Metoda VLM

7/26/2019 Metoda VLM

1/6

Metoda VLM

virtej XA XB, XP,( ) AP XP XA

BP XP XBAB XB XA

i

1

0

0

VlegatAP AB

AP

AB BPBP

AB AP

AB AP( ) 2

Vliber1 1i APAP

+

AP i

AP i( ) 2

Vliber2BP iBP

1+

i BP

i BP( ) 2

V1

4 Vlegat Vliber1+ Vliber2+( )

V

:=

Geometrie arip (dimensiunile n m)

ce 1.6:=c0 6.88:= b 10.:= 43.5180

:= 4

180:=

Incidenta ariiice c0b

2tan ! ":= ce 1.62=

Vin# 1:=$c0 ce+

2b:= $ 46.36315=

b2

$:= 2.5626=

c%a2

$

0

b

2

&c0

ce c0

b

2

&+

2

d:= c%a 4.797=

Ecuatia scheletului aripii

'( )! " i# 0 ) 40* 4 *)

40*! "2

2 40 * )! "

, 4*

1 )

1 40*! "2 1 )+ 2 40 *! ",

:=

) 0 0.01, 1..:=


2/6

Discretizare arip

+ 10:= nr. sectiuni pe semiplan

, 5:= nr. puncte pe sectiune

i 1 +..:= j 1 ,..:=

&(i

b

2

b

2

i 1+ 1

+:= )j

j 1, 1

:='

j'( )j( ):= zp in %

ci

c0

ce c0

0.5 b&(

i:=

)-i j, &( i tan ! " ci )j+:= '-i j, ci 'j:= aripa fara incidenta

)-2 + i j,

)-i j,:= '-2 + i j, '-i j,:=

coordonate aripa cu incidenta

)i j, )-i j, c( ! " '-i j, (in ! "+:= &i j, &( i:= 'i j, )-i j, (in ! " '-i j, c( ! "+:=

)2 + i j, )i j,:= &2 + i j, &! "i j,:= '2 + i j, 'i j,:=

0 0.2 0.4 0.6 0.8 10.1

0.05

0

0.05

0.1

'( )! "

)


3/6

) &, ',! "

j 1 ,..:=

Xi j, )i j, &i j, 'i j,( )

/:=i 1 2 + 1..:= coordonate puncte : X(x,y,z)

Vind vite'eind(e XA XB, XP, virtej, +, ,,( ):=

crd + ,, X, ,! "

ind i 1! " , 1! " j+

XPctind

Xi j, 0. 25 Xi j 1+, Xi j,( )+ 1i#

XPctind

Xi 1+ j, 0. 25 Xi 1+ j 1+, Xi 1+ j,( )+ 2i#

XPctind

0.5 Xi j, Xi 1+ j,+( ) 0.75 0.5 Xi j 1+, Xi 1+ j 1+,+( ) 0.5 Xi j, Xi 1+ j,+( )+ 3i#

j 1 , 1..#r

i 1 2 + 2..#r

XPct

:=

nr%alaan + ,, X,! "

ind i 1! " , 1! " j+

nanind

Xi j 1+, Xi j,( ) Xi 1+ j, Xi j,( )

Xi j 1+, Xi j,( ) Xi 1+ j, Xi j,( )

j 1 , 1..#ri 1 2 + 2..#r

nan

:=

n.r%ala n.r%ala0an + ,, X,! ":=

XA crd + ,, X, 1,! ":= XB crd + ,, X, 2,! ":= XP crd + ,, X, 3,! ":=

vite'eind(e XA XB, XP, virtej, +, ,, nrele% 2 + 2! " , 1! "

Viti j, virtej XAj

XBj

, XPi

,

j 1 nrele%..#r

i 1 nrele%..#r

Vit

:=


4/6

e# +at Vind +, ,, nr%ala,( ):=

/lib Vin# +, ,, nr%ala,( ) nrele% 2 + 2! " , 1! "

tlibi

Vin# nr%ala i( )1

i 1 nrele%..#r

tlib

:=

tlib /lib Vin# +, ,, nr%ala,( ):=

(l l(lve e# tlib,! ":=

i1 1 2 + 2..:= j1 1 , 1..:=

i1 j1, (l i1 1! " , 1! " j1+

:= )--i1 j1, XP i1 1! " , 1! " j1+1

:= &--i1 j1, XP i1 1! " , 1! " j1+2

:=

1.225:= kg/m

Vin#2

2:=

+at Vind +, ,, nr%ala,( ) nrele% 2 + 2! " , 1! "

ce#i j, nr%alai( )

1Vind

i j,1

nr%alai( )

2Vind

i j,2

+ nr%alai( )

3Vind

i j,+

j 1 nrele%..#r

i 1 nrele%..#r

ce#

:=

#rteaerd XAXB, (l, Vind, +, ,, ,( ) nrele% 2 + 2! " , 1! "c' 0

c%& 0

c)i 0

- 0

- - (lj

Vindi j,

3

+

j 1 nrele%..#r

i

-

i 1 nrele%..#r

d#' (li

XBi

2

XAi

2

c' c' d#'+

c%& c%& 0.5 X

Bi 1

X

Ai 1

+

d#'

c)i c)i i

XBi

2

XAi

2

(li

i 1 nrele%..#r

c' 1i#

c%& 2i#

c)i 3i#

:=


5/6

2

180:=

' #rteaerd XAXB, (l, Vind, +, ,, 1,( ):=

) #rteaerd XA XB, (l, Vind, +, ,, 3,( ):=

+& #rteaerd XA XB, (l, Vind, +, ,, 2,( ):=

' 0.30402= ) 0.75077= +& 8.72082=

'

2 '

$:= ' 0.01311=

)i

2 )

Vin#$:= )i 0.03239=

%&

2 +&

$ c%a:=

%& 0.07842=

0

180:=

' #rteaerd XAXB, (l, Vind, +, ,, 1,( ):=

) #rteaerd XAXB, (l, Vind, +, ,, 3,( ):=

+& #rteaerd XAXB, (l, Vind, +, ,, 2,( ):=

' 0.30402= ) 0.75077= +& 8.72082=

'

2 '

$:= ' 0.01311=

)i

2 )

Vin#$:= )i 0.03239=

%&

2 +&

$ c%a:= %& 0.07842=


6/6

4

180:=

' #rteaerd XA XB, (l, Vind, +, ,, 1,( ):=



' 0.30402= ) 0.75077= +& 8.72082=

'

2 '

$:= ' 0.01311=

)i

2 )

Vin#

$:= )i 0.03239=

%&

2 +&

$ c%a:= %& 0.07842=

8

180:=

'

#rteaerd X

A

X

B

, (l

, Vind

, +, ,, 1,( ):=



' 0.30402= ) 0.75077= +& 8.72082=

'

2 '

$:= ' 0.01311=

)i

2 )

Vin#$:= )i 0.03239=

%&

2 +&

$ c%a:= %& 0.07842=

Metoda VLM

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