Question

An airplane has its Neutral Point \(x_{NP}\) located at \(0.35c\) (35% of the Mean Aerodynamic Chord). The Current Center of Gravity (CG) \(x_{CG}\) is \(0.20c\) (20% of the Mean Aerodynamic Chord). The pilot wants to move the CG to a new position such that the Static Margin is reduced by exactly \(50\%\). Calculate the new location of CG?

• A. \(0.175c\)
• B. \(0.275c\)
• C. \(0.10c\)
• D. \(0.035c\)

Hint:

The static margin is \[ \boxed{ SM=x_{NP}-x_{CG}. } \] Moving the CG aft decreases the static margin, while moving it forward increases the static margin.

Answer 1

The Correct Option is B

Step 1: Write the expression for static margin. The static margin is given by \[ \boxed{ SM=x_{NP}-x_{CG}. } \]

Step 2: Calculate the initial static margin. Given, \[ x_{NP}=0.35c, \] \[ x_{CG}=0.20c. \] Hence, \[ SM=0.35c-0.20c=0.15c. \]

Step 3: Reduce the static margin by \(50\%\). The new static margin is \[ SM_{\text{new}} = \frac{0.15c}{2} = 0.075c. \] Using \[ SM_{\text{new}} = x_{NP}-x_{CG,\text{new}}, \] we obtain \[ 0.075c = 0.35c-x_{CG,\text{new}}. \] Therefore, \[ x_{CG,\text{new}} = 0.35c-0.075c = 0.275c. \] Hence, \[ \boxed{0.275c} \] is the new CG location. Thus, \[ \boxed{(B)} \] is the correct answer.