Vol Horizontal Uniforme Forces : Trois forces :

!
"
#
$
$
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 1
"
!
%
% #
#
= '+
=
&
&
"
α ≈*
( )
α
α ≈+)
= '
=
"
"
"
#
= '
"
ρ'
"
σ
,
,
,"
+
ρ ' . , - /'
+
=
ρσ . , - /'
+
=
ρσ . ," - /'
=
=
"
ρ'
"
σ
+
ρ' . , - /
+
=
ρσ . , - /
+
=
ρσ . ," - /
=
,
,
,"
0
α
1
)ρ
234 5).
-
,
4
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 2
"
+
ρσ . ," - /'
+
=
ρσ . ," - /
-
+ →
=
- →
+
=
-
=
/'
=
/
=
0
6
/
% 7
$
#
1
1
8
3
%
#
#
/
)
% 9 6 ,
9 =
×,
9
1
1
, #
9
4
/
/' 5
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 3
"
9
α5
α:
/ /' 5
/
/' 5
;
α-
!
<
/
/' 5 49
=
#
;
/' 5
/ -
,=
=
9 =
=
9
9
9
*
σ
,*
σ
9
=
#
,=
,+
5 4+
=
+
+
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 4
/
% 7>
8
9 = / ×ω
9 = 9 ×η
3
%
/
% 9 6
3
,
#
9
# ,
η
#
#
,
9
6/
,
3
)
η
9
)η = /
;
. <
/
9 =/
)η
9
%
%
!
%
9
9
/
/!
/
$
/
9
/
A
=
/
9
234
/#
/# +/#6 ?5@1
234
3
/
6
*)
- *)
5 234
/#
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 5
%
B 6B
B 6B
/
%
= B 9 −,
3
!
9 6,
, 6,
%
! C
!
6 ,
"
#
(
#
!
%
#
"
#
" 3
% C
#
D
#
;
. <
"
!
B
'
B
=
*σ
E
A
(
E 6+
3
!
/
% 9 6
,
0
#
/
9 6 , ! F9
6
,
/
/!
=
/
$
/
/
A
/
234
0
0 1
234
3
/
6
*)
*5G *)
*@234
0
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 6
%
/
H
9
9
% 9 6
,
69
= 9
9
9
/
=9
9
9
!
η
η
=
,
I9
,
+
/
J>
#
J
/
/!
/
$
/
9
/
A
=
/
9
234
/#
/# +/#6 ?5@1
234
3
/
6
*)
+G *)
+K 234
/#
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 7
H 3
/!
B
!
%
9 69
"
6
3
+
3
(
%
! #
#
9
3
,#
9
=
,#
#
J>
A
J
!
9
!
3
!
3
3
#
#
#
3
α5)
#
#
α-
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 8
α5
J
!
3
α- /
)
9
"
#
9
3
" #
( )
"
"
3
3
%
6"
=
+
-
3
I"
,- +
3
3 ' =/
" = " +" =/
∆, +
"
∆' = −
+
,
++)5
3 ∆' = *
∆,
'
),
,
2
&
"
=
+
-
L =
,- +
3 ' =/
,+
-3
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 9
&
$
#
+:*
;
(
# =
3 6 M)
K+ 4-
)#
%
G*** (
-?* / 6 *)
*+G I *)
*G /'-
!
/ 6 / I / 6 *)
*+GI *)
*G
! "#"$%
λ
&
/ =
/' -
πλ
→ *)
*G=
+
πλ
→ λ=
+
π *)
*G
→ λ =@)
5@@
'
λ=
N→ N = λ . → N = @)
5@@× -?* → N = :+):?
.
&
&
/
=-
/'
/
= - × *)*+G= *)*5
A
*)
*+G
= *)G:?
*)
*G
=
/'
=
=
%
=
+
: %
/' *)
G:?
=
= +K)-5
/
*)
*5
A
=
+
: %
=
+
= +K)-@
:×*)
*+G×*)
*G
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 10
(
&
(
&
"
=
+
ρ ' . , /' → , =
-
ρ' =
σ=
-* − G +G
=
= *)
@
-* + G -G
ρ'
→ ρ ' = ρ * σ → ρ ' =+)
--G×*)
*@
ρ*
=
,
()
A
ρ ' . /'
- × +:**** × M)
K+
=+GK)
@ 4
+)
--G× *)
*@× -?* × *)
GG
&
, =
()
,"
&
→ ," = ,
σ
σ
," = +GK)
@ *)
@ = +--)KG 4
*
&
&
"
=
=
→
=
+:**** × M)
K+
= ?G55?
+K)
-5
1
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 11
+
&
*
*
&
9 =
" /#=
, → 9 = ?G55? × +GK)@= ++M:K ::K 1
++M:K ::K
?5@
9 = ++M:K 29 = +@-5: /#
+
&
*
$""""&
*
&
σ G*** = *)@ → 9
G***
= +@-5: /#
-* −+*
= *)
555
-* ++*
E
9 G*** =
*)
@
9 G***
=
9 +****
E
9 +**** =
*)
555
σ +**** =
9
+****
=9
G***
E
*)
@
=
E
*)
555
*)
@
= +@-:5
*)
555
*)
555
*)
@
*)
@
= -+?M+ /#
*)
555
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 12
$""""&
#
&-&
$"
#
,
*
+
9
9
+:*
9
+5*
+5*
=
E +:* 5
→ 9
E +5* 5
= -+ ?M+
+5*
=9
+:*
+5* 5
+:*
+5* 5
= +M :MK /#= +: 5G+29
+:*
(
, G***
=
, +****
E
*)
@
=
E
*)
555
, +**** = , G***
*)
555
*)
@
*)
@
= +GK)
@
*)
555
, +:*
E +:*
=
→ , +5* = , +:*
, +5*
E +5*
, +5* = -+-)M
+5*
= -*G
+:*
*)
@
= -+-)
M
*)
555
4
+5*
+:*
4
()
," = ,
σ = -*G *)
555 = ++K)5* 4
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 13
"
!
%
% #
#
γ= '
&
=
&
3
+
γ
γ
+*O
+
=
+* ≈ *)MK
= '
=
+
"
"
γ
&
+*O)
∆ =
γ
! $."/012
#
3
+**
#
P
∆
= +***** M)K+
+*°
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 14
#
)#' #
γ=
#' =
9 −9
=
#'
,
∆9
γ)
3γ =
0
#'
=
,
−
Q = +**
−
+
H
, )
,)
3γ
+
=
#'
,
%
%
3γ
=
#'
,
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 15
/
% #' 6 ,
,γ
#
#
,
,'
#'
,
α5 9
α R α5 S
!
γ
!
9 )
9
! #
!
9
9
3
!
!
)!
α5
9
α5
9
;
&
3
/'
T
/
3
A
,'
γ
;
#
%
,'
%
3
#
3
! %
γ
3
#
)%
%
3
4 %
;
.
&# 0 +
#
3(
=
,'
#
,'
%
γ
=
! # 0
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 16
,γ
#
#
,
,'
#'
,
α U α- S
!
γ
α-
!
A
J
#
%
#
3δ)
#
% )
#
! #
!
!
3
9
)
3
)
%
α-
!
3
>
%
/
&!
)! #
!
'
'
'
#
α-)
#
=
*
!
=
σ
#
=
<
A
σ=
-* − <
=
-* + <
#'
"
*
γ
%
%
J
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 17
"
%
!
% #
#
γ= '
+
γ=
&
&
3
γ
+*O
=
+
= '
+
"
"
.
6* )
"
!
γ=
!
γ= '
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 18
γ=
"
#
)#!' #
#D' =
H
#D' =
!
9 −9
=
∆9
9
γ)
3γ =
0
+
−
H
, )
,)
3γ
=
#D'
,
%
%
3γ
=
#D'
,
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 19
H
/
3γ =
!
+
% #!' 6 ,
#D' =
9
#!'
&
α5
α-
!
γ
!
&
9
/D
&
#
<P
# =
<
#D'
#
#!'
3
&
3γ =
H
!
<
H
&
=
)
!
!
+
α5
9
<P
H 6<
α-
;
A
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 20
. 9
9
(
;
γ
#!'
(
#
%
γ
#!'
) #
9
#
#
%
3
#
%
3
#
,'
%
#
%
%
3
3
3
&
H
#
&
#
W
#
N
#
(
.
! #
#
=
#
,"
"
=
N)
&
WP
#
3
&
N
V
3
V
WP
3
#
W
!
"
#
&
+Q
C
3
3
)
+**
3
+**
≠ *)+ 4
*)+ 4 = *)- 2
H
*)+ 4
-
= *)- 2 4
-
+Q
→ ± *)- 2 4
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 21
&
&< 6 *
C
#
#
#
G
∆, = − *)
-2 4
H
%
+5* 2
)! #
P
GQ = −+2 4
∆, = − G2 → +-G2
G
3
=
GQ .
B
%
'
'
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 22
3
=
'
=
+
'=
=
ϕ
H
ϕ
# 3
ω=
3ϕ 3
,
, - ,ω ω3ϕ =
=
=
3
3
3
ω
=
,3ϕ 3
A
%
ω6
#
3
# 3
# 3
$
π
ω=
4
34
4
+K*O4
4
+K* °
= 5° 4
@*
ω=
π
@*
= *)*G
4
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 23
@O4
4 !
*)
+
%
# 3
9
#
ω6
+)5@*O4
4
<
=9
#
5
,# = ,
,
3
)
! # 3
%
!
! F
)%
!
#
)
(
H
,
&3
ϕ
3
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 24
,
3 3
)
! # 3
%
!
%
)%
!
! F
%
)
(
&3
3
H
,
ϕ
N
,
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 25
,3
" &
= ++
" /
=
,−+
3
=
,3
" N
H
!
!
C
3
X
= ++
,3
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 26
.
≤ +)
-
3
ω ≤
*)- 3
,
ω,
ω
)
ω °4 ≤
4)3
4-
O4
,
,
4
2
--*
, 2
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 27
.
(
+
=
ϕ
,#
,=
3ϕ 3
=,
ω=
,3
→ 3ϕ =
≤ *)-
ω
3ϕ =
.
3
3ϕ 3
,
=
4
=
*)- 3
,
4
=
"
= ++
&,
,3
= ++ -
N
$
,
,3
→
=
,3
ω° 4 =
--*
, 2
γ
=
,−+
3
&
&
= +− -
=
,3
$
,
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 28
5
+ ,
=
,
ρ ' . /'
,
- .
3
5 &
#
/'
α5
!
9
3
/!
=
#
! #
B
/
&
&
:
α:
!
α5
!
9
%
!
%
3
/!
&>
>
%
B
H=
/
!
!
,
,
,
#
/
/ =
,
!
α-
#
, 6*
α( , R * α R α( , U * α U α-
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 29
G
@>
,'
!
? H
,!'
γ
K .
α5
!
!
α5
α5
9
9
9
α R α 5)
9
α-
(
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 30
5
+ ,
J>
ρ ' . /'
=
,
,
α-
!
- .
3
5 &
#
3
/!
#
! #
B
=
/
&
>
α-
!
)
<
:
α-
!
#
%
#
0
!
3
/!
&>
0
>
%
B
H=
/
/
/ =
,
#
!
α+
!
/
/'
)
!
,
#
%
!
!
#
.
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 31
!
#
,
,
,
G
3
α+
, 6*
(
(
, R*
, U*
,
α R α+
α U α+
3
;
!
&>
3
@
-
,'
!
+Q
#
α-
!
? >
:Q
α R α-)
α -)
K H
,!'
γ
!
α5
9
α-
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 32
M .
(
5
!
#
J
J>
J
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 33
-(
!
+(
=
+
ρ ' . , - /'
-
-(
>
= *)
?
H
. /' > -
#
,
%
%
T
#
$
$
3 %
).
#
3
$
>+
!
3
#
>-
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 34
&
#
3
$
#
!
3
,
%
T
; !
;
; !
!
#
>
).
3 %
>
#
3 3
#
!
#
#
"
!
A&
%
#
5G***
&N
N/
C
C
(
! #
D
D
@* ***
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 35
;
.
!
#
3
3
>
>
3 %
3
3
#
;
3
3
.
3
!
#
>
>
3
3 %
3
!
3
#
&
3
! #
#
7=
#
!
!
3
%
"
/
#
%
%
3
3
!
3 )
!
T
___________________________________________________________________________
© 2005 HIESSE.COM / CPL (A) – 080 Mécanique du Vol - 36