The center of gravity (CG) plays a key role in flight safety and efficiency. Pilots and flight planners rely on accurate CG calculations to ensure that an aircraft operates within its safe envelope limitations.

In this blog, we’ll go through the basics of CG and a step-by-step of how to calculate center of gravity.

Or, you can bypass the complications and head straight to our streamlined Weight & Balance module.

Firstly, what is Center of Gravity?

The center of gravity is the exact point where the aircraft's total weight is considered to be concentrated.

An accurate CG calculation ensures the aircraft is correctly balanced and provides safe controllability. If the CG is too far forward or aft, the aircraft could become difficult to control, leading to unsafe flying conditions for the flight crew.

Why is CG important?

• Flight Stability: A correctly positioned CG ensures the aircraft is stable during flight.
• Control: CG affects how responsive the aircraft is to pilot inputs.
• Fuel Efficiency: Incorrect CG positioning can increase drag, leading to inefficient fuel usage.
• Safety: An out-of-balance aircraft may lead to dangerous flight dynamics like stalls or spins.

Learn more about the importance of weight & balance and center of gravity.

The formula of how to calculate Center of Gravity

CG is commonly calculated by dividing the total moment (the force of weight at a distance) by the total weight of the aircraft.

The formula is: CG=Total Moment /Total Weight

• Total Moment is the sum of the moments of all individual weights (passengers, fuel, cargo), calculated by multiplying each weight by its distance from a reference point, which is usually the aircraft’s datum.
• Total Weight is the sum of all individual weights on board the aircraft.

Step-by-step of how to calculate CG 

1 - Collate Data for:
Aircraft Empty Weight & CG: Obtain the aircraft's empty weight and its CG location from the aircraft's specific weight and balance configuration.
Weight of Passengers, Cargo, and Fuel: Determine the weight and location of all items being loaded on the aircraft.

2 - Calculate Moments:
For each weight (passengers, cargo, fuel, etc), multiply the weight by the distance from the datum to find the moment. Moment=Weight×Arm (Distance)

3- Sum the Moments & Total Weight:
Add up all the moments and the total weight to find the overall moment and total weight of the loaded aircraft.

4 - Apply the Formula:
Divide the total moment by the total weight to find the CG location. CG=Total Moment/Total Weight

5 - Check the CG Limits:
Compare the calculated CG with the aircraft’s allowable CG flight envelope range from the flight manual to ensure it’s within the safe operating limits.

These days, many weight calculations, like the basic operating weight, can be pre-configured and automatically integrated into the weight & balance section of an EFB app.

Here’s an example CG calculation

Aircraft Load:

• Empty weight: 10,000 lbs, located at an arm (distance from a reference point) of 300 inches
• Pilot and co-pilot: 400 lbs, located at an arm of 120 inches
• Passengers: 800 lbs, located at an arm of 160 inches
• Baggage: 200 lbs, located at an arm of 380 inches
• Fuel: 600 lbs, located at an arm of 310 inches

Step 1: Calculate Moment for Each Component

To find the moment, multiply the weight by the arm for each component:

• Empty weight: Moment = 10,000 lbs × 300 inches = 3,000,000 in-lbs
• Pilot and co-pilot: Moment = 400 lbs × 120 inches = 48,000 in-lbs
• Passengers: Moment = 800 lbs × 160 inches = 128,000 in-lbs
• Baggage: Moment = 200 lbs × 380 inches = 76,000 in-lbs
• Fuel: Moment = 600 lbs × 310 inches = 186,000 in-lbs

Step 2: Calculate the Total Weight & Total Moment

• Total weight: 10,000 lbs + 400 lbs + 800 lbs + 200 lbs + 600 lbs = 12,000 lbs
• Total moment: 3,000,000 in-lbs + 48,000 in-lbs + 128,000 in-lbs + 76,000 in-lbs + 186,000 in-lbs = 3,438,000 in-lbs

Step 3: Calculate the Center of Gravity (CG)

Divide the total moment by the total weight to find the CG:

• CG = 3,438,000 in-lbs ÷ 12,000 lbs = 286.5 inches

Answer

The aircraft’s center of gravity is located 286.5 inches from the reference point. This CG must fall within the aircraft's safe operational limits to ensure stable flight.
 

Other Considerations to factor in

• Fuel Burn: The CG can shift during the flight as fuel is consumed, so it's important to ensure it stays within acceptable limits for the entire duration of the flight.
• Trim Adjustments: If CG is slightly out of balance, some aircraft allow trim adjustments to maintain stable flight. 

Understanding and accurately calculating the center of gravity is essential for ensuring smooth and safe flight operations.

With modern tools like electronic flight bags (EFBs), pilots can access weight and balance data to perform these calculations more efficiently and accurately.

The W&B loadsheet data can then be signed off and synced to the ground system for secure data storage and providing flight summary reports. This also ensures a robust audit trail and provides extra safety checks if necessary.

Why not read more about how the EFB weight & balance calculator can save time for the flight crew.