Prop-fan with improved stability
CROSS REFERENCE 
     The invention described herein was made in the performance of work under NASA Contract No. NA3-22394 and is subject to the provisions of Section 305 of the National Aeronautics and Space Act of 1958 (72 Stat. 435; 42 U.S.C. 2457). 
    
    
     This application is a continuation of application Ser. No. 699,119, filed Feb. 7, 1985 and now abandoned. 
    
    
     DESCRIPTION 
     1. Technical Field 
     This invention relates generally to aircraft propellers and more specifically to high speed prop-fans. 
     2. Background Art 
     It has been long known that certain aircraft such as commercial airliners may be powered more efficiently with turbo-props than turbo-jets. However, in the 1950s, turbo-jet powered aircraft began replacing propeller driven aircraft on relatively long routes because of the low cost and availability of jet fuel and the relatively low noise and vibration levels of turbo-jet power plants. The extreme increase in the cost of jet fuel in the 1970s caused the airline industry to look to a new generation of propeller as a way of enhancing the efficiency of operation of commercial airliners on routes of from 500-1800 miles and at speeds in the range of Mach 0.7-0.8. Since engines capable of powering such aircraft rotated at much higher rates of speed than state of the art turbo-prop engines, the propeller tips of which were already running at sonic speeds, the diameter of the new generation propeller had to be reduced. Since power handling requirements were greatly increased over state of the art turbo-props, high solidity ratios (greater than 1.0) at the propeller root were required and, therefore, the new generation propeller required a relatively large number of wide chord blades. To reduce compressibility losses and thereby make up for additional swirl losses, the blades of the new generation propeller were required to be thinner than existing blades. Blade sweep was also required to reduce the effective Mach number at the blade tip to less than critical while minimizing blade noise levels. The resulting highly loaded, high solidity, multi-bladed swept propeller is referred to today as a prop-fan and is disclosed in U.S. Pat. No. 4,171,183 and American Institute of Aeronautics and Astronautics Paper No. 75-1208. Improvements to such prop-fans are disclosed in U.S. Pat. Nos. 4,358,246 and 4,370,097 to Hanson, et al. 
     Those skilled in the art of aerodynamics recognize flutter as a potential problem in the operation of an aerodynamic device such as an airplane wing or propeller blade. In the low speed operation of a propeller blade, the blade may vibrate in uncoupled flat-wise bending and torsional modes, such vibrations being damped by the propeller itself and the aerodynamic loading thereon. However, at higher speeds, the flat-wise bending and torsional modes may become coupled, thus extracting greater energy from the airstream than when uncoupled. Such increased energy extraction can result in sustained, neutrally stable vibration or, in the case of classical flutter, in energy extraction exceeding that dissipated by internal blade damping, thereby causing a vibration of increasing amplitude and ultimately structural failure of the blade. 
     While classical flutter is always a consideration in the design and development of conventional propellers, it is of particular concern in prop-fans since the sweep of prop-fan blades increases the tendency toward coupling of flat-wise bending at the blade tip and torsional modes of vibration, thereby increasing the risk of classical flutter at high operating speeds. Moreover individual modes of vibration may be characterized by a combination of both bending and torsion motion which can result in single-mode, high-speed, unstalled flutter. 
     DISCLOSURE OF INVENTION 
     It is therefore among the objects of the present invention to provide an improved prop-fan characterized by reduced coupling between flat-wise bending and torsional vibratory motion, both for separate modes which tend to couple, and individual modes which contain components of both bending and torsional motion. 
     It is another object of the present invention to provide such a prop-fan wherein such reduced coupling is achieved by a stiffening of the prop-fan blades in an edge-wise direction. 
     These objects are achieved in the present invention by providing each swept prop-fan blade with a leading edge which, from a location outwardly of the midpoint thereof, occupies substantially a single plane, thereby enhancing the edge-wise stiffness of the blade and reducing the tendency of the coupling of flat-wise bending and torsional modes of blades vibration. In other words, the outer portion of the leading edge is curved in a chordal direction (to define blade sweep), the edge exhibiting no significant offset (lateral curvature in a span-wise direction. In the preferred embodiment, the leading edge of the tip portion of the blade is statically predeflected normally to the local chord line in the general direction of blade rotation. Under operating conditions, aerodynamic forces on the blade tend to straighten this predeflected tip portion whereby the entire leading edge outwardly from the mid-span of the blade occupies essentially a common plane under normal operating conditions. 
    
    
     BRIEF DESCRIPTION OF DRAWINGS 
     FIG. 1 is a frontal elevation of a prior art aircraft prop-fan; 
     FIG. 2 is an isometric view of the prop-fan of FIG. 1; 
     FIG. 3 is an isometric view of a prop-fan of the present invention; 
     FIG. 4 is a plan view of one of the blades of the prop-fan of FIG. 3 taken in the direction of line 4--4 thereon; 
     FIG. 5 is a frontal elevation of one of the blades of FIG. 3; 
     FIG. 6 is a side elevation of the blade of FIG. 5; 
     FIG. 7 is a sectional view taken at the chordal centers of the airfoil sections which define the blade of FIG. 6, in a direction perpendicular to the chords of those airfoils as exemplified by line 7--7 of FIG. 8; 
     FIGS. 8-27 are a series of cross-sectional views of the airfoil sections which when stacked, define the blades of the prop-fan of the present invention, the sections being taken at the stations indicated in FIG. 6; 
     FIG. 28 is a side elevation of a prior art prop-fan blade in a graphical representation of a first resonance mode thereof; 
     FIG. 29 is a view similar to FIG. 28 but illustrating the effects of the first resonance mode on one of the blades of the prop-fan of the present invention; 
     FIG. 30 is a view similar to FIG. 28 but showing the effects of a fourth resonance mode on the prior art prop-fan blade; and 
     FIG. 31 is a view similar to FIG. 29 but illustrating the effects of the fourth resonance mode on the prop-fan blade of the present invention. 
    
    
     BEST MODE FOR CARRYING OUT THE INVENTION 
     Referring to FIGS. 1 and 2, a prior art prop-fan is shown generally at 10 and comprises a hub 15 on which a plurality of blades 20 are mounted for pivotal pitch change movement with respect thereto. The hub is covered by a spinner 25 and nacelle 30 which are shaped to reduce the effective velocity of the airflow adjacent to the spinner and nacelle so as to maintain an effective velocity through the inner airfoil sections of the blades equal to or less than the critical Mach number. Further details of the shape and structure of prop-fan 10 may be found in U.S. Pat. Nos. 4,171,183, 4,358,246 and 4,370,097 as well as American Institute of Aeronautics and Astronautics Paper No. 75-1208 noted hereinabove. 
     As perhaps best seen by reference to blade 20&#39; shown in the 11 o&#39;clock position in FIG. 2, each blade includes a leading edge which is swept back (for the reasons set forth hereinabove) and also curved in a circumferential direction generally opposite to the direction of rotation (indicated by arrows 35) of the propeller. This is in keeping with the aero-acoustic desire to sweep each of the high-speed outboard sections in a rearward direction, parallel to the local direction of air flow which describes a different helical path at each radial section. It has been shown that flat-wise vibration of the tip portions of blades 20 can result in a coupled torsional vibration thereof under certain operating conditions. Referring to blade 20&#39; it will be appreciated that displacement of the blade tips normal to the local chord lines thereof will, owing to the blade sweep and curvature of the leading edge in a direction opposite that of rotation, contribute toward a twisting of the blade generally about the mass centers of the airfoils which define the blade. Thus, it is seen that flat-wise vibration can, under certain operating conditions, couple with a torsional vibration of the blade, thereby risking classical flutter and mechanical failure of the blade. 
     In accordance with the present invention, the tendency toward coupling of flat-wise bending and torsional modes of blade vibration is significantly reduced by a modification of the stacking of the airfoil sections which form the blades of the prop-fan. Referring to FIG. 3, the prop-fan of the present invention is shown generally at 40, comprising a plurality of blades 45 mounted on a hub 50 for pivotal, pitch change movement with respect thereto, hub 50 being covered by a spinner 55. As illustrated in FIG. 3, blades 45 are, at radially outer portions thereof, generally thin and swept back as are known prop-fan blades. The blades are also highly loaded and cummulatively define a solidity factor of greater than 1.0 at the roots thereof and less than 1.0 at the tips thereof, also in accordance with known prop-fan teachings. However, unlike prop-fan blades 20 illustrated in FIGS. 1 and 2, the airfoils which form blades 45 are stacked such that for each blade, the outer portion of the leading edge lies substantially in a single plane. In other words, the outer portion of the leading edge is curved only in a chordal direction, thereby defining blade sweep, without being significantly curved or offset in a span-wise direction (normal to the direction of blade sweep). This is perhaps best illustrated in the enlargements of one of the blades in FIGS. 4 and 5. Referring to these drawings, blade 45 includes a relatively thick base or root portion 60 which fairs radially outwardly to a thin tip portion 65 including a free tip 70. The leading edge of the blade is illustrated at 75, the mid point of the leading edge (located at about the mid point of the blade span) being shown at 80. As set forth hereinabove, it will be noted that that portion of leading edge 75 between point 80 and tip 70 lies substantially in a single plane. This is to be contrasted with prior art prop-fan blades (the radially outer portion thereof being shown in FIG. 4 by phantom line 85) wherein the leading edge of the blade curves in a direction generally opposite to the direction of blade rotation (illustrated again by arrow 35). However, it will be noted that the leading edge of the tip portion of blade 45 may be slightly statically predeflected in a direction generally normal to the local chord lines at the tip. The magnitude of the predeflection of the blade tip 70 is generally on the order of from 1.0% to 5.0% of the blade span and allows the bending of the blade tip portion by aerodynamic forces on the blade to maintain the tip portion of the blade leading edge in a coplanar relationship to the remainder of the outer portion of the leading edge. 
     Referring to FIG. 6, a side elevation of blade 45 with twist removed therefrom is shown along with the locations of several stations along the blade span. The numbers of the stations indicate distances in inches from the radially innermost end of the blade spar outwardly, to the tip of the blade. Accordingly, it will be understood that the blade illustrated in FIG. 6 measures approximately 54 inches from tip to spar end. 
     Referring to FIGS. 8-27, a family of airfoils resulting from the sectioning of blade 45 along lateral planes at the stations noted on FIG. 6 is shown. The intersection of the axes shown in each of FIGS. 8-27 define, the pitch change axis of the blade. The following tables list precise coordinates of the airfoil sections. For each table, angle BA is the angular orientation of the airfoil chord from a reference stacking plane, LEA is a measurement of the distance between the leading edge of the airfoil and the pitch change axis, Z is a chordal measure from the pitch change axis, C is the location of the camber side of the airfoil measured normally from a corresponding chordal location and F is the location of the face side of the airfoil measured normally from a corresponding chordal location. See FIG. 12. 
     
                       TABLE I                                                     
______________________________________                                    
STA 11.10 BA° 75.86 LEA 8.199                                      
Z         C            Z        F                                         
______________________________________                                    
-8.1302   .1725        -8.1273  .2450                                     
-8.0714   .2423        -8.0714  .3071                                     
-7.9539   .3441        -7.9539  .4002                                     
-7.7580   .4718        -7.7580  .5127                                     
-7.4152   .6349        -7.4152  .6502                                     
-6.9255   .8416        -6.9255  .8237                                     
-6.2399   1.1010       -6.2399  1.0484                                    
-5.2604   1.4359       -5.2604  1.3407                                    
-4.2810   1.7391       -4.2810  1.6224                                    
-2.3221   2.2521       -2.3221  2.1972                                    
-.3632    2.6288       -.3632   2.7650                                    
1.5957    2.8229       1.5957   3.2132                                    
3.5545    2.7735       3.5545   3.3676                                    
5.5134    2.4744       5.5134   3.1589                                    
7.4723    1.9223       7.4723   2.5036                                    
9.4312    1.1129       9.4312   1.4060                                    
10.4106   .5939        10.4106  .7534                                     
10.9003   .2902        10.9003  .4062                                     
11.1942   .0996        11.1942  .1927                                     
11.3814   -.0219       11.3820  .0544                                     
______________________________________                                    
 
    
     
                       TABLE II                                                    
______________________________________                                    
STA 13.50 BA° 75.68 LEA 9.479                                      
Z         C            Z        F                                         
______________________________________                                    
-9.4249   .0598        -9.4227  .1946                                     
-9.3528   .1206        -9.3528  .2495                                     
-9.2362   .1906        -9.2362  .3100                                     
-9.0418   .2772        -9.0418  .3796                                     
-8.7017   .3874        -8.7017  .4620                                     
-8.2157   .5220        -8.2157  .5580                                     
-7.5354   .6849        -7.5354  .6726                                     
-6.5635   .8775        -6.5635  .8073                                     
-5.5915   1.0404       -5.5915  .9235                                     
-3.6477   1.3005       -3.6477  1.1271                                    
-1.7039   1.4855       -1.7039  1.3058                                    
.2399     1.5728       .2399    1.4413                                    
2.1838    1.5310       2.1838   1.4913                                    
4.1276    1.3709       4.1276   1.4265                                    
6.0714    1.0808       6.0714   1.1861                                    
8.0152    .6230        8.0152   .7245                                     
8.9871    .3157        8.9871   .4220                                     
9.4731    .1323        9.4731   .2479                                     
9.7647    .0207        9.7647   .1464                                     
9.9462    -.0483       9.9454   .0860                                     
______________________________________                                    
 
    
     
                       TABLE III                                                   
______________________________________                                    
STA 15.50 BA° 75.19 LEA 10.462                                     
Z         C            Z        F                                         
______________________________________                                    
-10.4138  .0187        -10.4096 .1826                                     
-10.3355  .0741        -10.3355 .2289                                     
-10.2186  .1333        -10.2186 .2763                                     
-10.0237  .2070        -10.0237 .3295                                     
-9.6827   .3021        -9.6827  .3908                                     
-9.1954   .4169        -9.1954  .4591                                     
-8.5133   .5555        -8.5133  .5390                                     
-7.5389   .7172        -7.5389  .6287                                     
-6.5645   .8509        -6.5645  .7026                                     
-4.6156   1.0520       -4.6156  .8202                                     
-2.6667   1.1744       -2.6667  .9025                                     
-.7178    1.2067       -.7178   .9351                                     
1.2311    1.1260       1.2311   .8922                                     
3.1799    .9455        3.1799   .7792                                     
5.1288    .6767        5.1288   .6010                                     
7.0777    .3332        7.0777   .3713                                     
8.0521    .1353        8.0521   .2414                                     
8.5394    .0314        8.5394   .1738                                     
8.8317    -.0310       8.8317   .1333                                     
9.0107    -.0692       9.0093   .1086                                     
______________________________________                                    
 
    
     
                       TABLE IV                                                    
______________________________________                                    
STA 18.50 BA° 73.85 LEA 11.763                                     
Z         C            Z        F                                         
______________________________________                                    
-11.7222  -.0339       -11.7148 .1889                                     
-11.6330  .0197        -11.6330 .2270                                     
-11.5130  .0717        -11.5130 .2615                                     
-11.3129  .1376        -11.3129 .2981                                     
-10.9628  .2249        -10.9628 .3369                                     
-10.4626  .3309        -10.4626 .3765                                     
-9.7624   .4586        -9.7624  .4204                                     
-8.7620   .6076        -8.7620  .4650                                     
-7.7617   .7292        -7.7617  .4991                                     
-5.7610   .9056        -5.7610  .5504                                     
-3.7603   1.0058       -3.7603  .5801                                     
-1.7595   1.0239       -1.7595  .5802                                     
.2412     .9443        .2412    .5351                                     
2.2419    .7777        2.2419   .4513                                     
4.2426    .5370        4.2426   .3416                                     
6.2433    .2381        6.2433   .2242                                     
7.2436    .0733        7.2436   .1673                                     
7.7438    -.0081       7.7438   .1465                                     
8.0439    -.0570       8.0439   .1340                                     
8.2272    -.0868       8.2248   .1265                                     
______________________________________                                    
 
    
     
                       TABLE V                                                     
______________________________________                                    
STA 21.50 BA° 71.71 LEA 12.741                                     
Z         C            Z        F                                         
______________________________________                                    
-12.7039  .0114        -12.6951 .1388                                     
-12.6058  .0379        -12.6058 .1686                                     
-12.4813  .0840        -12.4813 .1935                                     
-12.2739  .1435        -12.2739 .2184                                     
-11.9108  .2245        -11.9108 .2416                                     
-11.3921  .3245        -11.3921 .2623                                     
-10.6659  .4452        -10.6659 .2822                                     
-9.6286   .5874        -9.6286  .2979                                     
-8.5912   .7037        -8.5912  .3073                                     
-6.5164   .8718        -6.5164  .3202                                     
-4.4417   .9689        -4.4417  .3217                                     
-2.3670   .9881        -2.3670  .3083                                     
-.2922    .9162        -.2922   .2703                                     
1.7825    .7626        1.7825   .2150                                     
3.8573    .5386        3.8573   .1535                                     
5.9320    .2544        5.9320   .1056                                     
6.9694    .1011        6.9694   .0975                                     
7.4881    .0244        7.4881   .0934                                     
7.7993    -.0216       7.7993   .0910                                     
7.9896    -.0497       7.9867   .0895                                     
______________________________________                                    
 
    
     
                       TABLE VI                                                    
______________________________________                                    
STA 24.50 BA° 69.28 LEA 13.254                                     
Z         C            Z        F                                         
______________________________________                                    
-13.2141  .1373        -13.2047 -.0166                                    
-13.1146  .1769        -13.1146 .0026                                     
-12.9862  .2165        -12.9862 .0196                                     
-12.7723  .2695        -12.7723 .0365                                     
-12.3978  .3432        -12.3978 .0512                                     
-11.8629  .4340        -11.8629 .0632                                     
-11.1139  .5422        -11.1139 .0716                                     
-10.0441  .6690        -10.0441 .0752                                     
-8.9742   .7720        -8.9742  .0757                                     
-6.8344   .9202        -6.8344  .0758                                     
-4.6946   1.0093       -4.6946  .0666                                     
-2.5549   1.0309       -2.5549  .0489                                     
-.4151    .9735        -.4151   .0182                                     
1.7247    .8425        1.7247   -.0196                                    
3.8644    .6446        3.8644   -.0561                                    
6.0042    .3868        6.0042   -.0589                                    
7.0741    .2430        7.0741   -.0603                                    
7.6090    .1710        7.6090   -.0609                                    
7.9300    .1279        7.9300   -.0614                                    
8.1267    .1014        8.1238   -.0616                                    
______________________________________                                    
 
    
     
                       TABLE VII                                                   
______________________________________                                    
STA 27.00 BA° 67.34 LEA 13.313                                     
Z         C            Z        F                                         
______________________________________                                    
-13.2704  .3199        -13.2587 -.1989                                    
-13.1711  .3520        -13.1711 -.1880                                    
-13.0403  .3867        -13.0403 -.1767                                    
-12.8222  .4352        -12.8222 -.1646                                    
-12.4407  .5040        -12.4407 -.1542                                    
-11.8956  .5876        -11.8956 -.1467                                    
-11.1324  .6850        -11.1324 -.1436                                    
-10.0423  .7971        -10.0423 -.1434                                    
-8.9521   .8867        -8.9521  -.1437                                    
-6.7717   1.0122       -6.7717  -.1400                                    
-4.5913   1.0918       -4.5913  -.1466                                    
-2.4109   1.1159       -2.4109  -.1581                                    
-.2305    1.0754       -.2305   -.1762                                    
1.9498    .9699        1.9498   -.2000                                    
4.1302    .7997        4.1302   -.2268                                    
6.3106    .5659        6.3106   -.2485                                    
7.4008    .4260        7.4008   -.2465                                    
7.9459    .3531        7.9459   -.2455                                    
8.2729    .3105        8.2729   -.2450                                    
8.4735    .2844        8.4709   -.2446                                    
______________________________________                                    
 
    
     
                       TABLE VIII                                                  
______________________________________                                    
STA 29.00 BA° 65.85 LEA 13.147                                     
Z         C            Z        F                                         
______________________________________                                    
-13.1043  .4930        -13.0911 -.3741                                    
-13.0043  .5212        -13.0043 -.3681                                    
-12.8721  .5531        -12.8721 -.3606                                    
-12.6517  .5991        -12.6517 -.3520                                    
-12.2661  .6649        -12.2661 -.3446                                    
11.7153   .7431        -11.7153 -.3396                                    
-10.9440  .8312        -10.9440 -.3377                                    
-9.8423   .9305        -9.8423  -.3366                                    
-8.7406   1.0086       8.7406   -.3346                                    
-6.5371   1.1166       -6.5371  -.3253                                    
-4.3336   1.1884       -4.3336  -.3269                                    
-2.1301   1.2138       -2.1301  -.3300                                    
.0733     1.1860       .0733    -.3352                                    
2.2768    1.1008       2.2768   -.3467                                    
4.4803    .9530        4.4803   -.3673                                    
6.6837    .7357        6.6837   -.3948                                    
7.7855    .5987        7.7855   -.4102                                    
8.3364    .5234        8.3364   -.4105                                    
8.6669    .4782        8.6669   -.4106                                    
8.8699    .4505        8.8672   -.4107                                    
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                       TABLE IX                                                    
______________________________________                                    
STA 32.00 BA° 63.73 LEA 12.560                                     
Z         C            Z        F                                         
______________________________________                                    
-12.5203  .7784        -12.5072 -.6718                                    
-12.4159  .8052        -12.4159 -.6694                                    
-12.2828  .8351        -12.2828 -.6655                                    
-12.0610  .8788        -12.0610 -.6609                                    
-11.6728  .9408        -11.6728 -.6582                                    
-11.1182  1.0119       -11.1182 -.6567                                    
-10.3418  1.0906       -10.3418 -.6582                                    
-9.2327   1.1782       -9.2327  -.6592                                    
-8.1236   1.2430       -8.1236  -.6552                                    
-5.9053   1.3279       -5.9053  -.6385                                    
-3.6870   1.3904       -3.6870  -.6376                                    
-1.4688   1.4132       -1.4688  -.6321                                    
.7495     1.3956       .7495    -.6252                                    
2.9677    1.3301       2.9677   -.6246                                    
5.1860    1.2085       5.1860   -.6388                                    
7.4043    1.0166       7.4043   -.6707                                    
8.5134    .8897        8.5134   -.6939                                    
9.0679    .8139        9.0679   -.6981                                    
9.4007    .7697        9.4007   -.7007                                    
9.6052    .7420        9.6027   -.7022                                    
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                       TABLE X                                                     
______________________________________                                    
STA 35.00 BA° 61.65 LEA 11.521                                     
Z         C            Z        F                                         
______________________________________                                    
-11.4878  1.0954       -11.4769 -1.0064                                   
-11.3784  1.1239       -11.3784 -1.0044                                   
-11.2464  1.1512       -11.2464 -1.0019                                   
-11.0266  1.1923       -11.0266 -.9996                                    
-10.6419  1.2500       -10.6419 -1.0006                                   
-10.0922  1.3161       -10.0922 -1.0033                                   
-9.3228   1.3873       -9.3228  -1.0075                                   
-8.2235   1.4639       -8.2235  -1.0086                                   
-7.1242   1.5181       -7.1242  -1.0033                                   
-4.9257   1.5866       -4.9257  -.9855                                    
-2.7272   1.6400       -2.7272  -.9867                                    
-.5287    1.6552       -.5287   -.9810                                    
1.6698    1.6350       1.6698   -.9736                                    
3.8683    1.5745       3.8683   -.9720                                    
6.0668    1.4675       6.0668   -.9834                                    
8.2653    1.3021       8.2653   -1.0096                                   
9.3645    1.1944       9.3645   -1.0193                                   
9.9142    1.1305       9.9142   -1.0241                                   
10.2439   1.0921       10.2439  -1.0270                                   
10.4461   1.0686       10.4439  -1.0237                                   
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                       TABLE XI                                                    
______________________________________                                    
STA 38.00 BA° 59.62 LEA 9.937                                      
Z         C            Z        F                                         
______________________________________                                    
-9.9089   1.4088       -9.9015  -1.3346                                   
-9.7990   1.4347       -9.7990  -1.3315                                   
-9.6713   1.4596       9.6713   -1.3285                                   
-9.4584   1.4952       -9.4584  -1.3254                                   
-9.0859   1.5446       -9.0859  -1.3247                                   
-8.5538   1.6016       -8.5538  -1.3265                                   
-7.8088   1.6635       -7.8088  -1.3318                                   
-6.7446   1.7295       -6.7446  -1.3334                                   
-5.6803   1.7741       -5.6803  -1.3265                                   
-3.5518   1.8338       -3.5518  -1.3137                                   
-1.4232   1.8746       -1.4232  -1.3128                                   
.7053     1.8807       .7053    -1.3065                                   
2.8338    1.8564       2.8338   -1.3001                                   
4.9624    1.7993       4.9624   -1.2996                                   
7.0909    1.7064       7.0909   -1.3106                                   
9.2194    1.5713       9.2194   -1.3354                                   
10.2837   1.4864       10.2837  -1.3430                                   
10.8158   1.4375       10.8158  -1.3468                                   
11.1351   1.4082       11.1351  -1.3490                                   
11.3298   1.3903       11.3281  -1.3504                                   
______________________________________                                    
 
    
     
                       TABLE XII                                                   
______________________________________                                    
STA 41.00 BA° 57.73 LEA 7.748                                      
Z         C            Z        F                                         
______________________________________                                    
-7.7225   1.6569       -7.7167  -1.5929                                   
-7.6183   1.6788       -7.6183  -1.5904                                   
-7.4987   1.6992       -7.4987  -1.5874                                   
-7.2993   1.7284       -7.2993  -1.5837                                   
-6.9503   1.7685       -6.9503  -1.5811                                   
-6.4519   1.8147       -6.4519  -1.5799                                   
-5.7540   1.8654       -5.7540  -1.5814                                   
-4.7570   1.9186       -4.7570  -1.5807                                   
-3.7601   1.9560       -3.7601  -1.5747                                   
-1.7661   2.0088       -1.7661  -1.5670                                   
.2278     2.0358       .2278    -1.5596                                   
2.2217    2.0360       2.2217   -1.5506                                   
4.2156    2.0126       4.2156   -1.5427                                   
6.2095    1.9635       6.2095   -1.5418                                   
8.2035    1.8872       8.2035   -1.5529                                   
10.1974   1.7813       10.1974  -1.5821                                   
11.1943   1.7162       11.1943  -1.5933                                   
11.6928   1.6795       11.6928  -1.5988                                   
11.9919   1.6575       11.9919  -1.6022                                   
12.1727   1.6441       12.1715  -1.6042                                   
______________________________________                                    
 
    
     
                       TABLE XIII                                                  
______________________________________                                    
STA 43.50 BA° 56.42 LEA 5.431                                      
Z         C            Z        F                                         
______________________________________                                    
-5.4080   1.7746       -5.4034  -1.7182                                   
-5.3127   1.7922       -5.3127  -1.7168                                   
-5.2033   1.8089       -5.2033  -1.7139                                   
-5.0210   1.8329       -5.0210  -1.7102                                   
-4.7020   1.8661       -4.7020  -1.7073                                   
-4.2463   1.9051       -4.2463  -1.7055                                   
-3.6084   1.9493       -3.6084  -1.7068                                   
-2.6970   1.9972       -2.6970  -1.7081                                   
-1.7856   2.0261       -1.7856  -1.7013                                   
.0372     2.0719       .0372    -1.6956                                   
1.8600    2.0921       1.8600   -1.6867                                   
3.6828    2.0917       3.6828   -1.6780                                   
5.5055    2.0714       5.5055   -1.6708                                   
7.3283    2.0303       7.3283   -1.6700                                   
9.1511    1.9669       9.1511   -1.6804                                   
10.9739   1.8782       10.9739  -1.7068                                   
11.8853   1.8244       11.8853  -1.7165                                   
12.3410   1.7945       12.3410  -1.7213                                   
12.6144   1.7765       12.6144  -1.7241                                   
12.7780   1.7658       12.7769  -1.7258                                   
______________________________________                                    
 
    
     
                       TABLE XIV                                                   
______________________________________                                    
STA 46.00 BA° 55.40 LEA 2.625                                      
Z         C            Z        F                                         
______________________________________                                    
-2.6052   1.8050       -2.6009  -1.7576                                   
-2.5215   1.8195       -2.5215  -1.7580                                   
-2.4260   1.8336       -2.4260  -1.7565                                   
-2.2667   1.8540       -2.2667  -1.7548                                   
-1.9880   1.8826       -1.9880  -1.7550                                   
-1.5899   1.9156       -1.5899  -1.7546                                   
-1.0325   1.9504       -1.0325  -1.7524                                   
-.2362    1.9882       -.2362   -1.7485                                   
.5601     2.0141       .5601    -1.7479                                   
2.1527    2.0525       2.1527   -1.7435                                   
3.7453    2.0704       3.7453   -1.7377                                   
5.3379    2.0710       5.3379   -1.7314                                   
6.9304    2.0540       6.9304   -1.7259                                   
8.5230    2.0210       8.5230   -1.7251                                   
10.1156   1.9678       10.1156  -1.7323                                   
11.7082   1.8935       11.7082  -1.7521                                   
12.5045   1.8480       12.5045  -1.7565                                   
12.9026   1.8238       12.9026  -1.7587                                   
13.1415   1.8093       13.1415  -1.7600                                   
13.2820   1.8007       13.2809  -1.7608                                   
______________________________________                                    
 
    
     
                       TABLE XV                                                    
______________________________________                                    
STA 47.50 BA° 54.95 LEA .693                                       
Z         C            Z        F                                         
______________________________________                                    
-.6760    1.7855       -.6725   -1.7455                                   
-.5999    1.7990       -.5999   -1.7448                                   
-.5144    1.8116       -.5144   -1.7435                                   
-.3719    1.8291       -.3719   -1.7414                                   
-.1225    1.8535       -.1225   -1.7405                                   
.2338     1.8799       .2338    -1.7380                                   
.7327     1.9071       .7327    -1.7363                                   
1.4453    1.9387       1.4453   -1.7343                                   
2.1579    1.9669       2.1579   -1.7362                                   
3.5831    2.0021       3.4831   -1.7351                                   
5.0084    2.0191       5.0084   -1.7312                                   
6.4336    2.0189       6.4336   -1.7260                                   
7.8588    2.0051       7.8588   -1.7216                                   
9.2841    1.9774       9.2841   -1.7207                                   
10.7093   1.9299       10.7093  -1.7261                                   
12.1345   1.8649       12.1345  -1.7416                                   
12.8472   1.8253       12.8472  -1.7430                                   
13.2035   1.8043       13.2035  -1.7437                                   
13.4172   1.7917       13.4172  -1.7442                                   
13.5409   1.7844       13.5393  -1.7444                                   
______________________________________                                    
 
    
     
                       TABLE XVI                                                   
______________________________________                                    
STA 49.00 BA° 54.62 LEA -1.430                                     
Z         C            Z        F                                         
______________________________________                                    
1.4424    1.7294       1.4450   -1.6981                                   
1.5101    1.7423       1.5101   -1.6963                                   
1.5842    1.7535       1.5842   -1.6967                                   
1.7077    1.7684       1.7077   -1.6952                                   
1.9240    1.7885       1.9240   -1.6950                                   
2.2328    1.8109       2.2328   -1.6938                                   
2.6653    1.8383       2.6653   -1.6965                                   
3.2830    1.8665       3.2830   -1.6963                                   
3.9008    1.8904       3.9008   -1.6967                                   
5.1363    1.9192       5.1363   -1.6954                                   
6.3718    1.9338       6.3718   -1.6918                                   
7.6074    1.9315       7.6074   -1.6868                                   
8.8429    1.9209       8.8429   -1.6826                                   
10.0784   1.8984       10.0784  -1.6819                                   
11.3139   1.8576       11.3139  -1.6859                                   
12.5495   1.8023       12.5495  -1.6901                                   
13.1672   1.7677       13.1672  -1.6922                                   
13.4761   1.7504       13.4761  -1.6933                                   
13.6614   1.7401       13.6614  -1.6939                                   
13.7661   1.7342       13.7650  -1.6943                                   
______________________________________                                    
 
    
     
                       TABLE XVII                                                  
______________________________________                                    
STA 50.50 BA° 54.95 LEA -3.737                                     
Z         C            Z        F                                         
______________________________________                                    
3.7475    1.6643       3.7493   -1.6398                                   
3.8039    1.6749       3.8039   -1.6375                                   
3.8653    1.6842       3.8653   -1.6369                                   
3.9676    1.6962       3.9676   -1.6365                                   
4.1466    1.7116       4.1466   -1.6341                                   
4.4023    1.7296       4.4023   -1.6326                                   
4.7603    1.7507       4.7603   -1.6344                                   
5.2718    1.7725       5.2718   -1.6337                                   
5.7832    1.7904       5.7832   -1.6336                                   
6.8060    1.8130       6.8060   -1.6351                                   
7.8289    1.8290       7.8289   -1.6341                                   
8.8518    1.8290       8.8518   .6320                                     
9.8746    1.8240       9.8746   -1.6322                                   
10.8975   1.8088       10.8975  -1.6334                                   
11.9203   1.7781       11.9203  -1.6389                                   
12.9432   1.7338       12.9432  -1.6370                                   
13.4546   1.7039       13.4546  -1.6361                                   
13.7103   1.6889       13.7103  -1.6356                                   
13.8638   1.6800       13.8638  -1.6353                                   
13.9472   1.6751       13.9460  -1.6351                                   
______________________________________                                    
 
    
     
                       TABLE XVIII                                                 
______________________________________                                    
STA 52.00 BA° 54.51 LEA -6.231                                     
Z         C            Z        F                                         
______________________________________                                    
6.2398    1.5528       6.2412   -1.5332                                   
6.2827    1.5595       6.2827   -1.5325                                   
6.3300    1.5655       6.3300   -1.5319                                   
6.4089    1.5741       6.4089   -1.5311                                   
6.5470    1.5866       6.5470   -1.5300                                   
6.7442    1.6007       6.7442   -1.5295                                   
7.0202    1.6163       7.0202   -1.5295                                   
7.4146    1.6337       7.4146   -1.5298                                   
7.8090    1.6472       7.8090   -1.5303                                   
8.5978    1.6664       8.5978   -1.5311                                   
9.3866    1.6776       9.3866   -1.5317                                   
10.1754   1.6819       10.1754  -1.5325                                   
10.9642   1.6796       10.9642  -1.5341                                   
11.7530   1.6687       11.7530  -1.5367                                   
12.5418   1.6473       12.5418  -1.5338                                   
13.3306   1.6118       13.3306  -1.5350                                   
13.7250   1.5898       13.7250  -1.5317                                   
13.9222   1.5786       13.9222  -1.5300                                   
14.0406   1.5719       14.0406  -1.5291                                   
14.1002   1.5685       14.0989  -1.5286                                   
______________________________________                                    
 
    
     
                       TABLE XIX                                                   
______________________________________                                    
STA 53.00 BA° 54.32 LEA -7.987                                     
Z         C            Z        F                                         
______________________________________                                    
7.9937    1.4426       7.9946   -1.4263                                   
8.0271    1.4474       8.0271   -1.4257                                   
8.0646    1.4518       8.0646   -1.4250                                   
8.1269    1.4580       8.1269   -1.4241                                   
8.2361    1.4671       8.2361   -1.4229                                   
8.3921    1.4774       8.3921   -1.4220                                   
8.6104    1.4887       8.6104   -1.4213                                   
8.9223    1.5015       8.9223   -1.4208                                   
9.2342    1.5117       9.2342   -1.4208                                   
9.8580    1.5267       9.8580   -1.4214                                   
10.4818   1.5355       10.4818  -1.4218                                   
11.1059   1.5394       11.1059  -1.4229                                   
11.7294   1.5379       11.7294  -1.4222                                   
12.3532   1.5287       12.3532  -1.4226                                   
12.9770   1.5111       12.9770  -1.4233                                   
13.6008   1.4820       13.6008  -1.4184                                   
13.9127   1.4661       13.9127  -1.4150                                   
14.0686   1.4584       14.0686  -1.4136                                   
14.1622   1.4538       14.1622  -1.4128                                   
14.2043   1.4518       14.2047  -1.4125                                   
______________________________________                                    
 
    
     
                       TABLE XX                                                    
______________________________________                                    
STA 54.00 BA° 54.04 LEA 9.788                                      
Z         C            Z        F                                         
______________________________________                                    
9.7933    1.2873       9.7943   -1.2756                                   
9.8176    1.2915       9.8176   -1.2754                                   
9.8446    1.2955       9.8446   -1.2752                                   
9.8895    1.3014       9.8895   -1.2750                                   
9.9680    1.3101       9.9680   -1.2748                                   
10.0803   1.3201       10.0803  -1.2752                                   
10.2374   1.3306       10.2374  -1.2758                                   
10.4619   1.3406       10.4619  -1.2767                                   
10.6864   1.3460       10.6864  -1.2774                                   
11.1354   1.3524       11.1354  -1.2786                                   
11.5844   1.3610       11.5844  -1.2806                                   
12.0334   1.3657       12.0334  -1.2830                                   
12.4823   1.3673       12.4823  -1.2864                                   
12.9313   1.3630       12.9313  -1.2802                                   
13.3803   1.3505       12.3803  -1.2740                                   
13.8293   1.3296       13.8293  -1.2677                                   
14.0538   1.3161       14.0538  -1.2646                                   
14.1660   1.3085       14.1660  -1.2631                                   
14.2334   1.3037       14.2334  -1.2621                                   
14.2595   1.3018       14.2579  -1.2618                                   
______________________________________                                    
 
    
     The improvement in the vibration characteristics of the prop-fan of the present invention is illustrated in FIGS. 28-31. FIG. 28 illustrates the results of analytical vibration predictions, verified by test, of a prior art prop-fan blade. In this test, a two foot diameter, titanium prop-fan was rotated at 8636 rpm, lines 100 connecting points of equal vibratory motion on the leading and trailing edges of the blade at a first resonance point of 180 Hz. It is noted that at the tip, the angular displacement of lines 120 from the axis of rotation of the prop-fan is roughly indicative of the type of vibration experienced by the blade. A very small value of angle φ indicating substantially pure bending, while an angle φ of 90° indicating substantially pure torsion. Thus, it will be noted that the angle illustrated is indicative of substantial coupling between bending and torsional modes of vibration. This blade exhibited high-speed, unstalled flutter of the first mode illustrated in FIG. 28 during wind tunnel tests. A stability analysis was subsequently developed which successfully predicted the operating condition corresponding to the onset of the first mode, high-speed, unstalled flutter. 
     FIG. 29 illustrates the results of analytical vibration predictions of a blade of the present invention differing from the blade of FIG. 28 only in the restacking of the airfoil sections to define a leading edge orientation in a single plane. In this analysis a solid titanium, two foot diameter prop-fan was rotated at 8636 rpm and the mode shape at a 198 Hz first resonance point was predicted. Note that in FIG. 29, angle φ defined by lines connecting points of equal vibratory movement is substantially less than the corresponding angle in FIG. 28, indicating less coupling of flat-wise bending and torsional vibratory modes at the blade tip than experienced by the prior art blade of FIG. 28. In other words, the blade of the present invention illustrated in FIG. 29 experiences substantially less torsional vibration and hence less coupling between the modes of vibration than the prior art blade of FIG. 28, and thus improved high speed stability. 
     In FIG. 30, a node line 130 is shown for the prior art blade of FIG. 28 when experiencing a forth resonance point (710 Hz) at a rotational speed of 8636 rpm. Those skilled in the art will appreciate that a node line parallel to the blade spar indicates torsional vibration while a node line perpendicular to the blade spar indicates flat-wise bending vibration. Thus, node line illustrated in FIG. 30 being generally horizontal at the left end thereof and approaching a more vertical orientation at the right end thereof indicates coupling between torsional and bending in the circumferentially outer portion of the blade. 
     However, in FIG. 31 node lines 130 for the fourth resonance point (785 Hz) predicted by analysis for the blade of the present invention when rotated at 8636 rpm, indicate generally pure bending at the blade tip and generally pure torsion at the blade root further evidencing a general uncoupling of these modes of vibration and the enhanced high speed stability associated therewith. 
     The same high-speed stability analysis which successfully predicted the onset of first mode, high-speed unstalled flutter instability of the prior art blade of FIG. 28 was applied to the blade of the present invention illustrated in FIGS. 29 and 31. Results of that stability analysis indicate that the blade of the present invention has greatly improved high-speed stability. 
     It is thus apparent that the prop-fan of the present invention exhibits significantly less coupling between torsional and flat-wise bending modes of vibration, and thus less risk of classical flutter and improved stability over known prop-fan blade geometries. While the prop-fan of the present invention has been illustrated with eight blades, it will be appreciated that greater or lesser numbers of such blades may be employed without departing from this invention. Likewise, while a particular family of airfoils has been illustrated as defining blade geometry it will be understood that the invention herein may be practiced by the stacking of any suitable family of airfoils to achieve the generally planar orientation of the blade leading edge from the midpoint of the blade span to the blade tip. Accordingly, it is intended by the following claims to cover these and any other modifications which will be suggested to those skilled in the art by the disclosure herein.