Intro: How to Solve an Aerodynamics Problem
Aerodynamics, in relation to aviation, is the way air moves on an aircraft. The four forces that act on an aircraft are thrust, drag, lift, and weight. These different forces allow an aircraft to accelerate, decelerate, ascend, or descend. Lift, the component that allows an aircraft to move upwards and ascend, is responsible for allowing an aircraft to become airborne. With the lift equation, you can determine the proper angle (i.e. angle of attack) an aircraft's nose must be in order to sustain level flight at any given speed and altitude.
For this Instructable you will need: a pencil, scratch paper, a calculator and basic knowledge of mathematical conversions. It should take you approximately 10 minutes to complete.
Step 1: Become Familiar With the Lift Equation
The lift equation, pictured above, will help you determine what angle of attack is needed to sustain level flight. The aircraft you are using weighs 14,250 lbs and is flying at 150 knots at sea level pressure with a wing surface area of 250 ft. squared. The values below indicate what each variable within the equation represents.
- S=surface area of the wing
- Fl=force of lift
- ρ=density at sea level pressure
- Cl=coefficient of lift
(Note: density at sea level pressure is always .002378 slugs per feet cubed)
Step 2: Convert Knots to Feet Per Second
Convert 150 knots to feet per second by using conversation factors. You have to determine how many feet are in a nautical mile and how many seconds are in an hour. Once you know the numerical value divide the top values from the bottom. Your new speed should be approximately 253 feet/sec.
Keep track of which units you cross out and note that a conversion factor is always equal to 1.
Step 3: Rearrange the Equation to Solve for Cl
Rearrange the equation to isolate Cl then plug in your givens along with your speed and solve using a calculator. Be sure to square the speed value first then proceed to multiply and divide.
Your answer for the coefficient of lift should be approximately .76
Step 4: Determine the Angle of Attack (AoA)
The chart pictured above is a standard aerodynamics chart that shows the relationship between the coefficient of lift and the bank angle of an aircraft.
Starting with your lift coefficient of .76 move across the graph to intersect the line where you will then determine your angle of attack. Your answer should turn out to be approximately 7 degrees. This demonstrates that if the 14,250 lb aircraft is traveling at 253 feet/sec with a 7 degree angle of bank, level flight will be sustained.
Step 5: Additional Resources
Additional websites for further interest:
Video for how lift acts on an airplane: