Fuel Burn Impact: Calculating Cg Change Effectively

The centre of gravity (CG) of an aircraft is the point at which it would balance. Its position is calculated by supporting the aircraft on weighing scales or load cells and noting the weight shown on each. The CG affects the stability of the aircraft, and to ensure safety, it must fall within specified limits established by the manufacturer. The CG may change as the aircraft's weight changes due to fuel burn. The basic formula for calculating CG is: Weight x Arm = Moment, Total Moment / Total Weight = CG. To calculate the CG change for fuel burn, you need to know the original CG, the weight of the fuel consumed, the new total weight, and the distance between the original CG and the point where the weight is being removed.

Calculating the weight shift

Now, let's delve into a more comprehensive example to illustrate the process of calculating the weight shift.

Example Calculation:

Let's say you have the following details for an aircraft:

• Total weight: 4,037 lbs
• CG location station: 67.8
• Fuel consumption: 14.7 GPH
• Fuel CG station: 68.0

You want to determine the new CG location after 1 hour and 45 minutes of flight time. Here's how to calculate it:

• Find the amount of weight change due to fuel consumption: First, calculate the total fuel consumed by multiplying the fuel consumption rate by the duration of the flight. In this case, 14.7 GPH x 1.75 hr = 25.7 gallons. Next, convert gallons to pounds by multiplying by the weight of fuel per gallon (usually around 6 lbs/gal). So, 25.7 gallons x 6 lbs/gal = 154 lbs. This is the weight of fuel burned.
• Determine the new total weight: To find the new total weight, subtract the weight of the fuel consumed from the initial total weight. In this case, 4,037 lbs - 154 lbs = 3,883 lbs.
• Calculate the distance between the original CG and the fuel CG: To do this, simply subtract the original CG location from the fuel CG location. So, 68.0 - 67.8 = 0.2 inches.
• Apply the weight change formula: Now, you can use the weight change formula to find the change in CG. The formula is: Weight Removed = Change in CG / New Total Weight. Plug in the values: 154 lbs / 3,883 lbs = Change in CG / 0.2 in. Now, solve for Change in CG: 154 lbs x 0.2 in / 3,883 lbs = 0.01 in.

So, the CG shifted by approximately 0.01 inches. Since the weight was removed aft of the original CG (68.0 inches) by burning fuel, the CG shifted forward by 0.01 inches. To find the new CG location, subtract the forward shift from the original CG: 67.8 inches - 0.01 inches = 67.79 inches.

Alternative Method:

Another way to calculate the weight shift is by using the basic weight and balance equation: Weight x Arm = Moment, and then dividing the total moment by the total weight to get the CG.

In this case, the initial moment is: 4037 lbs x 67.8 in = 273,708.6 in-lbs. After burning the fuel, the new moment is: (4037 lbs - 154 lbs) x (67.8 in - 0.01 in) = 266,667.6 in-lbs.

Now, divide the new moment by the new weight: 266,667.6 in-lbs / 3883 lbs = 68.7 in. So, the new CG location is approximately 68.7 inches.

Using the weight change formula

To calculate the change in the centre of gravity (CG) of an aircraft as fuel is burned, you can use the weight change formula. This formula will help you determine the new CG after fuel burn.

Let's say an aircraft has a total weight of 4,037 lbs, a CG location of 67.8, and a fuel consumption rate of 14.7 gallons per hour. The fuel CG station is at 68.0. We want to find the new CG location after 1 hour and 45 minutes of flight time.

First, we need to find the amount of weight change due to fuel consumption. We know the aircraft consumes 14.7 gallons per hour, and we are considering a duration of 1 hour and 45 minutes, which is 1.75 hours. So:

7 GPH x 1.75 hr = 25.7 gallons of fuel consumed

Next, we need to convert the volume of fuel consumed to weight. Assuming a fuel weight of 6 lbs per gallon, we can calculate:

7 gallons x 6 lbs/gallon = 154 lbs

Now we can determine the new total weight of the aircraft by subtracting the weight of the fuel consumed from the initial total weight:

4,037 lbs - 154 lbs = 3,883 lbs

To find the change in CG, we also need to know the distance between the original CG and the point where the weight is being removed (the fuel CG).

0 (fuel CG) - 67.8 (original CG) = 0.2 inches

Now we have all the values we need to plug into the weight change formula:

154 lbs / 3,883 lbs = Change in CG / 0.2 inches

To isolate the "Change in CG" and solve for it, we can cross-multiply:

154 lbs x 0.2 inches / 3,883 lbs = 0.01 inches

So, the CG shifted approximately 0.01 inches forward.

New CG = 67.80 (original CG) - 0.01 (forward shift) = 67.79 (new CG)

This calculation assumes that the fuel tank is located aft of the CG. If the fuel tank is located exactly on the CG, there will be no change in CG position as fuel is burned.

Determining the new CG location

To determine the new CG location, you must first find the weight shift. This is done by calculating the amount of weight change and the new total weight.

For example, if an aircraft has consumed 14.7 gallons of fuel per hour for 1 hour and 45 minutes, you would first calculate the total fuel consumed:

> 14.7 GPH x 1.75 hr = 25.7 gal

> 25.7 gal x 6 lbs/gal = 154 lbs

Next, you determine the new total weight by subtracting the weight of the fuel consumed from the aircraft's original total weight:

> 4,037 lbs – 154 lbs = 3,883 lbs new total weight

Now, you can find the new CG location by using the following formula:

> Weight Removed = Change in CG

> ______________

> __________________

> New Total Weight = Distance between weight and old CG

Plugging in the values, you get:

> 154 lbs = x

> _______

> 3,883 lbs = 0.2 in

Solving for x, you find the change in CG:

> 154 lbs x 0.2 in / 3,883 lbs = 0.01 in

Finally, you can calculate the new CG location by subtracting the change in CG from the original CG location:

> 67.80 (original CG) – 0.01 (forward shift) = 67.79 (new CG)

It's important to note that the CG will shift in the opposite direction of the weight removal. In this case, since the weight was removed aft of the CG, the CG shifted forward.

Calculating the moment

The moment is the moment of force, or torque, that results from an object's weight acting through an arc that is centred on the zero point of the reference datum distance. In other words, it is the tendency of an object to rotate or pivot about a point. The moment is calculated by multiplying the weight of an object by its arm (the distance from the reference datum to the centre of gravity of an item).

The moment can be calculated using the following formula:

Moment = Weight x Arm

For example, if an aircraft's total weight was 8,600 pounds, and you shifted 100 pounds from station (or, arm) 100 to arm 150, the moment would be calculated as follows:

100 x 150 / 8,600 = 0.06 inches

So, the CG shifts 0.06 inches aft.

When calculating the moment for fuel burn, the weight of the fuel consumed needs to be subtracted from the total weight of the aircraft. For example, if an aircraft has a total weight of 4,037 lbs and has consumed 14.7 GPH of fuel for 1 hour and 45 minutes, the total fuel consumed would be calculated as follows:

• 7 GPH x 1.75 hours = 25.7 gallons
• 7 gallons x 6 lbs/gallon = 154 lbs

The new total weight of the aircraft would then be calculated by subtracting the weight of the fuel consumed from the original total weight:

4,037 lbs - 154 lbs = 3,883 lbs

The moment can then be calculated by multiplying the weight of the fuel consumed by the distance between the original CG and the point where the weight was removed (the fuel CG):

154 lbs x 0.2 inches = 30.8 inch-pounds

So, the moment for the fuel burn is 30.8 inch-pounds.

It's important to note that the moment calculations for fuel burn will vary depending on the specific aircraft and flight conditions. The above examples are meant to provide a general understanding of how to calculate the moment for fuel burn.

Adjusting the CG within limits

When adjusting the CG within limits, it is important to consider the placement of the fuel tanks in relation to the centre of gravity (CG) of the aircraft. The CG will shift as fuel is burned, depending on the location of the fuel tanks. If the fuel tanks are positioned exactly on the CG, there will be no change in CG during the flight. However, if the CG is calculated relative to a datum, such as the leading edge of the wing, the CG position will appear to change as fuel is consumed.

The customary method is to calculate the CG with the fuel tanks empty, as this ensures the aircraft is stable during landing. Typically, the fuel tanks are located forward of the CG, so when they are full, the aircraft is more stable. This is especially important for pattern planes, where consistent performance is crucial. By placing the fuel tanks on the CG, any variation in fuel level will not impact the CG, eliminating this variable.

The pitch stability of an aircraft depends on the CG location in relation to the Neutral Point (NP). The NP is influenced by factors such as tail location and tail efficiency, and it can vary significantly between different aircraft. Therefore, it is essential to determine the CG relative to the NP to ensure stable flight.

When calculating the CG, it is important to consider all the forces and moments acting on the aircraft. Forces and moments are vectors, and they can be added together. The CG can be determined by dividing the total moment by the total weight (ΣM/W=x̅). The moment is the cross product of position and force (r×F), which simplifies to the arm (distance) multiplied by weight for fuel burn calculations.

By taking into account the initial weight and moment, as well as the change in weight due to fuel burn, the new CG position can be calculated. This calculation involves finding the difference in CG position and then removing the moment of the burned fuel. The new weight is calculated by subtracting the weight of the fuel consumed from the total weight. The distance between the original CG and the point where weight is removed (fuel CG) is also considered.

It is important to note that the CG limits may change with different loadings, and this can impact whether the CG remains within the acceptable range during the flight. Therefore, pilots should always compute the weight and balance at the beginning and end of the flight to ensure the CG remains within safe limits.

Frequently asked questions