This instructable explains the process of finding the center of gravity for the weight and balance of an aircraft. This is an important process when piloting an aircraft because the location affects performance characteristics of the aircraft and if it is out of acceptable limits the aircraft may be uncontrollable. Having this information calculated and on hand is, in fact, a requirement for every flight you make.
What you will need:
Aircraft information manual
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Step 1: Find Your Aircraft's Empty Weight and Moment.
Each aircraft's weight and moment are different. This information will be found in the Pilot's Operating Handbook (POH) specific to the aircraft you are flying. It will be in the weight and balance chapter which is standard chapter six.
Step 2: Find Weights of Everything Loaded.
This includes pilot, all passengers, baggage, and the fuel that will be loaded into the aircraft. You will find the fuel load in the first chapter of the POH. Keep in mind that you will use the amount labeled "usable fuel" because unusable fuel is included in the aircraft's weight and that fuel weighs six pounds per gallon.
Step 3: Calculate the Moment for the Load.
In chapter 6 of the POH you will find either a chart similar to the one on the left or a figure like the one shown on the right. If you have the chart you can follow the weight to the appropriate line to find the moment. If you have the figure, you need to multiply the weight of each position by the number given as the arm to find the moment. Calculate the moments for the pilot, all passengers, fuel, and baggage.
Using the graph above, if the pilot and front passenger weighed 300 pounds, you would find 300 on the vertical axis. You then follow that over to where it intersects the line labelled "Pilot and front passenger". You then follow that down to the horizontal axis to get your moment value of about 11. Using the other method with the same 300 pounds you would multiply by the value given for the pilot and front passenger which gives you 300*37=11,100
Step 4: Total Up the Weights and the Moments
Add together the weights for the aircraft, people, fuel, and baggage. Also add the moments found in the previous step (pilot, passengers, fuel, and baggage) to the moment of the empty aircraft.
Step 5: Determine If Center of Gravity Is Within Limits
In chapter 6 of the POH find the chart that shows the acceptable limits of the center of gravity. It will look like one of the charts pictured above. One compares the total weight to the total moment and one compares the total weight to the arm of the center of gravity. If your chart uses the arm all you need to do is divide the total moment by the total weight to find that value. If the intersection falls within the area outlined on the chart you are within acceptable limits to fly.
If your total weight was 2500 and total moment was 105 (105,000) you would find these values on their specific axes on the second chart pictured and their intersection lies within the outlined area. Using the arm you would find 105,000/2500=42 which when found on the first chart also falls withing the border.