Math & the U.S. Flag

1. Math & the U.S. Flag Official flags for government agencies are required to have specific hoist (width), fly (length) measurements. They all have a fly:hoist ratio of 1.9:1. Measure the flags on your tables and see if they are an “official” size. Be ready to defend your decision. hoist f l y Strand: Number & Operations/Standard 1: Number Sense Strand: Algebra/Standards 4 & 6: Patterns, Relations & Functions and Algebraic Models

2. Using the hoist:fly ratio answer the following… • Explain what it means for the fly:hoist ratio to be 1.9:1. _____________ • _____________________________________________________________ 2. If an official flag has a hoist of 5 feet, what is the fly? ________________ • How would you find the appropriate hoist if the fly is given? ________ • ____________________________________________________________ 4. If the fly is 19 feet, what is the hoist? ___________________ • There was a small flag in each of the cupcakes you made for the Fourth of July picnic. It measured 1 in. by 1 ¾ in. Which measurement would be the hoist? _________ The fly?_______ Could this be an official flag? _______. • Why or why not? _____________________________________ • Write an equation for the fly(“f”) where “h” represents any measurement for the hoist. _________________________

3. Name: ______________________ Math the Red, White & Blue

5. Student Work

6. Name: ___________________________________ Symbols of our Freedom...

7. Math & the Military? CENTER OF GRAVITY A small mistake in the CENTER OF GRAVITY can lead to much bigger problems!

8. Math & the Military Before a military aircraft can take off, the ground crew must be sure that the Center of Gravity (CG) is within certain safe limits. If it is, the pilot is ready for takeoff. If it is not, the weight must be rebalanced. Use the table to find the center of gravity for this small aircraft. The safe limit for this aircraft is 137.5.To find the MOMENT for each location the WEIGHT and the ARM must be MULTIPLIED.ADD the MOMENTS, DIVIDE by the TOTAL WEIGHT, and round to the nearest tenth to find the CENTER OF GRAVITY. Is the aircraft listed in the table safe for takeoff? If not, how could they remedy the problem? Problem Solving Addition of Integers Weight (pounds) Arm (inches) Moment Solving for the Unknown Dividing Rational Numbers Rounding & Comparing Decimals

9. CENTER OF GRAVITY Complete the charts. Formulas: (Weight)(Arm) = Moment Total Moment ÷ Gross Aircraft Weight = CG Name: ___________________________________ Aircraft 1 Safe limit: 82.1 Center of Gravity ______, Is this within the limit? ______ Aircraft 2 Safe limit: 98.7 Center of Gravity _____, Is this within the limit? ______ Aircraft 3 Safe limit: 43.3 Center of Gravity ______, Is this within the limit? ______ Aircraft 4 Safe limit: 74.9 Center of Gravity _____, Is this within the limit? ______

10. Center of gravity (aircraft) From Wikipedia, the free encyclopedia Center of Gravity The center-of-gravity (CG) is the point at which an aircraft would balance if it were possible to suspend it at that point. It is the mass center of the aircraft, or the theoretical point at which the entire weight of the aircraft is assumed to be concentrated. [1] Its distance from the reference datum is determined by dividing the total moment by the total weight of the aircraft.[2] The center-of-gravity is an important point on an aircraft, which significantly affects the stability of the aircraft. To ensure the aircraft is safe to fly, it is critical that the center-of-gravity fall within specified limits. • Terms • Ballast • Removable or permanently installed weight in an aircraft used to bring the center of gravity into the allowable range. • CG Limits • The specified longitudinal (forward and aft) or lateral (left and right) points within which the CG must be located during flight. These limits are indicated in the aircraft operator manuals. • CG Range • The distance between the forward and aft (or left and right) CG limits indicated in the aircraft operator manuals. • Weight and Balance • The aircraft is said to be in weight and balance when the gross weight of the aircraft is under the max gross weight, and the center of gravity is within limits and will remain in limits for the duration of the flight. • Reference Datum • A reference plane that allows accurate, and uniform, measurements to any point on the aircraft. • Arm • The horizontal distance from the datum to any component. Another term that can be used interchangeably with arm is station. • Moment • If the weight of an object is multiplied by its arm, the result is known as its moment. You may think of moment as a force that results from an object’s weight acting at a distance. Moment is also referred to as the tendency of an object to rotate or pivot about a point. The farther an object is from a pivotal point, the greater its force. • Center-of-gravity Computation • By totaling the weights and moments of all components and objects carried, you can determine the point where a loaded aircraft would balance. This point is known as the center-of-gravity.