Aerodynamic Forces
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Aerodynamic Forces Lift and Drag Aerospace Engineering © 2011 Project Lead The Way, Inc. Lift Equation Lift Coefficient of Lift, Cl – Determined experimentally – Combines several factors • Shape • Angle of attack 2πΏ πΆπ = π΄ππ£ 2 Alternate format πΏ πΆπ = ππ΄ Direction of Flight πΆπ = πΆππππππππππ‘ ππ πΏπππ‘ π· = π·πππ π π΄ = ππππ π΄πππ π2 ππ π = π·πππ ππ‘π¦ π3 π π£ = πππππππ‘π¦ π π = π·π¦πππππ ππππ π π’ππ ππ Applying the Lift Equation The Cessna 172 from Activity 1.2.2 step #2 takes off successfully from Denver, CO during an average day in May (22 OC) with a standard pressure (101.3 kPa). Assume that the take-off speed is 55 knots (102 kph). What is the minimum coefficient of lift needed at the point where the aircraft just lifts off the ground? The Cessna wing area is 18.2 m2 and weight is 2,328 lb (1,056 kg). Applying the Lift Equation Convert mass into weight π€ = ππ π π€ = (1,056 ππ) 9.81 2 π π€ = 10,359 π Convert velocity π 102 ππβ 1000 ππ π= πππ π 60 60 πππ βπ π π = 28.3 π Applying the Lift Equation Calculate Air Density π= 0.2869 π½ ππ πΎ π πΎ π + 273.1β β 101.29 πππ π= 0.2869 π½ ππ πΎ ππ π = 1.196 3 π πΎ 22 β + 273.1β β Applying the Lift Equation Calculate coefficient of lift assuming that lift equals weight 2πΏ πΆπ = π΄ππ£ 2 πΆπ = 18.2 π2 πΆπ = 1.19 2(10,359 π) ππ π 1.196 3 28.3 π π 2 Boundary Layer • Fluid molecules stick to object’s surface • Creates boundary layer of slower moving fluid • Boundary layer is crucial to wing performance Boundary Layer and Lift • Airflow over object is slower close to object surface • Air flow remains smooth until critical airflow velocity • Airflow close to object becomes turbulent Reynolds Number, Re • Representative value to compare different fluid flow systems • Object moving through fluid disturbs molecules • Motion generates aerodynamic forces Airfoil1 Comparable to Airfoil2 when Re1 = Re2 Angle of Attack (AOA) Affects Lift Lift increases with AOA up to stall angle Airflow Lift Lift Airflow Direction of Flight Lift Stall Direction of Flight Angle of Attack Reynolds Number • Ratio of inertial (resistant to change) forces to viscous (sticky) forces • Dimensionless number π vπ πvπ ν= π π = π π = or π ν π π = πΏππππ‘β ππ π π = π ππ¦πππππ ππ’ππππ πΉππ’ππ ππππ£ππ π ππ ππ π = πΉππ’ππ π·πππ ππ‘π¦ π = πΉππ’ππ πππ πππ ππ‘π¦ π3 π2 π 2 v = πππππππ‘π¦ π π ν = πΎππππππ‘ππ πππ πππ ππ‘π¦ π Applying Reynolds Number A P-3 Orion is cruising at 820 kph (509 mph) at an altitude of 4,023 m (13,198 ft). Assume a fluid viscosity coefficient of 1.65x10-5 N(s)/m3. What is the average Reynolds Number along a wing cross section measuring 1.1 m (3.6 ft) from leading edge to trailing edge? Need components to calculate Re πvπ π π = π Applying Reynolds Number Calculate Air Temperature β π = 15.04β − 0.00649 β π β π = 15.04β − 0.00649 (4,023 π) π π = −11.1β Calculate Air Pressure π = 101.29πππ π = 61.5 πππ πΎ −11.1β + 273.1β β 288.08 πΎ 5.256 Applying Reynolds Number Calculate Air Density π π= 0.2869 π½ ππ πΎ π + 273.1 61. 5 πππ π= 0.2869 π½ ππ πΎ ππ π = 0.818 3 π πΎ −11.1 β + 273.1 β Applying Reynolds Number Convert Velocity π 820 ππβ 1000 ππ π= πππ π 60 60 πππ βπ π π = 227.8 π Applying Reynolds Number Calculate Re πvπ π π = π ππ π 0.817 3 227.8 (1.1 π) π π π π = ππ −5 1.65 × 10 π2 π π = 12,408,000 Drag Equation Drag Coefficient of drag, Cd – Determined experimentally – Combines several factors • Shape • Angle of attack 2×π· πΆπ = π΄ × π × π£2 Alternate format π· πΆπ = π ×π΄ Direction of Flight πΆπ = πΆππππππππππ‘ ππ π·πππ π· = π·πππ π π΄ = ππππ π΄πππ π2 ππ π = π·πππ ππ‘π¦ π3 π π£ = πππππππ‘π¦ π π = π·π¦πππππ ππππ π π’ππ ππ Coefficient of Drag (Cd) Object shape affects Cd Applying the Drag Equation The same Cessna 172 from Activity 1.2.2 step #2 takes off under the same conditions as described earlier in this presentation. How much drag is produced when the wing is configured such that the coefficient of drag is 0.05? Applying the Drag Equation Calculate drag 2π· πΆπ = π΄ππ£ 2 πΆπ π΄ππ£ 2 π·= 2 0.05 18.2 π2 π·= π· = 436 π ππ 1.196 3 π 2 π 28.3 π 2 Downwash and Wingtip Vortices • Pressure difference at wing tips • Air to spill over wingtip perpendicular to main airflow • Air flows both upward and rearward, forming a vortex • Decreases lift • Increases drag Wingtip Vortices • Air flows both upward and rearward, forming a vortex • Winglets are vertical airfoils that limit vortices and improve fuel efficiency Reference National Aeronautics and Space Administration (2011). Aerodynamic forces. Retrieved from http://www.grc.nasa.gov/WWW/K12/airplane/presar.html National Aeronautics and Space Administration (2011). Reynolds number. Retrieved from http://www.grc.nasa.gov/WWW/BGH/reynolds.html National Aeronautics and Space Administration (2011). Winglets. Retrieved from http://www.nasa.gov/centers/dryden/about/Organizations/Technolog y/Facts/TF-2004-15-DFRC.html Raymer, P. (2006). Aircraft design: A conceptual approach. Reston, VA: American Institute of Aeronautics and Astronautics.
