Dartmouth Flying Club October 10, 2002 Andreas Bentz Basic Aerodynamics Dartmouth Flying Club October 10, 2002 Andreas Bentz

Bernoulli’s Principle Lift Bernoulli’s Principle

Energy Definition: Energy is the ability to do work. Energy cannot be created or destroyed. We can only change its form. A fluid in motion has (mainly) two forms of energy: kinetic energy (velocity), potential energy (pressure).

The Venturi Tube and Bernoulli’s Principle kinetic energy (velocity) potential energy (pressure) velocity increases pressure decreases

Lift: Wing Section Air flows toward the low pressure area above the wing: upwash and downwash. Newton’s third law of motion: to every action there is an equal and opposite reaction. “The reaction to downwash is, in fact, that misunderstood force called lift.” Schiff p. 8 relative low pressure upwash downwash

Angle of Attack The angle of attack is the angle between the chord line and the average relative wind. Greater angle of attack creates more lift (up to a point). total lift chord line average relative wind

Lift and Induced Drag Lift acts through the center of pressure, and perpendicular to the relative wind. This creates induced drag. chord line average relative wind total lift effective lift induced drag

Got Lift? Flaps Flaps increase the wing’s camber. Some also increase the wing area (fowler flap). Almost all jet transports also have leading edge flaps.

Too Much Lift? Spoilers Spoilers destroy lift: to slow down in flight (flight spoilers); for roll control in flight (flight spoilers); to slow down on the ground (ground spoilers).

There is no such things as a free lunch. Side Effects There is no such things as a free lunch.

Drag: Total Drag (Power Required) Curve 50 100 150 200 Indicated Airspeed (knots) Drag (lbs) 1,400 1,200 1,000 800 600 400 200 max. lift/drag best glide induced drag parasite drag resistance total drag

Wingtip Vortices and Wake Turbulence relative low pressure Wingtip vortices create drag: “ground effect”; tip tanks, drooped wings, “winglets”.

Longitudinal: Static, Dynamic Lateral Stability Longitudinal: Static, Dynamic Lateral

Longitudinal Stability lift down lift weight Static stability (tendency to return after control input) up elevator increases downward lift, angle of attack increases; lift increases, drag increases, aircraft slows; less downward lift, angle of attack decreases (nose drops).

Aside: CG and Center of Pressure Location lift down lift weight Aft CG increases speed: the tail creates less lift (less drag); the tail creates less down force (wings need to create less lift). This also decreases stall speed (lower angle of attack req’d).

Lateral Stability If one wing is lowered (e.g. by turbulence), the airplane sideslips. The lower wing has a greater angle of attack (more lift). This raises the lower wing. relative wind relative wind

Directional Stability As the airplane turns to the left (e.g. in turbulence), the vertical stabilizer creates lift toward the left. The airplane turns to the right.

Speed Stability v. Reverse Command Power curve: Power is work performed by the engine. (Thrust is force created by the propeller.) Suppose airspeed decreases. “Front Side”: Power is greater than required: aircraft accelerates. “Back Side”: Power is less than required: aircraft decelerates. 1,400 1,200 1,000 800 600 400 200 100% 50% max. endurance ca. 75% of max. lift/drag Percent horsepower Drag (thrust required) 50 100 150 200 Indicated Airspeed (knots)

Turning Flight Differential Lift

Turning Flight More lift on one wing than on the other results in roll around the longitudinal axis (bank). Lowering the aileron on one wing results in greater lift and raises that wing.

Turning Flight, cont’d More lift on one wing than on the other results in roll around the longitudinal axis (bank). Lowering the aileron on one wing results in greater lift and raises that wing. This tilts lift sideways. The horizontal component of lift makes the airplane turn. (To maintain altitude, more total lift needs to be created: higher angle of attack req’d) Centrifugal Force

Adverse Yaw and Frise Aileron However, more lift on one wing creates more induced drag on that wing: adverse yaw. Adverse yaw is corrected by rudder application. Frise ailerons counter adverse yaw: They create parasite drag on the up aileron.

Stalls Too Much of a Good Thing

Stalls A wing section stalls when its critical angle of attack is exceeded. Indicated stall speed depends on how much lift the wing needs to create (weight, G loading).

Stalls, cont’d The disturbed airflow over the wing hits the tail and the horizontal stabilizer. This is the “buffet”. Eventually, there will not be enough airflow over the horizontal stabilizer, and it loses its downward lift. The nose drops: the stall “breaks”. weight lift

Stalls, cont’d The whole wing never stalls at the same time. Power-on stalls in most light singles allow the wing to stall more fully. Why? Where do you want the wing to stall last? Ailerons

Stalls, cont’d (Stalls with one Engine Inop.) Stalls in a twin with one engine inoperative lead to roll or spin entry: Propeller slipstream delays stall.

Stalls, cont’d Stall strips make the wing stall sooner.

Stalls, cont’d Definition: The angle of incidence is the acute angle between the longitudinal axis of the airplane and the chord line of the wing. Twist in the wing makes the wing root stall first: The angle of incidence decreases away from the wing root.

Preventing Stalls Slats direct airflow over the wing to avoid boundary layer separation. Slots are similar but fixed, near the wingtips. Delays stall near the wingtip (aileron effectiveness).

Stalls and Turns Greater angles of bank require greater lift so that: the vertical component of lift equals weight (to maintain altitude), the horizontal component of lift equals centrifugal force (constant radius, coordinated, turn)

Stalls and Turns, cont’d Load factor (multiple of aircraft gross weight the wings support) increases with bank angle. limit load factor: acrobatic 6G Normal 3.8G Stall speed increases accordingly.

Turns As bank increases, load factor increases. But: as airspeed increases, rate of turn decreases. In order to make a 3 degree per second turn, at 500 Kts the airplane would have to bank more than 50 degrees. Uncomfortable (unsafe?) load factor. This is why for jet-powered airplanes, a standard rate turn is 1.5 degrees per second.

High and Fast In the Flight Levels

High and Fast Mach is the ratio of the true airspeed to the speed of sound. Speed of sound decreases with temperature. Temperature decreases with altitude. At higher altitudes, the same indicated airspeed leads to higher Mach numbers. Conversely: at higher altitudes, a certain Mach number can be achieved at a lower indicated airspeed. The indicated stall speed increases with altitude (compressibility).

High and Fast, cont’d At high subsonic speeds, portions of the wing can induce supersonic airflow (critical Mach number Mcrit). Where the airflow slows to subsonic speeds, a shockwave forms. The shockwave causes boundary layer separation. High-speed buffet, “aileron snatch”, “Mach tuck”. velocity increases velocity decreases, shockwave forms boundary layer separates

High and Fast, cont’d Vortex generators delay boundary layer separation.

High and Fast, cont’d With altitude: coffin corner indicated stall speed (low speed buffet) increases; indicated airspeed that results in critical Mcrit decreases. coffin corner

References De Remer D (1992) Aircraft Systems for Pilots Casper: IAP FAA (1997) Pilot’s Handbook of Aeronautical Knowledge AC61-23C Newcastle: ASA Lowery J (2001) Professional Pilot Ames: Iowa State Univ. Press Schiff B (1985) The Proficient Pilot vol. 1 New York: Macmillan U.S. Navy (1965) Aerodynamics for Naval Aviators Newcastle: ASA