1.2.5.A-AerodynamicForces-1l8jtb4.pptx
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The document discusses aerodynamic forces of lift and drag. It provides the lift and drag equations, which relate these forces to factors like airspeed, wing shape, angle of attack, and coefficients of lift and drag. It also discusses boundary layers, Reynolds number, and how these impact lift. An example calculation is shown applying the equations to a Cessna 172 aircraft taking off.
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Meanwhile, viscous friction between the air and the airfoil surface slows the airflow to some extent next to the surface.
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1.2.5.A-AerodynamicForces-1l8jtb4.pptx
- 1. Aerodynamic Forces Lift and Drag © 2011 Project Lead The Way, Inc. Aerospace Engineering
- 2. Lift Equation Coefficient of Lift, Cl – Combines several factors • Shape • Angle of attack Lift Direction of Flight
- 3. 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).
- 4. Applying the Lift Equation Convert mass into weight Convert velocity
- 5. Applying the Lift Equation Calculate Air Density
- 6. Applying the Lift Equation Calculate coefficient of lift assuming that lift equals weight
- 7. Drag Equation Coefficient of drag, Cd – Determined experimentally – Combines several factors • Shape • Angle of attack Drag Direction of Flight
- 8. 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?
- 9. Applying the Drag Equation Calculate drag
- 10. Boundary Layer •Fluid molecules stick to object’s surface •Creates boundary layer of slower moving fluid •Boundary layer is crucial to wing performance
- 11. 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
- 12. Reynolds Number, Re •Representative value to compare different fluid flow systems •Object moving through fluid disturbs molecules •Motion generates aerodynamic forces = Re1 Re2 Comparable to Airfoil1 Airfoil2 when
- 13. Angle of Attack (AOA) Affects Lift Lift increases with AOA up to stall angle Lift Direction of Flight Airflow Lift Direction of Flight Airflow Lift Angle of Attack Stall
- 14. Reynolds Number •Ratio of inertial (resistant to change) forces to viscous (sticky) forces •Dimensionless number 𝑅𝑒 = 𝜌v𝑙 𝜇 𝑅𝑒 = v𝑙 ν ν = 𝜇 𝜌 or 𝑅𝑒 = 𝑅𝑒𝑦𝑛𝑜𝑙𝑑𝑠 𝑁𝑢𝑚𝑏𝑒𝑟 𝜌 = 𝐹𝑙𝑢𝑖𝑑 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 𝑘𝑔 𝑚3 v = 𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑚 𝑠 𝑙 = 𝐿𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝐹𝑙𝑢𝑖𝑑 𝑇𝑟𝑎𝑣𝑒𝑙 𝑚 𝜇 = 𝐹𝑙𝑢𝑖𝑑 𝑉𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦 𝑁𝑠 𝑚2 ν = 𝐾𝑖𝑛𝑒𝑚𝑎𝑡𝑖𝑐 𝑉𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦 𝑚2 𝑠
- 15. 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 𝑅𝑒 = 𝜌v𝑙 𝜇
- 16. Applying Reynolds Number Calculate Air Temperature Calculate Air Pressure 𝑇 = 15.04℃ − 0.00649 ℃ 𝑚 ℎ 𝑇 = 15.04℃ − 0.00649 ℃ 𝑚 (4,023 𝑚) 𝑇 = −11.1℃ 𝑝 = 101.29𝑘𝑃𝑎 −11.1℃ + 273.1℃ 𝐾 ℃ 288.08 𝐾 5.256 𝑝 = 61.5 𝑘𝑃𝑎
- 17. Applying Reynolds Number Calculate Air Density 𝜌 = 𝑝 0.2869 𝐽 𝑘𝑔 𝐾 𝑇 + 273.1 𝜌 = 61. 5 𝑘𝑃𝑎 0.2869 𝐽 𝑘𝑔 𝐾 −11.1 ℃ + 273.1 𝐾 ℃ 𝜌 = 0.818 𝑘𝑔 𝑚3
- 18. Applying Reynolds Number Convert Velocity 𝑉 = 820 𝑘𝑝ℎ 1000 𝑚 𝑘𝑚 60 𝑚𝑖𝑛 ℎ𝑟 60 𝑠 𝑚𝑖𝑛 𝑉 = 227.8 𝑚 𝑠
- 19. Applying Reynolds Number Calculate Re 𝑅𝑒 = 𝜌v𝑙 𝜇 𝑅𝑒 = 0.817 𝑘𝑔 𝑚3 227.8 𝑚 𝑠 (1.1 𝑚) 1.65 × 10−5 𝑁𝑠 𝑚2 𝑅𝑒 = 12,408,000