1. Aerodynamic Forces
Lift and Drag

2. 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

3. Applying the Lift Equation
Presentation Name
Course Name
Unit # – Lesson #.# – Lesson Name
Applying the Lift Equation
The Cessna 172 from Activity 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 =

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

5. Applying the Lift Equation
Calculate Air Density
𝜌= 𝑝 𝑇+273.1
𝜌= 𝑘𝑃𝑎 ℃+273.1
𝜌=1.196 𝑘𝑔 𝑚 3

6. 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) 𝑚 𝑘𝑔 𝑚 𝑚 𝑠 2
𝐶 𝑙 = 1.09

7. 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:

8. 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

9. 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:
Comparable to
when
Re1 =
Re2

10. 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:
Stall
Lift
Angle of Attack

11. 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:
𝜌=𝐹𝑙𝑢𝑖𝑑 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 𝑘𝑔 𝑚 3
𝜇=𝐹𝑙𝑢𝑖𝑑 𝑉𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦 𝑁𝑠 𝑚 2
v=𝑉𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑚 𝑠
ν=𝐾𝑖𝑛𝑒𝑚𝑎𝑡𝑖𝑐 𝑉𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦 𝑚 2 𝑠