V-n diagram and gust diagram

Dr Jian Wang

08/02/201008/02/2010

No. ID No First name Surname No. ID No First name Surname

1

0958093/1 FADL SULIMAN

2

0820488/1 SHEM SASI

0934040/1 SANDEEP SINGH 0852679/1 RAJASOORIYAG E RAJASOO RIY

0961487/1 DILESH BHARDWA 0808462/1 NICOLE JAROSINSKI

0642335/1 BARDYA ADIB 0819603/1 TOBIAS RICHARDS

0849989/1 MANPREET SIDHU 0818632/1 FREDERICO BENGE

0814047/1 EMMANUEL BAJOWA 0601933/1 ANTHONY OFORI

No. ID No First name Surname No. ID No First name Surname

0802909/1 DAVINDER MAHI 0835515/1 QINHONG CHEN

0808248/1 THOMAS GILBERT 0805625/1 LEAH WAIRIA

Group List

3 4

0808248/1 THOMAS GILBERT 0805625/1 LEAH WAIRIA

0830347/1 ADEKUNLE KARUNWI 0720885/1 SAGAR PATEL

0810415/1 ABDUL SHARIFI 0641619/1 ELIAS EZUZ0640259/1 DUARTE DA COSTA 0803682/1 MATTHEW HENTLEY-RI CHOLD0815031/1 QADEER KHAN 0803866/1 JIGAR PATEL0800916/1 Hashan Hettiarach 0640096/1 IRFAN KHAN

No. ID No First name Surname No. ID No First name Surname

5

0714407/2 HAMMAD WASIM

0609502/1 ROSS PARRY

0701487/1 SAMUEL TANNER

0820141/1 MUHAMMAD KHATTAK

0631753/1 NASSER AJJA

0724402/2 SHAUN SUNNY

0630485/1 FRANCIS MLANDA0830307/1 ABHINIVESH BEECHOOK

Content

• What is V-n diagram• Aerodynamic & structural limits• How do we construct the V-n diagram• What is gust diagram• What is gust diagram• How do we draw the gust diagram• Work out the V-n, gust diagram for your

design

What is V-n diagram

What is V-n diagram

• In general, aircraft are limited in their performance capabilities by aerodynamics (for example, stall), structure and/or engine capabilities.structure and/or engine capabilities.

• A V-n diagram captures an aircraft’s operation envelope—means enclosures shown the limits

Aerodynamic & structural limits• Aircraft are limited aerodynamically by stall:

The stall speed

• An aircraft can only withstand a finite amount of g load until it structurally fails,

1;2

max

===∞

nnWLwithSC

WV

Ls ρ

which is represented by load factor. • Then we have• Combine these two equations,

1; ≠= nnWL

max

2

Ls SC

nWV

∞

=ρ

We will have our V-n diagram

Aerodynamic & structural limits

• Some definition of velocities1. Design cruise speed: VC, a minimum value of

the maximum speed to be considered for straight and level flight.

2. Design dive speed (maximum structure speed): VD the maximum speed for structure design.VD the maximum speed for structure design.

3. Manoeuvring speed: Va the speed of the aircraft is operated

4. Corner velocity or Maximum elevator deflection: VA the speed of a aircraft is operating at the brink of stall.

General characteristics of a V-n diagram

• The following figure is a typical V-n diagram• Stall speed limits the aerodynamic capacity• Load factor confines the structure capacity

• Four velocities

Va

speedstructureDesign

speedcruiseDesign

speedCorner

speedStall

D

C

A

S

V

V

V

V

Key points about an aircraft’s V-n diagram1. A V-n diagram is good for one weight, altitude, and

one configuration2. The area inside is called the operating envelope in

which the aircraft can be safely operated at combination of airspeed and load factor

3. Refer to the positive and negative stall limits—again, the higher the load factor, the higher the stall again, the higher the load factor, the higher the stall speed. At a load factor of 1.0 (L=W), the 1-g stall limit is quickly identified.

4. The corner speed VA is shown, which is the “corner” (intersect) of aircraft’s stall limit and structure limit

Key points about an aircraft’s V-n diagram5. A positive and negative limit load fact are identified—the

aircraft will sustain damage if these are exceeded. Structurally, the aircraft is typically designed to handle more positive than negative gs

6. At high airspeed the aircraft reach the structure limit, also called q-limit or redline. Not as straightforward, this could be an aeroelastic limit or a temperature limit. Something undesirable, in terms of structure and handling qualities, undesirable, in terms of structure and handling qualities, happens if this limit is exceeded

7. When weight and altitude change, the V-n diagram will change

8. If equivalent velocity Ve is used on horizontal axis of the V-n diagram, then the Ve-n diagram will not be affected by altitude changes

How do we construct the V-n diagram• To construct the V-n diagram, you need to know

1. The stall speed, corner speed, design cruise speed and structure speed

2. Maximum positive load factor and negative load factor

• Procedures:1. Locate structure speed, corner speed, and design cruise speed

2. Draw two horizontal lines represented maximum ± load factors

3. Calculate stall speed for n=1:

4. Set up equations:

5. For positive and negative load factor, CLmax can be different

max1,

2

Ls SC

WV

∞

=ρ

nVV sns 1,, =

What is gust diagram

• The gust velocity: V is the original airspeed; Ude is the gust velocity.

• Because of the gust velocity, the real velocity for the aircraft will be VR.

VR • The consequence Sharp-edged gustVR • The consequence is that angle of attack will change ∆α; the load factor will change as well

Sharp-edged gust

V

U

d

dCd

dCC

dL

LL

×±=

∆=∆

α

αα

How do we draw the gust diagram

• What should we find out before construct the gust diagram�The change of the angle of attack:

�The increase of load

V

U d=∆α

αρ ∆=∆ SCVL 21�The increase of load

�The increase of load factor:

αρ α ∆=∆ ALSCVL 2

2

( )SW

CV

W

SCV

W

Ln AL

AL

221

22

αραρα

α ∆=∆

=∆=∆

How do we draw the gust diagram

• Some discussions�The above equation does not include alleviation

effects resulting from real unsteady aerodynamics;

�In reality, the lift does not change instantaneously when an airplane enters a gust, nor is a gust ever when an airplane enters a gust, nor is a gust ever truly sharp-edged.

�Therefore, the gust velocity is tempered by a “gust alleviation factor,”

dgd UKU ′=

How do we draw the gust diagram

• Construction of the gust diagram�The increase of load factor:

( )SW

CVK

W

SCVK

W

Ln AL

g

AL

g 221

22

αα αραρ ∆=

∆=∆=∆

�The load factor—velocity relationship:

( ) ( )SW

UVCK

V

U

SW

CVK dAL

gdAL

g 22

2αα ρρ =×=

( )SW

UVCKn dAL

g 21 αρ+=

How do we draw the gust diagram

• The gust alleviation factor

+=

supersonic

subsonic3.5

88.0

03.1µ

µµ

gK

• The mass ratio

+supersonic

95.6 03.1µµ

( )ALCcg

SW

αρµ 2=

How do we draw the gust diagram

• Gust load factors must be determined at three speeds:

• VB is determined by the intersection of the stall curve with the maximum gust velocity curve (with Ud = the maximum gust speed).

How do we draw the gust diagram

• The other points:�Intersection

with VC

�Intersection with VD

How do we draw the gust diagram• How to work out CLαA

�Based on NACA Report No. 1206, 1954, and

�NACA Rep. No. 921, 1948

• Graphic method

Graphic method

Work out the V-n, gust diagram for your designfor your design