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.

f l yStrand: Number & Operations/Standard 1: Number Sense

Strand: Algebra/Standards 4 & 6: Patterns, Relations & Functions and Algebraic Models

Measure the flags on your tables and see if they are an “official” size. Be ready to defend your decision.

Using the hoist:fly ratio answer the following…

2. If an official flag has a hoist of 5 feet, what is the fly? ________________

3. How would you find the appropriate hoist if the fly is given? ________

____________________________________________________________

4. If the fly is 19 feet, what is the hoist? ___________________

5. 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? _____________________________________

1. Explain what it means for the fly:hoist ratio to be 1.9:1. _____________

_____________________________________________________________

6. Write an equation for the fly(“f”) where “h” represents any measurement for the hoist. _________________________

Name: ______________________

Name: ___________________________________

CENTER OF GRAVITY

A small mistake in the CENTER OF GRAVITY can

lead to much bigger problems!

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?

Weight (pounds)

Arm (inches)

Moment

LocationWeight

(pounds)Arm

(Inches) Moment

Empty Weight 2,181 80 ________

Front seats 340 85 ________

Rear seats 125 117 ________

Oil 30 24 ________

Fuel 444 75 ________

Aircraft 1 Safe limit: 82.1 Center of Gravity ______,

Is this within the limit? ______

Location

Weight (pound

s)Arm

(Inches)Momen

t

Empty Weight 1,489 38.8 _______

Front seats 325 _______ 12,025

Rear seats 180 73 _______

Oil 11 _______ 154

Fuel 240 48

_______

Aircraft 3 Safe limit: 43.3 Center of Gravity ______,

Is this within the limit? ______

LocationWeight

(pounds)Arm

(Inches)Moment

Empty Weight 2,789 _______ 284,478

Front seats 400 _______ 40,000

Rear seats 170 _______ 27,030

Oil 54 _______ 2,322

Fuel 650 _______ 71,500

Aircraft 2 Safe limit: 98.7 Center of Gravity _____,

Is this within the limit? ______

Location

Weight (pound

s)

Arm (Inches

) Moment

Empty Weight 1903 67.7 ________

Front seats 364 91 ________

Rear seats 172 _______ 27,692

Oil 26 _______ 541

Fuel 347 _______

20,339

Aircraft 4 Safe limit: 74.9 Center of Gravity _____,

Is this within the limit? ______

CENTER OF GRAVITY Complete the charts.

Formulas: (Weight)(Arm) = Moment Total Moment ÷ Gross Aircraft Weight = CG

Name: ___________________________________

Center of GravityThe 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.