Aerodynamic Forces Lift and Drag

Lift Equation Lift Coefficient of Lift, Cl Direction of Flight Presentation Name Course Name Unit # – Lesson #.# – Lesson Name Lift Equation Lift Direction of Flight Coefficient of Lift, Cl Determined experimentally Combines several factors Shape Angle of attack 𝐶 𝑙 =𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝐿𝑖𝑓𝑡 𝐷=𝐷𝑟𝑎𝑔 𝑁 𝐶 𝑙 = 2𝐿 𝐴𝜌 𝑣 2 𝐶 𝑙 = 𝐿 𝑞𝐴 𝐴=𝑊𝑖𝑛𝑔 𝐴𝑟𝑒𝑎 𝑚 2 Rearranging the coefficient of lift equation shows that lift is increased by wing area, air density, and velocity. Velocity is a squared function, giving it a more significant impact on lift. 𝜌=𝐷𝑒𝑛𝑠𝑖𝑡𝑦 𝑘𝑔 𝑚 3 Alternate format 𝑣=𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑘𝑔 𝑚 3 𝑞=𝐷𝑦𝑛𝑎𝑚𝑖𝑐 𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑃𝑎

Applying the Lift Equation Presentation Name Course Name Unit # – Lesson #.# – Lesson Name 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 day (101.3 kPa). Assume that the take off speed is 55 knots (102 kmph). 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) Average temperature source = http://www.weather.com/outlook/health/fitness/wxclimatology/monthly/graph/USCO0105

Applying the Lift Equation Convert mass into weight Convert velocity 𝑤=0.92𝑚𝑔 𝑤=0.92(1,056 𝑘𝑔) 9.81 𝑚 𝑠 2 𝑤=9,531 𝑁 𝑉= 102 𝑘𝑚𝑝ℎ 1000 𝑚 𝑘𝑚 60 𝑚𝑖𝑛 ℎ𝑟 60 𝑠 𝑚𝑖𝑛 𝑉=28.3 𝑚 𝑠

Applying the Lift Equation Calculate Air Density 𝜌= 𝑝 0.2869 𝑇+273.1 𝜌= 101.29 𝑘𝑃𝑎 0.2869 22 ℃+273.1 𝜌=1.196 𝑘𝑔 𝑚 3

Applying the Lift Equation Calculate coefficient of lift assuming that lift equals weight 𝐶 𝑙 = 2𝐿 𝐴𝜌 𝑣 2 𝐶 𝑙 = 2(9,531 𝑁) 18.2 𝑚 2 1.196 𝑘𝑔 𝑚 3 28.3 𝑚 𝑠 2 𝐶 𝑙 = 1.09

Boundary Layer Fluid molecules stick to object’s surface Presentation Name Course Name Unit # – Lesson #.# – Lesson Name Boundary Layer Fluid molecules stick to object’s surface Creates boundary layer of slower moving fluid Boundary layer is crucial to wing performance More information is available through the NASA Reynolds Number webpage: http://www.grc.nasa.gov/WWW/BGH/reynolds.html.

Boundary Layer and Lift Presentation Name Course Name Unit # – Lesson #.# – Lesson Name 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

Presentation Name Course Name Unit # – Lesson #.# – Lesson Name Reynolds Number, Re Representative value to compare different fluid flow systems Object moving through fluid disturbs molecules Motion generates aerodynamic forces Airfoil1 Airfoil2 More information is available through the NASA Reynolds Number webpage: http://www.grc.nasa.gov/WWW/BGH/reynolds.html. Comparable to when Re1 = Re2

Angle of Attack (AOA) Affects Lift Presentation Name Course Name Unit # – Lesson #.# – Lesson Name Angle of Attack (AOA) Affects Lift Lift increases with AOA up to stall angle Lift Direction of Flight Airflow Lift Direction of Flight Airflow Airflow becomes turbulent at the critical angle of attack. Airflow separates from airfoil, and lift decreases dramatically. NASA developed an applet to show how the angle of attack impacts lift. It can be accessed through this link: http://www.grc.nasa.gov/WWW/K-12/airplane/incline.html Stall Lift Angle of Attack

Presentation Name Course Name Unit # – Lesson #.# – Lesson Name Reynolds Number Ratio of inertial (resistant to change) forces to viscous (sticky) forces Dimensionless number 𝑅 𝑒 = 𝜌v𝑙 𝜇 𝑅 𝑒 = v𝑙 ν ν= 𝜇 𝜌 or 𝑙=𝐿𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 𝐹𝑙𝑢𝑖𝑑 𝑇𝑟𝑎𝑣𝑒𝑙 𝑚 𝑅 𝑒 =𝑅𝑒𝑦𝑛𝑜𝑙𝑑𝑠 𝑁𝑢𝑚𝑏𝑒𝑟 More information is available through the NASA Reynolds Number webpage: http://www.grc.nasa.gov/WWW/BGH/reynolds.html. 𝜌=𝐹𝑙𝑢𝑖𝑑 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 𝑘𝑔 𝑚 3 𝜇=𝐹𝑙𝑢𝑖𝑑 𝑉𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦 𝑁𝑠 𝑚 2 v=𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑚 𝑠 ν=𝐾𝑖𝑛𝑒𝑚𝑎𝑡𝑖𝑐 𝑉𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦 𝑚 2 𝑠