CA1270802A - Prop-fan with improved stability - Google Patents
Prop-fan with improved stabilityInfo
- Publication number
- CA1270802A CA1270802A CA000488883A CA488883A CA1270802A CA 1270802 A CA1270802 A CA 1270802A CA 000488883 A CA000488883 A CA 000488883A CA 488883 A CA488883 A CA 488883A CA 1270802 A CA1270802 A CA 1270802A
- Authority
- CA
- Canada
- Prior art keywords
- prop
- blade
- fan
- blades
- tip
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired - Fee Related
Links
Classifications
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B64—AIRCRAFT; AVIATION; COSMONAUTICS
- B64C—AEROPLANES; HELICOPTERS
- B64C11/00—Propellers, e.g. of ducted type; Features common to propellers and rotors for rotorcraft
- B64C11/16—Blades
- B64C11/18—Aerodynamic features
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T50/00—Aeronautics or air transport
- Y02T50/60—Efficient propulsion technologies, e.g. for aircraft
Landscapes
- Physics & Mathematics (AREA)
- Fluid Mechanics (AREA)
- Engineering & Computer Science (AREA)
- Aviation & Aerospace Engineering (AREA)
- Structures Of Non-Positive Displacement Pumps (AREA)
- Percussion Or Vibration Massage (AREA)
- Nitrogen And Oxygen Or Sulfur-Condensed Heterocyclic Ring Systems (AREA)
Abstract
Abstract Prop-Fan With Improved Stability Improved prop-fan stability is achieved by providing each blade of the prop-fan with a leading edge which, outwardly, from a location thereon at the mid-span of the blade, occupy generally a single plane.
Description
~escription Ti~le Prop-~an With Improved Stability Technical Field S This invention relates generally to aircraft prop011ers and more specifically to high speed prop-fans.
~aokground Art It has been long known that certain aircraft such as commercial airliners may be powered more e~ficiently 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 Euel in the 1970s caused the airline industry to look to a new genera tion of propeller as a way of enhancing the ef~iciency of operation of commercial airliners on routes of from 500-180Q miles and at speeds in the range of Mach 0.7-0.8~ Since engines capahle of powering such aircraft rotated at much higher ra~es of cpeed than state o the art turbo~prop engines, the propeller tips of which were already running at sonic speeds, th6 diameter of the new generation propeller had to be reduced. Since power handling requirements were ~,'7 greatly increased o~er state o~ the art turho-props, high solidlty ratios (greater than 1.0) at the propeller root were required and, therefore, the new genaration propeller required a relatively large numbsr of wide chord blades. To reduce compress-ibility losses and thereby make up for additional swirl losses, the blades of the new generation propeller were required to be thinner than exi~ting blad~sO ~lade sweep wa5 also required to reduce the effective Mach number at the blade ~ip to le55 than critical while minimizin~ blade noise levels. The reculting highly ioaded, ~igh solidity, multi-bladed swept propeller is referred to today as a prop~fan and is disclosed in U~S. Patent No. 4,171,183 and American Institute o~ Aeronautics and Astronautics Paper No.
.
75-1208. Improvements to such prop-fans are disclosed in U.S. Patent Nos. 4,25~,246 and 4,370,0g7 to Hanson, et al.
Those skilled in the art of aerodynamics recognize ~lutter as a potential problem in the operation of an aerodynamic device such as an air21ane wing or propeller blade. In the low speed operation of a propeller blade, the blade may vibrate in un-coupled flat-wise bending and torsional modes, such vibrations being damped by the propeller itself and the aerodynamic loading thereon. However, a~ higher speeds, the flat wise bending and torsional modes may become coupled~ thus extracting greater energy ~rom the airstream than when uncouple~. Such increased energy extraction can resùlt in sustained, neutrally stable vibration or, in the case o~ classical ~lutter, ~;'f~
in energy extraction e~ceedinq that dissipated by internal blade dampln~, thereby causing a vibration of increasing amplitude and ul-timately structural f a ilure of the blade.
While clas~ical flutter is always a consid-eration in the design and deve]opmen-t 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 vibra-tion, 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 ~or separate ~odes which tend to couple, and individual modes which contain components of both bending and torsional motion.
It is another object of the present inven-tion 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 subs-tantially 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 blade vibration. In the preferred embodiment, the leading edge of the tip portion Of the blade iS statically ~'7(~
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 pred~flected tip po~tion wher~by the entire leading ~dge outwardly from the mid-span of the blade occupi~s essQntially a common plane unde~
normal operating conditionq.
Brief Description of Drawings Fig. l is a frontal elevation of a prior art aircraft prop-fan;
Fig. 2 is an isometric view of the prop-fan of Fig. l;
Fig. 3 i5 an isome~ric view of a prop-~an 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. S is a frontal elevation of one of the blades of Fîg. 3;
Fig. 6 is a side elevation of ~he blaAe o~ Fig.
5;
Fig, 7 is a sectional view taken at the chordal centers of the airfoil section~ which de~ine the blade of Fig~ 6, in a direction perpendicular to the chords of those airfoils as exemplified by line 7~7 o~ Fig.
8;
Figs. 8-27 are a serie~ of cross-sectional views of the airfoil sections which when stacked, define t~e blades of the prop-fan of the present invention, the scctions being taken at the stations indicated in Fig.
6s Fig. 28 is a side elevation of a prior art prop-S fan blade in a graphical representation of a firstresonance mode thereof;
Fi~ 29 is a view similar to ~ig. 28 but illu.strating the effects Oe the first resonance mode on one of the blade~ of the prop-fan of the pr~ent inventiOn;
Fiq. 30 is a view similar to Fig. 28 but showing the ef~ect 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 co~prise~ a hub 15 on which a plurality of blades 20 are mounted Eor pivotal pitch change movement with respect thereto. ~hc huh 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 blade~ equal to or less than ~he critical M3ch number. Further details of the shape and structure of prop-fan l0 may be found in U.S.
Patent Nos. 4,171,183, 4,358,246 and 4,370,097 as well as merican Institute of A~ronautics and Astro-nautics Paper No. 75-1208 noted hereinabove.
As perhaps best seen by reference to blade 20' shown in the 11 o'clock positlon in Fiy. 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' 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, compris-ing a plurality of blades 45 mounted on a hub 50 for ,~' ..'. .
...
(3~
pivotal~ pitch change movement with respect thereto, ~ub 50 being covered by a spinner 55. A3 illustrated in Fig~ 3, blades 45 are, at radially out~r portion~
thereof, generally thin and swept ~ack as are known prop-fan blades. The blade~ are also highly loaded and cu~mulatively ~efine a solidity factor of greater than l~0 at the roots thereof and less than 1.0 a~ the tips thereof, also in accordance with known prop-fan teachings. However, unlike prop-fan blades 20 illustrated in Figs. l and 2, the airfoils which form blade~ 45 are stacked such that for each blade, the outer portion of the leading edge lies subctantially in a single plane. 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 fr~e tip 70. The leading edge of the blade is illustrated at 75, the mid point of t~e leading edge (located at about the mid point of the blade span~
being shown at 80. As set forth hereinabove, it will be noted tha~ that portion ot laading edge 75 between point 8~ and tip 70 lie~ substantially in a single plane. This is to be contrasted with prior art prop-fan blades (the radially outer portion thereof beingshown in Fig. 4 by phantom lin~ 85) wherein the leading edge of the blade curves in a direction generally opposite to the direction of blade rotation (illustrated again hy arrow 35). However, it will be noted that the leading edge of the tip portion o~
blade 45 may ~e slightly statically predeflected in a ~ 3~
direction generally normal to the local chord lines at ~he 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 S blade tip portion by aerodynamic ~orces on the hlade 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. ~ is shown. The intersection of the axes shown in each of Figs. 8-27 define, the pitch change axis of the blade.
The ~ollowing 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 3 ~
9 _ pitch change axis, C is the location of the camber side of the airfoil measured normally from a corres-pondins 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 -8.1302.1725 -8.1273 .2450 -8.0714.2423 -8.0714 .30~1 -7.9539.3441 -7.9539 . ~002 -7.7580. q718 7.7580 .5127 -7.4152. ~349 -7.4152 .6502 -6,92~ .8416 -6.9255 .8237 6.23991.1010 -6.2399 1.0484 -5.26041.4359 ~5.2604 1.3407 -4.2~101.7391 -4.2810 1.6224
~aokground Art It has been long known that certain aircraft such as commercial airliners may be powered more e~ficiently 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 Euel in the 1970s caused the airline industry to look to a new genera tion of propeller as a way of enhancing the ef~iciency of operation of commercial airliners on routes of from 500-180Q miles and at speeds in the range of Mach 0.7-0.8~ Since engines capahle of powering such aircraft rotated at much higher ra~es of cpeed than state o the art turbo~prop engines, the propeller tips of which were already running at sonic speeds, th6 diameter of the new generation propeller had to be reduced. Since power handling requirements were ~,'7 greatly increased o~er state o~ the art turho-props, high solidlty ratios (greater than 1.0) at the propeller root were required and, therefore, the new genaration propeller required a relatively large numbsr of wide chord blades. To reduce compress-ibility losses and thereby make up for additional swirl losses, the blades of the new generation propeller were required to be thinner than exi~ting blad~sO ~lade sweep wa5 also required to reduce the effective Mach number at the blade ~ip to le55 than critical while minimizin~ blade noise levels. The reculting highly ioaded, ~igh solidity, multi-bladed swept propeller is referred to today as a prop~fan and is disclosed in U~S. Patent No. 4,171,183 and American Institute o~ Aeronautics and Astronautics Paper No.
.
75-1208. Improvements to such prop-fans are disclosed in U.S. Patent Nos. 4,25~,246 and 4,370,0g7 to Hanson, et al.
Those skilled in the art of aerodynamics recognize ~lutter as a potential problem in the operation of an aerodynamic device such as an air21ane wing or propeller blade. In the low speed operation of a propeller blade, the blade may vibrate in un-coupled flat-wise bending and torsional modes, such vibrations being damped by the propeller itself and the aerodynamic loading thereon. However, a~ higher speeds, the flat wise bending and torsional modes may become coupled~ thus extracting greater energy ~rom the airstream than when uncouple~. Such increased energy extraction can resùlt in sustained, neutrally stable vibration or, in the case o~ classical ~lutter, ~;'f~
in energy extraction e~ceedinq that dissipated by internal blade dampln~, thereby causing a vibration of increasing amplitude and ul-timately structural f a ilure of the blade.
While clas~ical flutter is always a consid-eration in the design and deve]opmen-t 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 vibra-tion, 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 ~or separate ~odes which tend to couple, and individual modes which contain components of both bending and torsional motion.
It is another object of the present inven-tion 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 subs-tantially 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 blade vibration. In the preferred embodiment, the leading edge of the tip portion Of the blade iS statically ~'7(~
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 pred~flected tip po~tion wher~by the entire leading ~dge outwardly from the mid-span of the blade occupi~s essQntially a common plane unde~
normal operating conditionq.
Brief Description of Drawings Fig. l is a frontal elevation of a prior art aircraft prop-fan;
Fig. 2 is an isometric view of the prop-fan of Fig. l;
Fig. 3 i5 an isome~ric view of a prop-~an 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. S is a frontal elevation of one of the blades of Fîg. 3;
Fig. 6 is a side elevation of ~he blaAe o~ Fig.
5;
Fig, 7 is a sectional view taken at the chordal centers of the airfoil section~ which de~ine the blade of Fig~ 6, in a direction perpendicular to the chords of those airfoils as exemplified by line 7~7 o~ Fig.
8;
Figs. 8-27 are a serie~ of cross-sectional views of the airfoil sections which when stacked, define t~e blades of the prop-fan of the present invention, the scctions being taken at the stations indicated in Fig.
6s Fig. 28 is a side elevation of a prior art prop-S fan blade in a graphical representation of a firstresonance mode thereof;
Fi~ 29 is a view similar to ~ig. 28 but illu.strating the effects Oe the first resonance mode on one of the blade~ of the prop-fan of the pr~ent inventiOn;
Fiq. 30 is a view similar to Fig. 28 but showing the ef~ect 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 co~prise~ a hub 15 on which a plurality of blades 20 are mounted Eor pivotal pitch change movement with respect thereto. ~hc huh 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 blade~ equal to or less than ~he critical M3ch number. Further details of the shape and structure of prop-fan l0 may be found in U.S.
Patent Nos. 4,171,183, 4,358,246 and 4,370,097 as well as merican Institute of A~ronautics and Astro-nautics Paper No. 75-1208 noted hereinabove.
As perhaps best seen by reference to blade 20' shown in the 11 o'clock positlon in Fiy. 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' 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, compris-ing a plurality of blades 45 mounted on a hub 50 for ,~' ..'. .
...
(3~
pivotal~ pitch change movement with respect thereto, ~ub 50 being covered by a spinner 55. A3 illustrated in Fig~ 3, blades 45 are, at radially out~r portion~
thereof, generally thin and swept ~ack as are known prop-fan blades. The blade~ are also highly loaded and cu~mulatively ~efine a solidity factor of greater than l~0 at the roots thereof and less than 1.0 a~ the tips thereof, also in accordance with known prop-fan teachings. However, unlike prop-fan blades 20 illustrated in Figs. l and 2, the airfoils which form blade~ 45 are stacked such that for each blade, the outer portion of the leading edge lies subctantially in a single plane. 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 fr~e tip 70. The leading edge of the blade is illustrated at 75, the mid point of t~e leading edge (located at about the mid point of the blade span~
being shown at 80. As set forth hereinabove, it will be noted tha~ that portion ot laading edge 75 between point 8~ and tip 70 lie~ substantially in a single plane. This is to be contrasted with prior art prop-fan blades (the radially outer portion thereof beingshown in Fig. 4 by phantom lin~ 85) wherein the leading edge of the blade curves in a direction generally opposite to the direction of blade rotation (illustrated again hy arrow 35). However, it will be noted that the leading edge of the tip portion o~
blade 45 may ~e slightly statically predeflected in a ~ 3~
direction generally normal to the local chord lines at ~he 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 S blade tip portion by aerodynamic ~orces on the hlade 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. ~ is shown. The intersection of the axes shown in each of Figs. 8-27 define, the pitch change axis of the blade.
The ~ollowing 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 3 ~
9 _ pitch change axis, C is the location of the camber side of the airfoil measured normally from a corres-pondins 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 -8.1302.1725 -8.1273 .2450 -8.0714.2423 -8.0714 .30~1 -7.9539.3441 -7.9539 . ~002 -7.7580. q718 7.7580 .5127 -7.4152. ~349 -7.4152 .6502 -6,92~ .8416 -6.9255 .8237 6.23991.1010 -6.2399 1.0484 -5.26041.4359 ~5.2604 1.3407 -4.2~101.7391 -4.2810 1.6224
-2.32212.2521 -~.3221 2.1972 -.36322.6288 -.3~32 2.7650 1.59572.822g 1.5957 3.2132
3.55~52.7735 3.5545 3.3fi76 5.51342.4744 5.5134 3.1589 7.47231.9223 7.4723 2.503~
9.43121.1129 9.4312 1.4060 1~.4106.5939 10.4106 .7534 10.9003.2902 10.9003 .40fi2 11.1942.0996 11.1942 .1927 11.3814-. ~219 11.3820 .0544 3~3~
TABLE II
STA 13.50 BA 75~ fi8 LEA 9~ 479 -Z - -C - -Z - -F--g.4249.0598 ~9.4227 .19~6 -9.3528.1206 -9. ~528 .2495 -9.23h2.1906 -9.2362 .3100 -9.0418. 2772 -9. 0418 . 3796 -8.7017.3874 -8.7nl7 .4620 -8.2~57.5220 -~.2157 .5580 -7.5354.6~49 -7.5354 ~ 6726 -6.5635.8775 -6.5635 .8073 -5.59151.0404 -5.5915 .9235 -3.64771.3005 -3.6477 1.1271 -1.70391.4855 -1.7039 1.3058 .23991.5728 .2399 1.4413 2.1~381.5310 2.1838 1.4913
9.43121.1129 9.4312 1.4060 1~.4106.5939 10.4106 .7534 10.9003.2902 10.9003 .40fi2 11.1942.0996 11.1942 .1927 11.3814-. ~219 11.3820 .0544 3~3~
TABLE II
STA 13.50 BA 75~ fi8 LEA 9~ 479 -Z - -C - -Z - -F--g.4249.0598 ~9.4227 .19~6 -9.3528.1206 -9. ~528 .2495 -9.23h2.1906 -9.2362 .3100 -9.0418. 2772 -9. 0418 . 3796 -8.7017.3874 -8.7nl7 .4620 -8.2~57.5220 -~.2157 .5580 -7.5354.6~49 -7.5354 ~ 6726 -6.5635.8775 -6.5635 .8073 -5.59151.0404 -5.5915 .9235 -3.64771.3005 -3.6477 1.1271 -1.70391.4855 -1.7039 1.3058 .23991.5728 .2399 1.4413 2.1~381.5310 2.1838 1.4913
4.12761.3709 4.1276 1.4265 6.07141.080~ 6.071~ 1.1861 ~3.0152.6230 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 ~7~
TABLE III
STA 15.50 BA 75.19 LEA 10.462 -z - -C- -Z - -F--10.4138. ~187 -10.4096 .1826 -10.3355.0741 -10.3355 .2289 -10.2186.1333 -10.2186 .2763 -lOo 0237.2070 -10.0237 .3295 -9.6827 .3021 -9.6827 .3908 -9.1954 .4169 -~.1954 .4591 -8.5133 .5555 -8~ 5133 ~ 5390 -7.5389 .7172 -7.5389 .6287 -6.564~ .8509 -~.5645 .7026 -4.61561.0520 -4.6156 .82n2 -2.66671.1744 -2.6667 .9~25 -.7178 1.2067 -.7178 .9351 1.23111.1260 1.2311 ,8922 3.1799 .9455 3.1799 .7792
TABLE III
STA 15.50 BA 75.19 LEA 10.462 -z - -C- -Z - -F--10.4138. ~187 -10.4096 .1826 -10.3355.0741 -10.3355 .2289 -10.2186.1333 -10.2186 .2763 -lOo 0237.2070 -10.0237 .3295 -9.6827 .3021 -9.6827 .3908 -9.1954 .4169 -~.1954 .4591 -8.5133 .5555 -8~ 5133 ~ 5390 -7.5389 .7172 -7.5389 .6287 -6.564~ .8509 -~.5645 .7026 -4.61561.0520 -4.6156 .82n2 -2.66671.1744 -2.6667 .9~25 -.7178 1.2067 -.7178 .9351 1.23111.1260 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. ~ 521 A 2414 8.5394 .0314 8.5394 .173~
8.8317 -.0310 8.8317 .1333 9.0107 -.0692 9.0093 .1086 7~
TABLE IV
STA 18.5() ~A 73.85 LEA 11.763 _z _ -C- -Z- -F-~ 7222-.0339 -11.7148 .1889 -11.6330.0197 -11.6330 .2270 -11.5130.0717 -11.513~ .2615 ~ 3129.1376 -11.3129 ~ 2981 -10.9628.224S -10.962~ .33fi9 -10.4626.3309 -10.462~ .37fi5 -9.7~24.4586 -4.7624 .4204 -8.7620.6076 -8.7620 .4650 -7.7617.7292 -7. ~17 . ~991 -5.7610.9056 -5.7610 .5504 -3.76031.0058 -3.7603 .5801 -1.75951.0239 -1.7595 .5802 .2412.9443 .2412 c 5351 2.2419.7777 2.2419 .4513 4.2426.5370 4.2426 .3416
8.8317 -.0310 8.8317 .1333 9.0107 -.0692 9.0093 .1086 7~
TABLE IV
STA 18.5() ~A 73.85 LEA 11.763 _z _ -C- -Z- -F-~ 7222-.0339 -11.7148 .1889 -11.6330.0197 -11.6330 .2270 -11.5130.0717 -11.513~ .2615 ~ 3129.1376 -11.3129 ~ 2981 -10.9628.224S -10.962~ .33fi9 -10.4626.3309 -10.462~ .37fi5 -9.7~24.4586 -4.7624 .4204 -8.7620.6076 -8.7620 .4650 -7.7617.7292 -7. ~17 . ~991 -5.7610.9056 -5.7610 .5504 -3.76031.0058 -3.7603 .5801 -1.75951.0239 -1.7595 .5802 .2412.9443 .2412 c 5351 2.2419.7777 2.2419 .4513 4.2426.5370 4.2426 .3416
6.2433.2381 h.2433 .2242
7.2436.0733 7.2436 .1673 7.7438-.0081 7.743~ .1465
8.0439-.0570 8.0439 .1340 8.2272-.0868 ~.2248 .1265 TABLE V
STA 21.50 ~A 71.71 LEA 12.741 ~Z - -C- -Z - -F--12.7039~ ~114-12.6951 .1388 -12.6058 .0379-12.6058 .1686 -12.4813 .0840-12.4813 .1935 -12.2739 .1435-12.2~39 .2184 -~1,9108 .2245-11.9108 .2416 -11.3921 .3245-11.3921 .2623 -10.6659 4452 -10.6659 .2822
STA 21.50 ~A 71.71 LEA 12.741 ~Z - -C- -Z - -F--12.7039~ ~114-12.6951 .1388 -12.6058 .0379-12.6058 .1686 -12.4813 .0840-12.4813 .1935 -12.2739 .1435-12.2~39 .2184 -~1,9108 .2245-11.9108 .2416 -11.3921 .3245-11.3921 .2623 -10.6659 4452 -10.6659 .2822
-9.6286 .5874 -9.6286 .2979 -8. S912 .7037 -8.5912 .3~73 -6.5164 . ~3718-~.5164 .3202 -4.441~ .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 .153S
5.9320 o 2544 5.932n . lOS~
6.9694 .1011 6.9~94 . ~975 7.4881 .0244 7.4881 .0934 7.7993 -.0216 7.7993 .0910 7.9896 -.0497 7.986~ .0895 ~J'7 TABLE VI
STA 24.50 BA 69.28 LEA 13.254 -Z - -C- -Z - -F--13.2141.1373 -13.2047 -.0156 -13.1146.1769 -13.1146 .0026 -12.9862.21h5 -12.9862 .0196 -12.7723~ 2695 -12.7723 .0365 -12.3978.3432 -12.3978 .0512 -11.8629.4340 -11.8629 .0~32 11.1139.5422 -11.1139 .0716
5.9320 o 2544 5.932n . lOS~
6.9694 .1011 6.9~94 . ~975 7.4881 .0244 7.4881 .0934 7.7993 -.0216 7.7993 .0910 7.9896 -.0497 7.986~ .0895 ~J'7 TABLE VI
STA 24.50 BA 69.28 LEA 13.254 -Z - -C- -Z - -F--13.2141.1373 -13.2047 -.0156 -13.1146.1769 -13.1146 .0026 -12.9862.21h5 -12.9862 .0196 -12.7723~ 2695 -12.7723 .0365 -12.3978.3432 -12.3978 .0512 -11.8629.4340 -11.8629 .0~32 11.1139.5422 -11.1139 .0716
-10.0441.6690 -1~.0441 . ~752 -8.9742 .7720 -8.9742 .0757 -6.8344 .9202 -~.8344 .0758 -4.6946l. OOg3 -4.6946 . ~666 -2.55491.0309 -2.5549 , ~489 -.4151 .9735 -.4151 . ~182 1.7247 .8425 1.7247 -.019fi 3.8644 .6446 3.8644 -.0561 6.0042 .3868 6.0042 -. ~589 7.0741 .2430 7. ~741 -.0603 7,6090 .1710 7.6090 -,0609 7.9300 .1279 7.9300 -.0~14 ~.1267 .1014 ~.1238 -.0~16 ~ABLE VI]
STA 27000 BA 67.34 LEA 13.313 -Z - -C `- -Z - -F --13.2704 .31~9-13.2587 -.1989 -13.1711 .3520-13.1711 -.1880 -13.0403 .38h713~ n403 -.1767 -12.8222 .4352~12.822~ -.16~6 -12~ 4407.5040-12.4407 -.1542
STA 27000 BA 67.34 LEA 13.313 -Z - -C `- -Z - -F --13.2704 .31~9-13.2587 -.1989 -13.1711 .3520-13.1711 -.1880 -13.0403 .38h713~ n403 -.1767 -12.8222 .4352~12.822~ -.16~6 -12~ 4407.5040-12.4407 -.1542
-11.8956 .5876 ~ 5~ -.1467 -11.1324. ~850-11.1~24 -.1436 -10.0~23 .7971-10.0423 -.1434 -8. g~21 .8867 -8.9521 -.1437 -6,77171. l?122-6.7717 -.1400 -4.591~ 1. osla-4.5913 -.1466 -2.4109 1.1159 -2.4109 -.1581 -.2305 1.0754 -.2305 -.1762 1.9498 .9699 1.9498 -.200n 4.1302 .7997 4.1302 -.2268 6.3106 .5~59 ~.310~ -.2485 7.4008 .4260 7.4008 -.24h5 7.9459 .3531 7.9459 -.2455 8.2729 .3105 802729 -.2450 8.4735 .2844 8.4709 -.244~
1 ~`d 7 ~
TAB LE VI I I
srA 29.00 ~A hS.85 LEA 13.147 -13.1043 .4930 -13.0911 -.3741 -13.0043 .5212 -13.0043 -.3681
1 ~`d 7 ~
TAB LE VI I I
srA 29.00 ~A hS.85 LEA 13.147 -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 -10.944n .8312-10. ~440 -.3377 -9.8423 .9305 -9.8423 -.336Ç
-8.7406 1. ~0~6 8.7406 -o 3346 -6.5371 1.1166 -6.5371 -.3253 4.3336 1.1884 -4.3336 -.3269 -2.13~1 1.2138 -2.1301 -.3300 .0733 1.18hO .0733 -~ 3352 2.2768 l. l()O8 2.2768 -.3467 4.4803 .9530 4.4803 -.3673 6.6837 .7357 6.6837 -.3948 7.7855 .5987 7.7855 -.4102 8.3364 .5234 ~.3364 -.4105 8.6669 .4782 8,6669 -.4106 8.8699 .4505 8.8672 -.4107 TABLE IX
STA 32.00 ~A 63.73 LEA 12~560 -12.5203 .7784-12.5072 -o671~
-12.4159 .8052-12.4159 -.6694 -12.2828 .8351-12.282~ -.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 -1.46~8 1.4132-1. 4688 -. 6321 .7495 1.3956 .7495 -. 62S2 2.9677 1.3301 2.9677 -.6246 5.1860 1.2085 5.1860 -.6388 7.4043 1.0166 7.4043 -.6707 8.5134 .889~ 8.5134 -.6939 -9.0679 .8139 9.0679 -.6981 9.4007 .7697 9.4007 -.7007 9.6052 .7420 9.~027 -.7022 ~ ~ 7 ~
STA 35.00 BA 61. fi5 LEA 11.521 -11.4~378 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-ln. 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 1.63501.6698 -.9736 3.8683 1.57453.8683 -.9720 6.0668 1.46756.0668 -.9834 8.2653 1.30218,2653 -1. nO96 9.3645 1.19449.3645 -1.0193 9.9142 1.13059.9142 -1.02~1 lt).2439 1.092110.2439 -1.0270 1~.4461 1.068~10.4439 -1.0~37 ~`7~3~(3;~
TAB LE XI
STA 38.00 BA 59.62 LEA 9.937 -9.90891.4~88 -9.9015 -1.3346 -9.79901.4347 -9.7990 -1.3315 -9.67131.4596 9.6713 -1.3285 -9.45841.4~52 -9.4584 -1.3254 -9.08591.5446 -9.0859 -1.3247 -8.55381.6016 -8.5538 -1.3265 -7.80881.6635 -7.8088 -1.3318 -6.74461.7295 -6.7446 -1.3334 -5.68031.7741 -5.6803 -1.3265 -3.551~ 338 -3.5518 -1.3137 -1.42321.874~ -1.4232 -1.3128 ,70531.8807 .7053 -1.3065 2. ~3381.85642. ~338 -1.3nOl 4.96241.7g93 4.962~ -1.2996 7.09091.7064 7.0909 -1.3106 9.21941.5713 9.2194 -1.3354 10.28371.486410.2837 -1.3430 10.81581.437510.8158 -1.346~
11.13511.408211.1351 -1.34gO
11.32981.390311.3281 -1.3504 ~7~
TABLE XI I
STA 41.00 ~A 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 -6.9533 1.76~35-6.9503 -1. S811 -~.4519 1.8147-6.451~ -1.5799 -S.7540 1.8654-5.7540 -1.5814 -4.7570 1.9186-4.7570 -1.5807 -3.76()l 1.9560-3. ~601 -1.57~7 1.7661 2.0088-1.7661 -1.5~70 .2278 2.0358.2278 -1.5596 2.2217 2.03602.2217 -1.5506 4.2156 2. ~1 ~64.2156 -1.5427 6.2095 1.96356.2095 -1.541~
8.2035 1.88728.2035 -1.5529 lO. lg74 1.781310.1974 ,-1.5821 11.1943 1.716211.1943 -1.5933 11.6928 1.679511.6928 -1.5988 11.9919 1. fi57511.9919 -1.6022 12.1727 1.644112.1715 -1~ 6042 TAE3LÆ XIII
STA43. 50 8A56. 42 LEA 5. 431 ~Z - -C - -Z - -F--5.4080 1.7746 -S.4034 -1.7182 -5.3127 1.7922 -5.3127 -1.7168 -5.2033 1.8089 -5.2033 -1.7139 -S.0210 1.8329 -5.02~0 -1.7102 -4.71)20 1.8661 -4.7020 -1.7073 -4.2463 l.90Sl -4.2463 -1.7055 -3. 6084 1. 949~ -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. ~600 2.0921 1.8600 -1.6867 3.6828 2.0917 3.682~ -1.6780 5.5055 2.0714 5.5055 -1.6708 7.32~3 2.0303 7.3283 -1.6700 9.1511 1.9669 9.1511 -1.6804 10.9739 1.8~82 1~.9739 -1.7068 11.8853 1.8244 11.8853 -1.7165 12.3410 1.7945 12.3410 -1.7213 12,6144 1.7765 1~.6144 -1.7241 12.7780 1.7658 120 7769 -1.72~58 {~
TABL~ XIV
STA 46.00 BA 55.4n LEA 2.625 -Z- -C- -Z- -F--2.6052 1. 8050-2. 6009 -1.7576 -2.5215 1.819S-2.5215 -1.7580 -2.4260 1.8336-2.4260 -1.7565 -2.2667 1.85~0-2.2667 -1.7S48 -1.988~ 1.8826-1.9~80 -1.7550 -1.5899 1.9156-1.5899 -1.7546 -1.0325 1.9504-1.0325 -1.7524 -.23h2 1.9882-.2362 -1.1485 .5601 2.0141.5601 -1.7479 2~1527 2.05252.1527 -1.7435 3.7453 2.07043.7453 -1.7377 5.3379 2.07105.3379 -1.7314 6.9304 2.05406.9304 -1.7259 8.5230 2.0210~.5230 -1.7251 10.1156 1.9~7810.1156 -1.7323 11.7082 1.893511.7082 -1.7521 12.5045 1.848012.5045 -1.7565 12.9026 1.823a12.9n26 -1.7587
-8.7406 1. ~0~6 8.7406 -o 3346 -6.5371 1.1166 -6.5371 -.3253 4.3336 1.1884 -4.3336 -.3269 -2.13~1 1.2138 -2.1301 -.3300 .0733 1.18hO .0733 -~ 3352 2.2768 l. l()O8 2.2768 -.3467 4.4803 .9530 4.4803 -.3673 6.6837 .7357 6.6837 -.3948 7.7855 .5987 7.7855 -.4102 8.3364 .5234 ~.3364 -.4105 8.6669 .4782 8,6669 -.4106 8.8699 .4505 8.8672 -.4107 TABLE IX
STA 32.00 ~A 63.73 LEA 12~560 -12.5203 .7784-12.5072 -o671~
-12.4159 .8052-12.4159 -.6694 -12.2828 .8351-12.282~ -.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 -1.46~8 1.4132-1. 4688 -. 6321 .7495 1.3956 .7495 -. 62S2 2.9677 1.3301 2.9677 -.6246 5.1860 1.2085 5.1860 -.6388 7.4043 1.0166 7.4043 -.6707 8.5134 .889~ 8.5134 -.6939 -9.0679 .8139 9.0679 -.6981 9.4007 .7697 9.4007 -.7007 9.6052 .7420 9.~027 -.7022 ~ ~ 7 ~
STA 35.00 BA 61. fi5 LEA 11.521 -11.4~378 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-ln. 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 1.63501.6698 -.9736 3.8683 1.57453.8683 -.9720 6.0668 1.46756.0668 -.9834 8.2653 1.30218,2653 -1. nO96 9.3645 1.19449.3645 -1.0193 9.9142 1.13059.9142 -1.02~1 lt).2439 1.092110.2439 -1.0270 1~.4461 1.068~10.4439 -1.0~37 ~`7~3~(3;~
TAB LE XI
STA 38.00 BA 59.62 LEA 9.937 -9.90891.4~88 -9.9015 -1.3346 -9.79901.4347 -9.7990 -1.3315 -9.67131.4596 9.6713 -1.3285 -9.45841.4~52 -9.4584 -1.3254 -9.08591.5446 -9.0859 -1.3247 -8.55381.6016 -8.5538 -1.3265 -7.80881.6635 -7.8088 -1.3318 -6.74461.7295 -6.7446 -1.3334 -5.68031.7741 -5.6803 -1.3265 -3.551~ 338 -3.5518 -1.3137 -1.42321.874~ -1.4232 -1.3128 ,70531.8807 .7053 -1.3065 2. ~3381.85642. ~338 -1.3nOl 4.96241.7g93 4.962~ -1.2996 7.09091.7064 7.0909 -1.3106 9.21941.5713 9.2194 -1.3354 10.28371.486410.2837 -1.3430 10.81581.437510.8158 -1.346~
11.13511.408211.1351 -1.34gO
11.32981.390311.3281 -1.3504 ~7~
TABLE XI I
STA 41.00 ~A 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 -6.9533 1.76~35-6.9503 -1. S811 -~.4519 1.8147-6.451~ -1.5799 -S.7540 1.8654-5.7540 -1.5814 -4.7570 1.9186-4.7570 -1.5807 -3.76()l 1.9560-3. ~601 -1.57~7 1.7661 2.0088-1.7661 -1.5~70 .2278 2.0358.2278 -1.5596 2.2217 2.03602.2217 -1.5506 4.2156 2. ~1 ~64.2156 -1.5427 6.2095 1.96356.2095 -1.541~
8.2035 1.88728.2035 -1.5529 lO. lg74 1.781310.1974 ,-1.5821 11.1943 1.716211.1943 -1.5933 11.6928 1.679511.6928 -1.5988 11.9919 1. fi57511.9919 -1.6022 12.1727 1.644112.1715 -1~ 6042 TAE3LÆ XIII
STA43. 50 8A56. 42 LEA 5. 431 ~Z - -C - -Z - -F--5.4080 1.7746 -S.4034 -1.7182 -5.3127 1.7922 -5.3127 -1.7168 -5.2033 1.8089 -5.2033 -1.7139 -S.0210 1.8329 -5.02~0 -1.7102 -4.71)20 1.8661 -4.7020 -1.7073 -4.2463 l.90Sl -4.2463 -1.7055 -3. 6084 1. 949~ -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. ~600 2.0921 1.8600 -1.6867 3.6828 2.0917 3.682~ -1.6780 5.5055 2.0714 5.5055 -1.6708 7.32~3 2.0303 7.3283 -1.6700 9.1511 1.9669 9.1511 -1.6804 10.9739 1.8~82 1~.9739 -1.7068 11.8853 1.8244 11.8853 -1.7165 12.3410 1.7945 12.3410 -1.7213 12,6144 1.7765 1~.6144 -1.7241 12.7780 1.7658 120 7769 -1.72~58 {~
TABL~ XIV
STA 46.00 BA 55.4n LEA 2.625 -Z- -C- -Z- -F--2.6052 1. 8050-2. 6009 -1.7576 -2.5215 1.819S-2.5215 -1.7580 -2.4260 1.8336-2.4260 -1.7565 -2.2667 1.85~0-2.2667 -1.7S48 -1.988~ 1.8826-1.9~80 -1.7550 -1.5899 1.9156-1.5899 -1.7546 -1.0325 1.9504-1.0325 -1.7524 -.23h2 1.9882-.2362 -1.1485 .5601 2.0141.5601 -1.7479 2~1527 2.05252.1527 -1.7435 3.7453 2.07043.7453 -1.7377 5.3379 2.07105.3379 -1.7314 6.9304 2.05406.9304 -1.7259 8.5230 2.0210~.5230 -1.7251 10.1156 1.9~7810.1156 -1.7323 11.7082 1.893511.7082 -1.7521 12.5045 1.848012.5045 -1.7565 12.9026 1.823a12.9n26 -1.7587
13.1415 1.809313.1415 -1.7hOO
13.2820 1.800713.2809 -1.7608 TA~LE XV
STA 47.50 BA 54.95 LEA . fi93 -z - -C- -Z- -F--.6760 1.7855-.6725 -1,7455 -.5999 1.7990-.5999 1.744~
-.5144 1.8116-.5144 -1.7435 -.3719 1.8291-.3719 -1.7414 -.1225 1. ~535-.12~5 -1.7405 .2338 1.8799.2338 -1.738 .7327 1. 9071.732~ ~1.7363 1.4453 ~.93871.4453 -1.7343 2.1579 1.96692.1579 -1.7362 3.5831 2.00213.4831 -1. ~351 5.00B4 2.01915.00B4 -1.7312 6.4336 2. ~189~.4336 -1.7260 7.8588 2. ~0517.8588 -1.7216 9.2841 1.97749.2841 -1.7207 10.7093 1.929910. 7093 -lc 7261 12.1345 1.864~12~ 1345 -1.7416 12.8472 1. ~25312.8472 -1.7430 13.2035 1.804313.2035 -1.7437 13.4172 1.791713.4172 -1.7442 13. S409 1. ~84413.5393 -1.7444 ~'7~
TABLE XVI
STA 49.00 BA 54.62 LEA -1. 430 -2 ~ -C- -Z - -F -1.4424 1.7294 1.4450 ~ 981 1.5101 1.7423 1.51~1 -1.69~
1.5~42 1.7535 1.5842 -1.6967 1.7077 1.76~4 1,7077 -1.6952 1.924Q 1.7885 1.9240 -1.6950 2,2328 1.8109 2. ~328 -1.6938 2.6653 1.8383 2. h653 -1.6965 3.2830 lo 86653.2830 -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 8.8~29 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 13.47hl 1.7504 13.4761 -1.6933 13.6614 1.7401 1306614 -1.6939 13.7661 1.7342 13.7650 -1.6943 - 2fi -TA~ LE XVI 1 STA 50.50 BA 54.95 LEA -3.737 -Z - -C- -Z ~ -F-3.7475 1.6643 3.7493 -1.6398 3.8Q39 1.6749 3.8039 -1.6375 3.8653 1. fi8423.8653 -1.636~
3.9676 1.6962 3.9676 -1.63~5 4.1456 1.7116 4.1466 -1.6341 4.4023 1.7296 4.4023 -1.632fi 4.76~3 1.7507 4.7503 -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 7.828g 1.8290 7.8289 -1.6341 8.8518 1.8290 8.8518 .6320 9.8746 1. ~2~0 9.8746 -lo 6322 10.8975 1.8038 10.8975 -1.6334 11.9203 1.7781 11.9203 -1.6389 12.9432 1.7338 1~.9432-1.637() 13.4546 1.7039 13.454fi -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 ~VIII
STA 52.00 BA 54.51 LEA -6.231 ~ - -C- -2 - -F-6.2398 1.5528 6.2412 -1.5332 6. ~827 1.5595 6.2827 -1.5325 6.3300 1.5655 6.3300 -1.5319 6.40a9 lo 5741fi. ~089 -1.5311 fi.5~70 1.58~6 6.5470 -1.5300 6.7~42 1.6007 6.7442 -1.5295 7.0202 1.6~fi3 7.0202 -1.5295 7.41~6 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 10.9h42 -1.5341 11.7530 1.6687 11.7530 -1.5367 12.5418 1.6473 12.5418 -1.5338 13.3306 1.6118 13.3306 -1.535~
13.7250 1.5898 13.7250 -1.5317 13.9222 1.5786 13. ~222 -1.5300
13.2820 1.800713.2809 -1.7608 TA~LE XV
STA 47.50 BA 54.95 LEA . fi93 -z - -C- -Z- -F--.6760 1.7855-.6725 -1,7455 -.5999 1.7990-.5999 1.744~
-.5144 1.8116-.5144 -1.7435 -.3719 1.8291-.3719 -1.7414 -.1225 1. ~535-.12~5 -1.7405 .2338 1.8799.2338 -1.738 .7327 1. 9071.732~ ~1.7363 1.4453 ~.93871.4453 -1.7343 2.1579 1.96692.1579 -1.7362 3.5831 2.00213.4831 -1. ~351 5.00B4 2.01915.00B4 -1.7312 6.4336 2. ~189~.4336 -1.7260 7.8588 2. ~0517.8588 -1.7216 9.2841 1.97749.2841 -1.7207 10.7093 1.929910. 7093 -lc 7261 12.1345 1.864~12~ 1345 -1.7416 12.8472 1. ~25312.8472 -1.7430 13.2035 1.804313.2035 -1.7437 13.4172 1.791713.4172 -1.7442 13. S409 1. ~84413.5393 -1.7444 ~'7~
TABLE XVI
STA 49.00 BA 54.62 LEA -1. 430 -2 ~ -C- -Z - -F -1.4424 1.7294 1.4450 ~ 981 1.5101 1.7423 1.51~1 -1.69~
1.5~42 1.7535 1.5842 -1.6967 1.7077 1.76~4 1,7077 -1.6952 1.924Q 1.7885 1.9240 -1.6950 2,2328 1.8109 2. ~328 -1.6938 2.6653 1.8383 2. h653 -1.6965 3.2830 lo 86653.2830 -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 8.8~29 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 13.47hl 1.7504 13.4761 -1.6933 13.6614 1.7401 1306614 -1.6939 13.7661 1.7342 13.7650 -1.6943 - 2fi -TA~ LE XVI 1 STA 50.50 BA 54.95 LEA -3.737 -Z - -C- -Z ~ -F-3.7475 1.6643 3.7493 -1.6398 3.8Q39 1.6749 3.8039 -1.6375 3.8653 1. fi8423.8653 -1.636~
3.9676 1.6962 3.9676 -1.63~5 4.1456 1.7116 4.1466 -1.6341 4.4023 1.7296 4.4023 -1.632fi 4.76~3 1.7507 4.7503 -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 7.828g 1.8290 7.8289 -1.6341 8.8518 1.8290 8.8518 .6320 9.8746 1. ~2~0 9.8746 -lo 6322 10.8975 1.8038 10.8975 -1.6334 11.9203 1.7781 11.9203 -1.6389 12.9432 1.7338 1~.9432-1.637() 13.4546 1.7039 13.454fi -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 ~VIII
STA 52.00 BA 54.51 LEA -6.231 ~ - -C- -2 - -F-6.2398 1.5528 6.2412 -1.5332 6. ~827 1.5595 6.2827 -1.5325 6.3300 1.5655 6.3300 -1.5319 6.40a9 lo 5741fi. ~089 -1.5311 fi.5~70 1.58~6 6.5470 -1.5300 6.7~42 1.6007 6.7442 -1.5295 7.0202 1.6~fi3 7.0202 -1.5295 7.41~6 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 10.9h42 -1.5341 11.7530 1.6687 11.7530 -1.5367 12.5418 1.6473 12.5418 -1.5338 13.3306 1.6118 13.3306 -1.535~
13.7250 1.5898 13.7250 -1.5317 13.9222 1.5786 13. ~222 -1.5300
14.0406 1.5719 14. ~406 -1.5291 14.1002 1.5685 14.0989 -1.5286 3L~7 ~ 2~ ~
TA~LE XIX
STA 53.00 BA 54.32 LEA -7.987 -Z - -C- -Z - -F-7.9937 1.44267.9946 -1.4263 8.0271 14 4474~. ~271 -1.4257 ~.0646 1. ~51~8.06~6 -1.4250 8.1269 1.4580~.1269 ~ 241 8.2361 1.46718.2361 -1,422g ~.3921 1.47748.3921 -1.4220 8. ~10~ 1.48878,6104 -1.4213 8.9223 1.50158.9223 -1.4208 9.2342 1.51179.2342 -1.4208 9. 85B0 1.52679.8580 -1.4214 10.4818 1.535510.4818 -1.4218 11.1059 1.539411.1059 -1.4229 11.7294 1.537911.7294 -1.4222 12.3532 1~ 528712.3532 -1.4226 12.9770 1.511112.9770 -1.4233 13.6008 1.482013.6008 -1.4184 13.9127 1.466113.9127 -1.4150 14.0686 1.458414. Ofi86 -l.4136 14.1622 1.453814.1622 -1.4128 14.2043 1.451814.2047 -1.4125 ~L ~ 7 ~
TABLE XX
STA 54.00 BA 54004 LE~ 9.788 -Z - -C- -Z - -F-g.7933 102873 9~ 7943 -1.2756 9. ~176 1.2915 9.8176 ~1.2754 9.8~46 1. ~55 9. ~446 -1.2752 9.8~95 1.3014 9.8895 -1.2750 9.9680 1.3101 9.9680 -1.2748 10.0803 1.3201 10.0~03 -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 12.3~03 -1.2740 13.8293 1.3296 13. ~293 -1.2677 14.0538 1.3161 14.0538 -1.2646 14.16fiO 1.3085 14.1660 -1.2631 14.2334 1.3037 14.2334 -1.2621 14.2595 1.3018 14.2579 -1.261~
~ ~ f~
The improvement in the vibration character-istics of the prop-fan of the present invention is illustrated ln 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 vibra-tory motion on the ]eading and trailing edges of the blade at a first resonance point of 180 H~. I-t is noted that at the tip, the angular dis-placement 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 ~ indicating substantially pure bending, while an angle ~ 90 indicating s~bstan-tially 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, un-stalled 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 analy-tical 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 ti-tanium, 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 ~ 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 ~' .~
~'~''71~
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 vibra-tion 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 appre-ciate that a node line parallel to the blade spar indicates torsional vibration while a node line perpendicular to the blade spar indicates flat-wise lS 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 i.s thus apparent that the prop-fan of -the present lnvention exhibits sl.gnificantly less coupling between torsional and fl.at-wise bending modes of ~ibration, and thus less ri.sk of classical flutter and i.mproved stability over known prop-fan blade geometries. While the prop-fan of the present invention has been illustrated with ei~ht blades, it will be appreciated that greater or lesser numbers of such blades may be ernployed without departing from this invention. I.ikewise, 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 ori.entation of the blade leading edge from the midpoint of -the blade span to the blade tip. Accord-ingly, it is intended by the following claims to cover these and any other modifications which will be suggested to those ski.lled in the art by the dis-closure herein.
.~
TA~LE XIX
STA 53.00 BA 54.32 LEA -7.987 -Z - -C- -Z - -F-7.9937 1.44267.9946 -1.4263 8.0271 14 4474~. ~271 -1.4257 ~.0646 1. ~51~8.06~6 -1.4250 8.1269 1.4580~.1269 ~ 241 8.2361 1.46718.2361 -1,422g ~.3921 1.47748.3921 -1.4220 8. ~10~ 1.48878,6104 -1.4213 8.9223 1.50158.9223 -1.4208 9.2342 1.51179.2342 -1.4208 9. 85B0 1.52679.8580 -1.4214 10.4818 1.535510.4818 -1.4218 11.1059 1.539411.1059 -1.4229 11.7294 1.537911.7294 -1.4222 12.3532 1~ 528712.3532 -1.4226 12.9770 1.511112.9770 -1.4233 13.6008 1.482013.6008 -1.4184 13.9127 1.466113.9127 -1.4150 14.0686 1.458414. Ofi86 -l.4136 14.1622 1.453814.1622 -1.4128 14.2043 1.451814.2047 -1.4125 ~L ~ 7 ~
TABLE XX
STA 54.00 BA 54004 LE~ 9.788 -Z - -C- -Z - -F-g.7933 102873 9~ 7943 -1.2756 9. ~176 1.2915 9.8176 ~1.2754 9.8~46 1. ~55 9. ~446 -1.2752 9.8~95 1.3014 9.8895 -1.2750 9.9680 1.3101 9.9680 -1.2748 10.0803 1.3201 10.0~03 -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 12.3~03 -1.2740 13.8293 1.3296 13. ~293 -1.2677 14.0538 1.3161 14.0538 -1.2646 14.16fiO 1.3085 14.1660 -1.2631 14.2334 1.3037 14.2334 -1.2621 14.2595 1.3018 14.2579 -1.261~
~ ~ f~
The improvement in the vibration character-istics of the prop-fan of the present invention is illustrated ln 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 vibra-tory motion on the ]eading and trailing edges of the blade at a first resonance point of 180 H~. I-t is noted that at the tip, the angular dis-placement 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 ~ indicating substantially pure bending, while an angle ~ 90 indicating s~bstan-tially 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, un-stalled 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 analy-tical 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 ti-tanium, 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 ~ 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 ~' .~
~'~''71~
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 vibra-tion 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 appre-ciate that a node line parallel to the blade spar indicates torsional vibration while a node line perpendicular to the blade spar indicates flat-wise lS 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 i.s thus apparent that the prop-fan of -the present lnvention exhibits sl.gnificantly less coupling between torsional and fl.at-wise bending modes of ~ibration, and thus less ri.sk of classical flutter and i.mproved stability over known prop-fan blade geometries. While the prop-fan of the present invention has been illustrated with ei~ht blades, it will be appreciated that greater or lesser numbers of such blades may be ernployed without departing from this invention. I.ikewise, 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 ori.entation of the blade leading edge from the midpoint of -the blade span to the blade tip. Accord-ingly, it is intended by the following claims to cover these and any other modifications which will be suggested to those ski.lled in the art by the dis-closure herein.
.~
Claims (6)
1. A prop-fan comprising a plurality of swept, rotatable airfoil blades pivotally mounted to a hub for pitch change movement with respect thereto, and having a solidity ratio of 1.0 or greater at the roots of said blades and less than 1.0 at the tips of said blades, said prop-fan being operable at or above critical Mach numbers and at transonic or supersonic tip speeds, and being characterized by:
each of said blades having a leading edge, said leading edge, from a location thereon at approximately a midportion of the span and said blade, outwardly to the tip thereof, being curved in a chordal direction to define blade sweep while exhibiting no significant offset curvature in a span-wise direction.
each of said blades having a leading edge, said leading edge, from a location thereon at approximately a midportion of the span and said blade, outwardly to the tip thereof, being curved in a chordal direction to define blade sweep while exhibiting no significant offset curvature in a span-wise direction.
2. The prop-fan of claim 1 characterized by said leading portions of those airfoil sections defining tip portions of each of said blade being slightly bent normal from the local chord lines thereof generally in the direction of rotation of said prop-fan under normal operating conditions.
3. The prop-fan of claim 2 characterized by each of said blades including a radially outermost tip, the leading edge of each of said tips being offset from said common plane, a distance approx-imately equal to between 1% and 5% of said blade span.
4. The prop-fan of claim 1 characterized by said leading edge at a tip portion of said blade being slightly statically predeflected normal to the local chord line in the direction of rotation of said prop-fan.
5. The prop-fan of claim 4 characterized by said static predeflection being sufficient to effect a straightening of said tip portion of said blade by the aerodynamic loading thereof under normal operating conditions.
6. A prop-fan comprising a plurality of swept, rotatable airfoil blades pivotally mounted to a hub for pitch change movement with respect thereto, and having a solidity ratio of 1.0 or greater at the roots of said blades and less than 1.0 at the tips of said blades, said prop-fan being operable at or above critical Mach numbers and at transonic or supersonic tip speeds, and being characterized by:
each of said rotatable blades, outwardly from approximately the midpoint of the span thereof, comprising a plurality of stacked airfoil sections defined substantially by the coordinate system of Tables VIII
through XX set forth hereinabove.
each of said rotatable blades, outwardly from approximately the midpoint of the span thereof, comprising a plurality of stacked airfoil sections defined substantially by the coordinate system of Tables VIII
through XX set forth hereinabove.
Applications Claiming Priority (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| US69911985A | 1985-02-07 | 1985-02-07 | |
| US699,119 | 1991-05-13 |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CA1270802A true CA1270802A (en) | 1990-06-26 |
Family
ID=24808020
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CA000488883A Expired - Fee Related CA1270802A (en) | 1985-02-07 | 1985-08-16 | Prop-fan with improved stability |
Country Status (7)
| Country | Link |
|---|---|
| JP (1) | JPS61181798A (en) |
| BR (1) | BR8504907A (en) |
| CA (1) | CA1270802A (en) |
| DE (1) | DE3535399A1 (en) |
| FR (1) | FR2576872B1 (en) |
| GB (1) | GB2170868B (en) |
| IT (1) | IT1185996B (en) |
Families Citing this family (34)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| FR2605588B1 (en) * | 1986-10-24 | 1989-04-28 | Onera (Off Nat Aerospatiale) | IMPROVEMENTS ON AIR PROPELLERS, ESPECIALLY FOR AIRCRAFT PROPELLERS |
| DE3738785A1 (en) * | 1986-11-19 | 1988-05-26 | Gen Electric | CONTRA-ROTATING AIRPLANE DRIVE BLADES |
| USRE34207E (en) * | 1986-11-19 | 1993-03-30 | General Electric Company | Counterrotating aircraft propulsor blades |
| US5165856A (en) * | 1988-06-02 | 1992-11-24 | General Electric Company | Fan blade mount |
| US5102302A (en) * | 1988-06-02 | 1992-04-07 | General Electric Company | Fan blade mount |
| GB2220712B (en) * | 1988-07-13 | 1992-12-09 | Rolls Royce Plc | Open rotor blading |
| US4971641A (en) * | 1988-11-14 | 1990-11-20 | General Electric Company | Method of making counterrotating aircraft propeller blades |
| US6071077A (en) * | 1996-04-09 | 2000-06-06 | Rolls-Royce Plc | Swept fan blade |
| GB2469516A (en) * | 2009-04-17 | 2010-10-20 | Insensys Ltd | Rotor blade with optical strain sensors covered by erosion shield |
| US20130340406A1 (en) | 2012-01-31 | 2013-12-26 | Edward J. Gallagher | Fan stagger angle for geared gas turbine engine |
| US10465702B2 (en) | 2014-02-19 | 2019-11-05 | United Technologies Corporation | Gas turbine engine airfoil |
| WO2015126715A1 (en) | 2014-02-19 | 2015-08-27 | United Technologies Corporation | Gas turbine engine airfoil |
| EP3108110B1 (en) | 2014-02-19 | 2020-04-22 | United Technologies Corporation | Gas turbine engine airfoil |
| WO2015175058A2 (en) | 2014-02-19 | 2015-11-19 | United Technologies Corporation | Gas turbine engine airfoil |
| EP3108109B1 (en) | 2014-02-19 | 2023-09-13 | Raytheon Technologies Corporation | Gas turbine engine fan blade |
| US9567858B2 (en) | 2014-02-19 | 2017-02-14 | United Technologies Corporation | Gas turbine engine airfoil |
| EP3108101B1 (en) * | 2014-02-19 | 2022-04-20 | Raytheon Technologies Corporation | Gas turbine engine airfoil |
| US10519971B2 (en) | 2014-02-19 | 2019-12-31 | United Technologies Corporation | Gas turbine engine airfoil |
| WO2015175052A2 (en) | 2014-02-19 | 2015-11-19 | United Technologies Corporation | Gas turbine engine airfoil |
| EP3114321B1 (en) | 2014-02-19 | 2019-04-17 | United Technologies Corporation | Gas turbine engine airfoil |
| EP3108106B1 (en) | 2014-02-19 | 2022-05-04 | Raytheon Technologies Corporation | Gas turbine engine airfoil |
| WO2015126824A1 (en) | 2014-02-19 | 2015-08-27 | United Technologies Corporation | Gas turbine engine airfoil |
| EP3108116B1 (en) | 2014-02-19 | 2024-01-17 | RTX Corporation | Gas turbine engine |
| WO2015126450A1 (en) | 2014-02-19 | 2015-08-27 | United Technologies Corporation | Gas turbine engine airfoil |
| EP3108115B8 (en) | 2014-02-19 | 2023-11-08 | RTX Corporation | Turbofan engine with geared architecture and lpc blades |
| WO2015175073A2 (en) | 2014-02-19 | 2015-11-19 | United Technologies Corporation | Gas turbine engine airfoil |
| US10502229B2 (en) | 2014-02-19 | 2019-12-10 | United Technologies Corporation | Gas turbine engine airfoil |
| EP3108113A4 (en) | 2014-02-19 | 2017-03-15 | United Technologies Corporation | Gas turbine engine airfoil |
| US10393139B2 (en) | 2014-02-19 | 2019-08-27 | United Technologies Corporation | Gas turbine engine airfoil |
| US10590775B2 (en) | 2014-02-19 | 2020-03-17 | United Technologies Corporation | Gas turbine engine airfoil |
| US10605259B2 (en) | 2014-02-19 | 2020-03-31 | United Technologies Corporation | Gas turbine engine airfoil |
| WO2015126454A1 (en) | 2014-02-19 | 2015-08-27 | United Technologies Corporation | Gas turbine engine airfoil |
| FR3045564B1 (en) | 2015-12-21 | 2018-08-17 | Airbus Helicopters | AIRCRAFT ROTOR BLADE WITH GEOMETRY ADAPTED FOR ACOUSTIC IMPROVEMENT DURING APPROACH FLIGHTS AND PERFORMANCE IMPROVEMENT IN STATIONARY AND ADVANCED FLIGHTS |
| FR3045565B1 (en) | 2015-12-21 | 2018-07-27 | Airbus Helicopters | AIRCRAFT ROTOR BLADE WITH GEOMETRY ADAPTED FOR ACOUSTIC IMPROVEMENT DURING AN APPROACH FLIGHT AND PERFORMANCE IMPROVEMENT IN FLYING |
Family Cites Families (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US3989406A (en) * | 1974-11-26 | 1976-11-02 | Bolt Beranek And Newman, Inc. | Method of and apparatus for preventing leading edge shocks and shock-related noise in transonic and supersonic rotor blades and the like |
| US4171183A (en) * | 1976-09-24 | 1979-10-16 | United Technologies Corporation | Multi-bladed, high speed prop-fan |
| US4358246A (en) * | 1979-07-16 | 1982-11-09 | United Technologies Corporation | Noise reduction means for prop-fan and the construction thereof |
-
1985
- 1985-08-16 CA CA000488883A patent/CA1270802A/en not_active Expired - Fee Related
- 1985-10-02 GB GB08524280A patent/GB2170868B/en not_active Expired
- 1985-10-03 DE DE19853535399 patent/DE3535399A1/en not_active Withdrawn
- 1985-10-04 BR BR8504907A patent/BR8504907A/en not_active IP Right Cessation
- 1985-10-07 FR FR8514818A patent/FR2576872B1/en not_active Expired
- 1985-10-07 IT IT22377/85A patent/IT1185996B/en active
- 1985-10-07 JP JP60223447A patent/JPS61181798A/en active Pending
Also Published As
| Publication number | Publication date |
|---|---|
| FR2576872B1 (en) | 1987-07-24 |
| FR2576872A1 (en) | 1986-08-08 |
| GB8524280D0 (en) | 1985-11-06 |
| IT8522377A0 (en) | 1985-10-07 |
| IT1185996B (en) | 1987-11-18 |
| GB2170868A (en) | 1986-08-13 |
| DE3535399A1 (en) | 1986-08-07 |
| BR8504907A (en) | 1986-12-16 |
| GB2170868B (en) | 1988-07-13 |
| JPS61181798A (en) | 1986-08-14 |
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| Date | Code | Title | Description |
|---|---|---|---|
| MKLA | Lapsed |