Aero Engineering 315

Lesson 15

3-D (Finite) Wings Part I

Airfoil Lab Review Due Thursday (lesson 17) Use spreadsheet template (posted on k: drive) Closely follow lab handout directions Review Excel tutorial if needed Compare to published data for NACA 0012

provided in supplemental hand out Re = 3.0 x 106

Key Formula: Px = Pref – [oil x 32.2 x (hx –href)/12]

Airfoil Lab Spreadsheet

Lessons 15 and 16 Objectives Define and calculate aspect ratio Explain wing tip effects on lift and drag Describe design techniques to reduce induced

drag State which planform shape minimizes

induced drag Describe span efficiency factor Calculate the 3-D lift curve slope and lift

coefficient Calculate induced and total drag coefficients

3-D Wing Geometry

S

bAR

2

Aspect Ratio (AR):

High AR Low AR Typical Values

Fighters: 2-5Transports: 6-10Gliders: 10-15

Wing Twist Wing twist is applied to create a delay in stall for

outboard portions of wings Two types of twist:

1. Geometric twist – wing is physically twisted to change the angle-of-attack at the tip

2. Aerodynamic twist – not a physical twist, but a different airfoil at the tip (usually one with a higher stall – i.e. thinner or less camber at tip)

Root

Angle of TwistTip

NACA 6716

-0.06

-0.01

0.04

0.09

0.14

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x/c

y/c

Remember the A-10?

at wing root

NACA 6713 at wingtip

So what’s up with a “real wing”?

Wingtip Vortices

Wingtip Vortices

upper surface flow (inboard) lower surface flow (outboard)

The pressure imbalance at the wingtip sets up a spanwisecomponent of flow, strongest at the tips, weakest in the

center.

TOP SURFACE

BOTTOM SURFACE

(relative low pressure)

(relative high pressure)

Downwash

Front View

Top View

A Cessna Citation was flown above a cloud bank at approximately 165 knots. The trailing vortices descended over the fog layer due to downwash, and were made visible by the distortion at the interface.

Tip effects and lift curve

Notice the slope is decreased for the wing, but thezero lift angle of attack is unchanged—these 3-D effects are directly a result of lift (i.e. pressure differential) being created on the wing

Airfoil

cl

cland CL

Wing

CL

Caused by:• Pressure loss at tip

• Pressure simply “leaks” to top of the wing

• Downwash• Local flow is diverted down by vortices

DownwashSpanwise flow comes off each wingtip and creates a trailing vortex. These vortices, in turn, deflect the local flow over the wing downward. This deflection is called “downwash.” One result is reduced lift!

V

DownwashEffective flow direction over wing

eff is the downwash angle

Induced drag — big picture Wingtip vortex is an unavoidable

consequence of wingtips and results in reduced lift & increased drag

Induced drag is greatest when the pressure difference between upper and lower surfaces is greatest High angles of attack Takeoff and landing

Induced drag will be zero when there is no pressure difference (i.e. at zero lift)

Next Lesson (16)…

Prior to class Complete reading (4.1 – 4.2)

In Class Calculate 3-D lift and drag Span efficiency factor Design strategies to minimize induced

drag