We read your photo as:

Calculate the center of gravity (CG) location of a loaded aeroplane in Mean Aerodynamic Chord (MAC) percentage.

Physics

ScanSolve AI Answer

Answer

D) 27.2% MAC\text{D) 27.2\% MAC}

Step-by-step solution

5 steps

To find the center of gravity (CG) location of the loaded aeroplane in MAC%, we need to calculate the total mass, total moment, the overall CG in inches, and then convert it to a percentage of the Mean Aerodynamic Chord (MAC).

  1. Calculate the moment for each component.

    The moment is calculated as mass multiplied by its arm (station).

    • Basic Empty Mass (BEM) moment: M1=1000 kg×92 inches=92000 kg-inchesM_1 = 1000 \text{ kg} \times 92 \text{ inches} = 92000 \text{ kg-inches}
    • Pilot's mass moment: M2=80 kg×100 inches=8000 kg-inchesM_2 = 80 \text{ kg} \times 100 \text{ inches} = 8000 \text{ kg-inches}
    • Fuel mass moment: M3=120 kg×130 inches=15600 kg-inchesM_3 = 120 \text{ kg} \times 130 \text{ inches} = 15600 \text{ kg-inches}
  2. Calculate the total mass of the loaded aeroplane.

    Total Mass=1000 kg+80 kg+120 kg=1200 kg\text{Total Mass} = 1000 \text{ kg} + 80 \text{ kg} + 120 \text{ kg} = 1200 \text{ kg}
  3. Calculate the total moment of the loaded aeroplane.

    Total Moment=92000 kg-inches+8000 kg-inches+15600 kg-inches=115600 kg-inches\text{Total Moment} = 92000 \text{ kg-inches} + 8000 \text{ kg-inches} + 15600 \text{ kg-inches} = 115600 \text{ kg-inches}
  4. Calculate the overall Center of Gravity (CG) in inches.

    CGinches=Total MomentTotal Mass=115600 kg-inches1200 kg=96.333... inches\text{CG}_{\text{inches}} = \frac{\text{Total Moment}}{\text{Total Mass}} = \frac{115600 \text{ kg-inches}}{1200 \text{ kg}} = 96.333... \text{ inches}
  5. Convert the CG location to a percentage of MAC.

    The 0% MAC is at station 80 inches, and the length of the MAC is 60 inches.

    \text{CG}_{\%MAC} = \frac{\text{CG}_{\text{inches}} - \text{Station of 0% MAC}}{\text{Length of MAC}} \times 100\% CG%MAC=96.333... inches−80 inches60 inches×100%\text{CG}_{\%MAC} = \frac{96.333... \text{ inches} - 80 \text{ inches}}{60 \text{ inches}} \times 100\% CG%MAC=16.333...60×100%\text{CG}_{\%MAC} = \frac{16.333...}{60} \times 100\% CG%MAC=0.27222...×100%\text{CG}_{\%MAC} = 0.27222... \times 100\% CG%MAC≈27.2%\text{CG}_{\%MAC} \approx 27.2\%

    Comparing this to the given options, the closest answer is D.

    The final answer is \text{D) 27.2% MAC}.

Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp