DE102009028820A1 - Wind turbine, has axial surfaces partially covered with flow conducting device, so that axial inflow opening is formed, and turbine blades blowing against flow directed on axial surfaces by axial inflow opening - Google Patents

Abstract

The turbine has a vertical rotor (1) covered by a cylindrical cover surface (5) and by an axial surface (6) and another axial surface. The axial surfaces run perpendicular to an axis. A radial flow region is partially covered with a flow conducting device e.g. flow conducting units (7, 8), radial flow conducting unit (10) and axial flow conducting unit, and is directed on the cover surface. The axial surfaces are partially covered with the conducting device, so that an axial inflow opening is formed. Turbine blades (4) blow against flow directed on the axial surfaces by the opening.

Description

The The invention relates to a wind turbine according to the preamble of the claim 1.

Such a wind turbine is out of the DE 30 497 64 A1 known. The known wind turbine comprises a vertical rotor, which is surrounded by a housing-like flow guide. The vertical rotor is closed at its opposite axial surfaces each with a closure plate. The flow guide has funnel-like guide plates which direct an air flow in the direction of turbine blades, which are provided between the end plates of the vertical rotor. The well-known wind turbine is not very efficient.

task The invention is to the disadvantages of the prior art remove. It should in particular a wind turbine with improved Efficiency can be specified. For a further object of the invention should also be a wind turbine arrangement with improved Efficiency be provided.

These The object is achieved by the features of claims 1 and 15 solved. Advantageous embodiments of Invention will become apparent from the features of the claims 2 to 14 and 16 to 19.

To According to the invention, it is provided that at least one the axial surfaces with the flow guide only partially covered, so that a first axial inflow opening is formed, through which the turbine blades through an oblique Flow directed towards the axial surface can be flowed on are.

By the provision of a first axial inflow opening the vertical rotor can additionally with currents be flown, which have axial direction components. The usable for driving the vertical rotor inflow surface is enlarged. This is the energy yield elevated. Such a wind turbine can be particularly efficient operate. It is also suitable for use in low wind areas.

To An embodiment of the invention, the flow guide first Strömungsleitmittel, which the first inflow opening overlap in the axial direction and at least in sections are directed obliquely to the axial surface, so that a flow area formed by the first flow guide downsized in the flow direction. Through the first flow guide can be radial currents and also currents passed with axial components through the first axial inflow opening become. This further improves the efficiency of the wind turbine.

To In a further embodiment of the invention, the first flow guiding means bend downstream in a direction substantially parallel to the axial surface Direction around. A nozzle effect generated thereby contributes continue to improve the efficiency of the wind turbine.

advantageously, the flow guide covers each of the axial surfaces partially off, so that in each axial surface one each axial inflow opening is formed, through which the turbine blades through an oblique to the respective Axial surface directed flow can be flowed against are. Such a configuration allows a flow both axial surfaces. The usable for driving the vertical rotor Flow area can thus be further increased. An energy inherent in the flow can thus be better be used to drive the vertical rotor.

To a further embodiment of the invention, the flow guide at least partially obliquely on the lateral surface directed second Strömungsleitmittel on. By the second Strömungsleitmittel can a wind flow in radial Direction to the turbine blades of the vertical rotor be redirected. Such a design allows a further increase in efficiency.

To an expedient embodiment bend the second Flow guide downstream in a substantially tangent to the lateral surface direction. Thereby In turn, an advantageous nozzle effect is achieved.

To In a further embodiment of the invention, the first flow-guiding means form and the second flow guiding means in the flow direction Tapered inlet funnel or a funnel-like Structure. Through the inlet funnel becomes the flow directed to the turbine blades of the vertical rotor and accelerates.

Between the first flow guiding means and the axial surface a gap with a width of 2 to 20 cm can be provided.

Conveniently, the vertical rotor has at least one substantially perpendicular to the axis extending rotor bottom. From a top of the rotor bottom can first turbine blades in the axial direction extend. From a bottom of the rotor bottom can extending second turbine blades in the axial direction. By the Providing a rotor bottom increases the mechanical Stability of the vertical rotor. It can too be provided several rotor bottoms.

To a further advantageous embodiment of the invention is attached at least one of the radial edges of the turbine blades a recess intended. In this embodiment, one through the rotation the radial edge of the turbine blades defined axial surface no flat surface. The axial surface is here by rotation of the recesses having radial edges of the Defined turbine blades. By providing the recesses can the flow to the at least one axial inflow opening be further improved.

To Another embodiment of the invention is the wind turbine attached to a mast and is with respect to another Axis of the mast by means of a pivoting device about a horizontal Axis pivotable or oblique by a predetermined angle posed. The wind turbine can thus control the direction of a wind flow be set. The wind flow can then be the at least one axial flow opening of the vertical rotor flow directly.

To Another embodiment of the invention is the axis of the vertical rotor drivingly connected to at least one generator. Thus, the mechanical energy of the vertical rotor in electrical Energy to be transformed.

It is also possible several inventive Wind turbines stacked, the wind turbines over a common shaft drivingly with a Generator are connected. The number of wind turbines can z. B. two, four or more.

alternative can the kinetic energy of the vertical rotor / the vertical rotors over a transmission for driving a machine, for. As a pump transferred become.

To Another requirement of the invention is a turbine arrangement provided with four wind turbines according to the invention, in which about a substantially vertical axis rotatable vertical rotors and a vertical rotors sections surrounding flow guide are provided. There are two first vertical rotors with respect to a mainstream direction given by a wind direction upstream arranged two second vertical rotors. First axles of the first Vertical rotors and second axes of the second vertical rotors are with respect to the main flow direction offset from one another. The flow guide is configured such that one of the first vertical rotors outflowing Sub-flow downstream to the downstream directed to the second vertical rotors. Because of the use of the secondary stream flowing out of the first vertical rotors for driving the second vertical rotors, one of the wind flow inherent energy exploited to a very high degree become. The proposed wind turbine arrangement is particularly efficient.

To An embodiment of the invention is the flow guide further formed so that the second vertical rotors in addition subjected to a main current flowing in the main flow direction become. As a result, the energy yield of the wind turbine assembly be further improved.

To Another embodiment is the flow-guiding device designed so that a direction of the secondary flow in the Beaufschlagungsbereich the second vertical rotors with the main flow direction forms an angle of 20 to 120 °, preferably from 45 to 100 °.

To In another embodiment, the axes of the second vertical rotors spaced farther apart than the axes of the first vertical rotors. In this case, a position of the axes of the vertical rotors the vertices correspond to an isosceles trapezium.

following Embodiments of the invention with reference to the drawings explained in more detail. Show it:

1 a partially broken plan view of a wind turbine;

2 a first side view according to 1 ;

3 a second side view according to 1 ;

4 a plan view of a first vertical rotor;

5 a sectional view taken along the line AA in 4 ;

6 a plan view of a turbine blade;

7 a side view of a turbine blade;

8th a sectional view through a second vertical rotor;

9 an arrangement of turbine blades;

10 a sectional view through a third vertical rotor;

11 a side view of a fourth vertical rotor;

12 a plan view of a first wind turbine assembly;

13 a schematic side view of the first wind turbine assembly;

14 a front view of the first wind turbine assembly;

15 a flow path in the first wind turbine assembly;

16 a plan view of a second wind turbine assembly;

17 a flow path in the second wind turbine assembly;

18 a side view of a third wind turbine assembly;

19 a side view of a fourth wind turbine assembly;

20 a front view of the fourth wind turbine assembly;

21 a front view of a fifth wind turbine assembly; and

22 a front view of a sixth wind turbine assembly.

In 1 is with the reference numeral 1 generally called a vertical rotor of a wind turbine. The vertical rotor 1 is about a vertical axis 2 rotatably mounted and has a hub 3 and a variety of turbine blades 4 on. A cylindrical lateral surface and a planar upper axial surface of the vertical rotor 1 are with the reference numerals 5 and 6 designated. The wind turbine has a vertical rotor 1 partially surrounding flow guide on. The flow guide forms a kind of housing of the vertical rotor 1 and can z. B. made of sheet metal or plastic. A main flow is indicated by an arrow designated by the reference H. The direction of rotation of the vertical rotor 1 is indicated by an arrow denoted by the reference D.

The flow guide has first 7 and second flow guiding means 8th on. The first flow guide 7 form with the axial surfaces 6 an acute angle. The first flow guide 7 go through the axis 2 , The second flow guide 8th are obliquely on the lateral surface 5 directed. The first 7 and second flow guiding means 8th each form an inlet funnel. A section of the vertical rotor located in the inlet funnel 1 can be flowed through by the main flow H. A section of the upper axial surface located outside the inlet funnel 6 is covered by the flow guide. Furthermore, a portion of the lateral surface facing the main flow H is located outside of the inflow funnel 5 covered by the flow guide. This ensures that the counter to the main flow H running turbine blades 4 not be flown. One with the reference numeral 9 designated lateral surface portion is for outflow of a secondary flow N from the vertical rotor 1 not covered.

As in particular in 1 can be seen, direct the second flow guide 8th the main flow H on the radially outer portions of the turbine blades 4 , To improve this effect, the flow guiding device has additional radial flow guiding means 10 on.

2 shows a side view of the wind turbine. Here is particularly good to see that the upper axial side 6 , a lower axial side 11 and the lateral surface 5 in a section of the axial rotor shown by dotted lines 1 are covered by the flow guide. The uncovered section can be flowed through by a flow through the inlet funnel.

How out 3 As can be seen, the uncovered portions of the upper 6 and the lower axial surface 11 each axial inflow openings 12 through which the turbine blades 4 can be flown. The axial inflow openings 12 are from each obliquely to the top 6 or lower axial surface 11 directed first flow guides 7 overlaps. The first flow guide 7 direct the main flow H to the axial inflow openings 12 , To improve this effect, the flow guide has additional Axialströmungsleitmittel 13 on. The vertical rotor 1 Thus, in addition to radially on the turbine blades 4 directed flows are also driven by flows with axial components. The axis 2 of the vertical rotor 1 is with a generator 14 for converting the mechanical energy into electrical energy.

The approach streamline tapers in the direction of the main stream H. As out 1 it can be seen, the inlet funnel is formed like a snail shell. This is the flow of the vertical rotor 1 further improved.

4 shows a plan view of a first vertical rotor 1 , The vertical rotor 1 has twelve here Turbine blades 4 on. Of course, a different number of turbine blades 4 be provided. The turbine blades 4 each have in the radially outer region of a kink at an angle of 135 ° to 170 °. They can also be bent.

How out 5 can be seen, the vertical rotor 1 a rotor bottom 15 on. From the rotor bottom 15 Turbine blades extend in both axial directions 4 , A first height H1 of the turbine bucket blades 4 on the upper axial side 6 here is equal to a second height H2 of the turbine blades on the lower axial side 11 , The turbine blade leaves each have a recess at their radial edges 16 which facilitates an inflow of wind with axial components. Such a vertical rotor 1 can on both axial sides 6 . 11 be streamed.

6 shows a plan view of a turbine blade 4 , The turbine bucket blade 4 shows one from the hub 3 extend radially outward radial section 17 on. This is followed by a first inclination section bent counter to the direction of rotation D. 18 as well as an angled against the direction of rotation D second slope section 19 at. A first angle α between the radial section 17 and the first slope section 18 is between 120 ° and 160 °, preferably about 140 °, a second angle β between the first 18 and the second slope portion 19 is between 110 ° and 150 °, preferably about 130 °. The length L1 of the radial section 17 is between 70% and 90%, preferably about 80%, of the radius of the vertical rotor 1 , The length L2 of the second slope section 19 is between 1% and 5%, preferably about 2%, of the radius of the vertical rotor 1 ,

7 shows a side view of a turbine blade 4 with a recess 16 , The recess 16 is in the radial section 17 intended. A height of the turbine bucket 4 is denoted by A. The height of the recess 16 is about A / 2.

At the in 8th illustrated second vertical rotor 1 is the first height H1 of the turbine bucket blades 4 on the upper axial side 6 greater than the second height H2 of the turbine blades 4 on the lower axial side 11 , Only the turbine blades 4 on the upper axial side 6 are with a recess 16 Mistake.

As in 9 are shown, the turbine blades are 4 on an axial side 6 . 11 each spaced apart at a third angle γ. The third angle γ is determined by its on the vertical axis 2 lying vertex S1 and two adjacent vertices S2 of the angle α defined. The turbine blades 4 on the other axial side 11 . 6 are each offset by an angle in the range of γ / 4 to 3γ / 4, preferably γ / 2. In an axial rotor 1 with twelve turbine blades, the angle γ is about 30 °.

The in 10 illustrated third vertical rotor 1 points only on the upper axial side 6 each with a recess 16 provided turbine blades 4 on.

The in 11 illustrated fourth vertical rotor 1 has three rotor bottoms 15 on. The vertical rotor 1 has several segments 20 . 21 . 22 . 23 on, with the axially outer segments 20 . 23 can be flown both radially and axially. Such a vertical rotor 1 is very stable.

In 12 is shown a first wind turbine arrangement with four wind turbines. The first wind turbine assembly has two first vertical rotors 24 and two second vertical rotors 25 on. The wind turbine assembly has one of the first 24 and second vertical reds 25 each partially surrounding flow guide on. The first vertical rotors 24 are upstream of the second vertical rotors with respect to the direction of the main flow H. 25 arranged. The axes 2c . 2d the second vertical rotors 25 are more widely spaced than the axes 2a . 2 B the first vertical rotors 24 , The first wind turbine assembly is rotatable about a system axis 26 stored. The first wind turbine assembly may be provided by means of wind direction tracking, e.g. B. a wind direction sensor or connected to a wind direction sensing sensor actuator, to the system axis 26 be aligned in the wind direction. The first vertical rotors 24 have opposite directions of rotation D1, D2. The second vertical rotors 25 also have mutually opposite directions of rotation D3, D4, wherein the rotational direction D3 or D4 of a second vertical rotor 25 in each case opposite to the direction of rotation D1 or D2 of the first vertical rotor arranged upstream thereto 24 is. As a result, backlash losses can be avoided. The first vertical rotors 24 have one of the first 7 and second flow guiding means 8th comprehensive common inlet funnel on. The second vertical rotors 25 each have a snail shell-shaped inlet funnel. Through the inlet funnel become the first 24 and the second vertical rotors 25 in the direction of the main flow H flows. The first wind turbine assembly further comprises approximately corresponding to the lateral surface curved third Strömungsleitmittel 27 on. The third flow guide 27 are between the first two vertical rotors 24 arranged. They meet against the main flow H at an acute angle to each other and form egg NEN flow divider.

In 13 is the first wind turbine arrangement on a mast 28 appropriate. The axes 2 B . 2d the vertical rotors 24 . 25 are each drivingly with a generator 14 connected. Both axial sides 6 . 11 the first 24 and second vertical rotors 25 have axial inlet openings 12 on. By the oblique to the direction of the main flow H directed first flow 7 can cause a flow with axial components on the axial surfaces 6 . 11 the first 24 and second vertical rotors 25 be directed.

14 shows a front view of the first wind turbine assembly. Here is particularly good to see that the lateral surfaces 5 and the axial surfaces 6 . 11 the first 24 and second vertical rotors 25 are partially covered by the flow guide. Furthermore, they are the first 7 and second flow guiding means 8th comprehensive, for each of the first 24 and second vertical rotors 25 formed inlet funnel visible.

15 shows a flow path in the first wind turbine assembly. The first 24 and second vertical rotors 25 are respectively flowed through by the main flow H. Through the third flow guide 27 becomes one of the first vertical rotors 24 outflow side stream N on the turbine blades 4 the second vertical rotors 25 directed. The second vertical rotors 25 are thus driven by both the main flow H and by the secondary flow N. The direction of the secondary flow N forms in the loading area of the second vertical rotors 25 with the direction of the main flow H an angle of 20 to 120 °, preferably from 45 to 100 °, here about 90 °. Such a flow pattern is particularly efficient.

16 shows a second wind turbine assembly. Here are the axes 2a . 2 B the first vertical rotors 24 spaced farther apart than the axes 2c . 2d the second vertical rotors 25 , The first vertical rotors 24 are partially surrounded by a snail-like inflow funnel. For the second vertical rotors 25 is a first 7 and second flow guiding means 8th comprehensive inlet funnel provided. The third flow guide 27 is between the second vertical rotors 25 intended.

The flow pattern of the second wind turbine device is in 17 shown. The first 24 and second vertical rotors 25 are in turn flowed through by the main flow H. The flow guiding device is designed such that one of the first vertical rotors 24 outflow secondary flow N, the second vertical rotors 25 drives. The second flow guide 8th the first vertical rotors 24 have to one with a distance along the lateral surface 5 the first vertical rotors 24 extend section. The angle between the direction of the secondary flow N and the direction of the main flow H in the loading area of the second vertical rotors 25 is here again about 90 °.

In 18 a third wind turbine arrangement is shown. The flow guiding device serves here simultaneously as a roof of the third wind turbine arrangement. As a result, on the one hand reduces the production cost and on the other hand, the system can be protected from the weather. The first 24 and second vertical rotors 25 are skewed with respect to the direction of the main flow H. This allows the upper axial surface 6 the vertical rotors 24 . 25 be streamed directly. For tilting a suitable pivoting means may be provided with a motor and a sensor, which aligns the wind turbine assembly to the main flow direction H. The pivoting movement may, for. B. in a range of +/- 25 ° relative to the horizontal.

19 shows one on a mast 28 attached fourth wind turbine assembly in which two wind turbine assemblies according to the invention are combined. Here are the axis 2 B the first 24 and the axis 2d the second vertical rotors 25 each drivingly with a common generator 14 connected. The entire arrangement can be about a pivot axis 29 be pivoted in relation to the horizontal and a servomotor 30 be aligned in the wind direction. By combining several wind turbine arrangements, the z. B. can be designed in modular design, particularly powerful systems can be realized.

In 20 is a front view of the fourth wind turbine assembly is shown. The structure and function of the individual modules corresponds to the wind turbine arrangement of 14 ,

21 shows a fifth wind turbine assembly in which four wind turbines according to the invention are arranged one above the other. The vertical rotors 1 The wind turbines are over a common wave 31 drivingly with a generator provided below the four wind turbines 14 connected.

22 shows a sixth wind turbine arrangement in the two wind turbines according to the invention above and below a generator 14 are arranged. The vertical rotors 1 the above and below the generator 14 arranged wind turbines are in turn via a common shaft 31 drivingly with the generator 14 connected.

LIST OF REFERENCE NUMBERS

1

vertical rotor

2, 2a, 2b, 2c, 2d

vertical axis

3

hub

4

Turbine blades

5

lateral surface

6

upper axial surface

7

first flow guide

8th

second flow guide

9

Lateral surface section

10

Radialströmungsleitmittel

11

lower axial surface

12

axial inflow

13

Axialströmungsleitmittel

14

generator

15

rotor base

16

recess

17

radial section

18

first slope portion

19

second slope portion

20

first segment

21

second segment

22

third segment

23

fourth segment

24

first vertical rotor

25

second vertical rotor

26

system axis

27

third flow guide

28

mast

29

swivel axis

30

servomotor

31

wave

A

height of turbine blade

B

width the recess

D D1, D2, D3, D4

direction of rotation

H

mainstream

H1

first height

H2

second height

N

secondary flow

L1

length of the tangential section

L2

length of the second slope section

S1

first vertex

S2

second Vertex first angle

β

second Angle third angle

QUOTES INCLUDE IN THE DESCRIPTION

This list The documents listed by the applicant have been automated generated and is solely for better information recorded by the reader. The list is not part of the German Patent or utility model application. The DPMA takes over no liability for any errors or omissions.

Cited patent literature

• - DE 3049764 A1 [0002]

Claims (19)

Wind turbine with at least one about a substantially vertical axis ( 2 ) rotatable vertical rotor ( 1 ), whereby from a hub ( 3 ) of the vertical rotor ( 1 ) radial turbine blades ( 4 ), wherein the vertical rotor ( 1 ) by an imaginary substantially cylindrical lateral surface ( 5 ) and imagined substantially perpendicular to the axis extending axial surfaces ( 6 . 11 ), and wherein one on the lateral surface ( 5 ) directed radial Anströmbereich partially with a flow guide ( 7 . 8th . 10 . 13 ), characterized in that at least one of the axial surfaces ( 6 . 11 ) with the flow guiding device ( 7 . 8th . 10 . 13 ) is only partially covered, so that a first axial inflow opening ( 12 ) is formed, through which the turbine blades ( 4 ) by an oblique on the axial surface ( 6 . 11 ) directed flow are flowed. Wind turbine according to claim 1, wherein the flow guiding device ( 7 . 8th . 10 . 13 ) first flow guide ( 7 ), which the inflow opening ( 12 ) overlap in the axial direction and at least partially obliquely to the axial surface ( 6 . 11 ) are directed so that through the first flow guide ( 7 ) formed in the flow direction decreases in size. Wind turbine according to one of the preceding claims, wherein the first flow guiding means ( 7 ) downstream in a substantially parallel to the axial surface ( 6 . 11 ) turn direction. Wind turbine according to one of the preceding claims, wherein the flow guiding device ( 7 . 8th . 10 . 13 ) each of the axial surfaces ( 6 . 11 ), so that in each axial surface ( 6 . 11 ) each have an axial inflow opening ( 12 ) is formed, through which the turbine blades ( 4 ) by an oblique on the respective axial surface ( 6 . 11 ) directed flow are flowed. Wind turbine according to one of the preceding claims, wherein the flow guiding device ( 7 . 8th . 10 . 13 ) at least partially obliquely on the lateral surface ( 5 ) directed second flow guiding means ( 8th ) having. Wind turbine according to one of the preceding claims, wherein the second flow guiding means ( 8th ) downstream in a substantially tangential to the lateral surface ( 5 ) turn direction. Wind turbine according to one of the preceding claims, wherein the first flow guiding means ( 7 ) and the second flow guiding means ( 8th ) form a direction of flow (H) tapered inlet funnel. Wind turbine according to one of the preceding claims, wherein between the first flow guiding means ( 7 ) and the axial surface ( 6 . 11 ) a gap with a width of 2 to 20 cm is provided. Wind turbine according to one of the preceding claims, wherein the vertical rotor ( 1 ) at least one substantially perpendicular to the axis ( 2 ) running rotor bottom ( 15 ) having. Wind turbine according to one of the preceding claims, wherein first turbine blades ( 4 ) in the axial direction from an upper side of the rotor bottom ( 15 ). Wind turbine according to one of the preceding claims, wherein second turbine blades ( 4 ) in the axial direction from an underside of the rotor bottom ( 15 ). Wind turbine according to one of the preceding claims, wherein on at least one of the radial edges of the turbine blades ( 4 ) a recess ( 16 ) is provided. Wind turbine according to one of the preceding claims, wherein the wind turbine on a mast ( 28 ) and with respect to another axis of the mast ( 28 ) by means of a pivoting device about a horizontal axis ( 29 ) is pivotable or inclined by a predetermined angle. Wind turbine according to one of the preceding claims, wherein the axis ( 2 ) of the vertical rotor ( 1 ) drivingly with at least one generator ( 14 ) connected is. Wind turbine arrangement with four wind turbines according to one of the preceding claims, wherein about a substantially vertical axis ( 2a . 2 B . 2c . 2d ) rotatable vertical rotors ( 24 . 25 ) and one the vertical rotors ( 24 . 25 ) sectionally surrounding flow guiding device ( 7 . 8th . 10 . 13 . 27 ) are provided, wherein two first vertical rotors ( 24 ) with respect to a main flow direction given by a wind direction (H) upstream of two second vertical rotors ( 25 ) are arranged, wherein first axes ( 2a . 2 B ) of the first vertical rotors ( 24 ) and second axes ( 2c . 2d ) of the second vertical rotors ( 25 ) with respect to the main flow direction (H) offset from one another, and wherein the flow guide ( 7 . 8th . 10 . 13 . 27 ) is configured such that one of the first vertical rotors ( 24 ) flowing secondary flow (N) on the downstream downstream second vertical rotors ( 25 ). Wind turbine assembly according to claim 15, wherein the flow guiding device ( 7 . 8th . 10 . 13 . 27 ) is further formed so that the second Vertikalro gates ( 25 ) are additionally acted upon by a main flow (H) flowing in the main flow direction. Wind turbine assembly according to claim 15 and 16, wherein the flow guide is formed so that a direction of the secondary flow (N) in the loading region of the second vertical rotors ( 25 ) with the main flow direction (H) forms an angle of 20 to 120 °, preferably from 45 to 100 °. Wind turbine arrangement according to one of claims 15 to 17, wherein the axes ( 2c . 2d ) of the second vertical rotors ( 25 ) are more widely spaced than the axes ( 2a . 2 B ) of the first vertical rotors ( 24 ), Wind turbine arrangement according to one of claims 15 to 18, wherein a position of the axes ( 2a . 2 B . 2c . 2d ) of the vertical rotors ( 24 . 25 ) corresponds to the vertices of an isosceles trapezium.

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