IP-AST-2013/14 - PROBLEM=1 (PIPER SEMINOLE)

PART-CMANEUVER & GUST DIAGRAM

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CMANEUVER & GUST DIAGRAM

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CONDITIONS:

Regulations: FAR-23 Airplane category: Normal Altitude: S/L

NOTE:

This text applies to the specified Airplane and Regulations

and shall be used only as reference
For all other applications the reader is referred to pertinent methodology
[1] AIRPLANE OVERALL DATA
We recall - for convenience - the airplane geometry and weight data to be used in calculations
(The various performance data are extracted from Jane's and will be used as reference values)
Table C-1: Airplane/wing geometry and weights + Performances
1700 [daN]
Airplane design weight
G(AV)
11.75
[m]
Wing span
2b
17.90
[m2]
Wing area (gross)
S
Wing stations & chords:
C0 = 2.1 [m]
The plane of symmetry (0)
y0 = 0
yr = 0.6 [m]
(Cr = 1.97 [m])
Wing root (R)
ym = 1.85 [m]
Cm = 1.7 [m]
Engine station (M)
ye = b = 5.875 [m]
Ce = 1.0 [m]
Wing tip (E)
yCMA = 2.50 [m]
CMA = 1.59 [m]
* CMA (calculated)
yCMG = 2.87 [m]
CMG = 1.52 [m]
* CMG (calculated)
Performance (at max T-O weight) (informative)
167 [knots] = 309 [km/h]
Max level speed at S/L
162 [knots] = 300 [km/h]
Cruising speed at optimum altitude (75% power)
63 [knots] = 117 [km/h]
Stalling speed flaps up
59 [knots] = 110 [km/h]
Stalling speed flaps down

[2] FLIGHT MANEUVER DIAGRAM

The flight envelope (flight maneuver diagram "plus" gust diagram) refers to symmetrical loading
conditions of an airplane. The object of this text is to explicitly show the construction of the flight
envelope for a conventional general civil aircraft for which FAR-23 applies. We proceed step-by-step
following the methodology presented in course. The various parameters are selected or derived according
to FAR-23 prescriptions through basic analytic considerations. All results are finally summarized in a
graphic representation drawn to scale
A. Design load factors
The maximum positive limit maneuvering load factor n1 is selected according to the following
two cumulative conditions (Normal category)

n1 2.1

11,000
G[daN] 4,500

(a)

with n1 2.5 and n1 3.8

Note. Throughout this text, the two symbols above stand for the words:

"may not be less than" ("nu va fi inferior valorii de")

"need not exceed" ("nu e nevoie s depeasc valoarea de")
This means that there exists a degree of freedom in selecting design values
It follows: n1 2.1

11,000
3.87 ; according to (a) we may select n1 3.8
1,700 4,500

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PART-CMANEUVER & GUST DIAGRAM

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With n1 selected, the negative limit maneuvering load factor will be (Normal category)
(b)
n 0.4 n
2

It follows: n2 0.4 3.8 1.52 ; according to (b) we may choose n2 1.6

B. Design speeds
VS - stalling speed with flaps retracted
We may adopt this from airplane performance data to
117
[m/s] 32.5[m/s]
Vs 117[km/h]
3.6
From this we compute the maximum lift coefficient *) to
!
2 G AV
2 17, 000
C z_ max

1.4386

1.44
S VS2 1.225 17.90 (32.5)2
VA - design maneuvering speed may be computed according to FAR as

V A VS n1

(c)

It follows (we retain exactly the theoretical value!...)

V A 32.5 3.8 63.4[m/s]
VC - design cruising speed may be selected from the following conditions (Normal category)

G daN
(1) ... VC [ EAS (m/s)] 7.7
S m2

(2) ... VC 0.9 (VH at S/L)

(d)

where VH denotes the maximum level speed at S/L with maximum continuous power
1700
75[m/s]
17.90
309[km / h ] 85.8 ; 0.9 VH 77.25[m/s]

(1) From the first definition we get VC 7.7

(2) From Table C-1 we read VH

From these two we retain VC 75[m/s] (since the diagram is computed at S/L, this value is also a
true air speed).
VD - design dive speed. For Normal category if no compressibility effects are present, the
following apply
(1) ... VD ( M D ) 1.25VD ( M D )

(e)
(2) ... with V
C _ min selected as above, VD _ min 1.40 VC _ min

The second definition is applicable; therefore we adopt VD 1.40 75 105[m/s]

VG - design maneuvering speed in "inverted" flight. This speed corresponds to point G on the
parabola defined by C z_ max ; since this last value is usually not known in a preliminary design, a purely

informative value may be selected from practical considerations in order to complete the diagram, for
instance
!

C z_ max (0.6 0.8) C z_ max

2 n2 G AV

Let C z_ max 0.7 C z_ max 1 ; then VG

*
The diagram is drawn to scale in Figure C-1

*)

In fact FAR uses the maximum normal force coefficient C N _ max

C z_ max

(f)

2 1.6 17, 000

49.8[m / s ]
1.225 17.90 1

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PART-CMANEUVER & GUST DIAGRAM

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n
4

n1

B'

Cz_ max

+ 20

C'
+ 15

D'
+ 7.5

S
1

-1

VB

VS
20

40

A1

C1

VA

VC

60

80

D1

V [m/s]

VD
- 7.5

100

110
D"

Cz_ max
- 20 B"

S'
n2

- 15

C"

-2

Fig. C-1 _ Numerical application: Flight envelope

Maneuver diagram
Gust diagram

[3] GUST DIAGRAM

A. Design conditions
According to FAR, the airplane is
assumed to be disturbed from an initial straight
and level flight at a given speed " V0 " (points B1,
C1 and D1 on the maneuver diagram) by a vertical
"1 cos" gust with the maximum intensity " w0 " as
in Figure C-2 (note that this gust is individualized
in the sense that its wavelength is considered to be
a multiple of the airplane wing CMA ). With all
these, the gust load factor is given by the following
general formula
n 1 G

SC z V0 w

wmax = w 0

(g)

1
2s
w ( s ) w 0 1 cos
2
L

s = V0 t

0
L= 25CMA
Fig. C-2: FAR "1-cos" gust

2G AV
in which, in accord with the gust shape in Fig. C-2, the gust alleviation factor has the expression
2 G Av / S
0.88 G
(i)
G
; G
5.3 G
Cz CMA g

In these expressions C z denotes the slope of the airplane lift coefficient *) while g is the earth
acceleration

*)

In fact FAR uses the slope of the normal force coefficient C N

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The gust load factor in (g) is seen to depend linearly on the product V0 w0 ; therefore, the gust
intensity is imposed in a rational manner resulting in the following *) combinations of V0 and w0 :
66 fps [20 m/s] at "VB ..."

w0 50 fps [15 m/s] at

VC
25fps[7.5 m/s] at
VD

(j)

*
B. Gust load factors; gust diagram
For the calculations, in the absence of a more detailed analysis, FAR suggests using (in some
conditions) the wing lift curve slope; further, this value can be computed from the corresponding
profile characteristic by conventional formulae (see theoretical section). For straight trapezoidal wings
of relatively large aspect ratios, the simple theoretical formula below can be used (this formula was
actually established in aerodynamics for elliptic wings!...)
C z

Cz

with Cz

(k)

For the wing of the given airplane and more rigorously by using for the profile lift curve slope,
as is recommended by experiments, only a k-fraction ( k 0.9 ) of the theoretical value 2 we get
(see theoretical section!...)
(2b)2 (11.75)2

7.71
S
17.90
(2k )
5.65
5.65 7.71
Cz

4.49
(2k ) 5.65 5.65 7.71
Further, the mass parameter is
2 G Av / S
2 17, 000 /17.90
G

22.14
Cz CMA g 1.225 4.49 1.59 9.81

0.88 G 0.88 22.14

G

0.71
5.3 G
5.3 22.14
Let's begin with the calculation at VC ; we get immediately

n 1 G

SC z VC w0
2G AV

1 0.71

(l)

(m)

3.31 (point C ')

1.225 17.90 4.49 75 15
1 0.71
3.258

2 17, 000
1.31 (point C ")
2.31

Note. The expression (g) represents in the coordinates (Vn) a straight line through point
(V 0 , n 1) with the slope determined by the gust intensity w0 . Although the calculation above is
valid strictly for V VC !, it is useful to draw this line on the maneuver diagram in Fig. C-1 indicating the
corresponding gust intensity; in this way, the two points C ' and C " are fully determined
In a similar manner, the values at VD can be established (note that G remains unchanged!):
n 1 G

SC z VD w0
2G AV

1 0.71

2.62 (point D ')

1.225 17.90 4.49 105 7.5
1 0.71
2.28

2 17, 000
0.62 (point D ")
1.62

0
The VB (or VB') is the design speed for maximum gust intensity*) wmax
66 fps ( 20 m/s) ;
the corresponding point B ' is determined (in principle!) as the intersection of the line (g) having a slope
0
and the parabola defined by C z_ max , that is from the following system of
proportional to wmax

equations

*)

FAR-23 does not impose the 20 m/s gust; this condition has been mentioned here for conformity with FAR-25

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PART-CMANEUVER & GUST DIAGRAM

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SCz wmax
VB
1.225 17.90 4.49 20
VB 1 0.0411 VB
1 0.71
n 1 G
2G AV
2 17, 000

SC z_ max VB2 1.225 17.90 1.44 2

n
VB 0.000929 VB2

2G AV
2 17, 000

This system is equivalent to an elementary quadratic equation with two real solutions, namely
V1 17.5 and V2 61.7 , of which only the positive one is realistic; thus we retain for B ' the values
B '(VB 61.7 ; n 3.53) (see Fig. C-1).

Note. The VB speed denotes the minimum speed at which an aircraft can be safely operated in
gusty weather (therefore it is even called "safety speed in gusts"); flying below this speed presents the
risk of "stalling" the aircraft in case it encounters a gust of maximum intensity, by simply raising the
aircraft angle of attack beyond the critical value
0
The point B " corresponding to negative wmax
is defined (cf. FAR-25) by the same speed VB and
the line (g) with a slope of opposite sign (see Fig. C-1); the values are B "(VB 61.7 ; n -1.53)
With the "isolated" points B ', C ', D ', etc. determined as above for discrete values of w0 , FAR
stipulate that, for intermediate values of the gust intensity, the loading conditions should correspond to
points lying on straight lines drawn through these points in the natural sequence; by this procedure, the
final gust diagram results as indicated on Figure C-1.
[4] FLIGHT ENVELOPE
A. Definition
The topological superposition of flight and maneuver diagrams results in the flight envelope.
FAR stipulate that an airplane structure should be investigated for the conditions corresponding
to any point inside and on the borders of the flight envelope
B. Discussion
From the example above it is apparent that the controlled maneuvers and the gusts lead to
comparable load factors and are therefore of equal importance for the design.
Experience shows that the gust loads can be more significant (and even critical) for Normal
airplanes (this explains by the relative smaller maneuver load factors imposed by FAR for these machines
as compared to the Utility and Acrobatic ones).