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NASA Contractor Report 3727
NASA CR 3726- v.2 C.1
LOAN COPY: RETURN TO AFWL TECHNICAL LIBRARY KIRTLAND AFB, NM 87117
Helicopter Rotor Wake Geometry and Its Influence in Forward Fligh Volume II - Wake Geometry Charts
T. Alan Egolf and Anton J. Landgrebe
CONTRACT NASl-14568 OCTOBER 1983
25th Anniversary 1958-1983
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https://ntrs.nasa.gov/search.jsp?R=19840004023 2020-04-26T11:37:19+00:00Z
NASA Contractor Report 3727
TECH LIBRARY KAFB. NM
Helicopter Rotor Wake Geometry and Its Influence in Forward Flight Volume II - Wake Geometry Charts
T. Alan Egolf and Anton J. Landgrebe
United Technologies Research Center East Hartford, Connecticut
Prepared for Langley Research Center under Contract NASl-14568
National Aeronautics and Space Administration
Scientific and Technical lnformatlon Branch
1983
PREFACE
This investigation was sponsored by the Structures Directorate, U. S. Army Research and Technology Laboratories, Langley Research Center, Virginia, and administered by the National Aeronautics and Space Administration at Langley Research Center under Contract NASl-14568. The Army technical representative for this contract was Wayne R. Mantay. Henry E. Jones was the technical representative during the initial period of the contract. The Principal Investigator was T. Alan Egolf, Research Engineer, United Technologies Research Center (UTRC). The Program Manager and Co-investigator was Anton J. Landgrebe, Manager, Aeromechanics Research, UTRC. Donna Edwards, Engineering Assistant, UTRC, contributed significantly to the development of the computer graphics used to provide the wake charts presented herein.
This report consists of two volumes:
Volume I - Generalized Wake Geometry and Wake Effect on Rotor Airloads and Performance
Volume II - Wake Geometry Charts
iii
SUMMARY
Wake geometry charts and figures are presented which provide the necessary information to estimate the location of tip vortices trailed from helicopter rotor blades for a range of parameters representative of steady level forward flight. The charts are based on theoretical wake geometries from the classical undistorted wake equations and the generalized distorted wake equations described in Volume I. The charts can be used for a variety of applications which require the geometric relationship between the tip vortices and spatial locations relative to the helicopter. In addition to tip vortex geometry, the geometry related to blade/tip vortex interactions and wake boundaries beneath the rotor can be rapidly defined using these charts. An example application is included as an instructional tool for the use of the charts.
V
TABLE OF CONTENTS
Page
PREFACE................................ iii
SUMMARY................................ v
TABLEOFCONTENTS........................... vii
LIST OF SYMBOLS. . . . . . . . . . . . :. . . . . . . . . . . . . . . ix
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
WARE CHART DESCRIPTION . . . . . . . . . . . . . . . . . . . . . . . . 3
Isometric and Projection View Plots . . . . . . ......... 3 Inflow Ratio Nomographs . . . . . . . . . . . . ......... 4 Undistorted Axial Displacement Nomographs . . . ......... 5 Undistorted Longitudinal and Lateral Coordinates ......... 5 Generalized Axial Distortion Nomographs . . . . ......... 7 Blade/Vortex Passage Charts . . . . . . . . . . ......... 8 Blade/Vortex Intersection Angle Nomographs . . . ......... 8 Fore and Aft Wake Boundary Charts . . . . . . . ......... 9
SAMPLE APPLICATION OF THE WAKE CHARTS . . . . . . . . . . . . . . . . . 11
Example Condition ........................ 11 Inflow Ratio ........................... 11 Undistorted Axial Location ................... 12 Longitudinal and Lateral Coordinates ............... 12 Axial Coordinate Distortions ................... 13 Blade/Tip Vortex Intersections .................. 14 Angle of Intersection ...................... 15 Fore and Aft Wake Boundaries ................... 15
FIGURES
vii
LIST OF SYMBOLS
b
GT
Ef
Gf
PR
Y
2
aTPP
8
AZ
'TPP
lJ
?lPP
lr
Number of rotor blades, dimensionless
Rotor thrust coefficient, dimensionless: T prRzL(GR)2
Generalized wake envelope function, nondimensional
Generalized wake shape function, nondimensional
Functional notation defining the operation of taking the positive residual of the specified quantity.
Rotor radius, dimensional
Rotor thrust, dimensional
Rotor flight speed, dimensional
Longitudinal coordinate in the tip path plane, dimensional - Eq. 3
Lateral coordinate in the tip path plane, dimensional - Eq. 4
Axial coordinate in the tip path plane, dimensional - Eq. 2 or Eq. 6
Rotor disk attitude in tip path plane, degrees
Angle of intersection between blade and tip vortex based on tip path plane plan view projection, degrees
Axial coordinate distortion, dimensional,Eq. 7
Rotor inflow ratio in tip path plane, Eq. 1
Rotor advance ratio, &
Tip path plane advance ratio, ucos oTpp
Pi, 3.1415926...
ix
LIST OF SYMBOLS (Cont'd)
P
J, age
*b
$0
T
QR
Air density, dimensional, slugsIft
Wake azimuth position or wake age, azimuth angle of vortex element (point on tip vortex) relative to the blade from which it originated; represents the blade azimuth travel between the time the vortex element was shed by the blade and the current blade azimuth, deg or rad
Azimuth position of the blade from which the tip filament is trailed, degrees or radians
Reference blade azimuth position, degrees
Positive residual of the relative wake azimuth position as defined by Eq. 5, degrees or radians
Rotor tip speed, dimensional
X
INTRODUCTION
The intent of this volume is to provide wake geometry data in the form of easily usable charts and figures which allow for the rapid estimation of the geometric position of the tip vortex of a specific rotor blade at any instant in time (blade azimuth). This information can then be used to determine the potential for rotor blade/tip vortex interactions and other spatial point/tip vortex interactions through comparison of the relative geometric position of the point of interest and the tip vortex position. These charts and figures provide this information based on both undistorted wake methodology and the generalized distorted tip vortex model developed and discussed in Volume I of this report. The charts and figures are presented progressing from the elementary to the more complex model. The charts consist of isometric and projection views of wake geometry, inflow ratio nomographs, undistorted axial displacement nomographs, undistorted, generalized longitudinal and lateral coordinate charts, generalized axial distortion nomographs, blade/vortex passage charts, blade/vortex intersection angle nomographs and fore and aft wake boundary charts . These charts and figures have been prepared as func- tions of the parameters found to be of primary interest in the first level wake generalization as described in Volume I of this report. The range of these parameters for most of the charts and figures is listed below.
Thrust Coefficient: 0.0025 < CT < .ol
Rotor Disk Attitude: -16” IC’TpPF 4’
Advance Ratio: 0 < u < 0.5
Number of Blades: 2 <b < 6
The charts are presented in a format which allows for the rapid estima- tion of the geometric positions of the tip vortex. They were developed such that they require only a minimum amount of hand calculations to obtain the desired information. All coordinate values on the charts are normalized by the rotor radius and are in a right handed tip path plane coordinate system. This coordinate system is illustrated in Fig. 1. Figures 2 to 10 are presented as an introduction to the wake charts and their application. These figures illustrate the variety and use of the wake charts that have been developed by way of an example application.
WARE CHART DESCRIPTION
Isometric and Projection View Plots
To provide for the fundamental understanding of the wake and its parametric variations and to provide a realistic pictorial wake representation which complements the wake information to follow, isometric and projection view plots of both the undistorted and distorted wake geometries for selected conditions are presented. These plots will give the wake chart user a physical feeling of the output from the two dimensional wake charts that follow in relation to the actual three dimensional wake geometry. All of the figures presented in this section will contain the standard projection views (top, side, and rear) and an isometric view. They are presented as functions of blade number, thrust level, tip path plane attitude, advance ratio, and blade azimuth position.
Figure 11 presents the effect of advance ratio on the wake geometry of a four bladed configuration for the undistorted wake model. The variation in advance ratio changes the inflow ratio for the condition selected (CT = .005,
%-PP = -2.0 deg). This effect results in both an axial and longitudinal variation in the wake geometry with increasing advance ratio, as seen in Fig. 11.
Figure 12 presents the effect of thrust level on the wake geometry of a two bladed configuration for the undistorted wake model. The influence of thrust level is limited to changes in the axial coordinate as seen in this figure. Higher thrust creates a larger inflow, and thus, a larger axial displacement from the rotor tip path plane. Figure 13 presents the effect of tip path plane attitude on the wake geometry of a two bladed configuration for an undistorted wake model. Changes in rotor tip path plane attitude with the other parameters held constant result in changes in both axial and longitu- dinal coordinates since the definition used for the rotor advance ratio does not include the cos oTpp term. The strongest influence of increasing (nega- tively) the tip path plane attitude is to displace the wake in an axially increasing (negative) direction. The effect of wake distortions as modeled by the generalized distorted tip vortex model is presented in Fig. 14 for the same conditions as presented in Fig. 12. As seen frcrm the comparison of the undistorted and distorted wake geometries presented in these two figures, the effect of the distortions is a tendency for the tip vortex to rollup on the lateral edges of the wake. The increase in thrust level (Fig. 14~) is seen also to result in larger wake distortions from the comparatively undistorted position at the lower thrust level (Fig. 14a). The effect of wake distortion with changes in tip path plane attitude can be seen in a comparison of Fig. 15, the distorted wake model, with Fig. 13, the undistorted model.
3
Figure 16 presents the effect of advance ratio on the distorted wake geometries for the same conditions presented in Fig. 11. A comparison of these two figures shows the influence of the distorted wake model on the tip vortex geometry for changes in advance ratio. The effect of increasing advance ratio is seen to change the character of the wake distortions. This effect is better demonstrated in a following section on the generalized wake shape function. Figure 17 presents the specific condition presented in Fig. llc for incremental values of the blade azimuth position using the distorted tip vortex model. From this figure, the variation of the wake geometry with blade azimuth position can be seen. A careful study of the plots of wake geometries presented in Figs. 11 to 17 should yield significant insight into the three dimensional representation of the tip vortex as modeled by either the undistorted or distorted wake models. This insight will be helpful in understanding the use of the following wake charts.
Inflow Ratio Nomographs
The first set of nomographic charts (Fig. 18) are used to determine the rotor tip path plane inflow ratio (XTPP ) to define the axial displacement of the rotor wake. The inflow ratio is defined by momentum considerations in the tip path plane as a function of the rotor thrust coefficient (defined in the conventional sense, (CT>>, the rotor advance ratio cl.11 defined as the ratio of the rotor flight speed to rotor tip speed, and the rotor tip path plane angle (negative nose down, aTPP). Given these parameters, the rotor inflow ratio can be determined quickly by graphical means from these charts, or by finding the first positive root (XTPP > of the following relationship
%PP = CT
psin OTPP - T-- I -l/2 (IJCOS ?pp)
2 + 'TPP2 1 (1)
These charts are presented in terms of the tip path plane inflow ratio as a function of the tip path plane rotor advance ratio (pcos uTpp) from 0 to .5 and the thrust coefficient (CT) from 0.0 to .OlO for two degree incremental values of the tip path plane angle from -16 to 4 degrees. This range of values should be adequate for mst conventional rotorcraft.
4
Undistorted Axial Displacement Nomographs
Once the tip path plane inflow ratio is known, the classical undistorted axial (normal) displacement of any tip vortex can be found. Figure 19 provides nomographic charts which are used to determine this normalized axial displacement of the tip vortex as functions of wake age and inflow.ratio. The wake age is defined as the azimuthal variation in time from the instant in time that the filament is trailed off the blade to its current position in time. Zero wake age is thus physically referenced to the blade tip (quarter chord1 ine) .
Z/R - ‘TPP *age (2)
The axial displacement referenced to the tip path plane is normalized by the blade radius and is plotted for four revolutions of wake age (1400 degrees) in Parts I and II of Fig. 19. The third part of this figure is a table of the normalized axial displacement versus inflow ratio for integer multiples of 360 degrees of wake age. With this table, and the graphs of Parts I and II, the axial displacement can be found for any wake age by the appropriate addition of the axial displacement for integer multiples of 360 degrees of wake age and .the displacement for the positive fractional remainder of the wake age for the condition of interest. Note that the variation of this displacement is linear in terms of either the inflow ratio or the wake age.
Undistorted Longitudinal and Lateral Coordinate
The axial displacement by itself does not allow for the determination of the relative distance between a point of interest and the tip vortex in three dimens ional space. The longitudinal and lateral positions of the tip vortex are also necessary to determine the relative geometry. As noted in Volume I of this report, the longitudinal and lateral positions are not highly
distorted from the undistorted helicoidal shape. Thus, the first order approximation to these coordinate positions can be simply determined by the use of the undistorted equations in the tip path plane.
X/R = COS ($B - *age) + Was DTPP *age
Y/R = sin ($B - $,,,I
(3)
(4)
5
. To avoid the necessity of calculating these functions to obtain the
coordinate values, the charts in Figs. 20 and 21 are provided. These charts present the data as functions of the wake age, the blade azimuth position of the blade from which the wake is trailing (I@, and the rotor advance ratio in the tip path plane ( uTRp = ucos aTRp) . Figure 20 provides sufficient information to determine the longitudinal position of the tip vortex. This figure has .two parts, corresponding to the cyclic and steady terms in the above equation for the longitudinal term (X/R). The steady part is determined in a manner similar to the method for axial displacement and is linear with wake age. The table in Fig. 20a provides for the determination of the steady longitudinal displacement for integer multiples of 360 degrees of wake age for various tip path plane advance ratios. The steady longitudinal displacement for the positive fractional remainder of the wake age for a given condition is obtained graphically from the nomograph of displacement versus wake age, presented in the graphic part of Fig. 20a as a function of the appropriate tip path plane advance ratio. The addition of these two displacements results in the total steady longitudinal coordinate for a given tip path plane advance ratio and wake age. The cyclic portion is obtained by the use of the second portion of this figure (Fig. 20b). This figure presents the cyclic portion of the longitudinal coordinate as a function of the positive residual of the relative wake azimuth position ($1. The relative wake azimuth position is defined as the difference between the instantaneous blade azimuth position from which the filament is trailing ($b) and the local wake age ($,,,I of interest of the actual filament. The positive residual (3) is defined as the remaining positive value after subtracting the largest integer multiple of 360 degrees which does not yield a negative fraction.
;G = PR [$, - $,,,I (5)
It can be seen that this figure is simply a plot of the cosine function versus a reference angular position <;G). For a given blade azimuth position ($b) from which a tip filament trails, interest,
and a particular wake age ($,,,) of the cyclic longitudinal position can then be obtained fran this
plot. The addition of the steady and cyclic portions results in the total longitudinal displacement of the tip vortex filament as a function of blade azimuth position, wake age and tip path plane advance ratio.
The lateral coordinate of the tip vortex is found by the use of the information presented in Fig. 21. Again, the positive residual of the relative blade wake azimuth position is used and the cyclic lateral position of the tip vortex is obtained from the plot for the particular combination of parameters of interest. These charts .provide sufficient. informat ion to quickly determine the location of an undistorted tip vortex with respect to the rotor tip path plane based on rotor momentum transport concepts.
6
Generalized Axial Distortion Nomographs
As noted in Volume I of this report, the actual tip vortex does not follow the trajectory of the undistorted momentum wake. Thus, the use of the axial distortions based on momentum definitions will not accurately define the potential for strong close blade/vortex interactions. As an improvement to the estimate of this potential based on the undistorted wake, the generalized distorted wake model can be used. However, the complex nature of the relationships used in this model requires the use of somewhat more complex wake charts. It should also be noted that the wake charts provided for this model provide only an approximation to the actual wake geometry and that the use of the charts must be made with this understanding. Because it is only an approximation, the results obtained should be used only as an indicator of potential blade/vortex interactions, and not as an accurate measure of the relative distance between the blade (or field point) of interest. The generalized wake coordinates for a tip vortex are comprised of two parts, one of which is the undistorted wake position (Fig. 19) already described. Thus, it is only necessary to present the additional axial distortions from this momentum wake position
Z/R = ‘TPP ‘#age + AZ/R*
The distortions from the momentum wake position (AZ/R) are modeled by the combination of an envelope function (Ef) and a geometric shape function (Gf).
AZ/R = Ef l Gf (7)
The exact expressions are presented in Volume I of this report and are func- tions of advance ratio, thrust level, blade number, blade azimuth position and wake age. Figures 22 through 25 present these functions as nomographic plots for the range in parameters for which they were developed. Figures 22 and 23 present the envelope function for 2 and 4 blades respectively at advance ratios of .05, .l, .15, .2, and .3, and for thrust coefficients of .0025 to .0075. Figures 24 and 25 present the generalized shape functions for 2 and 4 blades respectively for the same variation in parameters. Again, graphical means are used to obtain the appropriate values for these functions from the charts for the particular set of parameters of interest. The multiplication of these two values (Eq. 7) results in the axial displacement from the momentum wake position for the tip vortex. This value is then combined with the momentum wake position to define the axial position of the tip vortex (Eq. 6). With this information, an improved estimate can be made for the determination of the potential for close blade/vortex interaction.
7
Blade/Vortex Passage Charts
As noted earlier, the charts presented herein can be used to determine the relative position between a point in space and the tip vortex for any given time increment. The determination of the potential for a blade/tip vortex interaction to exist using these charts by themselves would be a tedious, time consuming task. To alleviate this tedious effort, the next set of charts was developed to simplify this task. These charts present the occurrence of an intersection of a rotor blade with the tip vortex of any of the blades of the rotor for a given tip path plane advance ratio. They are based only on the inplane projection of the longitudinal and lateral coordinates of the tip vortices and the intersection of the rotor blade of interest. The charts are presented in polar coordinate form where the axes represent the radial and azimuthal position of the blade of interest. These plots do not represent wake geometries, only the potential occurrence of an intersect ion. The occurrence of an intersection is represented by the solid lines and symbols. Superimposed at selected locations on these curves which correspond to the intersection occurrences are the wake ages for up to four revolutions of wake age (1440 degrees). Since these intersections are based on the projections of the tip vortices into the tip path plane, they do not recognize the axial displacement between the blade and vortex intersection of interest. However, the axial displacement for a potential intersection can be quickly obtained from the charts presented earlier if the thrust level, wake age, and rotor attitude are known (Figs. 18 and 19 and 22 through 25). Thus, the rapid determination for the potential for close blade/vortex interactions can be determined from these charts based on axially distorted wake considera- tions. These intersection plots are presented in polar coordinate format in Figs. 26 through 30 for two (2) through six (6) blades respectively as func- tions of the tip path plane advance ratios of .05, .l, .15, .2, .3 and .4. In addition, these results are also presented in rectilinear format, without the wake age indicated, on the plots in Figs. 31 and 32 for two (2) and four (4) blades respectively.
Blade/Vortex Intersection Angle Nomographs
The next set of charts, presented in Fig. 33, provides additional information about the intersections presented in Figs. 26 through 32. These charts provide the angle of intersection (8) of a potential blade/tip vortex intersection for the tip path plane advance ratios of .05, .l , .15, .2, .3 and .4. If the reference blade azimuth position (q,), wake age at the point of intersection (JI,,,), azimuthal position of the blade trailing the tip vortex (+b)r and the tip path plane advance ratio (ucos oTpp) are known, the angle of intersection can be obtained graphically from this figure. If the blade angle (JI,) is greater than 180 degrees, the .value for use with the chart must be reduced by 180 degrees. This is because of the periodicity of the solution
8
for multiples of 180 degrees of blade azimuth angle position. This angle of intersection information can be useful in determining the nature of the inter- sect ion; for example, a normal or parallel encounter.
Fore and Aft Wake Boundary Charts
The information provided in the axial distortion charts (Figs. 19 and 22 through 25) can also be used to define fore and aft wake boundary information. However, to expedite this task, a set of wake boundary charts has been provided in Figs. 34 through 50. The use of these charts can be helpful in the determination of rotor/empennage/stores/body interactions beneath the rotor disk. In Fig. 34, the fore and aft wake boundary charts are presented based on the undistorted axial wake model. These boundaries are functions of the rotor attitude, inflow rotor and advance ratio. The lines representing the fore and aft boundaries for the zero lateral position (Y/R=O) along the centerline of the outer disk are presented in these charts. The use of the lateral position indicators provided in these charts also allows for the determination of the fore and aft boundaries for non-zero lateral positions by the appropriate parallel translation of the fore and aft reference lines to the appropriate lateral reference position. This procedure will be discussed in the example application section which follows.
In Figs. 35 through 50 the fore and aft boundaries based on the general- ized distorted wake model are provided for various selected lateral positions, thrust levels, advance ratios, tip path plane attitudes, and two and four blades. A selection is necessary because the axial displacement based on the generalized distorted wake model must be determined numerically for each lateral position and would result in a very large number of plots. Careful examination of these selected charts indicates that the wake boundaries compress as the vertical and longitudinal sectional plane is moved in the lateral direction (advancing or retreating) toward the rotor tips. This is due to the wake rollup. It should also be noted that at the rotor centerline the distortions displace the wake toward the rotor.
The range of parameters is limited in scope due to the previously noted reason. Hopefully the selected range is sufficient for general applications and will give the user a “feel” for the distortion influence.
9
SAMPLE APPLICATION OF THE WARE CHARTS
Example Condition
An example of the use of the provided charts is demonstrated for a fictitious aircraft operating at a prescribed flight condition. In this example, the objective is to determine whether or not a tip vortex passes close to a blade at 160 degrees azimuth. The parameters and the values for this example which are necessary for the use of these charts are:
Blade radius 20 ft Blade number (b) 4 Thrust Coefficient (CT> .0075 Tip path plane attitude -3' QR 700 fps V 161 fps Advance ratio, IJ .23 Blade azimuth position, $B 160"
The tip path plane advance ratio is calculated as
PTPP = ucos %pp = 0.23
Inflow Ratio
The tip path plane inflow ratio (XTpp > for this particular condition is found by graphical means from Figs. 18g and 18h. This technique is demon- strated in Fig. 2, and the value obtained is approximately -.0283. An exact calculation for the inflow rotor to five places would yield -.02822 for this condition. This corresponds to a momentum induced velocity for the condition of 11.3 fps, using the relationship noted below.
-l/2 v* imom = + CT ($,p2)
11
Undistorted Axial Locat ion
With the above value for the tip path plane inflow ratio, the undistorted axial displacement of a tip vortex can be found using Fig. 19. To illustrate this procedure, consider a rotor blade’s relationship to the tip vortex trailed from the preceding blade (one of four). For this condition, the blade azimuthal spacing is 90 degrees (360*/b). Thus, the wake age is approximately 90 degrees. From Fig. 19, Part I, the axial displacement for 90 degrees wake age is found by graphical means. This procedure is demonstrated in Fig. 3 for two methods, one of which allows for an increased graphical accuracy. For this condition, the displacement is found to be about -.0425 R using the more accurate method. The exact value is -.044328 R. This represents a relatively close blade/vortex interaction. For example, if the magnitude of the induced velocity of such an encounter can be modeled for first order accuracy by a straight infinite vortex with circulation strength of 250 ft2/sec, not an unreasonable value for this aircraft, the induced velocity using the Biot- Savart law for an infinite vortex filament would be about 45 fps.
‘i : I- 1= 250 = 45.2 2nR h 2n*20*( .044)
This corresponds to four (4) times the momentum value for this condition. At the azimuthal position of 160 degrees at the .75 R radial location, this could represent a significant change in the induced angle of attack compared with that predicted based on the momentum value. As a result of this study, it is seen that a blade vortex interaction of potential significance could occur.
Longitudinal and Lateral Coordinates
Consider now that the preceding blade is at an azimuthal position ($I~) of 250 degrees for the above example, the longitudinal and lateral positions of the tip vortex shed from this blade near the reference blade of interest
= 160”) can approximately be found by the use of Figs. 20 and 21. Since fh”: approximate wake age ($ . ) in this example is known to be about 90 degrees for the close inter%ion noted above, the relative wake azimuth position (T) is simply 160”.
12
T p PR [$b - $,,,I = 250 - 90 m i60
From Fig. 20, Part I, the steady longitudinal component based on the wake age (90') is found to be .37 R. From Fig. 20, Part II, the cyclic portion based on the relative wake age position (3 = 160') is found to be -.93 R. The total of these two values results in a longitudinal coordinate of -.56 R. This technique is demonstrated in Fig. 4. The lateral coordinate is found from Fig. 21 in a manner similar to the cyclic portion of the longitudinal coordinate as shown in Fig. 5. The value obtained for the lateral coordinate is .34 R. The resulting undistorted coordinates for the tip vortex near the following blade at 160" for this condition are then:
Graphical Exact
X/R = -.56 -.57841 Y/R = .34 .34202 Z/R = -.043 -.04432
Axial Coordinate Distortions
Since it is known that the actual tip vortices trailed by the rotor blades can undergo significant axial distortions, the occurrence of such distortions should be considered when studying close blade/vortex interaction. In order to provide additional insight into this problem, the use of the UTRC Generalized Wake Model can be used to further refine the axial displacement. Figures 22 and 24, and 23 and 25, for two and four blades respectively, present the generalized wake modeling functions for a range of advance ratios and thrust loads. For the example condition, the envelope function, Ef, is 'I found by graphical means from Figs. 23d and 23e to be .035. This procedure is illustrated in Fig. 6. The generalized shape function, Gf, for this condi- tion is also found by graphical means from Fig. 25 to be .90. This procedure is illustrated in Fig. 7. The multiplication of these values results in the distortion, AZ/R, from the undistorted wake model.
AZ/R = Ef l Gf = .0350 x .90 = .0315
13
The addition of the undistorted and distorted displacement values results in the generalized wake distortion model value for the condition of interest,
‘JO = 160’,
‘Cb = 250”,
‘4 age = go”,
PTPP = .23,
XTpp = -.0283.
Z/R = +pp $age + AZ/R = -.043 + .0315 = -.0115
This value for the axial displacement places the tip vortex very near the rotor tip path plane for this condition. The implication of this result is that there is a very strong potential for a close blade/tip vortex interaction to occur. It should be noted that the exact wake age was not used, only an approximate value ( $Jage = 90”). The exact value will be obtained in the next section.
Blade/Tip Vortex Intersections
For the example condition, it has been shown that there is the potential for a blade vortex interaction to be occurring based on the tip vortex trailed from the preceding blade. The potential for blade/tip vortex intersections can quickly be determined for any azimuthal position due to any tip vortex by the use of Figs. 26 to 32. For the example condition, Figs. 28d and 28e are used to determine the desired information using graphical interpolation techniques. This procedure is illustrated in Fig. 8. The radial position of the blade at 160 degrees, which intersects the tip filament trailed by the preceding blade, is found to be about .68 R and the actual wake age noted at discrete intervals on the intersection curves is determined graphically to be about 84 degrees. For this wake age the exact value for the radial coordinate is .6781 R. This information could have been obtained from Figs. 32d and 32e which present the same information in a rectilinear format. With this more exact value for the wake age, a slightly more exact value for the axial displacement of the tip vortex can be found by repeating the above procedures.
14
These blade/vortex intersection plots (Figs. 26 to 32) are of significant value if the user is basically interested in only tip vortex intersections. By first using these figures to determine if any intersection is possible from
. a plan vrew projection basis, the axial position can be rapidly determined by the use of Fig. 18 for the inflow ratio, Fig. 19 for the undistorted axial displacement, and if desired, Figs. 22 to 25 for the generalized wake distor- tions. The longitudinal and lateral coordinates for the intersection point are determined graphically from Figs. ‘20 and 21, or by the use of the trigonometric relationships between polar and Cartesian coordinates, since the radial and azimuthal coordinates (polar) are now known from Figs. 26 to 32.
Angle of Intersection
Figure 33 can be used to obtain the relative angle of intersection between the blade and tip vortex for a plan view intersection obtained from the blade/tip vortex intersection plots. For the example condition, Fig. 9 illustrates this procedure, and the angle of intersection is found to be about 90 degrees. Note that 180 or 0 degrees represents a parallel blade/vortex encounter. As a further note, if the blade angle (I),) is greater than 180 degrees, the value should be reduced by 180 degrees for use on the chart as noted in the earlier section describing this type of chart.
Fore and Aft Wake Boundaries
Now assume that the wake boundary defined by the passage of the tip vortices beneath the rotor is of interest. For instance, the geometric relationship between the launch point location of rocket stores and the rotor wake boundary of an attack helicopter might be of importance because the strong downwash of the wake could influence the rocket trajectory. For this example, the wake boundary location is significant for low speed rocket firings, since the downwash can strongly affect the accuracy of the rocket. Assume for illustrative purposes that a rocket launcher is located in the tip path plane coordinate system .4 R beneath the rotor, .05 R ahead of the hub center, and displaced laterally on the advancing side by .5 R. For this example flight condition, the undistorted fore and aft wake boundaries can be determined using Fig. 34~. Figure 10 illustrates this procedure for the determination of the position of the wake boundary relative to the rocket launch locat ion. In this particular example, the results obtained in Fig. 10 indicate that there is no intersection of the rocket launch point, or trajectory with the wake boundary.
The wake boundaries are, in reality, changed due to the actual wake distortions. The approximate boundaries can be found for selected conditions by the use of Figs. 35 to 50. For the above example of a rocket launch point, the distorted wake boundaries can be found using a similar procedure (Fig. 5oc).
15
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3 an
d C
+ -
.007
5
the
inflo
w
ratio
fo
r a
-4’
tip
path
pl
ane
is
foun
d by
gr
aphi
cal
mea
ns
to
be
-.032
5.
0 B Fo
r vT
PP
a .2
3 an
d I+
0
.00?
5
the
inflo
w
ratio
fo
r a
-2’
tip
path
pl
ane
is
foun
d by
gr
aphi
cal
mea
ns
to
be
-.024
0,
0 C Si
nce
the
desi
red
valu
e is
fo
a
tip
path
pl
ane
of
-3’,
the
aver
age
of
the
two
valu
es
can
be
used
.
A~,,,
, l
(-.03
25
+ -.0
240)
/
2
l -.0
2R3
FIG
UR
E 2.
EX
AMI'L
E U
SE
OF
THE
INFL
OW
R
ATIO
N
OM
OG
RAP
IIS
QXI
AL
DIS
PLAC
EMEN
T O
f TI
P VO
RTE
X FI
LRH
ENT
F-R
OM
RLA
O~
TIP
PRTH
Pz
LFIN
E FI
S A
FUN
CTI
ON
O
F W
FIKE
FlG
b R
N0
INFL
OW
R
ATIO
.-
PRR
T I
d B d d
INFL
OY
RR
110
VALU
ES
Z/R
-
-0.3
4
, In
form
atio
n D
esire
d 1
Und
isto
rted
axia
l di
spla
cem
ent
Inst
ruct
ions
@
Det
erm
ine
Z/R
by
grap
hica
l in
terp
olat
ion
for
A -
-.028
3 at
+ ag
e of
9o
".
Z/R
Q -
0.04
@
Det
erm
ine
Z/R
by
grap
hica
l in
terp
olat
ion
for
A =
-.028
3 at
a
larg
er
* age
(72
0')
and
divi
de
answ
er b
y ap
prop
riate
va
lue
to
obta
in
mor
e ac
cura
te
estim
ate.
Z/R
(72
0)
- -0
.34
Div
ide
by 8
Z/
R
(90)
-
-0.0
425
FIG
UR
E 3.
EX
AMPL
E USE
OF
THE
AXIA
L D
ISPL
ACEM
ENT C
llhl?
T
MIK
E AG
E.+A
GE
CEN
E44L
!ZEO
LO
NG
ITU
OIN
RL
CO
OQ
OIY
R'E
rti
RQ
1
Info
rmat
ion
Des
ired
Long
itudi
nal
coor
dina
te,
X/R
whi
ch
the
tip
vorte
x tra
ils
($B)
Inst
ruct
io
ns
@
By
grap
hica
l m
eans
th
e st
eady
lo
ngitu
dina
l co
mpo
nent
is
fo
und
for
a gi
ven
pTpp
(.2
3)
and
&age
(9
OO
). X/
RS
- .3
6
@
By
grap
htca
l m
eans
th
e cy
clic
long
itudi
nal
com
pone
nt
is
foun
d fo
r th
e re
lativ
e w
ake
azim
uth
posi
tion
5 .
3-
PR
/tiB
- Ib
ag
1
i6-
PR
(250
-
90 T
- 16
0
X/R
C
- -.9
3
@
X/R
=
xlR
s +
xl%
=
-.56
FIG
UR
E 4.
EX
AMPL
E U
SE O
F Tl
IE C
EWER
ALIZ
ED LO
NG
ITU
DIN
AL C
OO
RD
INAT
E CH
ART
GEN
ERR
LIZE
O
LFIT
ERFI
L C
OO
RO
JNftT
E C
HAR
T
Y/R
*
0.34
R
io .o
o R
ELAT
IVE
WAK
E AZ
IMU
TH
PtlS
JTIO
N’,3
u PO
SJTI
VE
RES
IDU
AL
OF
RU
LTlP
LES
OF
360
DEC
REE
S
Info
rmat
ion
Des
ired
Late
ral
coor
dina
te
Info
rmat
ion
Req
uire
d
Rel
ativ
e w
ake
azim
uth
posi
tion,
II
@
By g
raph
ical
m
eans
, th
e
late
ral
coor
dina
te
for
the
rela
tive
wak
e az
imut
h po
sitio
n (&
- 16
0)
is
foun
d?
Y/R
-
0.34
’ *S
ee
Figu
re
4.
FIG
UR
E 5.
EX
AMPL
E U
SE O
F TH
E G
ENER
ALIZ
ED
LATE
RAL
C
OO
RD
INAT
E C
HAR
T
ENVE
LOPE
FU
NC
TIO
N
BLR
Ot3
=4.
rwro
.2
0
WR
KE A
GE
WR
KE R
CE
ENVE
LOPE
FU
NC
TIO
Y BL
9OES
z4.
PkO
.30
WAK
E R
CE
(Qp1
- 0.
030
l O
;“:”
1 0:
” (0
.23
- 0.
2)
- 0.
035
Info
rutio
n D
esire
d
Enve
lope
fu
nctio
n fo
r
l pe
rticu
ler
thru
mt
and
ukc
egc.
I In
form
erio
n R
equi
red
Thru
st
coef
ficie
nt
(Cf>
, w
ake
sgc
(1’.
e),
num
ber
of
bled
es
(b P
, an
d l l
vmcc
ratio
(p
-
Inst
ruct
ionr
@
Inte
rpol
ate
by
srap
hice
l m
eans
on
th
e th
rurt
leve
l (5
-
.007
5).
wak
e ag
e (+
. c
- 90
0),
blad
e
num
ber
(b
- f)
, an
d ad
vanc
e
ratio
(c
- .2
).
$ -
.038
@
Inte
rpol
ete
by
grap
hica
l m
ens
on
the
thN
It le
vel
(5
-.m75
).
wak
e r8
c (1
’. l
- 90
0),
blad
e nu
mbe
r (b
-
b ,
and
adva
nce
ratio
(~
0 .3
).
@
Usi
ng
linea
r in
terp
olat
ion
in
the
edva
nce
ratio
(c
-
.23)
an
d
enve
lope
fu
nctio
nr
foun
d in
A
end
B,
ths
l ctu
el
enve
lope
fu
nctio
n ir
foun
d.
4 -
.035
FIG
UR
E 6.
EX
AMPL
E U
SE O
F Tl
lE
GEN
ERAL
IZED
WAK
E EN
VELO
PE FU
NC
TIO
N C
HAR
T
4 C
HAR
ACTE
RJS
TJC
H
AKE
1-
BLR
OES
-4
SHR
PE
FUN
CTI
ON
2N0
RH
O A
LL
SUBS
LOU
ENT
REV
S M
IKE
RG
E
-
Info
rmat
ion
Req
uire
d
I Rot
or
adva
nce
ratio
(c
- $
0,
wak
e ag
e (ti
age)
, an
d nu
mbe
r of
I
blad
es.
-
Inst
ruct
ions
@
For
the
sele
cted
w
ake
age
(IGgg
e - 90
0),
the
shap
e fu
nctio
n (G
F) i
s fo
und
by g
raph
ical
in
terp
olat
ion
betw
een
the
adva
nce
ratio
s w
hich
bo
und
the
actu
al
valu
e (p
= .
23).
I G
F =
.90
FIG
UR
E 7.
EX
AMPL
E USE
OF
THE
GEN
ERAL
IZED
WAK
E SH
APE
FUN
CTI
ON
CH
ART
‘b t .W
=1
. .
*b
t .a
* r1
90 ~
~VFW
IHC
sln
t
- .6
FIG
UR
E 8.
EX
AMPL
E U
SE O
F TH
E BL
ADE/
TIP
VOR
TEX
INTE
RSE
CTI
ON
PLO
TS
RN
GLE
O
F IN
lER
SEC
TlO
N
CH
RR
T R
OVR
NC
E R
ATIO
z
0.20
. Pl
‘l,llI
“II
IMI
0,
rrmrrr
,LS
64 3
.0 B
LCIL
LS
RN
OLE
O
F IN
TER
SEC
TIO
N
CH
ART
RO
VRN
CE
RAT
IO
z 0.
30
REL
@
P -
98
+ 1;
; 1
‘; (.2
3 -
.2)
- 99
.2
Info
rmtio
n D
ealre
d
Angl
e of
in
tcrrc
ctio
n I
Info
rmat
ion
Req
uire
d
Tip
path
pl
ane
adva
nce
ratio
, (P
C-&
I
refe
renc
e bl
ade
azim
uth
porit
ion
(tc,),
an
d bl
ade
azim
uth p
oriti
on
from
uh
ich
tip
filam
ent
treilr
(Q
.
Inrtr
uctio
nr
@
The p
oriti
ve
rerid
ual
of
the
rela
tive
wak
e az
imut
h po
ritio
n (ti
B -
3;
c -
250
- 84
-
166)
on
th
e bo
un Ii ing
ad
vanc
e ra
tio
(p-
.2)
ir de
term
ined
, an
d th
e an
gle
of
inte
rrect
ion
(fl)
ir fo
und
b,-
grap
hica
l m
eam
fo
r th
e #e
lect
ed
refe
renc
e bl
ade
l rim
th
porit
ion
(to
- 16
0).
8'
98O
@
Whi
r pr
oced
ure
18 r
epea
ted
for
the
othe
r bo
undi
ng
adva
nce
ratio
(P
- .3
) to
de
tem
ine
the
corre
rpon
ding
an
gle
of
inte
rrect
ion.
b l
102O
@
The
angl
e of
in
terre
ctim
fo
r th
e ec
tum
l ad
vanc
e ra
tio
(c-
.23)
is
th
en
dete
rmin
ed
by
inte
rpol
atio
n.
p 8
99.2
O
FIG
UR
E 9.
EX
AMPL
E U
SE
OF
THE
ANG
LE
OF
INTE
RSE
CTI
ON
C
IIAR
T
?Fl!!O 5 0.20
'(If60
0.020 0.015 0.010 0 .oos -0 CO
-0 .G05 -0 -010 -0.015 -0 .G20 IiT -&23 -0 .G30 '-iI 333 -0 .G40 -0 c45 -c G50 -0 G55 -0 .C60 -0 G65 -0 -t70 -0 .G75 -KG60
-5.711 -4.269
1: :::; 0 coo I .432 2 ,862 4.269
-++g
8 53i - P.Vs-6
11.310 12.660 lI.C36 15.376 16.699 18 .GO4 19.290 20 556 21 6Oi
Y
:t- -0
reference locations if needed.
Xnstruct ions
0 A With a known loceral reference @ The parallel translation of the
value (Y/R - .5) the lateral graphically obtained wake boundary
reference guide can be used to lines for the fore and aft coordi- determine, by construction, the nates is made to the appropriate appropriate lateral reference lateral position @ .
location @ on the Z/R axis.
@DO G The determination of the rocket
0 C For the desired inflow ratio launch point in the tip path
(A - -.0283) the indices can be plane is made on tne selected
determined which define the fore graph (X/R - -.05, Z/R 9 .4),
and aft wake boundary reference resulting in 0.
lines. (Symbol from col. 1.) @ From this determination it is found
@ The wake boundary lines can be that the wake has been displaced
determined by graphical inter- rearward fran the launch point.
polation for the zero lateral Since the p - .23 condition will
location. have the wake displaced further rearward there ir no need to use any additional figures for inter- polation on advance ratio.
FIGURE 10. EXAMPLE iJSE OF THE FORE AND AFT WAKE BOUNDARY CHARTS
26
TOP
VIEH
N
UH
BER
OF
BLR
OES
=
4 ..-
.~
C
T =
0.00
5
+I3
= 0.
0
-
SIO
E VI
EW
ISO
MET
RlC
VI
EU R
EAR
VIE
W
FIG
UR
E 1l
A.
PRO
JEC
TIO
N
AND
IS
OM
ETR
IC
VIEW
S O
F U
ND
ISTO
RTE
D
TIP
VOR
TEX,
VA
RYI
NG
AD
VAN
CE
RAT
IO
(V/n
R
= .0
5>
NU
flBER
O
F BL
PDES
=
4 C
T =
o.uu
s Q
LPH
Fl =
-2
.0
flu
= 0.
10
SID
E Vf
EW
lSC
WEJ
RIC
VI
EH
FIG
UR
E 11
B.
V~yI
f’C
ADVA
NC
E R
ATIO
(V
/OR
=
.10)
PR
OJE
CTI
ON
AN
D IS
OPI
ETR
IC V
IEW
S O
F ~J
DIS
TOR
TED
TI
P VO
RTE
X,
TOP
VIEW
TO
P VI
EW
NU
MBE
R O
F BL
FIO
ES =
4
NU
MBE
R O
F BL
FIO
ES =
4
CT
= 0.
005
CT
= 0.
005
RLP
HFI
=
-2.0
R
LPH
FI =
-2
.0
MU
“B
=
0.20
=
0.0
SID
E VI
EW
FIG
UR
E 11
C.
ISO
tlETR
IC
VIEW
w
REA
R V
IEW
PRO
JEC
TIO
N A
ND
ISO
MET
RIC
VIE
WS
OF
UN
DIS
TOR
TED
TIP
VOR
TEX,
VA
RYI
NG
AD
VAN
CE R
ATIO
(V/
OR
=
.ZO
)
TOP
VIEW
N
UM
BER
OF
BLR
DES
=
4 C
T =
0.00
5 AL
PHA
= -2
.0
MU
q
0.30
+B
=
o-0
SID
E VI
EW
REl
7R V
IEW
ISO
MET
RIC
VI
EW
FIG
UR
E 11
D.
PRO
JEC
TIO
N A
ND
ISO
MET
RIC
VIE
WS
OF
UN
DIS
TOR
TED
TIP
VOR
TEX,
VA
RYI
NG
AD
VAN
CE
RAT
IO (
V/R
R
= .3
0>
TOP
VIEW
2
NU
MBE
R O
F BL
RD
ES
= 2
CT
c 0.
0025
R
LPH
R
= -2
.0
MU
=
0.10
'B
=
0.0
ISO
flETR
IC
VIEW
zis!
dis
x Y
RER
R V
IEW
SI
DE
VIEW
FIG
UR
E 12
A.
PRO
JEC
TIO
N AN
D IS
OM
ETR
IC.V
IEW
S O
F U
ND
ISTO
RTE
D TI
P VO
RTE
X,
VAR
YIN
G T
HR
UST
LEVE
L (C
T =
.002
5)
TOP
VIEW
2
NU
MBE
R O
F BL
ADES
=
2 C
T‘ =
0
.oos
o FI
LPH
R =
-2
.q
MU
=
0.10
*B
=
0.0
SID
E VI
EW
REf
lR
VIEW
ISO
MET
RI'C
VI
EW
FIG
UR
E 12
R.
PRO
JEC
TIO
N A
ND
ISO
MET
RIC
VIE
WS
OF
UN
DIS
TOR
TED
TIP
VOR
TEX,
VA
RYI
NG
TH
RU
ST L
EVEL
(C
T =
.005
0)
NU
Wf3
O
F 8~
~0~5
C
T =
O.O
U~?
~ Q
LPH
R
= 2
MU
=
= -2
.0
93
= 0.
0 0.
10
FIQ
JRE
12~.
PR
OJE
CTI
ON
AND
“m
yI&
T~~R
UST
LEVE
L (c
T =
, oo7
5j
Isoa
TRW
VI
EWS
oF
UN
DIS
TOR
TED
TIP
VO
RTE
X,
TOP
VIEW
N
UtlB
ER
OF
.BLF
IOES
=
2
2
CT
= 0.
005
RLP
HR
=
0.0
MU
=
0.10
tB
q
0.0
SI’O
E VI
EW
ISO
HET
RIC
VI
EU R
ERR
VIE
W
FIG
UR
E 13
A.
PRO
JEC
TIO
N
AND
IS
OM
ETR
IC
VIEW
S O
F U
ND
ISTO
RTE
D
TIP
VOR
TEX,
VA
RYI
NG
TI
P PA
TH
PLAN
E AL
TITU
DE
(a
= 0.
0)
-
TOP
VIEH
N
UM
BER
OF
BCR
OES
=
2 C
T =
0.00
5 R
LPH
A z
-4.0
H
U =
0.
10
tB
= 0.
0
SID
E VI
EW
ISO
MET
RIC
VI
EW RER
R V
rEW
FIG
UR
E 13
B.
PRO
JEC
TIO
N
AND
ISO
MET
RIC
VI
EWS
OF
UN
DIS
TOR
TED
TI
P VO
RTE
X,
VAR
YIN
G
TIP
PATH
PLA
NE
ALTI
TUD
E (9
=
-4.0
)
NU
MBE
R U
F‘BL
ADES
=
2 c-
r =
0.00
s R
LPH
R
= -1
3.0
MU
=
0.10
tg
=
0.0
SlO
E VI
’EW
I‘SO
MET
RIC
VJ
EU
RER
R
VI’E
W
FIG
UR
E 13
C.
VAR
YIN
G T
IP
PATH
PLA
NE
ALTI
TUD
E (a
=
-8.0
) PR
OJE
CTI
ON
AN
D IS
OM
ETR
IC V
IEW
S O
F U
ND
ISTO
RTE
D TI
P VO
RTE
X,
-
TOP
VIEW
N
UM
BER
OF
BLFI
DES
=
2 C
T =
0.00
25
FILP
HA
= -2
.0
MU
=
0.10
+B
=
0.0
SID
E VI
EW
ISO
HET
RIC
VI
EW REA
R V
IEW
FIG
UR
E 14
A.
PRO
JEC
TIO
N
AND
ISO
Mk'I
'RIC
VI
EWS
FOR
GEN
ERAL
IZED
D
ISTO
RTE
D
TIP
VOR
TEX,
VA
RYI
NG
TH
RU
ST L
EVEL
(C
T =
.002
5)
TOP
VIEW
N
UH
BER
O
F BL
FID
ES
CT
= 0.
0050
R
LPH
R
= -2
-D
HU
=
0.10
+B
=
0.0
2
SID
E VI
EW
ISO
MET
RIC
VI
EW REA
R
VIEW
FIG
UR
E 14
B.
PRO
JEC
TIO
N
AND
IS
OM
ETR
IC
VIEW
S FO
R
GEN
ERAL
IZED
D
ISTO
RTE
D
TIP
VOR
TEX,
VA
RYI
NG
TH
RU
ST
LEVE
L (C
T =
.005
0)
TOP
VIEW
2
NU
MBE
R O
F BL
RD
ES
= 2
CT
= 0.
0075
AL
PHA
= -2
.0
MU
=
0.10
“B
q
0.0
SID
E VI
EW
ISO
MET
RIC
VI
EW
- R
EAR
VIE
W
FIG
UR
E 14
C.
PRO
JEC
TIO
N
AND
ISO
MET
RIC
VI
EWS
FOR
GEN
ERAL
IZED
D
ISTO
RTE
D
TIP
VOR
TEX,
VA
RYI
NG
TI
IRU
ST
LEVE
L (C
T =
.007
5)
TOP
VIEW
N
UM
BER
O
F R
LflO
iZS
: 2
CT
I 0.
0050
F\
Lf'H
Q
= 0.
0 M
U
= 0.
10
SJD
E VI
EW
REF
lR
VIEW
JSO
MET
RJC
VI
EW
FIG
UR
E 15
A.
PRO
JEC
TIO
N
AND
IS
OM
ETR
IC
VIEW
S FO
R G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X,
VAR
YIN
G
TIP
PATH
PL
ANE
ALTI
TUD
E (a
, =
0.0)
TOP
VIEW
N
UM
BER
O
F BL
FlD
ES
- 2
CT
= 0.
0050
Q
LPH
R
= -4
.0
MU
=
0.10
2 +B
=
0.0
SID
E VI
EW
JSO
MET
RJC
VI
EW
'?EF
IR
VIE3
FIG
UR
E 15
B.
PRO
JEC
TIO
N
AND
ISO
MET
RIC
VI
EWS
FOR
GEN
ERAL
IZED
D
ISTO
RTE
D
TIP
VOR
TEX,
VA
RYI
NG
TI
P PA
TH P
LAN
E AL
TITU
DE
(a
= -4
.0)
TOP
VJLW
2
NU
MBE
R
OF
BtR
OES
=
2 C
T z
0.00
50
RLP
HFl
=
-8.0
M
U
q 0.
10
If)
z 0.
0
SJO
E VI
EW
REQ
R
VJEW
ISO
MET
RJC
VJ
LW
FIG
UR
E 15
C.
PRO
JEC
TIO
N
AND
IS
OM
ETR
IC
VIEW
S FO
R
GEN
ERAL
IZED
D
ISTO
RTE
D
TIP
VOR
TEX,
VA
RYI
NG
TI
P PA
TH
PLAN
E AL
TITU
DE
(Cu
= -8
.0)
-
TOP-
VIEW
2
NU
MBE
R
OF
BLR
OES
=
4 C
T =
0.00
50
FlLP
HA
= -2
.0
MU
=
0.05
+B
=
0.0
ISO
MET
RIC
VI
EW
2 I
FIG
UR
E 16
A.
PRO
JEC
TIO
N
AND
ISO
MET
RIC
VI
EWS
FOR
GEN
ERAL
IZED
D
ISTO
RTE
D
TIP
VOR
TEX,
VA
RYI
NG
AD
VAN
CE
RAT
IO
(V/n
R
= .0
5)
TOP
VIEW
N
UM
BER
O
F BL
R0E
.S
= 4
CT
= 0.
0050
R
LPH
R
= -2
.0
MU
=
0.10
$B
=
0.0
SID
E VI
EW
RER
R
VIEW
ISO
MET
RIC
VI
EW
FIG
UR
E 16
8.
PR9J
ECTI
ON
Af
JD I
SOM
ETR
IC
VIEW
S FO
R G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X,
VAR
YIN
G
ADVA
NC
E R
ATIO
(V
/OR
=
..lO
)
TOP
VIEW
N
UM
BER
O
F EL
fIDES
:
4 C
T =
0.00
50
RLP
HA
= -2
.0
MU
=
0.20
+t
YJ
q 0.
0
ISO
MET
RIC
VI
EW REF
lR
VIEW
SI
OE
VIEW
FIG
UR
E 16
C.
PRO
JEC
TIO
N
AND
ISO
MET
RIC
VI
EWS
FOR
GEN
ERAL
IZED
D
ISTO
RTE
D
TIP
VOR
TEX,
VA
RYI
NG
AD
VAN
CE
RAT
IO
(V/O
R
= .2
0)
TOP
VIEW
N
UM
BER
O
F BL
RO
ES
= 4
CT
= 0.
0050
R
LPH
A =
.-2.0
M
U
= 0.
30
+B
= 0.
0 2
ISO
MET
RlC
VI
EW
SIO
E Vl
EW
QER
R
VIEW
FIG
UR
E 16
D.
PRO
JEC
TIO
N
AND
IS
OM
ETR
IC
VIEW
S FO
R G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X,
VAR
YIN
G
ADVA
NC
E R
ATIO
(V
/OR
=
.30)
TOP
VfEW
N
UM
BER
O
F BL
FIO
ES
q 4
CT
= 0
.oos
o Q
LPH
R
= -2
.0
MU
=
0.20
IS
OM
ETR
IC
VIEW
SIO
E VI
EW
RER
R
VIEW
FIG
UR
E 17
A.
PRO
JEC
TIO
N
AND
ISO
MET
RIC
VI
EWS
FOR
GEN
ERAL
IZED
D
ISTO
RTE
D
TIP
VOR
TEX,
VA
RYI
NG
BL
ADE
AZIM
UTH
PO
SITI
ON
($
B =
0.0)
TOP
VIEW
N
UM
BER
O
F BL
RO
ES
= 4
CT
r. 0.
0050
R
LPH
R
= -2
.0
MU
=
0.20
SID
E VI
EW
RE.
QR
'.'T
EW
ISO
MET
RTC
Vl
EW
FIG
UR
E 17
B.
PRO
JEC
TIO
N
AND
IS
OM
ETR
IC
VIEW
S FO
R G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X,
VAR
YIN
G
BLAD
E AZ
IMU
TH
POSI
TIO
N
($B
= 15
.0)
TOP
VIEW
N
UM
BER
O
F BL
RD
ES
= 4
CT
= 0.
0050
Fl
LPH
Q
z -2
.0
MU
=
Cl.2
0 $B
=
30.0
SID
E VI
EW
ISO
MET
RIC
VI
EW SE
RR
VI
Eid
FIG
UR
E 17
C.
PRO
JEC
TIO
N
AND
ISO
MET
RIC
VI
EWS
FOR
GEN
ERAL
IZED
D
ISTO
RTE
D
TIP
VOR
TEX,
VA
RYI
NG
BL
ADE
AZIM
UTH
PO
SITI
ON
($
B =
30.0
)
TOP
V1E.
W
NU
MBE
; ;F
&QO
ES
= 4
Cl=
.
RLP
HR
zz
-2.
0 M
U
= 0.
20
“6
= 45
.0
ISO
VETR
JC
VIEW
KER
R
VIEW
SID
E VI
EW
FIG
UR
E 17
D.
PRO
JEC
TIO
N
AND
IS
OM
ETR
IC
VIEW
S FO
R
GEN
ERAL
IZED
DIS
TOR
TED
TI
P VO
RTE
X,
VAR
YIN
G
BLAD
E AZ
IMU
TH
POSI
TIO
N
($$j
= 4
5.0)
-
TOP
VIEW
N
UPB
ER
OF
BLFI
DES
=
4 C
T =
0.00
50
RLf
'HFl
z
-2.0
M
U
= 0.
20
tB
= 60
.0
SID
E VI
EW
TSO
PETR
IC
VIEW
REF
IR
VIEW
FIG
UR
E 17
E.
PRO
JEC
TIO
N
AND
IS
OM
ETR
IC
VIEW
S FO
R
GEN
ERAL
IZED
D
ISTO
RTE
D
TIP
VOR
TEX,
VA
RYI
NG
BL
ADE
AZIM
UTH
PO
SITI
ON
(q
+j
= 60
.0)
TOP
VIEW
2
NU
MBE
R
OF
BLflO
ES
: 4
CT
= 0.
0050
fK
PHF\
=
-2.0
M
U
= 0.
20
'&
= 75
.0
SID
E VJ
EW
FEFI
S VT
EW
JSU
t-fET
RJC
VJ
EW
A /,
FIG
UR
E 17
F.
PRO
JEC
TIO
N
AND
IS
OM
ETR
IC
VIEW
S FO
R G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X,
VAR
YIN
G
BLAD
E AZ
IMU
TH
POSI
TIO
N
($B
= 75
.0)
flLF'
Hf3
q
-16a
OO
CO
RR
ESPO
ND
lNG
FKIV
QN
CE
RFI
TIO
+pp
FIG
UR
E 18
A.
INFL
OW
RAT
IO
NO
MO
GR
APII
(CYT
pP =
-1
6.0)
\ .
nn\
flLPH
F1
=-14
JO
FIG
UR
E 18
B.
IIJFL
OW
R
ATIO
N
OM
OG
RAP
H (O
TPp
= -1
4.0)
e CL
I- A
L
0 H
FILP
Hfl
=--1
2nO
o
T VF
lLU
ES
WR
ITTE
N
FIBW
E
WlV
flNC
E R
FITl
thrp
p
FIG
UR
E 18
C.
INFL
OW
Ih
4TIO
N
OM
OG
RAP
H (+
Pp
= -1
2.0)
FlLP
Hfl
=-lO
a
CT
VQLU
ES
WR
ITTE
N
QBO
VE
CO
RR
ESPO
ND
ING
C
UR
VES
00
fJ~.
us
U‘.l
O
u-.1
5 u-
.20
0..2
5 0.
.30
0.. 3
5 0.
. 40
cl‘.r
15
1
FID
VQN
CE
RR
TIO
A,,,
FIG
UR
E 18
D.
INFL
OW
R
ATIO
N
OM
OG
RAP
H (@
TPp
= -1
0.0)
-
x c;
H
l- a CK
3 (3
-J
Ll-
7 H
FILP
HFI
=-
8000
CT
VQLU
ES
WR
ITTE
N
FlBO
VE
CO
RR
ESPO
ND
ING
C
UR
VES
I I
1 I
I I
I IO
0.
05
0.10
0.
15
0.20
0.
25
0.30
0.
35
0.40
0.
45
MIV
FIN
CE
RFI
TIO
ar
pp
.SO
FIG
UR
E 18
E.
INFL
OW
R
ATIO
N
OM
OG
MPH
(@
y~pp
=
-8.0
)
VI
cn
F\LP
t-iR
=-
6aO
O
CL.
a I-
/f (3
H I- a 11
1
iT
VQLU
ES
WR
ITTE
N
FJBO
VE
CO
RR
ESPO
ND
ING
C
UR
VES
E 1
I c_
1
I I
I I
I
p ,
.oo
0.05
0
.lO
0.15
0.
20
0.25
a.
30
0.35
a
.4a
0 ,4
53
0 .s
o
FIO
VflN
CE
RR
TIO
,U,,~
FIG
UR
E 18
F.
INFL
OW
R
ATIO
N
OM
OG
RAP
H ("
TPP
= -6
.O
>
QLP
Hf7
=-
4.00
CT
VFlL
UES
W
RIT
TEN
FI
BOVE
C
OR
RES
PON
DTN
G
CU
RVE
S
DO
0.
05
0.10
0.
15
0.20
0.
25
0.30
0.
35
0.40
0.
45
(
FID
VFIN
CE
Rf7
TIO
p>
urpp
FIG
UR
E 18
G.
INFL
OW
RAT
IO
NO
HO
GR
APll
(aTP
P =
-4.0
)
, I- I_
I I- 1 L-
, -
, , I :I I
: 1 I , -I-
O.
FlLP
Hfl
=--2
.O
O
CT
VflL
UES
W
RIT
TEN
R
BOVE
C
OR
RES
PON
DIN
G
CU
RVE
S
00
o-.o
s 0.
. 10
o- 1
5 o-
.20
o-.2
5 0.
. JO
o-
.35
0.. 4
0 0'
.45
FlD
VFlN
CE
R~~
TIO
A+~~
.so
FIG
UR
E 18
11.
INFL
OW
R
ATIO
N
OH
OC
RAP
H (
@Tp
p =
-2.0
)
FlLP
Hfl
=OoO
O
5 ,- C
OR
RES
PON
DIN
G
CU
RVE
S s:
: ,--
c$.o
o r
1 1
1 I
I I
0.0s
0.
1s
I 0.
10
0 LO
0.
25
0.30
0.
35
0.40
0.
15
0.50
FIC
UKE
181
. IN
FLO
W P
ATIO
NO
NO
CR
APII (a
TPP
= 0
.0)
flLPH
fl =Z
aOO
T Vf
JLU
ES
WR
ITTE
N
FIBO
VE
CO
RR
ESPO
ND
ING
C
UR
VES
QIIV
QN
CE
RFl
TIO
+,,
FIG
UR
E 18
5.
INFL
OW
RAT
IO N
OM
OC
RAP
H (m
TPP
= 2.
0)
& Ul
=I
,
(I /I
CT
VFIL
UES
W
RIT
TEN
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OVE
:]
CO
RR
ESPO
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ING
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UR
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0 I E r
&GO
0
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,
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0.
30
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0.40
I 0.45
0.
50
FJD
VQN
CE
RFI
TIO
au
Tpp
FIG
UR
E 18
K.
INFL
OW
RAT
IO f
JOM
OG
PdPI
1 (@TP
P =
4.0)
FIXI
FIL
DIS
PLAC
EMEN
T O
F TI
P VO
RTE
X FI
LFIM
ENT
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M
BLR
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OF
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KE
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R
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1
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UR
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T NO
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APH
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57
-I :3
\9
-l.SO
B -1
.696
-1
.885
-I .'1
59
-2.0
11
-2.2
62
-2.5
13
-2.1
99
-2.5
13
-2.8
27
-3.1
42
-2.6
39
-3.0
16
-3.3
93
-3.7
70
-3.0
79
-3.5
19
-3.9
58
-4.3
98
-3.5
19
-4.0
21
-4.5
24
-5.0
27
-3.9
58
-4.5
24
-5.0
89
-5.6
55
-4.3
98
-5.0
27
-5.6
55
-6.2
83
-4.8
38
-5.5
29
-6.2
20
-6.9
12
-5.2
78
-6.0
32
-6.7
86
-7.5
40
-5.7
18
-6.5
35
-7.3
51
-8.1
68
-6.\5
8 -7
.037
-7
.91'
1 -8
.796
-6.5
97
-7.5
40
-8.4
82
-9.4
25
FIG
UR
E 19
C.
UN
DIS
TOR
TED
AXI
AL
DIS
PLAC
EMEN
T N
OM
OG
RAP
HS -
PAR
T III
GEN
ERR
LIZE
D
LON
GlT
UD
INfIL
C
OO
RD
INH
TE
CH
RR
T lO
NG
JTU
DIN
flL
OlS
PLAC
EfltN
T FO
R
flULT
JPltS
O
F 36
0 D
tCR
tES
nULT
O:P
LES
TIP
PATH
PL
RN
E R
OTO
R
RO
VAN
CE
RR
TIO
36
0 O
EG
IY
\ X
W
l- a Z
Y
0.05
0.
10
0.15
0.
20
0.30
0.
40
I 0.
314
0.62
8 0.
942
1.25
7 1.
665
2.51
3 2
0.62
8 1.
257
I.885
2.
513
3.77
0 5.
027
3 0.
942
I.885
2.
827
3.77
0 5.
G55
7.
540
4 1.
257
2.51
3 3.
7.10
5.
027
7.54
0 10
.053
5
I.571
3.
142
4.71
2 6.
283
9.42
5 12
.566
G
1.
885
3.17
0 5.
655
7.54
0 II.
310
15.0
80
7 2.
199
4.39
8 6.
597
8.79
6 13
.195
17
.593
8
2.51
3 5.
027
7.54
0 10
.053
IS
.080
20
.106
2.
827
5.65
5 8.
482
II .3
10
16.9
65
22.6
19
3.14
2 6.
283
9.42
5 12
.566
18
.850
25
.133
u-l
.30
FIG
UR
E 20
A.
GEN
ERAL
IZED
LON
GIT
UD
INAL
CO
OR
DIN
ATE C
HAR
T -
PAR
T I,
STEA
DY
POR
TIO
N
GEN
ERR
LIZE
D
LON
GIT
UD
INQ
L C
OO
RO
INFI
TE
CH
FIR
T
* PO
C,IT
IVt
REr
,lDU
FlI
OF
flUl.T
lPltS
O
F 36
0 O
tGR
ttS
FIG
UR
E 20
B.
GEN
ERAL
IZED
LO
NG
ITU
DIN
AL C
OO
RD
INAT
E CH
ART
- PA
RT
II,
CYC
LIC
PO
RTI
ON
GEN
ERFI
LIZE
D
LFIT
ERFI
L C
OO
RD
INFl
TE
CH
FIR
T
50.0
0
REL
flTlV
E W
FlKk
FI
ZIM
UTH
f'O
SlT~
ON
=.~
I P’
l’.’
r I V
I. R
I ‘i
lflcl
nl
OF
tllll
1 IP
I t’;
O
F 36
0 0t
C;R
LtS
FIG
UR
E 21
. G
ENER
ALIZ
ED LA
TER
AL C
OO
RD
INAT
E CH
ART
ENVEjJIIPE FUNCTION BLADES=P, PU=o .Gs
H
HAKi RGE UfiKE AGE
FIGURE 22A. GENERALIZED WAKE ENVELOPE FUNCTION CHARTS FOR TWO BLADES (p = .05>
70
ENVELOPE FUNCTION 6LfmES=z, MU=O.OS
WRKE F\GE
FIGURE 22A. CONTINUED 71
ENVELOPE FUNCTJON BLRDES=P. HU=O.kO
r “7
WAKE AGE
ENVELOPE FUNCTION CHARTS FOR FIGURE 22B. GENERALIZED WAKE
TWO BLADES (p = .lo>
72
ENVELOPE FUNCTION BLROES=Z. MJ=O.~O
--
-- I- - :: --
FIGURE 22B. CONTINOED
73
ENVELOPE FUNCTION BLADESz2, HU=O .I5
c d
1
WRKE RGE
FIGURE 22C. GENERALIZED WAKE ENVELOPE FUNCTION CHARTS FOR TWO BLADES (/J = .15)
74
I
ENVELOPE FUNCTJO/,j UtDES=2, rwzo.~S
FIGURE 22C. CONTINUED
75
ENVELOPE FUNCTJON BLflOES=2. HlJ=O .20
cr
B
.cc,s
4 .CC?O
, pxcsr
WRKE RGE
FIGURE 22D. GENERALIZED WAKE ENVELOPE FUNCTION CHARTS FOR TWO BLADES (cl = .20)
76
ENVELOPE FUNCTION BLAOES=2, MU=O.20
10 .co 160 .co 640 .co YOO .co Y60 .co 1020 .co 1060 .GO 1140 .co 1200 .co 126O.CO 132O.CC ’ i36C .cc illO.CC
WAKE AGE
FIGURE 22D. CONTINUED
77
ENVELOPE FUNCTJON BLADES=P, t?U=O .30
WRKE AGE
K 460.1X 6lO.CC - 610 - 01 560 .cc 600.00 153 .:C 11o.co
WAKE RGE
FIGURE 22E. GENERALIZED WAKE ENVELOPE FUNCTION CHARTS FOR TWO BLADES (p - .30)
78
EWELOPE F-UNCTION BLADES=2 , MU=0 .30
CD Fc .cc:s -I
~zo.co 7io.m ~;o.~~ ,bo.co *
sso.cu ' 102o.cc 10sc.c0 '
116O.CO - 1100.00 '
&WE RGE l*so-QO l%O.CE ljsc.cc ' 14~O.CC
FRXmE 22E. CONTINUED
79
FIGURE 22F. GENERALIZED WAKE ENVELOPE FUNCTION CHARTS FOR TWO BLADES (/.i= .40)
80
ENVELOPE FUNCTION BLRDES=2, MU=0 .40
“0 cj;o.io -i&z- -&j :co- sKic- - -9io .CC
lb20 .cc ,OlC .co 114o.cu 1200 .co 1260 .co i320 .CO 136C .co 1440 .cc WAKE FlGE
FIGURE 22F. CONTINUED
81
WRKE RGE
ENVELOPE FUNCTION 8LADES=4, MU=0 .GEi
r d
FIGURE 23A. GENERALIZED WAKE ENVELOPE FUNCTION CHARTS FOR FOUR BLADES (cc = ,051
82
ENVELOPE FUNCTION BCRDESz4, f!U=O .05
0 N d
FIGURE 23A. CONTINUED 83
ENVELOPE FUNCTION BLRDES=4, NU=o .10
r d
WRKE RGE
s %8.CO 4io .CI 480 .OO rio .cc 800 .cc 880 .cc 720 .cc
WRKE RGE
FIGURE 23B. GENERALIZED WAKE ENVELOPE FUNCTION CHARTS FOR FOUR BLADES (p = .lo>
84
:: d 1
ENVELOPE FUNCTION BLADES=4, MU=O. io
FIGURE 23B. CONTINUED
85
ENVELOPE FUNCTION 9LAOESz4, tlU=0-15
"c d
WAfiE RGE
8, Srs .oo 610 .OP b#a .ac 64O.CO rba .ca rio.cc ?ZD.CC
WRKE RGE
FIGURE 23C. GENERALIZED WAKE ENVELOPE FUNCTION CHARTS FOR FOUR BLADES (p - .15)
86
I
d ,b I d P I
ENVELOPE FUNCTION BLADES=4, rwo.15
FW~E 23C. CONTINUED
87
ENVELOPE FUNCTJON BLFIDES=4, HlJ=O -20
-: 0 1
d’
e d’
WRKE RGE
FIGURE 23D. GENERALIZED WAKE ENVELOPE FUNCTION CHARTS FOR FOUR BLADES (p - .20)
88
I
ENVELOPE FUNCTION BLAOESz4, fiU=O.zO
FIGURE 230. CONTINUED
89
ItNVELOPE FUNCTION BLRDESz4, f%.J=O.30
t? d P d I
WAKE RGE
s 4SC.EU ’ bZU SC ,,o .CI S&O .cc 6CC .co C6C .tC ,ao.cc
WAKE AGE
FIGURE 23E. GENERALIZED WAKE ENVELOPE FUNCTION CHARTS FOR FOUR BLADES (p = .30)
90
ENVELOPE FUNCTlON BLAOESz4, fiU=O.30
Ei W .CCiI -8
~2o.co 7ic.co ,;o.co ’ s00.c0 ’ 86O.CC ’ 1020.c0 ’ lO~~.CO 114D.C~ ’
1200.c0 -
&IKE FlGE lZCO.Co - 13ZQ.CO ’ 13Ml.cc ’ 144c.cc
FIGURE 23E. CONTINUED
91
ENVELOPE FUNCTJON BLROESz4 a MU=0 -40
d 1 / LQ .cc,s ,-+.oc70
WAKE AGE
d :: d I
WAKE RGE
FIGURE 23F. GENERALIZED WAKE ENVELOPE FUNCTION CHARTS FOR FOUR BLADES (p - .40)
92
P d P d I? I
ENVELOPE FUNCTJON 5LfNlES=4, nu=o .40
A
%c.cc 7it.cc ~(O.CC w sOc.cC v ¶SO.CC p lOZO.CO 10B0.C~ li*o.oo ’
NRKE RGE l~~C.CU ~26C.C.J ’
11zc.co ’ 13bC.W ’ 14w.cc
FIGURE 23F. CONTINUED
93
----
--
lJ:o
.2
0 ,I c i
r .oo
60
.OO
12
0.00
18
0 .o
o 2b
O.C
O
- IS
1 30
0 .o
o 36
0 R
EV
.OO
42
0 .o
o 48
0 .o
o 51
0 .a
0 60
0 .O
O
I 12
0 .c
o .
2N0
RN
0 R
LL
SUBS
EQU
ENT
REV
y.O
O
WR
KE F
1GE
FIG
UR
E 24
. G
ENER
ALIZ
ED
WAK
E SH
APE
FUN
CTI
ON
C
HAR
T FO
R T
WO
BLA
DES
9,
CH
FIR
FIC
TER
ISTI
C
WR
KE
SHFI
PE
FUN
CTI
ON
BL
FID
ES=4
0,
If'
'o.c
o I
60.0
0 12
0.00
18
0.00
54
0.00
60
0.00
66
0.00
72
0.00
-
IS1
REV
2N
O
RN
0 FI
LL.
SUBS
EQU
ENT
REV
S __
01
------
-- M
=o JO
--
- x0
.15
----
----
ur
ro
$I0
------
ur
o .3
0
’ I
, I
I : :
1,
’
FIG
UR
E 25
. G
ENER
ALIZ
ED
WAK
E SH
APE
FUN
CTI
ON
C
HAR
T FO
R F
OU
R B
LAD
ES
‘E R
Qrlo
r~
O
f BL
RD
ES.
P.P.
, ;
2 -
0.05
0
FIG
UR
E 26
~.
muR
FO
RM
iT)
poTE
NTI
AL
BTAW
TU
VOR
TEX
INTE
RSE
CTI
O~J
PL
OT
FOR
m
. Bt
mEs
,
p =
005
.P.P
.I =
0.10
0 =
2
-0
WR
KE F
RO
II SY
tmO
L BL
ADE
ON
BLR
OE
cl
1 0
: I
d ,260
FIG
UR
E 26
B.
POTE
NTI
AL
BLAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N
PLO
T FO
R T
WO
BLA
DES
(P
OLA
R
FOR
MAT
), p
= .lO
90
RD
VRN
CIN
G
SID
E R
R11
0 I1
.P.P
.) =
OF
Et1 Q
OES
=
2
UR
KE
FRO
H
swm
BL
FlO
E
cl
Q
:
0.15
0
ON
BL
FlO
E
2’70
R
ETR
EFIT
INC
5
I DE
FIG
UR
E 26
C.
POTE
NTI
AL
BLAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N
PLO
T FO
R T
WO
BLA
DES
(P
OLA
R
FOR
MAT
), /.i
=
.15
90
RD
VFIN
ClN
G
SlD
E
270
RET
REF
lTlN
C
SID
E
QO
VFIN
CE
RF1
110
IT.P
.P.1
E
0.
200
NU
tIBER
O
F BL
AOES
=
2
HR
KE
FRO
tl SY
HBO
L BL
AOE
ON
BLR
OE
0 I
Q
: 1
584
FIG
UR
E 26
D.
POTE
NTI
AL B
LAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N
PLO
T FO
R T
WO
BLA
DES
(P
OLA
R F
OR
MAT
), p
= .2
0
I FI
DVF
INC
ING
SI
DE
NU
IIEIE
R
2’70
R
ETR
E,FI
TlN
G
SID
E
RR
TIO
(1
.P.P
.I =
OF
BLAD
ES
q 2
WR
KE F
RO
H
SYH
l3O
L BL
flOE
cl
0 :
0.30
0
ON
BL
ADE
I I
FIG
UR
E 26
E.
POTE
NTI
AL
BLAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N
PLO
T FO
R T
WO
BLA
DES
(P
OLA
R
FOR
MAT
), p
= .3
0
90
RD
VFIN
CIN
G
SID
E Q
OVF
INC
E R
RTI
O
IT.P
.P.1
=
0.40
0 N
UIIB
ER
OF
RLR
OES
r
2
WAK
E FR
Otl
Srn
aOl
ElLF
lOE
ON
BLF
IOE
8 1
8 :
I
FIG
UR
E 26
F.
POTE
NTI
AL B
LAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N P
LOT
FOR
TW
O B
LAD
ES
(PO
LAR
FO
IWAT
), p
= .4
0
90
FlO
VRN
CIN
G
SID
F
QO
VAN
I-E
RR
T IO
I
NU
MBE
R
OF
ELR
OE
SYH
BOL
IIf
0
// .
237
270
Rk
rRLH
T IN
I; <I
lIE
T.P.
P.J
1.
s-3
MIK
E FR
OR
BL
ADE
: 3
0.05
0
ON
R
LRO
E
FIG
UR
E 27
A.
POTE
NTI
AL B
LAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N P
LOT
FOR
TH
REE
BLA
DES
(P
OLA
R F
OR
MAT
), p
= .0
5
VU
3 IIJ
C
RO
VRN
CL
RR
TIO
I
NU
flEIh
R
OF
RI
RO
E
7 125
2'70
R
ETR
EFIT
ING
SI
DE
T.P.
P.1
z s-
-3
MR
KE F
RO
H
EIL I
DE
: 3
FIG
UR
E 27
B.
POTE
NTI
AL B
LAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N P
LOT
FOR
TH
REE
BLA
DES
(P
OLA
R F
OR
MAT
), p
= .lO
0.10
0
ON
RLR
IJE
90
FID
VFIN
CIN
G
SID
E Q
OVA
NI-I
F N
UN
i3tR
712
t 253
I
270
RET
REF
ITIN
G
SID
E
RR
TIO
I
.OF
BLR
OE
T.P.
P.1
= 5=
3
SY tl
EiO
L
I3
0 .
WR
KE F
RO
H
BLR
OE
: 3
0.15
0
ON
BL
RO
E
FIG
UR
E 27
C.
POTE
NTI
AL B
LAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N P
LOT
FOR
TH
REE
BLA
DES
(P
OLA
R F
OR
MAT
), p
= .I5
199 l 20
9
SYrlB
OL
I3
Q
T.P.
P.1
: s-
-3
WAK
E FR
Otl
BLR
OE
: 3
2’70
R
ETR
ERTI
NC
SI
DE
FIG
UR
E 27
D.
POTE
NTI
AL B
LAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N P
LOT
FOR
TH
REE
BLA
DES
(P
OLA
R F
OR
MAT
), p
= .2
0
0.20
0
ON
BLR
OE
FID
VFIN
CIN
G
SID
k R
OVR
NC
t R
RTI
O
lT.P
.P.1
=
NU
MEl
tR
OF
RLR
OES
=
3
/ --
6’ 12
.
/
UAK
E FR
Otl
SYtlF
JOL
BL R
OE
0 0 :
. 3
‘2.7
0 R
ETR
EFiT
INC
Sl
DE
0.30
0
ON
EI
L RO
E
FIG
UR
E 27
E.
POTE
NTI
AL B
LAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N P
LOT
FOR
TH
REE
BLA
DES
(P
OLA
R F
OR
MAT
), p
= .3
0
2’70
R
ETR
EFlT
lNC
SI
DE
RO
VRN
CE
RAT
IO
lT.P
.P.1
=
0.40
0 N
Utl!
3ER
O
F BL
ADES
I
3
HR
KE
FRO
H
SYH
BOL
RLR
OE
ON
BL
RC
IE
I3
Q
: I I
. 3
I
FIG
UR
E 27
F.
POTE
NTI
AL B
LAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N P
LOT
FOR
TH
REE
BLA
DES
(P
OLA
R F
OR
MAT
), c1
=
.40
: W
TIO
IT
.P.P
O
F &R
OES
=
4 .’
= O
-OS0
cl
I Q
. +
3’
I I 4
I I
FIG
UR
E 28
A.
(PO
LAR
FO
RM
AT),
/f =
.05
POTE
NTI
AL B
LAW
TZP
VOR
TEX
INTE
RSE
CTI
ON
PL
OT
FOR
FO
UR
BLA
DES
90
FlO
VFIN
ClN
r: Sl
nF
2;
W
RFl
TlO
I1
.P.P
.) =
OF
BLAD
ES
: 4
HAK
E FR
OH
SY
Hl3
OL
RLA
OE
cl
0 :
. 3
+ 4
1260
FIG
UR
E 28
B.
POTE
NTI
AL B
LAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N P
LOT
FOR
FO
UR
BLA
DES
(P
OLA
R F
oR~T
), v
= .I0
0.10
0
ON
EI
LAO
E
QD
VRN
CE
RR
1 IO
I
NU
HR
LR
OF
RLF
lOE
90
FlLl
VFlN
ClN
r =l
nc
/ /
L Y
/ ’
’ \
hq6
SYH
BOL
767
i
2’70
R
ETR
EFIT
INC
SI
DE
T.P.
P.)
= s-
4 WAK
E FR
OH
fiL
ADE
: 3 4
0.15
0
ON
BL
AOE
I I
FIG
UR
E 28
C.
POTE
NTI
AL B
LAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N P
LOT
FOR
FO
UR
BLA
DES
(P
OLA
R F
OR
MAT
), c1
=
.15
757
/ /
40
ISo/
/ / I
/
180i
--y-y
F-
106
u
113
240
I FI
DVF
lNC
lNG
SI
DE
9OVF
lNC
.E k
FI1
IO
IT
.P .
P.
I z
NU
NR
tR
OF
BL.R
OES
+
4
MA
KE
FR
OH
SY
HBO
L BL
RO
E
cl
I
/ /
x
1 369
t/ 33
0 47
0
/
S107
a 2
/ 56
4 . +
3 4
0 63
0
i
2’70
R
ETR
EFIT
IN
C
S I D
E
FIG
UR
E 28
D.
POTE
NTI
AL B
LAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N P
LOT
FOR
FO
UR
BLA
DES
(P
OLA
R F
OR
MAT
), p
= .2
0
0.20
0
ON
BLR
I’IE
90
FID
VFIN
CIN
G
SID
E
324
/
QD
VAN
CE
RR
110
lT.P
.P.1
=
0.30
0 lV
UH
BLR
O
F BL
RO
ES
= 4
2’70
R
ETR
EFlT
INC
SI
DE
/
392
0
WR
KE F
RO
H
SYH
BOL
BLR
OE
ON
BL
RO
E
8 I
I 0
2 I
. 3
I +
4 I
FIG
UR
E 28
E.
POTE
NTI
AL B
LAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N P
LOT
FOR
FO
UR
BLA
DES
(P
OLA
R F
OR
MAT
), j.t
=
.30
90
FlD
VFIN
C
120
4
TY
150
69
f I
I 1 I2
4
NG
SI
DE
AOVA
NC
E R
FlTl
O
1T.P
.P.)
z N
UM
BER
O
F BL
RD
ES
q 4
WR
KE F
RO
tl SY
HR
OL
BLR
OE
30
PJ
0
/
235
\
: I
3 /
+ 4
2’70
R
ETR
EFIT
INC
SI
DE
0.40
0
ON
BL
RO
E
FIG
UR
E 28
F.
POTE
NTI
AL B
LAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N P
LOT
FOR
FO
UR
BLA
DES
(P
OLA
R F
OR
MAT
), p
= .4
0
90
FlD
VflN
ClN
G
SID
E T.
P.P.
1 z
0.05
0 :s
=
5
WR
KE F
RO
H
RLR
DE
ON
BL
RO
E
270
RET
RtC
JTlN
G
SIU
E
FIG
UR
E 29
A.
POTE
NTI
AL B
LAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N P
LOT
FOR
FIV
E BL
ADES
(P
OLA
R F
OR
MAT
),p
= .0
5
RO
VRN
CE
RR
TIO
1T
.P.P
.j 2
WH
RER
O
F R
LRO
ES
z 5
6528
/
C(R
KE F
RO
H
SYH
l3O
L AL
RO
E
90
80
,FIG
UR
E 29
B.
POTE
NTI
AL B
LAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N P
LOT
FOR
FIV
E BL
ADES
(P
OLA
R F
OR
MAT
), p
= .I0
0.10
0
ON
RLR
DE
L 18
ot
I I!r
r .a
h;
*r
\
0 R
OVR
NC
ING
SI
I-IF
m
0 R
ETR
EFIT
INC
SI
DE
WR
KE F
RO
H
SYH
BOL
BLAD
E
cl
cl
: .
3 +
4 x
5
0.15
0
ON
BL
RO
E
FIG
UR
E 29
C.
POTE
NTI
AL B
LAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N P
LOT
FOR
FIV
E BL
ADES
(P
OLA
R F
OPJ
AT),/
t =
.15
90
FID
VRN
C’“‘
P “n
r
l7n
/m
1 N
W
J I
IJ L
‘JD
VRN
CE
RR
TIO
1T
.p.p
.1
z N
lJIIR
kR
OF
BLR
OES
=
S
MR
KE
FRO
H
65
SYH
BOL
BLAD
E
150
cl
I
0.20
0
ON
BLR
DE
/
623
2’70
R
ETR
EFIT
INC
SI
DE
FIG
UR
E 29
D.
POTE
NTI
AL B
LAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N P
LOT
FOR
FIV
E BL
ADES
(P
OLA
R F
OR
MAT
), p
= .2
0
. IN
U
51U
t
QO
VRN
Ct
RQ
TII’I
If
.t’.b
’. I
: O
.JO
O
YUH
RER
O
F R
lRO
tS
: 5
““~:R
~~oH
O
N
BLR
OE
SYM
BOL
I R
ETR
EFlT
lNG
SI
DE
FIG
UR
E 29
E.
POTE
NTI
AL B
LAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N P
LOT
FOR
FIV
E BL
ADES
(P
OLA
R F
OR
MAT
), p
= .3
0
90
RO
VRN
CIN
CI
SIO
F.
/-----
-t-s=
40
VAN
CE
RR
110
l1.p
.P.1
=
YUM
RER
O
f BL
AOES
-
5
MIK
E FR
OH
SY
MBO
L R
LFlO
E
cl
0 :
. 3
+ 4
Y
5
0.40
0
ON
BLR
OE
I I I I I
2’;O
R
ETR
EFIT
ING
SI
DE
FIG
UR
E 29
F.
POTE
NTI
AL B
LAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N P
LOT
FOR
FIV
E BL
ADES
(P
OLA
R F
OR
MAT
), /A
=
.40
I
90
RO
VFIN
C I
NC
,
UR
KE
f~on
SY
rlBO
L R
LRO
E O
N
BLR
OE
CI
0 :
I I l
3 I
+ :
I x
I e
6 I
2’70
R
kTR
t-firI
N
SIU
E
FIG
UR
E 30
A.
POTE
NTI
AL B
LAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N P
LOT
FOR
SIX
BL
ADES
(P
OLA
R F
OR
MAT
), /.L
=
.05
90
AOVF
INC
ING
SI
nF
SYH
RO
L
cl
T.P.
P.,
: :s
:
G
WKE
FR
OH
BL
RO
E
2’10
R
F_TR
tQTI
NG
SI
UF.
FIG
liRE
30B.
PO
TEN
TIAL
BLA
DE/
TIP
VOR
TEX
INTE
RSE
CTI
ON
PLO
T FO
R S
IX
BLAD
ES
(PO
LAR
FO
RM
AT),
p =
.lO
0.10
0
ON
BLA
DE
90
QD
VFIN
CIN
I; SI
DE
c. -A
lI Q
0VR
NC
.t R
QTI
O
1 O
F Bl
RO
t
SYl?
BOL
cl
0 .
2’70
R
ETR
EfiT
IN
C
SID
E
T.P.
P.1
: s
= G
UR
KE
FRO
H
BLW
E
0.15
0
ON
BL
ADE
FIG
UR
E 30
C.
POTE
NTI
AL B
LAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N P
LOT
FOR
SIX
BL
ADES
(P
OLA
R F
OR
MAT
), p
= .1
5
I.”
.J
I LI
I-
QllV
RN
l-t.
RR
T IO
I
rJU
tIRER
O
F R
I.AO
E
2.70
R
F. T
RliQ
T I N
r, S
I OF_
T.P.
P.,
: .s
:
G
WKE
FR
OH
BL
AOE
0.20
0
ON
BLR
OE
FIG
UR
E 30
D.
POTE
NTI
AL B
LAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N P
LOT
FOR
SIX
BL
ADES
(P
OLA
R F
OR
MAT
), /.L
=
.20
90
FIO
VQN
CIN
C
SID
E T.
P.P.
1 z
S=G
0.
300
QO
VHN
CE
RAT
IO
I W
UH
HLR
O
F Pl
AO
E
WFI
KE
FRO
M
flL A
OE
ON
R
LAO
E
I I
0 2
1 .
3 I
+ I
x
/
392
: I
e G
I
Ya 18
0.
2’70
R
F. T
RF.
RT
INT;
‘;
I nE
FIG
UR
E 30
E.
POTE
NTI
AL B
LAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N P
LOT
FOR
SIX
BL
ADES
(P
OLA
R F
OR
MAT
), p
= .3
0
90
QD
VRN
CIN
C
SID
E
fl--
RAT
IO
I 'O
F BL
RD
E T.
P.P.
I
r :S
=
6
HR
KE
FRO
H
SnlR
OL
I31
fH.lE
cl
1 0
2 .
3 + x
: e
6
2’70
R
ETR
EFIlI
NG
SI
DE
FIG
UR
E 30
F.
POTE
NTI
AL B
LAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N P
LOT
FOR
SIX
BL
ADES
(P
OLA
R F
OR
MAT
), p
= .4
0
0.40
0
ON
BL
RO
E
E3LR
DE/
TIP
VOR
TEX
INTE
RSE
CTI
ON
C
HQ
RT
ADVF
lNC
E R
flTIO
fT
.P.P
.1
= 0.
050
NU
MBE
R
OF
BLFI
DES
=
2
I I
1 1
I I
45 .
oo
90 .
oo
I35
.oo
I60
.oo
225
.oo
270
.OO
31
5 .o
o 36
0 .O
O
BLflD
E AZ
IMU
TH
POSJ
TIO
N.+
B (D
EG]
FIG
UR
E 31
A.
POTE
NTI
AL B
LAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N P
LOT
FOR
TW
O B
LAD
ES
(RE(
;TIL
INEA
R
FOR
MAT
),/&
= .0
5
z 0 ;I 0 W
m
cl5
W
I- Z -
BLFI
DE/
TIP
VOR
TEX
INTE
RSE
CTI
ON
C
HFl
RT
FlD
VFlN
CE
RQ
TJO
IT
.P.P
.1
= 0.
100
NU
MBE
R
OF
BLAD
ES
= 2
0 N I
ii.00
1
I I
I I
45.0
0 90
.oo
13
5.00
16
0.00
22
5.00
27
0.00
31
5.00
36
0.00
BLFl
DE
WIM
UTH
PO
SITI
DN
~+B
(DEG
]
FIG
UR
E 31
B.
POTE
NTI
AL B
LAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N P
LOT
FOR
TW
O B
LAD
ES
(REC
TILI
NEA
R F
OR
MAT
), p
= .I0
BLF1
DE/
TIP‘
VO
RTE
X IN
TER
SEC
TIO
N
CH
FlR
T
ADVA
NC
E R
ATIO
fT
.P.P
.1
= 0.
150
NU
MBE
R
OF
BLFI
DES
=
2
‘i.
00
4k .
oo
9b .
oo
1'35
.oo
180
.oo
2i5
.OO
2i
o .o
o 3'
15 .o
o
BLIX
IE
WIM
UTH
PO
SITI
ON
v+~
(DEG
]
, I 50.0
0
FIG
UR
E 31
C.
POTE
NTI
AL B
LAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N P
LOT
FOR
TW
O B
LAD
ES
(REC
TILI
NEA
R
FOW
lAT)
, ,x
=
.15
BLFI
DE/
TIP
VOR
TEX
INTE
RSE
CTI
ON
C
HFI
RT
FlD
VRN
CE
RFi
TIO
tT
.P.P
.1
= 0.
200
NU
MBE
R
OF
BLR
DES
=
2
I
00
I I
I
45 .o
o 90
.oo
13
5.00
18
0 .o
o 22
5 .O
O
270
.oo
315.
00
:
BLAD
E AZ
IMU
TH
POSI
TIO
N,+
B (D
EGI
, io .o
o
FIG
UR
E 31
D.
POTE
NTI
AL B
LAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N P
LOT
FOR
TW
O B
LAD
ES
(REC
TILI
NEA
R F
OR
MAT
), p
= .2
0
BLfX
lE/T
IP
VOR
TEX
INTE
RSE
CTI
ON
CHFIRT
flDVf
lNC
E R
ATIO
(T
.P.P
.) =
0.30
0 N
UM
BER
O
F BL
QO
ES
= 2
1 1
1 I
1 1
I 00
45
.oo
90
.oo
13
5.00
I8
0 .o
o 22
5 .O
O
210
.oo
at5
-00
BLR
DE
AZIM
UTH
PO
SITI
ON
,+B
(DEG
)
id .6
0
FIG
UR
E 31
E.
POTE
NTI
AL B
LAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N P
LOT
FOR
TW
O B
LAD
ES
(RE~
ILIN
EAR
Fo
mA
T),p
=
.30
BLR
DE/
TIP
VOR
TEX
INTE
RSE
CTI
ON
C
HFl
RT
QO
VFIN
CE
RAT
IO
(T.P
.P.1
q
0.40
0 N
UM
BER
O
F BL
ADES
=
2
Z w
u W
CD
lx
BLAD
E Fl
ZIM
UTH
PO
SITI
ON
,+B
(BEG
]
FIG
UR
E 31
F.
POTE
NTI
AL B
LAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N P
LOT
FOR
TW
O B
LAD
ES
(REC
TILI
NEA
R F
oRM
T),
p =
.40
BLQ
DE/
TIP
VOR
TEX
INTE
RSE
CTI
ON
C
HFl
RT
RD
VAN
CE
RR
TIO
IT
.P.P
.1
= 0.
050
NU
MBE
R
OF
BLAD
ES
= 4
T
%.O
O
I I
45 .
oo
I 90
.o
o I
135
I .o
o 18
0 .o
o 22
5 .o
o 1
I 27
0 .o
o 31
5.00
36
0 Y
BLAD
E AZ
IMU
TH
POSI
TIO
N,+
B ~D
EGI
.OQ
FIG
UR
E 32
A.
POTE
NTI
AL B
LAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N P
LOT
FOR
FO
UR
BLA
DES
(R
ECTI
LIN
EAR
FO
RM
AT),
p =
.05
BLFI
DE/
TIP
VOR
TEX
INTE
RSE
CTI
ON
C
HFl
RT
RD
VRN
CE
RR
TJO
IT
.P.P
.1
= 0.
100
NU
MBE
R
OF
BLAD
ES
= 4
I fY
ii.
00
I r
I I
I I
45.0
0 90
.o
o 13
5.00
16
0.00
22
5.00
27
0.00
31
5.00
36
0.00
BLR
DE
RZI
MU
TH
POSI
TIO
NAR
(D
EG]
FIG
UR
E 32
B.
POTE
NTI
AL B
LAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N P
LOT
FOR
FO
UR
BLi
DES
(R
ECTI
LIN
EAR
FO
KMAT
), p
= .lO
BLfiD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N
ADVA
NC
E R
RTI
O
IT.P
.P.1
=
0.15
0 N
UM
BER
O
F BL
RD
ES
= 4
CH
QR
T
I 1
I I
I 00
45
.o
o 90
.00
135.
00
160
.oo
225
.OO
21
0 .o
o 31
5.00
36
0 .O
O
BLFl
OE
AZIM
UTH
PO
SITI
UN
.+B
(DEG
)
FIG
UR
E 32
C.
POTE
NTI
AL B
LAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
Ii P
LOT
FOR
FO
UR
BLA
DES
(R
ECTI
LIN
EAR
Fo
Rm
T),
p =
.15
t; ln
BLFI
DE/
TTP
VOR
TEX
INTE
RSE
CTI
ON
C
HFI
RT
9DVR
NC
E R
FlTI
O
lT.P
.P.1
=
0.20
0 N
UPl
BER
O
F BL
AOES
=
4
.- 0
BLAD
E AZ
IMU
TH
POSI
TIO
N.+
B (B
EG)
.oo
FIG
UR
E 32
D.
POTE
NTI
AL
BLAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N
PLbT
FO
R F
OU
R B
LAD
ES
(REC
I'ILI
NEA
R
FOR
MAT
), p
= .2
0
BLflD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N
CH
RR
T
flDVR
NC
E R
FITI
O
lT.P
.P.1
z
0.30
0 N
UM
BER
O
F BL
FIO
ES
= 4
I- 1 .( IO
45
.oo
90
.o
o 13
5 .o
o 16
0 .o
o 22
5 .O
O
270
.OO
31
5.00
I
BLAD
E Fl
ZIM
UTH
PO
SITI
ON
9+B
(DEG
)
FIG
UR
E 32
E.
POTE
NTI
AL B
LAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N P
LOT
FOR
FO
UR
BLA
DES
(R
ECTI
LIN
EAR
FO
RM
AT),
Jo =
.3
0
BLFI
DE/
TIP
VOR
TEX
INTE
RSE
CTI
ON
C
HFl
RT
F)O
VF)N
CE
RFI
TIO
IT
.P.P
.1
= 0.
400
NU
HBE
R
OF
BLR
DES
=
4
z a:
=:
t
OL
4.00
I
I 1
I I
I 45
.oo
90
.00
135.
00
1eo.
00
225
.OO
27
0.00
31
5.00
3
BLAD
E W
IMU
TH
POSI
TIO
N.+
B (D
EGI
io.0
0
FIG
UR
E 32
F.
POTE
NTI
AL
BLAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N
PLO
T FO
R F
OU
R B
LAD
ES
(RE~
ILw
EAR
Fo
wT)
,p
= .4
0
REL
QN
r,lF
I-lF
INTE
RSE
CTI
ON
C
HFl
RT
FlD
VRN
C :E
R
flTIO
=
0.05
180
. oc’
:,,
45 .a
0 90
.o
o 13
s .o
o 18
0 .o
o 22
s .o
o 21
0 .o
o 31
5.uo
36
0 7 .c
o
.eflT
IVE
WFl
KE
FlZI
MU
TH
POSI
TIO
N.~
~,-~
RG
Flu~
DEG
. PO
S!l
IVE
RES
ICIU
~I.
OF-
tVJ
CTl
PLES
O
F 3F
O
OEC
REE
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S
FIG
UR
E 33
A.
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P VO
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X IN
TER
SEC
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FIG
UR
E 33
B.
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P VO
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X IN
TER
SEC
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t =
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FIG
UR
E 33
C.
BLAD
E/TI
P VO
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X IN
TER
SEC
TIO
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NG
LE,p
=
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RN
GLE
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TER
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OF
360
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S
FIG
UR
E 33
D.
BLAD
E/TI
P VO
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X IN
TER
SEC
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=
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180.
0
rl W
w
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TER
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RES
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OF
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OF
360
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S
FIG
UR
E 33
E.
BLAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N A
NG
LE,p
=
.30
LL
180.
0 (3
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GLE
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F IN
TER
SEC
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RR
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1
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5.00
36
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REL
ATIV
E W
RKE
R
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UTH
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EG
m P
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TIVE
R
ESIO
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L O
F tlU
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0 O
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FIG
UR
E 33
F.
BLAD
E/TI
P VO
RTE
X IN
TER
SEC
TIO
N A
NG
LE,p
=
.40
.REE
S
LRTE
RAL
W
AKE
BOU
NO
ARY
REF
EREN
CE
GU
IDE
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0.0
I .o
f3D
VFIN
CE
RFl
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LON
GIT
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L C
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TE.,
X/R
0.02
0 -2
1.80
1 0.
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699
0.01
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1.31
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11
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5
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11
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16
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21
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01
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26.5
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52
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54
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56
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57
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Z 0.
05
FIG
UR
E 34
A.
FOR
E AN
D A
FT W
AKE
BOU
ND
ARIE
S FO
R T
llE
UN
DIS
TOR
TED
WAK
E M
OD
EL, ~
1 =
.05
LATE
RR
L W
AKE
BOU
NO
FlR
Y R
EFER
ENC
E G
UI
-1 .o
0.
0 1 .
o
I I
I I
I I
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I
DE
+a
RD
VAN
CE
RFl
T
LON
GIT
UD
INR
L C
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RD
INR
TE,
X/R
;YN
EOL
R
8 c z F G
H J ii 1.
N
i L R
S 1 U
.50
0 =
0.10
0.02
0 -1
1.31
0 0.
015
-8.5
31
0 .O
lO
-5.7
11
0 .o
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62
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l 0
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5.
711
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15
8.53
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310
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36
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30
16.6
99
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35
19 -
290
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01
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28
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55
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65
33.0
24
-0.0
70
34.9
92
-0.0
75
36.8
70
-0.0
80
36.6
60
FIG
UR
E 34
B.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
IES
FOR
TH
E U
ND
ISTO
RTE
D
WAK
E M
OD
EL,
p =
.lO
LRTE
RAL
W
FlKE
BO
UN
OAR
Y R
EFER
ENC
E G
UIO
E -1
.o
0.0
1 .o
ADVA
NC
E R
RTI
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= 0.
15
; I
I I
I I
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I I
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l I
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3 ,
I- -I
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0 o.
ca
0.50
I
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I .s
o 2.
00
2.50
LON
GIT
UD
INR
L C
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RO
INR
TE,
X/R
i ii E
F G
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015
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10
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lS
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20
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25
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40
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45
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,
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0
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909
3.81
4 5.
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7.59
5 9.
462
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10
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14.9
31
16.6
99
18.4
35
20.1
36
21.6
01
23.4
29
! 25
.617
26
.565
28
.072
FIG
UR
E 34
C.
FOR
E AN
D
AFT
WAK
E,BO
UN
DAR
IES
FOR
TH
E U
ND
ISTO
RTE
D
WAK
E.
MO
DEL
, p
= .1
5
-
LRTE
RR
L H
AKE
BOU
NO
RR
Y R
EFER
ENC
E G
UID
E -1
.o
0.0
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R
R
C
0 E
F G
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L N
N
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T U
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00
0.50
1
.oo
1 .s
o 2.
00
2.~0
1
LON
GIT
UD
JNR
L C
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RD
INR
TE,
X/R
RFl
TIO
0.02
0 0.
015
0.01
0 0
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10
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15
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20
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25
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35
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40
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50
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55
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60
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65
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70
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80
I
I C
0.20
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11
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89
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62
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0 .o
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1.43
2 2.
862
4.28
9 5.
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O
12.6
80
14.0
36
15.3
76
16.6
99
18.0
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19.2
90
20 .
S56
21 .
801
FIG
UR
E 34
D.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
IES
FOR
TH
E U
ND
ISTO
RTE
D
WAK
E M
OD
EL,
p =
.20
ERR
L W
AKE
BOU
NO
RR
Y R
EFER
ENC
E G
UID
E -I
.o
0.0
1 .o
‘QN
CE
RFl
TIO
=
0.30
f-1
.oo
-0
.bO
0.
00
0.50
1
.oo
I .b
O
2.00
2
, .bO
LON
GIT
UD
INFI
L C
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RD
INfiT
E,
X/R
;YllB
OL
0.02
0 -3
.614
0.
015
-2.8
62
0 .O
lO
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09
0.00
5 -0
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o 0
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0.95
5 -0
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lO
1.90
9 -0
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2.
662
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20
3.61
4 -0
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4.
764
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30
5.71
1 -0
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6.
654
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40
7.59
5 -0
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8.
531
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50
9.46
2 -0
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IO
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9 -0
.G60
Il.
310
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6s
12.2
25
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70
13.1
34
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75
14.0
36
-0.0
80
14.9
31
FIG
UR
E 34
E.
FOR
E AN
D A
FT W
AKE
BOU
ND
ARIE
S FO
R T
HE
UN
DIS
TOR
TED
WAK
E M
OD
EL, p
=
.30
'AN
CE
RflT
lO
L
7.
WI
.oo
I -0
.so
0.00
0.
50
I .o
o I
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2
.oo
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O
LON
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INQ
L C
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RD
TNflT
E,
Y/R
;Yns
Ol
R
8 C
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0 i R
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ll
1-
0.02
0 -2
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0
.Ol5
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0.
010
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32
0.00
5 -0
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Ol
0 .o
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05
0.71
6 -0
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I
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2.
140
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20
2.86
2 -0
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3.
576
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O?O
4.
289
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35
5 .O
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5.71
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6.
419
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7.
125
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620
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I I .
3lO
FIG
UR
E 34
F.
FOR
E AN
D A
FT W
AKE
BOU
ND
ARIE
S FO
R T
HE
UN
DIS
TOR
TED
WAK
E M
OD
EL, p
=
.40
9OVA
NC
E R
ATIO
q
0.10
N
UM
BER
OF
BLAO
ES
q 2
vp\
CT
= 0.
004
(Lfll
lBO
F\
= -0
.023
0)’
TIP
PATH
PL
FlN
E =
-2.0
00
LATE
RqL
PO
SITI
ON
=
0.00
0
Q
GEY
ERR
LJZE
O
WAK
E BO
UN
OAR
Y In
-C
LFIS
SJC
AL
UR
KE
BOU
NO
ARY
N
0
1
i’l -1
.o
o 4.
50
d.00
0
.so
1 .to
1
.so
2 .o
o 1 2
.so
LON
GIT
UD
INFI
L C
OO
RD
INQ
TE,
X/R
FIG
UR
E 35
A.
FOR
E AN
D A
FT W
AKE
BOU
ND
ARY C
HAR
TS FO
R T
HE
GEN
ERAL
IZED
DIS
TOR
TED
TI
P VO
RTE
X (II
,=
.I,
B =
2,
CT
= .0
04,
Ly =
-2)
, Y/
R
= 0.
0
AOW
NC
E R
F\TI
O
= 0
.lO
NU
MBE
R O
F BL
FlO
ES =
2
Lp\
CT
- 0.
004
tLAf
lBO
FI
= -0
.023
01
TIP
PFIT
H P
LAN
E =
-2.0
00
LATE
RAL
PO
SJTJ
ON
=
0.25
9
CJ
GEN
ERAL
JZEO
WAK
E BO
UN
OR
RY
v)
N
-CLA
SSIC
AL
WR
KE B
OU
NO
RR
Y
LON
GTT
UD
INf3
L C
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RD
INQ
TE,
X/R
FIG
UR
E 35
B.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (p
=
.l,
B =
2,
c;r
= .0
04,
Os!
= -2
), Y/
R
= .2
59
AOVA
NC
E R
QTI
O
= 0.
10
%'u
\ N
UM
BER
OF
BLFI
OES
=
2 C
T =
0.00
4 tL
AMBO
f7
= -0
.023
01
TIP
PFIT
H P
LAN
E =
-2.0
00
LFIT
ERAL
PO
SITI
ON
=
0.50
0
Q
OEY
ERR
LJZE
O
WAK
E BO
UN
OR
RY
: -
CLA
SS IC
RL
WR
KE B
OU
NO
RR
Y
LON
GIT
UC
JIN
FIL
CO
OR
OIN
QTE
, X/
R
FIG
UR
E 35
C.
FOR
E AN
D
AFT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (C
L =
.I,
B =
2,
CT
= .0
04,
Cy =
-2
), Y/
R
= ,5
00
ADVA
NC
E R
ATIO
=
0.10
N
UM
BER
OF-
BLF
lOES
=
2 C
T =
0.00
6 IL
FlflB
Ofl
= -0
.032
11
TIP
PFlT
H P
LAN
E =
-2.0
00
LATE
RflL
PO
SITI
ON
=
0.00
0
-.I
a r; a Lo
w
‘-1
.oo
-0.5
0 0.
00
0.50
1
.oo
1 .s
o 2’
. 00
2 1 .so
LON
GYf
UO
INfIL
C
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RD
INflT
E,
X/R
Q
GEN
ERAL
IZED
W
AKE
BOU
ND
ARY
- C
LRSS
I C
AL
WR
KE
BOU
NO
RR
Y
FIG
UR
E 36
A.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (/L
=
.l,
B =
2,
CT
= .0
06,
oI=
-2),
Y/R
=
0.0
ADVF
INC
E R
ATIO
=
0.10
N
UM
BER
OF
BLFI
DES
=
‘2
CT
q 0.
006
(LAt
lBD
A =
-0.0
321
1 TI
P PA
TH
PLFI
NE
q -2
.000
LQ
TER
f7l.s
PO
SlTI
ON
=
0.25
9
Q
GEN
ERAC
SZEU
W
RKE
R
GU
NO
FIR
Y Q
G
E?IE
RAC
SZEU
W
RKE
R
GU
NO
FIR
Y
m
m
-CL4
SS!C
AL
WR
KE
EIO
UN
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Y -C
L4SS
!CAL
W
RKE
EI
OU
NO
ARY
N
N 7
I -I
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0 0.
00
0.50
1
.oo
1.50
2
.oo
2 .s
o .S
O
LON
GIT
UO
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L C
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RO
INQ
TE,
X/R
LO
NG
ITU
OIN
RL
CO
OR
OIN
QTE
, X/
R
FIG
UR
E 36
B.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (p
=
.l,
B =
2,
CT
= .0
06,
a =
-2),
Y/R
=
.259
FID
VFIN
CE
RAT
IO
q 0.
10
NU
IIBER
O
F BL
ADES
=
2 C
T =
0 -0
06
(LAf
lBD
A =
-0.0
321
I TI
P PA
TH
PLAN
E =
-2
.OO
O
LRTE
RFI
L PO
SJTI
ON
=
0.50
0
0 G
ENER
ALIZ
ED
WR
KE t3
OU
ND
ARY
In
-CLR
SSIC
AL
WR
KE B
OU
ND
ARY
x
LON
GIT
UO
INf4
L C
OO
RO
TNfJ
TE,
X/R
FIG
UR
E 36
C.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED DIS
TOR
TED
TI
P VO
RTE
X (/L
= .l,
B
= 2,
C
T =
.006
, a
= -2
), Y/
R
= .5
00
ADVA
NC
E R
f3TI
D
= 0.
10
NU
MBE
R O
F BL
ADES
=
2 C
T =
0.00
4 (L
AflB
DA
= -0
.026
4)
TIP
PRTH
PL
ANE
= -4
.000
LR
TER
QL
POSI
TIO
N
= 0.
000
o G
ENER
RLJ
ZEO
W
AKE
BOU
NO
RR
Y -C
LRSS
!CR
L W
RKE
BO
UN
OR
RY
-I ‘-1 .o
o -b
.so
0.00
0.
Sf.l
l-00
1 .s
o 2.
00
I 2 .s
a
LON
GIT
UO
TNR
L C
OO
RO
INfiT
E,
X/R
FIG
UR
E 37
A.
FOR
E AN
D
AFT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (/J
=
.I.
B =
2.
C’T
=
.004
. a
= -4
). Y/
R
= 0.
0
RD
VRN
CE
RR
TIO
=
0.10
N
UM
BER
OF
BLAD
ES
= 2
CT
= 0.
004
(LR
MR
OR
=
-0.0
264)
TI
P PA
TH
PLAN
E =
-4.0
00
LRTE
RR
L PO
SITI
ON
=
0.25
9
0 G
ENER
RLJ
Z~D
W
AKE
BOU
NO
RR
Y -C
LRSS
ICR
L W
RKE
BO
UN
DR
RY
LON
GIT
UO
INQ
L C
OO
RO
INFI
TE,
X/R
FIG
UR
E 37
B.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
T: G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (p
= .I,
B
= 2,
C
T =
.004
, (Y
=
-4),
Y/R
=
.259
-I a r; a
RD
VRN
CE
RR
TJO
=
0.10
N
UM
BER
OF
BLAD
ES
= 2
CT
= 0.
004
ILR
flBD
R
= -0
.026
41
TIP
PATH
PL
RN
E =
-4.0
00
LRTE
RR
L PO
SITI
ON
=
0.50
0
E)
GEN
ERR
L!ZE
G
WR
KE
RO
UN
OR
RY
2 -C
LASS
!CR
L W
RKE
R
OU
NO
RR
Y
‘: ‘-1
.oo
4.50
0.
00
o.so
I
.a0
1 1
.so
2.00
2
.so
LON
GIT
UO
INflL
C
OO
RO
INf3
TE,
X/R
FIG
UR
E 37
C.
FOR
E AN
D
AFT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (c
c =
.1,
B =
2,
CT
= .0
04,
a =
-4),
Y/R
=
.500
ADVA
NC
E R
RTI
O
= 0.
10
NU
MBE
R O
F BL
ADES
=
2 "v
\ C
T=
0.00
6 IL
RM
BDR
'-:
-0.
0353
1 TI
P PA
TH
PLR
NE
= -4
.000
LR
TER
RL
POSI
TIO
N
= 0.
000
o G
ENER
ALJZ
EO
HR
KE
RO
UN
OR
RY
- C
LASS
IC
RL
WR
KE
EIO
UN
OR
RY
‘-I
.oo
-0.5
0 0.
00
0.50
1
.oo
1.50
2.
00
2.50
LON
GIT
UO
INflL
C
OO
RO
INR
TE,
X/R
FIG
UR
E 38
A.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (p
=
.I,
R =
2,
C
T =
.006
, (Y
=
-4),
Y/R
=
0.0
LON
GTT
UO
INQ
L C
OO
RO
INf7
TE,
X/R
ADVA
NC
E R
ATIO
-
0.10
-++-
+\
NU
MBE
R O
F- B
LRD
ES
= 2
CT
= 0.
006
(LR
MBD
R
= -0
.035
31
TIP
PATH
PL
RN
E =
-4.0
00
LRTE
RR
L PO
SITI
ON
=
0.25
9
o G
ENER
ALIZ
ED
WAK
E BO
UN
OR
RY
-CLR
SSIC
RL
WR
KE
BOU
NO
RR
Y
FIG
UR
E 38
B.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
JIAK
TS F
OR
TJI
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (p
=
.l,
H =
2,
C
T =
.OO
h,
a =
-4),
Y/R
=
.259
-
ADVA
NC
E R
RTJ
O
= 0.
10
"v\
NU
MBE
R O
F BL
RD
ES
= 2
CT
= 0.
006
!LR
MBD
R
= -0
.035
31
TIP
PATH
PL
ANE
q -4
.000
LR
TER
RL
POSI
TIO
N
= 0.
500
4 l-1
.oo
I
-0
.so
0.00
o.
so
1 .o
o 1
.50
2 .o
o 2.
50
LON
GTT
UO
INFI
L C
OO
RO
INFI
TE,
X/R
d G
ENER
AL I Z
tO
WAK
E BO
UN
OAR
Y -C
LASS
ICR
L YQ
KE B
OU
ND
ARY
FIG
UR
E 38
C.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (p
= .l,
H
=
2,
CT
= .0
06,
a =
-4),
Y/R
=
.500
flDVQ
NC
E R
F\TI
O
- 0.
10
NU
MBE
R O
F BL
FID
ES
= 4
CT
q 0.
004
(LqM
BOF\
=
-0.0
230)
TI
P PA
TH
PLQ
NE
= -2
.000
L.
ATER
fIL
POSJ
TIO
N
= 0.
000
Q
GEN
ERAL
IZE0
U
FlKE
R
OiJ
ND
RR
Y -
CLA
SSIC
X.
UR
KE
9UU
ND
4RY
i T;.s
o -0
.50
LON
GIT
UD
INFI
L C
OO
RO
INFI
TE~
X/‘R
FIG
UR
E 39
A.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (c
l=
.I,
B =
4,
CT
= .0
04,
a=
-2),
Y/R
=
0.0
flDVF
)NC
E R
FlTJ
O =
0.
10
NU
MBE
R O
F BL
ADES
=
4 C
T =
0.00
4 (L
AMBO
R
= -0
.023
01
TIP
PQTH
PLF
lNE
= -2
.000
LF
ITER
RL
POSI
TIO
N
= 0.
259
CI
GEN
ERAL
JZtO
W
KE
BOU
NO
RR
Y In
C
-J
- C
I.RSS
ICR
L U
FlKt
R
OU
NO
RR
Y
2 ’ In
%
:-I 7 .o
o -0
.so
0.00
o.
so
1 .o
o I
.‘Jo
2 .o
o 2 I
.so
LON
GIT
UD
INflL
C
OO
RD
INW
E,
X/R
FIG
UR
E 39
B.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (/c
=
.l,
B =
4,
CT
= .0
04,
a =
-2),
Y/R
=
.259
. W
0 z a I- m
E;
J a x”
a
RD
VQN
CE
RFl
TIO
=
0.10
'"v\
NU
MBE
R O
F BL
FID
ES
= 4
CT
= 0.
004
(LR
MBD
F1 =
-0
.023
01
TIP
PGTH
PL
ANE
= -2
.000
LF
ITER
AL
POSI
TIO
N
= 0.
500
o FE
NER
FIL.
JZED
W
AKE
BOU
NLJ
RR
Y -
Cl.F
I.SS I
CR
L U
RKE
ElO
UN
OR
RY
:i,.i,
i_
1.50
2
.oo
2.50
LON
GIT
UD
INR
L C
OO
RO
INR
TE.
X/R
FIG
UR
E 39
C.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (p
=
.I,
B =
4,
CT
= .0
04,
cy =
-2
), Y/
R
= .5
00
RD
VRN
CE
RR
TIO
=
0.10
N
UtIB
ER
OF
BLAD
ES
= 4
CT
= 0.
006
ILR
F1BD
R =
-0
.032
1)
TIP
PRTH
PL
ANE
= -2
.000
LR
TER
RL
POSI
TIO
N
= 0.
000
Q
GEN
ERR
LIZE
O
UR
KE
BOU
NO
RR
Y -
CLR
SS
I CAL
U
RKt
l BO
UN
OR
RY
LON
GIT
UD
INflL
C
OO
RD
IWflT
E,
X/R
FIG
UR
E 40
A.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (c
c =
.I,
B =
4,
CT
= .0
06,
a =
-Z),
Y/R
=
0.0
LON
GIT
UD
IWIL
C
OO
RO
INFJ
TE~
X/R
RD
VRN
CE
RR
TID
=
0.10
N
UM
BER
OF
BLR
OES
=
4 C
T =
0.00
6 (L
RM
BOA
= -0
.03’
21
1 TI
P PA
TH
PLR
NE
= -2
.000
LR
TER
RL
POSI
TIO
N
= 0.
259
o G
ENER
RLJ
ZEO
W
AKE
AOU
NO
RR
Y .-
CLR
SS
I CR
I. H
RKE
BO
UN
OR
RY
FIG
UR
E 40
B.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (c
l =
.l,
B =
4,
CT
= .0
06,
(Y =
-2
), Y/
R
= .2
59
RD
VRN
CE
RR
TID
=
0.10
“p\
NU
MBE
R O
F BL
RD
ES
= 4
CT
= 0.
006
~Lfl~
BD~
= -0
,032
l) T
JP
PRfH
PL
ANE
q -2
.O
OO
LR
TER
RL
POSI
TIO
N
= O
.SO
O
LON
GIT
UD
INAL
C
OO
RD
INQ
TE,
X/R
c)
CC
’NER
RI
JZED
W
AKE
BOU
NO
RR
Y -
CLR
SS
I CAL
W
RKE
BO
UN
DR
RY
FIG
UR
E 40
C.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (c
l =
.l,
B =
4,
CT
= .0
06,
a =
-2),
Y/R
=
.500
RD
VRN
CE
RR
TID
=
0.10
N
UM
BER
OF
BLR
DES
=
4 C
T =
0.00
4 [L
RM
BDR
=
-0.0
2641
TI
P PA
TH
PLR
NE
q -4
.000
LR
TER
RL
PDS!
TIO
N
= 0.
000
E ’ v)
:Y
‘-1
-3 .oo
-0
.50
0 .o
o o.
so
1 .o
o 1
.so
2.00
2.
50
1
LON
GIT
UD
INflL
C
OO
RD
INflT
E,
X./R
GEY
ERR
I. I Z
EO
HAK
E BO
UN
DAR
Y C
LRSS
1 C
AL
UR
KE
RO
UN
OR
RY
FIG
UR
E 41
A.
FOR
E AN
D
AFT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (p
= .l,
B
= 4,
C
T =
.004
, a
= -4
>,
Y/R
=
0.0
ADVF
INC
E R
ATIO
=
0.10
N
UM
BER
OF
BLFi
DES
=
4 C
T q
0.00
4 (L
AMBO
R
= -0
.0'2
641
TIP
PATH
PL
RN
E =
-4.0
00
LFIT
ERAL
PO
SITI
ON
=
0.25
9
Q
GEN
ERAL
JZED
W
OKE
R
OU
NO
ARY
- C
I.ASS
IC
FIL
WKE
BO
UN
lJFl
RY
.d ;-1
.o
o -0
.50
0.00
O
.SO
i
.oo
1 .5
0 2
.oo
2.50
LON
GIT
UD
INFI
L C
OO
RD
I’WTE
, Y/
R
FIG
UR
E 41
B.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
llAR
TS
FOR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (/.
i=
.l,
B =
4,
CT
= .0
04,
a=
-4),
Y/R
=
.259
ADVR
NC
E R
fiTIO
=
0.10
Ik
v\
NU
MBE
R O
F BL
f3O
ES
= 4
CT
= 0.
004
(Lf7
MBl
JA
= -0
.026
41
TIP
PflT
H
PLF\
NE
= -4
.000
LQ
TER
F\L
POS!
TIO
N
= O
.SO
O
Q
GEY
ERR
LJZE
D
WR
KE
RO
UN
DR
RY
In
-CLF
IS:,J
C9L
W
RKE
BO
UN
UR
RY
TV
In
N
-7 ‘-1
.o
o -c
.s
o 0
.co
0 .s
o 1
.oo
1 .s
o 2
.oo
2.50
LON
GIT
UD
INQ
L C
OO
RD
INF\
TE
s K.
/R
FIG
UR
E 41
C.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TIIE
G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (/J
=
.I,
73 =
4,
C
T =
.004
, a
= -4
), Y/
R
= .5
00
ADVQ
NC
E R
FlTI
O
z 0.
10
++-J
\ N
UM
BER
OF
BLFl
DES
=
4 C
T =
0.00
6 [L
AMBD
A =
-0.0
3531
TI
P PA
TH
PLAN
E =
-4.0
00
LATE
RAL
PO
SITI
ON
=
0.00
0
LJ3N
GTT
UD
INfIL
C
OO
RD
INfIT
E,
S/R
(3
GEN
ERR
LIZE
D
WR
KE
BOU
ND
RR
Y -
C!-A
SS!
CAL
H
AKE
BOU
ND
RR
Y
FIG
UR
E 42
A.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (jw
b=
.1,
B =
4,
CT
= .0
06,
a =
-4),
Y/R
=
0.0
RD
VRN
CE
RR
TIO
=
0.10
N
UM
BER
OF
BLR
DES
-
4 C
T =
0.00
6 (L
AMBO
R
= -0
.035
31
TIP
PATH
PL
ANE
= -4
.000
LR
TER
RL
POS!
TIO
N
= 0.
259
Q
GEY
ERAL
JZED
H
AKE
RO
UN
OR
RY
- I-l
.455
JC
RL
HAK
t 6O
UN
OR
P.Y
LON
GIT
UD
INAL
C
OO
RO
INFI
TE,
X/R
FIG
UR
E 42
B.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (/L
= .1
, B
= 4,
C
T =
.006
, cr
= -4
), Y/
R
= .2
59
-
RO
VRN
CE
RAT
IO
= 0.
10
Lv\
NU
MBE
R O
F BL
RD
ES
= 4
CT
= 0.
006
(LR
MBD
R
= -0
.035
3)
TIP
PATH
PL
ANE
= -4
.000
LR
TER
RL
POSl
TJO
N
= O
.SO
O
0 G
ENER
ALIZ
ED
WR
KE
RO
UN
OAR
Y
VJ
-CLR
SSIC
RL
WR
KE
BOU
ND
RR
Y N
LON
GIT
UD
INf3
L C
OO
RD
IN9T
E,
X/R
FIG
UR
E 42
C.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (p
=
.l,
B =
4,
CT
= .O
OG
, a
= -4
), Y/
R
= .5
00
RO
VRN
CE
RR
T!O
=
0.20
N
UM
BER
OF-
BLR
OES
=
2 C
T q
0.00
4 IL
RM
BOR
=
-0.0
170)
TI
P PR
TH
PLAN
E =
-2.0
00
LRTE
RR
L PO
SITI
ON
=
0.00
0
0 G
ENER
RLI
ZEC
W
AKE
BOU
ND
dRY
- C
LRSS
ICR
L W
AKE
FJO
UN
DR
RY
LON
GIT
UD
INQ
L C
OO
RD
INQ
TE,
X/‘R
FIG
UR
E 43
A.
FOR
E AN
D
AFT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (p
=
.2,
B =
2,
CT
= .0
04,
a =
-2),
Y/R
=
0.0
RO
VRN
CE
RR
TIO
=
0.20
++J-
\ N
UM
BER
OF'
BLR
OES
=
2 C
T =
0.00
4 (L
AMBD
A =
-0.0
1701
TI
P PA
TH
PLAN
E =
-2.0
00
LRTE
RR
L PO
SITI
ON
=
0.25
9
o G
ENER
RLI
ZED
W
AKE
BOU
NO
RR
Y
In
- C
LRSS
I C
RL
WAK
E SO
UN
DR
RY
w
-I a D-4
:: 2
’ In
(II
.- :-I
1 .o
o -0
.50
o.co
o.
so
I .o
o I
.50
2 .o
o 2.
50
LON
GIT
UD
INflL
C
OO
RD
INFI
TE,
Si’R
FIG
UR
E 43
B.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (j.
h=
.2,
B =
2,
Ck
= .0
04,
(Y =
-2
), Y/
R
= .2
59
RO
VRN
CE
RR
TIO
=
0.20
N
UM
BER
OF
BLAD
ES
= 2
yv-
CT
= 0.
004
lLR
MBD
R
= -0
.017
0)
TIP
PATH
PL
ANE
q -2
.000
l.R
TER
Rl
POSI
TIO
N
= O
.SO
O
B G
tNER
RI.I
ZEO
l4
RKE
BO
UN
OR
3Y
s --
CI.R
SS:
CR
L H
AKE
SOU
NO
RR
Y
. W
u Z a I- m
E;
r; a
& 9 In
r- + ifi a I WI
N .a ‘-1
.oo
-b
0’.
1 .s
o 0
.oo
50
1 .o
o 1
.so
2.00
2.
50
LON
GIT
UD
INf7
L C
OO
RD
INFI
TE,
Y/R
FIG
UR
E 43
C.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (/b
= .2
, B
= 2,
C
;r =
,004
, /Iy
=
-2),
Y/R
=
.500
ADVA
NC
E R
RTI
O
= 0.
20
NU
MBE
R O
F BL
ADES
=
2 C
T =
0.00
6 !L
RM
BOR
=
-0.0
219)
TI
P PR
TH
PLR
NE
= -2
.000
l.R
TE?R
L PO
SITI
ON
= 0
.000
Q
GEN
ERR
L!ZE
O
HAK
E SO
UN
DR
RY
Lo
- C
I.RSS
IC
R!.
HAK
E R
OU
NC
RR
Y N
J-
1 *z
OS I In
P 0. I :: .A
I 2 7 -1 .o
o -0
.s
o 0.
00
0 .S
G
I .o
o I
.50
2.00
2’
.50
LON
GIT
UD
INFI
L C
OO
RD
TNR
TE,
K/R
FIG
UR
E 44
A.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENET
MLI
ZED
D
ISTO
RTE
D
TIP
VOR
TEX
(p
= .2
, B
= 2,
C
T =
.006
, a
= -2
), Y/
R
= 0.
0
RO
VRN
CE
RR
TIO
=
0.20
N
UM
BER
OF
BLR
OES
=
2 &v
\ C
T =
0.00
6 (L
AMBD
A =
-0.0
219)
TI
P PR
TH
PLR
NE
= -2
.000
LR
TER
RL
POSI
TIO
N
= 0.
259
Q
GEN
ERR
LJZE
O
HAK
E BO
UN
DAR
Y -
CLR
SS
ICR
L H
AKE
BOU
ND
ARY
t .o
o -0
.w
0.00
0.
50
1 .o
o 1
.so
2 .o
o 1 2 .s
o
LON
GTT
UD
INR
L C
OO
RD
INR
TE.
X/R
FIG
UR
E 44
B.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (/m
h =
.2,
B =
2,
CT
= .0
06,
Q( =
-2
), Y/
R
= .2
59
FlD
VFlN
CE
RFI
TIO
=
0.20
N
UM
BER
O
F BL
FIO
ES
= 2
CT
= 0.
006
(LR
MBO
A =
-0.0
2191
TI
P PR
TH
PLG
NE
= -2
.000
Lf
iTER
FIL
POSI
TIO
N
= 0.
500
t; L:
z:
7 2 b-
4::
2 .- ’ In
?.
I -l ‘-I .o
o 1
-0 .s
o 0 .
oo
0.50
I
.aa
1.50
2.
00
2.50
LON
GIT
UD
INf3
L C
OO
RD
INFI
TE,
X/R
a G
ENER
ACIZ
tO
WAK
E R
OU
NO
ARY
- tl.
RSS
I C
AL
WR
KE
BOU
ND
ARY
FIG
UR
E 44
C.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
MR
TS
FOR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (/.
.t =
.2,
B =
2,
CT
= .0
06,
a =
-2),
Y/R
=
.500
FID
VflN
CE
RQ
T!O
q
0.20
N
UM
BER
O
F BL
FlD
ES
= 2
CT
= 0
.004
(L
RtiB
Dfl
= -0
.023
9)
TIP
PRTH
PL
QN
E =
-4.0
00
LATE
RR
L PO
SITI
ON
=
0.00
0
a G
ENER
RLI
ZtIO
W
AKE
RO
UN
OAR
Y
y:
- C
I.RSS
I C
RL
WFI
KE
ElO
UN
DFl
RY
z -I ‘-I
.a0
7 -0
.so
a.00
a.
so
1 00
i
.SO
2
.oo
2 .s
a
L.O
NG
ITU
DIN
flL
CO
OR
DIN
f3TL
Y/
R
FIG
UR
E 45
A.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (p
=
.2,
B =
2,
CT
= .0
04,
a =
-4),
Y/R
=
0.0
FlO
VFlN
CE
RAT
IO
= 0.
20
NU
MBE
R O
F BL
FlD
ES =
2
CT
= 0.
004
ILFl
HBO
A =
-0.0
239)
TI
P PR
TH
PLAN
E =
-4.0
00
LFIT
ERAL
PO
SITI
ON
q
0.25
9
a VI
N
4 ‘-1 .
co
1 -a
.sa
a.00
0
.so
I .a
a I
.so
2 .a
a 2
.so
L~N
GIT
UD
INR
L C
OO
RD
TN~T
E~
Y/R
b G
EYER
ALIZ
EIJ
WAK
E EO
UN
OR
RY
--ITL
RSS
ICAL
W
AKE
BOU
ND
ARY
FIG
UR
E 45
B.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (/m
I =
.2,
B =
2,
CT
= .0
04,
a =
-4),
Y/R
=
.259
FlO
VAN
CE
RFl
TIO
=
0.20
N
UM
BER
OF
BLAD
ES
= 2
CT
q 0.
006
(LFI
HBD
Q
= -0
.026
81
TIP
PFlT
H P
LF)N
E =
-4.0
00
Lf3T
ERR
L. P
OSl
TIO
N
= 0.
259
L”
GEN
ERR
LIZE
O
HAK
E BO
UN
DAR
Y m
-
CLA
SS IC
FlL
WAK
E .B
OU
NO
RR
Y N
vi -I ‘-1
.o
o -a
.5
0 0.
00
0.50
1
.OO
I
.so
2.00
z’
.su
LON
GIT
UD
INf7
L C
OO
RD
INf4
TE,
S.‘R
FIG
UR
E 46
B.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (II
=
.2,
B =
2,
CT
= .0
06,
a=
-4),
Y/R
=
.259
FlO
VRN
CE
RFl
TIO
=
0.20
N
UM
BER
OF
SLR
OES
=
2 C
T =
0.00
6 (L
RH
BDFI
q
-0.0
2881
TI
P PA
TH
PLR
NE
= -4
.000
LR
TER
RL
POSI
TIO
N
= 0.
500
Q
GEN
ERAL
IZE0
U
AKE
RO
UN
OR
RY
‘22
- C
I.RSS
ICR
L W
RKE
EO
UN
OR
RY
3 0 In
3 .- ‘-1 .co
-0.5
0 0.
00
a.sa
1
.ca
t I
.ba
2.00
2.
50
LON
GIT
UD
INFI
L C
OO
RD
INflT
E,
K/R
FIG
UR
E 46
C.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (c
l =
.2,
B =
2,
CT
= .0
06,
Cy =
-4
), Y/
R
= .5
00
QO
VRN
CE.
RQ
T.10
q
0. ‘
20
NU
MBE
R. O
F BL
FIO
ES =
4
CT
= 0
.004
(L
F\fl6
DF\
=
-0.0
1701
TI
P PF
I.TH
PLF
lNE
= -2
.000
t.R
TER
AL
POSI
TIO
N
= 0.
000
a G
ENER
RL!
IEO
U
flKE
0OU
NO
RR
Y --C
LRSS
IC
-RL.
WlK
E BO
UN
OAR
Y
1 I
.oo
-0
.so
0.00
o.
so
I .o
o I
.50
2 .o
o 2
.so
LON
GIT
UD
INI7
L C
OO
RD
INFI
TE,
X/R
FIG
UR
E 47
A.
FOR
E AN
D
AFT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (y
= .2
, B
= 4,
C
T =
.004
, C
Y=
-2),
Y/R
=
0.0
ADVA
NC
E R
ATIO
=
0.20
N
UH
BER
OF
BLFK
IES
= 4
CT
= 0.
004
t LAf
lBD
R
= -0
.0’1
70)
TIP
PQTH
PLF
lNE
= -2
.000
LA
TER
FIL
POSI
TIO
N
z 0.
259
0 G
ENER
RLI
ZEO
W
RKE
BO
UN
DAR
Y -C
LRSS
lCR
L W
RKE
BO
UN
OR
RY
.oo
-0.5
0 0.
00
0.50
I
.oo
1.50
2.
00
1 2.50
LON
GIT
UD
INf4
L C
OO
RD
INR
TE,
X/R
FIG
UR
E 47
B.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y M
ARTS
FO
R T
IIE
GEN
ERAL
IZED
D
ISTO
RTE
D
TIP
VOR
TEX
(p=
.2,
R =
4,
C
T =
.004
, Q
=
-2),
Y/R
=
.259
RD
VAN
CE
RR
TIO
=
0.20
N
UM
BER
OF
BLR
DES
z
4 C
T =
0.00
4 (L
FIM
BOA
= -0
.017
01
TIP
PFlT
H P
I-fiN
E =
-2
.OO
O
LATE
RAL
PO
SI T
JON
:
0.50
0
0 G
ENER
RLI
ZEO
W
RKE
BO
UN
OR
RY
-CLR
SSlC
RL
WR
KE B
OU
NO
RR
Y
LON
GIT
UD
INFl
L C
OO
RD
INAT
E,
X/R
FIG
UR
E 47
C.
FOR
E AN
D
AFT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (C
L=
.2,
B =
4,
CT
= .0
04,
a =
-2),
Y/R
=
.500
-
AOVF
lNC
E R
FITI
O
= 0.
20
NU
tlBER
O
F BL
FIO
ES =
4
CT
= 0.
006
(!-flf
lBf,f
i =
-0.0
219)
TI
P PF
ITH
PLA
NE
= -2
.000
LF
ITER
RL
POSI
TIO
N
= 0.
000
8 G
ENER
ALIZ
E0
WR
KE B
OU
NO
RR
Y -C
LRSS
lCR
L W
AKE
BOU
ND
ARY
LON
GIT
UD
INFI
L C
OO
RO
INQ
TE,
X/R
FIG
UR
E 48
A.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TllE
G
ENER
ALIZ
ED DIS
TOR
TED
TI
P VO
RTE
X (/.L
= .
2,
B =
4,
CT
= .0
06,
a =
-21,
Y/
R
= 0.
0
FIJI
VAN
CE
RAT
IO
= 0.
20
NU
flSER
O
F BL
FIO
ES =
4
CT
= 0.
006
(LflM
BOA
= -0
.021
91
TIP
PFIT
H P
LfIN
E =
-2.0
00
LFlT
ERFl
L PO
SITI
ON
=
0.25
9
Q
GEN
ERR
Lli!E
O
UR
KE B
OU
ND
ARY
-CLR
SSIC
RL
WR
KE B
OU
NO
RR
Y
LON
GIT
UD
INFl
L C
OO
RD
INFI
TE,
X/R
FIG
UR
E 48
B.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (/.
L =
.2,
B =
4,
CT
= .0
06,
CY
= -2
1,
Y/R
=
.2%
QD
VAN
CE
RFI
TJO
’ =
0.20
“v\
NU
MBE
R O
F BL
f!DES
=
4 C
T =
0.00
6 (L
RflB
ofl
= -0
.021
9)
TIP
PATH
PL
RN
E =
-2 .
OO
O
L.AT
ERAL
PO
SITI
ON
=
0.50
0
0 G
ENER
RLI
ZEO
W
AKE
BOU
ND
RR
Y -C
LRSS
lCR
L H
RKE
BO
UN
OR
RY
LON
GIT
UD
INf7
L C
OO
RD
INI~
TE,
X/R
FIG
UR
E 48
C.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (c
c =
.2,
B =
4,
C'T
=
.006
, a
= -2
), Y/
R
= .5
00
RO
VRN
CE
RAT
IO
= 0.
20
NU
tlBER
O
F BL
RO
ES
= 4
CT
= 0.
004
ILR
MBO
R
= -0
.023
9)
TIP
PRTH
PL
RN
E =
-4.0
00
LATE
RR
L.
POSI
TIO
N
= 0.
000
CI
GEN
ERR
LIZE
O
WR
KE B
OU
NO
RR
Y -
CLR
SS IC
RL
HR
KE B
OU
NO
RR
Y
LlJ
z a 2 P
H
OF
o-
J ’
a x”
8 i- a
m
N -I :-1
I .o
o -0
.50
0 .o
o 0.
50
I .o
o I
.50
2’. 0
0 2
.so
LON
GIT
UD
INAL
C
OO
RO
TNflT
E,
X/R
FIG
UR
E 49
A.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (/h
=
.2,
B =
4,
CT
= .0
04,
(Y =
-4
), Y/
R
= 0.
0
RO
VAN
CE
RR
TJO
=
0.20
N
UM
BER
OF
BLR
OES
=
4 C
T q
0.00
4 (L
AMBO
R
= -0
.023
9)
TIP
PRTH
PL
ANE
= -4
.000
LR
TER
RL
POSI
TIO
N
= 0.
259
Q
GEN
ERAL
IZE0
H
AKE
BOU
NO
RR
Y
K
-CLA
SSIC
AL
WR
KE E
IOU
NO
RR
Y
I 5 :-I
.oo
I -0
.50
0 .o
o 0.
50
I .o
o I
.50
2 .o
o 2
.so
LON
GIT
UO
INf7
L C
OO
RO
TNFl
TE,
X/R
FIG
UR
E 49
B.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (C
L=
.2,
B =
4,
CT
= .0
04,
a =
-4),
Y/R
=
.2!%
RO
VRN
CE
TiR
TI0
= 0.
20
++J\
N
UM
BER
OF
BLR
OES
=
4 C
T q
0.00
4 (L
RM
BOR
=
-0.0
239)
TI
P PR
TH
PLAN
E =
-4.0
00
LRTE
RR
L PO
SITI
ON
=
0.50
0
c)
GEN
ERR
LIZE
O
WR
KE B
OU
ND
ARY
: -C
LRSS
lCR
L W
RKE
BO
UN
OR
RY
d Y)
N ‘-1
.o
o -b
.5
0 0.
00
0.50
I
.oo
I .s
o 2
.oo
2.50
1
LON
GIT
UO
INR
L C
OO
RO
INR
TE,
X/R
FIG
UR
E 49
C.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (/L
= .2
, B
= 4,
C
T =
.004
, a
= -4
), Y/
R
= .5
00
-
I; a
E
RO
VR.N
CE
RR
TIO
‘ =
0.20
N
UM
BER
OF
BLR
OES
=
4 C
T =
0.00
6 IL
AtIB
OR
=
-0.0
288)
TI
P PA
TH
PLAN
E =
-4..O
OO
LR
TER
RL
POSI
Tf
ON
=
0 .O
OO
o O
ENER
RLI
ZEO
W
RKE
BO
UN
DAR
Y -C
LRSS
lCR
L W
RKE
BO
UN
OR
RY
LON
GIT
UO
INflL
C
OO
RO
INf4
TE,
X/R
FIG
UR
E 50
A.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (c
l =
.2,
B =
4,
CT
= .0
06,
a! =
-4
), Y/
R
= 0.
0
RO
VRN
CE
RR
TJO
=
0.20
-!!a
p\
NU
flBER
O
F BL
RO
ES’
= 4
CT
= 0.
006
ILR
MBO
R.
= -0
.028
81
TIP
PRTH
PL
RN
E =
-4.0
00
L.AT
ERR
L PO
SITI
ON
=
0.25
9
o G
ENER
RLI
ZEO
W
RKE
BO
UW
OR
RY
E
-CLR
SSlC
RL
WR
KE B
OU
NO
RR
Y
E -I ‘-I
.oo
-0.5
0 0
.oo
0.50
I
.oo
1 .5
0 2
.oo
2.50
8
LON
GIT
UO
INR
L C
OO
RO
INf3
TE,
X/R
FIG
UR
E 50
B.
FOR
E AN
D
AFT
WAK
E BO
UN
DAR
Y C
HAR
TS FO
R T
HE
GEN
ERAL
IZED
DIS
TOR
TED
TI
P VO
RTE
X (/A
= .
2,
B =
4,
CT
= .0
06,
a =
-41,
Y/
R =
.25
9
-
ADVA
NC
E R
RTI
O
= 0.
20
NU
MBE
R O
F BL
RO
ES
= 4
CT
= 0.
006
tLR
M8O
R
= -0
.028
81
TIP
PRTH
PL
RN
E =
-4.0
00
LRTE
RR
L PO
SITI
ON
=
0.50
0
0 C
ENER
RLJ
ZEO
H
RKE
BO
UN
OR
RY
E
-CLR
SSJC
RL
HAK
E BO
UN
OR
RY
0
cfg
\ d-
I
I I
I I
I 1
J-4 m
z
w
p-
u z a!
J-
?-
m
E;: d.
I ii
z x”
i-
a 2 ‘-I
.oo
-0 .s
o 0.
00
o.so
I .o
o I
1 .so
2 .o
o 2
.so
LON
GIT
UO
INf4
L C
OO
RO
INf7
TE,
X/R
FIG
UR
E 50
C.
FOR
E AN
D A
FT
WAK
E BO
UN
DAR
Y C
HAR
TS F
OR
TH
E G
ENER
ALIZ
ED
DIS
TOR
TED
TI
P VO
RTE
X (/.
& =
.2,
B =
4,
CT
= .0
06,
a=
-4),
Y/R
=
.500
1. Report No. 2. Government Accuion No. 3. Aaipiont’s CIUlag No.
4. Title end Subtitle 5. Repon oate HELICOPTER ROTOR WARE GEOMETRY AND ITS INFLUENCE IN October 1983 FORWARD FLIGHT 5. Performing Orglnizrtion Coda
Volume II - Wake Geometry Charts
7. Author(s) 8. Porfwming Orgenitation Repon No.
T. Alan Egolf and Anton J. Landgrebe R83-912666-58 10. Work Unit No.
9. Performing Organization Name and Address
United Technologies Research Center 11. Contract or Grant No. East Hartford, CT 06108 NASl-14568
13. Type of Repot and Pnlod Covered
12. Sponsoring Agency Name and Addrnr
National Aeronautics and Space Administration Contractor Report
Washington, DC 20546 14. Sponsoring Agancy code
15. ~pplemen~arV Noter The contract research effort which has led to the results in this report was financially supported by the structures Laboratory, USARTL, (AVRADCOM). Langley Technical Monitor: Wayne R. Mantay, Final Report - Volume II of two Volumes
---_---- 16. Abstract An analytical investigation to generalize the wake geometry of a helicopter rotor in steady level forward flight and to demonstrate the influence of wake deforma- tion in the prediction of rotor airloads and performance is described.
In Volume I, a first level generalized wake model is presented which is based on theoretically predicted tip vortex geometries for a selected representative blade design. The tip vortex distortions are generalized in equation form as displacements from the classical undistorted tip vortex geometry in terms of vortex age, blade azimuth, rotor advance ratio, thrust coefficient, and number of blades. These equations were programmed in a computer module to provide distorted wake coordinates at very low cost for use in rotor airflow and airloads prediction analyses. The sensitivity of predicted rotor airloads, performance, and blade bending moments to the modeling of the tip vortex distortion are demonstrated for low to moderately high advance ratios for a representative rotor and the H-34 rotor. Comparisons with H-34 rotor test data demonstrate the effects of the classical, predicted distorted, and the newly developed generalized wake models on airloads and blade bending moments. The use of distorted wake models results in the occurrence of numerous blade-vortex inter- actions on the forward and lateral sides of the rotor disk. The significance of these interactions is related to the number and degree of proximity to the blades of the tip vortices. The correlation obtained with the distorted wake models (generalized and predicted) is encouraging. However, the resulting high sensitivity of the predicted airloads to small deviations in tip vortex position demonstrate the requirement for improved blade-vortex interaction modeling.
A set of wake geometry charts are presented in Volume II to provide a convenient, readily accessible source for approximating rotor forward flight wake geometry and identifying wake boundaries and locations of blade-vortex passage. 7. Key Words ISuggwed by Author(r)) 18. Distribution Statement
Rotor Wake Geometry Helicopter Distorted Wake Wake Geometry Charts Unclassified Generalized Wake Tip Vortex
- Unlimited
Rotor Airloads Rotor Performance Subject Category 02
9. Security Classif. (of this report1 20. Security Classif. (of this plgel 21. No. of Pagn 22. Price
Unclassified Unclassified 208 A10
For sale by the National Technical Information Serwce. Sprqfield. Virginia 22161
