AerodynamicsME-438

Spring’16ME@DSU

Dr. Bilal A. Siddiqui

Quiz 01The German Zeppelins of World War I were dirigibles with the followingtypical characteristics: volume = 15,000 m3 and maximum diameter =14 m. Consider a Zeppelin flying at a velocity of 30 m/s at a standard altitude of 1000 m (assume density 0.8 times sea-level density).The Zeppelin is at a small angle of attack such that its lift coefficient is0.05 (based on the maximum cross-sectional area). The Zeppelin is flying in straight-and-level flight with no acceleration. Calculate the total weight of the Zeppelin.

Stall Speed• In level, steady flight, we know that L=W and T=D • In most conventional aircraft, and .• For a given aerodynamic shape and velocity, M and Re are fixed.• In that case CL and CD are only functions of α.• Since, , this means for level flight • Therefore, the stall speed is given by • This means if the aircraft goes any slower than this it will start falling!• It may not be possible to sustain level flight at the stall speed due to

high drag. Why?

Why is stalling speed important

• The minimum or stall speed of an aircraft is purely a function of its weight and aerodynamic shape.

• It determines the minimum speed that an aircraft needs to attain for taking off the ground.

• It also determines the minimum speed which must be maintained during controlled landing (you have the option of crash landing!)

• Since we cannot muck around with the weight during flight (some fighters can jettison extra fuel tanks), the only thing we can do is to change the SHAPE and AREA of the aircraft wing when we need to go slower than the original stall speed. How?

High Lift Devices

• Flaps, slats, and slots on the wing which, when deployed by the pilot, serve to increase CL,max and Swing, hence decrease the stalling speed. High-lift devices are usually deployed for landing and take-off.

Maximum Velocity in Level Flight• Maximum velocity in level flight is of course determined by

• Maximum Engine Thrust• Minimum Drag

• Since, , this means for level flight • Therefore, maximum level speed is given by • This an aircraft with a given shape and engine cannot go any faster in

level flight, even if it tries.• But this speed may not be sustainable (look at the lift curve).

Actual Maximum Speed of the Aircraft

• This maximum velocity can easily be exceeded in dive!• There is also a structural limit of the aircraft speed due

to drag and lift which cannot be exceeded without breaking the craft in the air!

• The CL produced at CD,min may be not equal the weight, so may not be sustainable. It is only a theoretic speed for specifying an aircraft.

• It is clear that aerodynamic coefficients are important engineering quantities that dictate the performance and design of airplanes.

L/D ratio-A criterion for Aerodynamic Efficiency

• Obtaining raw lift on a body is easy-even a barn door creates lift at some

• The actual challenge is to do so at a low cost (drag).• A poor aerodynamic design (barn door) will produce the

required lift at a very high drag (which will require a large engine….and increase weight!)

• Therefore, the more the L/D ratio, the more aerodynamically efficient the shape.

Wind damage: Barn door blown around 40 yards away

L/D ratio as a function of Speed and AoA

• Since a particular aircraft's required lift is set by its weight, delivering that lift with lower drag leads directly to better fuel economy, climb performance, and glide ratio.

• Generally, we would like to cruise at or near best L/D velocity for max range.

Some Typical L/D ratiosFlight article Scenario L/D ratio

Virgin Atlantic GlobalFlyer Cruise 37[4]

Lockheed U-2 Cruise ~28

Rutan Voyager Cruise[4] 27

Albatross 20[5]

Boeing 747 Cruise 17

Common tern 12[5]

Herring gull 10[5]

Concorde M2 Cruise 7.14

Cessna 150 Cruise 7

Helicopter 100 kts speed 4.5[6]

Concorde Approach 4.35

House sparrow 4[5]

Assignment• Read Design Box in Chapter 1 of Anderson’s book, and try to

understand it. It is about the variation of CL and CD in flight and their importance in aerodynamics and flight.

• Solve Problem No. 1.15 in your book, with reference to the design box above. What is the stall speed?

• Also make a two page summary of historical notes 1.13 (CP) and 1.14 (coefficients)

Example 1.7Consider an executive jet transport patterned after the Cessna 560 Citation V. The airplane is cruising at a velocity of 492 mph at an altitude of 33,000 ft, where the ambient air density is 7.9656×10−4 slug/ft3. The weight and wing planform areas of the airplane are 15 kip and 342.6 ft2. The drag coefficient at cruise is 0.015. Calculate the lift coefficient and the lift-to-drag ratio at cruise.

Effect of Streamlining• We know that , but for M<0.3,

Drag Coefficients• Remember the composition of drag once again

• It is composed off pressure drag and skin friction drag. • Blunt bodies have big wake regions (of slow recirculating flow), and most of

their drag is due to pressure drag.• Streamlined bodies have smaller wake regions and most of the drag is due to

skin friction (much smaller)• The size of wake depends on flow separation point and turbulence.• More energetic (high Re) flows remain attached more and produce less drag

Effect of Reynold Number on Skin Friction

• Skin friction is a strong function of Reynold number.• Pressure drag is often just a function of the shape (it is aka form drag)• Turbulent Cf is much higher than laminar Cf. We like to promote slender

aerodynamic shapes (low form drag) and laminar flow (low skin friction drag)

Laminar Flow Airfoils• These are low speed airfoils designed to

have laminar flow over most of their length for low angle of attacks.

• Generally it is very difficult to ensure laminar flow due to

• Turbulence in upstream flow• Rivets, attachments on wings.• Vibrations in the aircraft• Need for higher angles of attack.

Drag increases at high AoA due to transition to turbulence

F-16XL Laminar Flow Aircraft

Drag Contributors