AE 2350 Lecture Notes #8

April 30, 1999

We have looked at..• Airfoil Nomenclature• Lift and Drag forces• Lift, Drag and Pressure Coefficients• The Three Sources of Drag:

– skin friction drag in laminar and turbulent flow– form drag– wave drag

• Read Chapter 8 of text.

Airfoil Drag Polar Cd vs. Cl

Rough airfoilshave turbulent flowover them, high drag.

Smooth airfoils havelaminar flow overat least a portionof the surface.Low Drag.

Form Drag

Source: http://www.allstar.fiu.edu/aerojava/flight46.htm

Form drag may be reducedby proper design, andstreamlining the shape.

Supersonic wave Drag

For a given airfoil or wing or aircraft, as the Mach numberis increased, the drag begins to increase above afreestream Mach number of 0.8 or so due to shock waves thatform around the configuration.

Shock waves

How can shock waves be minimized?

• Use wing sweep.• Use supercritical airfoils, which keep the flow

velocity over the airfoil and the local Mach number from exceeding Mach 1.1 or so.

• Use area rule- the practice of making the aircraft cross section area (from nose to tail, including the wing) vary as smoothly as possible.

How can shock waves be minimized?

Use sweep.

M= 0.80.

8cos

30

30 sweep

In your design...• The Maximum Mach number is 2.0• Wings for supersonic fighters are designed to

reduce wave drag up to 80% of the Maximum speed.

• In our case, 80% of 2 is 1.6.• If we use a wing leading edge sweep angle of

60 degrees or so, the Mach number normal to the leading edge is 1.6 cos 60°=0.8

Effect of Thickness and Sweep on Wave Drag

Source: http://www.hq.nasa.gov/office/pao/History/SP-468/ch10-4.htm

Supercritical Airfoils

Their shape is modified to keep the Mach number on the airfoilsfrom exceeding 1.1 or so, under cruise conditions.

Conventional vs. Supercritical Airfoils

Wing Drag

• Since a wing is made up of airfoils, it has– skin friction drag– form drag– wave drag at high speeds,

and– Induced drag due to tip vortices

TIP VORTICES

Effect of Tip Vortices

Downwash

V

Wind directionwithout downwash

Lift Direction without downwash

Downwash

New wind directionincluding downwash

New Lift Direction including downwash

Downwash changes lift direction

Induced Drag

Induced drag is caused by the downward rotation of the freestream velocity, which causes a clockwise rotation of the liftforce.

From AE 2020 theory, e

2

, ARCC L

iD

e= Oswald efficiency factor

Parasite Drag and Interference Drag

Parasite Drag is simply Skin Friction Drag+ Form Drag + Interference Drag + Wave Drag

Variation of Drag with Speed

Induced drag decreases as Vincreases, because we need lessvalues of CL at high speeds.

Other drag forces (form, skin friction , interference) increase.

Result: Drag first drops, then rises.

At High Values of Wings Stall

We need high CL to take-off and land at low speeds.

http://www.zenithair.com/stolch801/design/design.html

Achieving High Lift

One form of flaps, called Fowler flaps increase the chord length asthe flap is deployed.

High energy air from the bottom side of the airfoilflows through the gap to the upper side, energizes slow speedmolecules, and keeps the flow from stalling.

How do slats and flaps help?

1. They increase the camber as and when needed- duringtake-off and landing.

Leading Edge SlatsHelp avoid stall near the leading

edge

High Lift also Causes High Drag

MIG-29

Max T/O: 18 500kgMax Speed: Mach 2.3Range: 2100kmCeiling: 17 000mPowerplant: Two Klimov/Sarkisov RD-33 turbofansThrust: 98.8kN

Length: 14.87mWingspan: 11.36mHeight: 4.73mWeight Empty: 10 900kg