Aircraft Empty Weight CG Calculator
Calculate your aircraft's empty weight center of gravity (CG) accurately and understand its implications for safe flight.
Empty Weight CG Calculator
Enter the total empty weight of the aircraft in pounds (lbs) or kilograms (kg).
Enter the longitudinal distance of the empty weight CG from the datum line in inches (in) or centimeters (cm).
Enter the forward CG limit from the aircraft's POH/AFM.
Enter the aft CG limit from the aircraft's POH/AFM.
Calculation Results
Moment:
CG % MAC:
CG Location (Datum):
CG % MAC:
CG Location (Datum):
Formula: Empty Weight CG = (Empty Weight * Empty Weight CG Arm) / Empty Weight
Note: This calculator provides the Empty Weight CG. For the current CG of the aircraft, you must also account for installed equipment, crew, and fuel.
Aircraft CG Envelope Visualization
| Parameter | Value | Unit | Status |
|---|---|---|---|
| Empty Weight | N/A | N/A | – |
| Empty Weight CG Arm | N/A | N/A | – |
| Calculated Moment | N/A | N/A | – |
| Forward CG Limit | N/A | N/A | – |
| Aft CG Limit | N/A | N/A | – |
| Calculated Empty Weight CG | N/A | N/A | N/A |
| CG % MAC | N/A | % | – |
What is Aircraft Empty Weight CG?
The Aircraft Empty Weight CG (Center of Gravity) is a fundamental parameter in aviation safety and performance. It represents the point where the aircraft would balance if it were a rigid body, considering only its structure, fixed equipment, and unusable fuel. This CG is calculated based on the aircraft's empty weight and the arm (distance from a reference datum) of its center of gravity. Understanding and accurately calculating the empty weight CG is crucial because it forms the baseline for determining the aircraft's overall CG envelope, which dictates safe operating limits for weight and balance during flight.
Who should use it: Aircraft owners, pilots, maintenance personnel, and aviation engineers use the empty weight CG calculation. Pilots and owners need it to ensure that the aircraft's CG remains within the allowable limits throughout all phases of flight, from takeoff to landing, by accounting for variable loads like fuel, passengers, and cargo. Maintenance personnel use it when installing or removing equipment, as these changes affect the empty weight and its CG.
Common misconceptions: A common misconception is that the empty weight CG is the only CG that matters. In reality, it's just the starting point. The actual CG of the aircraft in flight changes dynamically with fuel burn, passenger and cargo loading, and even the configuration of the aircraft. Another misconception is that all aircraft have the same CG limits; these limits are highly specific to each aircraft model and are determined during its design and certification process.
Aircraft Empty Weight CG Formula and Mathematical Explanation
The calculation of the Aircraft Empty Weight CG is a straightforward application of the principle of moments. A moment is the product of a weight and its distance from a reference point (the datum). By summing the moments of all components that make up the empty weight and dividing by the total empty weight, we find the CG location of the combined mass.
The Core Formula:
The primary calculation for the empty weight CG is:
Empty Weight CG = (Empty Weight × Empty Weight CG Arm) / Empty Weight
This simplifies to:
Empty Weight CG = Empty Weight CG Arm
However, this is only if the "Empty Weight CG Arm" is the *resultant* arm of the empty weight. More commonly, we calculate the total moment of the empty weight components and then divide by the total empty weight.
Detailed Calculation Steps:
- Calculate the Moment of the Empty Weight: Multiply the total empty weight of the aircraft by the longitudinal distance of its center of gravity from the aircraft's datum. This gives you the empty weight moment.
- Determine the Empty Weight CG: Divide the calculated empty weight moment by the total empty weight. This yields the CG location relative to the datum.
Variable Explanations:
| Variable | Meaning | Unit | Typical Range |
|---|---|---|---|
| Empty Weight (EW) | The weight of the aircraft itself, including structure, engines, fixed equipment, and unusable fuel. | lbs or kg | Varies greatly by aircraft type (e.g., 500 lbs for ultralights to over 1,000,000 lbs for large airliners). |
| Empty Weight CG Arm (EWCA) | The horizontal distance from the aircraft's datum line to the center of gravity of the empty weight. | inches (in) or centimeters (cm) | Specific to aircraft design; often between 50-150 inches for light aircraft. |
| Moment (M) | The product of weight and its arm (M = W × Arm). Represents the turning effect of the weight. | lb-in or kg-cm | Product of EW and EWCA. |
| Empty Weight CG (EWCG) | The calculated center of gravity location of the aircraft in its empty configuration, relative to the datum. | inches (in) or centimeters (cm) | Must fall within the aircraft's specified CG limits. |
| Forward CG Limit | The most forward allowable CG position for safe flight. | inches (in) or centimeters (cm) | Defined in the aircraft's POH/AFM. |
| Aft CG Limit | The most aft (rearward) allowable CG position for safe flight. | inches (in) or centimeters (cm) | Defined in the aircraft's POH/AFM. |
| CG % MAC | Center of Gravity expressed as a percentage of the Mean Aerodynamic Chord. This is a standardized way to represent CG position, especially for swept wings. | % | Typically between 10% and 35% MAC for most aircraft. |
Practical Examples (Real-World Use Cases)
Understanding the Aircraft Empty Weight CG is vital for safe operations. Here are two examples:
Example 1: Light Single-Engine Aircraft
A Cessna 172 Skyhawk has an Empty Weight of 1,700 lbs. Its Empty Weight CG is located at 75.5 inches aft of the datum. The aircraft's POH specifies CG limits from 70.0 inches (forward) to 85.0 inches (aft).
- Inputs:
- Empty Weight: 1,700 lbs
- Empty Weight CG Arm: 75.5 in
- Forward CG Limit: 70.0 in
- Aft CG Limit: 85.0 in
- Calculation:
- Moment = 1,700 lbs * 75.5 in = 128,350 lb-in
- Empty Weight CG = 128,350 lb-in / 1,700 lbs = 75.5 in
- Results:
- Empty Weight CG: 75.5 inches aft of datum
- CG Status: Within limits (70.0 in ≤ 75.5 in ≤ 85.0 in)
- Interpretation: The empty weight CG of this particular Cessna 172 is well within its operational limits. This provides a good starting point for loading passengers, baggage, and fuel, ensuring the aircraft remains balanced throughout the flight.
Example 2: Experimental Aircraft with Equipment Change
An experimental aircraft builder has completed their aircraft. The initial empty weight is 1,200 lbs with a CG at 72 inches aft of the datum. They then install a new avionics package weighing 30 lbs, located 60 inches aft of the datum.
- Inputs:
- Initial Empty Weight: 1,200 lbs
- Initial Empty Weight CG Arm: 72.0 in
- Added Equipment Weight: 30 lbs
- Added Equipment Arm: 60.0 in
- (Assume CG Limits are 65.0 in to 80.0 in)
- Calculation:
- Initial Moment = 1,200 lbs * 72.0 in = 86,400 lb-in
- Added Equipment Moment = 30 lbs * 60.0 in = 1,800 lb-in
- New Total Empty Weight = 1,200 lbs + 30 lbs = 1,230 lbs
- New Total Moment = 86,400 lb-in + 1,800 lb-in = 88,200 lb-in
- New Empty Weight CG = 88,200 lb-in / 1,230 lbs = 71.71 in (approx.)
- Results:
- New Empty Weight CG: 71.71 inches aft of datum
- CG Status: Within limits (65.0 in ≤ 71.71 in ≤ 80.0 in)
- Interpretation: The addition of the avionics package shifted the empty weight CG slightly forward (from 72.0 in to 71.71 in) because the equipment was located forward of the original empty weight CG. This change is still within the aircraft's CG limits, but it's crucial to recalculate and document this new empty weight and CG for future weight and balance calculations. This highlights the importance of tracking every modification that affects the aircraft's weight and balance.
How to Use This Aircraft Empty Weight CG Calculator
Our calculator simplifies the process of determining your aircraft's Aircraft Empty Weight CG. Follow these steps:
- Enter Empty Weight: Input the total empty weight of your aircraft. Ensure you use consistent units (e.g., pounds or kilograms) as specified by your aircraft's documentation.
- Enter Empty Weight CG Arm: Input the distance of your aircraft's empty weight CG from the datum line. Again, maintain consistent units (e.g., inches or centimeters). This value is typically found in your aircraft's Pilot's Operating Handbook (POH) or Aircraft Flight Manual (AFM).
- Enter CG Limits: Input the forward and aft CG limits provided in your aircraft's POH/AFM. These define the safe operating envelope for your aircraft's CG.
- Calculate: Click the "Calculate CG" button.
- Review Results: The calculator will display:
- Main Result: The calculated Empty Weight CG location.
- Intermediate Values: The calculated Moment, CG % MAC (if applicable and calculable), and CG Location relative to the datum.
- Status: An indication if the calculated Empty Weight CG falls within the specified limits.
- Interpret: Compare the calculated Empty Weight CG to the forward and aft limits. If it's outside these limits, your aircraft is not airworthy in its current empty configuration, and adjustments (like adding or removing equipment) may be necessary.
- Reset: Use the "Reset" button to clear all fields and start over.
- Copy Results: Use the "Copy Results" button to copy the calculated values and key assumptions for documentation or sharing.
Decision-making guidance: A calculated Empty Weight CG that falls outside the specified limits indicates a potential issue with the aircraft's configuration. It might mean that even without any payload, the aircraft is unbalanced. This requires immediate attention, potentially involving re-weighing the aircraft, verifying equipment installations, or consulting with aviation maintenance professionals.
Key Factors That Affect Aircraft Empty Weight CG Results
While the calculation itself is simple, several factors influence the accuracy and relevance of the Aircraft Empty Weight CG and its impact on flight safety:
- Datum Line Selection: The choice of the datum (reference point) is critical. All measurements for weight arms must be taken from this same datum. A different datum will result in different arm values, though the actual CG location relative to the aircraft structure remains the same. Consistency is key.
- Accuracy of Weighing: The empty weight and the CG arm must be determined accurately. This often involves weighing the aircraft using calibrated scales at specific points (e.g., main landing gear and nose gear) and calculating the resultant CG. Inaccurate weighing leads to an incorrect empty weight CG.
- Installed Equipment: Any equipment permanently installed in the aircraft (avionics, interior furnishings, modifications) contributes to the empty weight and its CG. Changes in installed equipment necessitate recalculating the empty weight and CG.
- Unusable Fuel: The weight and location of unusable fuel (fuel that cannot be safely consumed) are included in the empty weight. This is a fixed value for a given aircraft type.
- Aircraft Configuration: The empty weight CG is a static value representing the aircraft without crew, passengers, or usable fuel. However, the *actual* CG during flight is dynamic and depends heavily on how the aircraft is loaded. The empty weight CG is the baseline for these dynamic calculations.
- POH/AFM Accuracy: The accuracy of the CG limits provided in the Pilot's Operating Handbook (POH) or Aircraft Flight Manual (AFM) is paramount. These limits are determined through rigorous flight testing and analysis to ensure safe flight characteristics across the entire operational envelope.
- Units of Measurement: Inconsistent use of units (e.g., mixing pounds and kilograms, or inches and centimeters) will lead to erroneous calculations. Always ensure all inputs use the same units or are converted correctly.
- Mean Aerodynamic Chord (MAC): For many aircraft, especially jets and complex designs, CG is expressed as a percentage of the MAC. This requires knowing the MAC length and the location of its forward and aft limits, in addition to the datum-based CG. Our calculator provides this if the necessary data is available.
Frequently Asked Questions (FAQ)
Q1: What is the difference between Empty Weight CG and Actual CG?
A1: The Empty Weight CG is the CG of the aircraft with only its fixed equipment and unusable fuel. The Actual CG is the CG at any given time during flight, which includes the empty weight plus crew, passengers, baggage, and usable fuel.
A1: The Empty Weight CG is the CG of the aircraft with only its fixed equipment and unusable fuel. The Actual CG is the CG at any given time during flight, which includes the empty weight plus crew, passengers, baggage, and usable fuel.
Q2: Can my aircraft's Empty Weight CG be outside the limits?
A2: No. If the calculated Empty Weight CG falls outside the forward or aft limits specified in the POH/AFM, the aircraft is considered overweight and unbalanced, and it is not legally airworthy until the configuration is corrected.
A2: No. If the calculated Empty Weight CG falls outside the forward or aft limits specified in the POH/AFM, the aircraft is considered overweight and unbalanced, and it is not legally airworthy until the configuration is corrected.
Q3: How often should I recalculate my aircraft's Empty Weight CG?
A3: You should recalculate the Empty Weight CG whenever significant modifications are made to the aircraft, such as installing new avionics, changing interior configurations, or repairing major structural components that might affect weight distribution. Regular weighing (e.g., every few years or after major work) is also recommended.
A3: You should recalculate the Empty Weight CG whenever significant modifications are made to the aircraft, such as installing new avionics, changing interior configurations, or repairing major structural components that might affect weight distribution. Regular weighing (e.g., every few years or after major work) is also recommended.
Q4: What happens if my aircraft's CG is too far forward?
A4: A forward CG can make the aircraft less stable and harder to control, potentially leading to stall issues or difficulty achieving rotation speed during takeoff. It generally results in heavier control forces.
A4: A forward CG can make the aircraft less stable and harder to control, potentially leading to stall issues or difficulty achieving rotation speed during takeoff. It generally results in heavier control forces.
Q5: What happens if my aircraft's CG is too far aft?
A5: An aft CG can make the aircraft unstable and difficult to control, especially at slower speeds. It can lead to a loss of control, particularly during landing or stall recovery, as the aircraft may have a tendency to pitch up uncontrollably.
A5: An aft CG can make the aircraft unstable and difficult to control, especially at slower speeds. It can lead to a loss of control, particularly during landing or stall recovery, as the aircraft may have a tendency to pitch up uncontrollably.
Q6: Does fuel burn affect the Empty Weight CG?
A6: No, the Empty Weight CG itself does not change with fuel burn. However, the *actual* CG of the aircraft *does* change as usable fuel is consumed, because fuel is typically located in specific points within the aircraft's structure, and its weight and arm change.
A6: No, the Empty Weight CG itself does not change with fuel burn. However, the *actual* CG of the aircraft *does* change as usable fuel is consumed, because fuel is typically located in specific points within the aircraft's structure, and its weight and arm change.
Q7: What is the datum line?
A7: The datum line is an imaginary vertical line established by the manufacturer from which all horizontal measurements (arms) for weight and balance calculations are taken. Its location is defined in the aircraft's POH/AFM.
A7: The datum line is an imaginary vertical line established by the manufacturer from which all horizontal measurements (arms) for weight and balance calculations are taken. Its location is defined in the aircraft's POH/AFM.
Q8: Can I use this calculator for any aircraft?
A8: This calculator is a tool to help you understand the calculation process. Always refer to your specific aircraft's POH/AFM for the correct empty weight, CG arm, and CG limits. The principles apply broadly, but exact values are aircraft-specific.
A8: This calculator is a tool to help you understand the calculation process. Always refer to your specific aircraft's POH/AFM for the correct empty weight, CG arm, and CG limits. The principles apply broadly, but exact values are aircraft-specific.