 2 814.615 0.517 31 378 121.247 17 323 59 192 i 844.288 1.079 5 354 202.425 17 557 88 901 13 075 13 126 I 940.624 0.931 139 747 179.366 17 021 -55 713 968.466 0.444 105 197 114.060 17.147 -17 853 13 108 13 094 i 991.286 0.470 37 916 116.219 17.295 52 141 86 706 13 078 2 1020.240 0.996 7 132 189.172 17.523 -58 200 13 128 2 1116.671 1.012 141.763 192.052 17.012 111.927 117.738 17.133 -24.915 13 ii0 I 1145.488 0.482 17.273 44.772 13096 2 1168.332 0.434 44.888 112.940 13080 I 1196.402 0.918 9.100 176.989 17.494 84.320 13.130 i 1292 717 1.094 143.478 205.115 17.004 -60.387 -30.932 13111 2 1322 510 0.525 117.613 122.476 17.120 37.025 13098 I 1345615 0.408 52.312 110.906 17.253 81,581 13 082 2 1372 577 0.841 11.419 165.293 17.465 16.992 -62312 13.133 2 1468 716 1.178 144.973 218.640 128.388 17.105 -36206 13.113 I 1499 432 0.575 122.537 60.580 109.677 17.234 28,433 13.099 2 1522 898 0.390 14.197 154.153 17.436 78,384 13.084 I 1548.753 0.766 232.774 16.972 -63985 13.135 I 1644.609 1.264 146.307 17.086 -41415 13.116 2 1675.819 0.637 127.302 136.459 19 236 13.101 i 1700.180 0.380 69.453 109.126 17.214 74,602 13.086 2 1724.938 0.694 17.558 143.744 17.406 -45.752 13.118 I 1852.205 0.703 131.194 145.536 17.067 9.819 13.103 2 1877.463 0.380 78.547 109.154 17.195 17.379 70.484 13.088 i 1901.608 0.633 21.164 135.534 17.628 92.735 13.070 2 1932.792 1.257 2.394 231.246 -49.407 13.121 2 2028.591 0.772 134.404 155.419 17.049 0.547 13.104 i 2054.721 0.390 87.494 109.770 17.176 13.090 2 2078.280 0.576 25.511 128.169 17.352 65.623 TABLE 5 CONTINUED M.R. 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