Understanding the Weight Change Formula

The weight change formula is an essential tool for pilots, allowing for quick recalculation of weight and balance when changes occur in the aircraft’s load. This formula helps avoid complex recalculations and ensures accurate adjustments to the center of gravity (C of G).

Components of the Weight Change Formula

The formula involves four key components:

1. Weight Lost/Gained: The amount of weight added or removed from the aircraft.
2. New Airplane Weight: The aircraft’s weight after the load change.
3. Change in C of G: The movement of the center of gravity due to the weight shift.
4. Distance from Original C of G: The distance between the original center of gravity and the location where the weight was added or removed.

The Weight Change Formula

Formula:

​

Example Calculation:

1. Current Weight of Airplane: 2,700 lbs
2. Weight of Fuel Burned: 150 lbs
3. Initial C of G: 95.0 inches
4. Fuel Station: 50 inches

Step-by-Step Calculation:

Explanation:

After burning 150 lbs of fuel, the center of gravity will move forward by approximately 2.94 inches. This formula can also be applied to changes in passenger or cargo weights, providing a quick and efficient way to adjust the weight and balance calculations.

Case Study: Weight Change Impact on Aircraft Balance

Background:

Sarah, a private pilot, was preparing for a cross-country flight with her Cessna 172. Before departure, she needed to account for the fuel burn and its effect on the aircraft’s balance.

Scenario:

• Aircraft Weight Before Flight: 2,800 lbs
• Fuel Burned: 180 lbs
• Initial C of G: 97.5 inches
• Fuel Station: 55 inches

Calculation:

1. Determine the New Weight:$$\text{New Weight}=2,800\text{ lbs}-180\text{ lbs}=2,620\text{ lbs}$$
2. Apply the Weight Change Formula:X=180 lbs×55 inches2,620 lbsX = \frac{{180 { lbs} \times 55 { inches}}}{{2,620 { lbs}}}X=2,620 lbs180 lbs×55 inches​ X=9,9002,620≈3.78 inchesX = \frac{9,900}{2,620} \approx 3.78 \text{ inches}X=2,6209,900​≈3.78 inches

Outcome:

The center of gravity shifted forward by approximately 3.78 inches due to the fuel burn. Sarah used this information to ensure that her aircraft remained within the safe C of G range throughout the flight.

Conclusion:

The weight change formula is a valuable tool for pilots to efficiently manage aircraft balance and ensure safe operations. By applying this formula, pilots can quickly adjust for changes in load and maintain proper weight and balance throughout their flights.