Weight and Balance Calculation

This article deals with weight and balance calculation for aircraft, a crucial pre-flight skill for pilots. it’s a basic and easy calculation that becomes second nature. As pilots move into larger aircraft, the task becomes more challenging. Practice makes it non-negotiable. Weight and balance calculations don’t require complex math or hours of hard work, and can be done quickly with a step-by-step guide. New technology like ForeFlight makes these calculations easier.

Why Calculate Weight and Balance?

Weight and balance are crucial for aircraft performance and safety, as they limit the aircraft’s capabilities. Regulations do not explicitly require calculations of weight and balance before every flight, but they are implied. The maximum takeoff weight is the most important number, and operating beyond this can result in negative flight characteristics such as higher takeoff speeds, longer landing rolls, reduced performance, higher stall speeds, exceeded limits on landing gear and brakes, and more load on the aircraft’s structure.

To ensure balance, find the loaded airplane Center of Gravity (CG) and compare it to the manufacturer’s charts or tables. The CG should not be too far forward or too far back, as either can make the airplane dangerous and unstable. A CG located forward of the forward limit can cause a nose-down tendency, increasing stall speed and making cruise flight slower. A CG located too far aft can cause a nose-up tendency, increasing cruise speed but making the aircraft less stable. If the airplane begins pitching up and slowing, it may be impossible for the pilot to lower the nose, reduce the angle of attack, and recover. A rearward out-of-limits CG is associated with unrecoverable stalls and spins.

Weight and Balance Terms

Standard empty weight — The weight of the airframe, engines, and permanently installed fixtures and fluids (including unusable fuel and full engine oil)

Basic empty weight — Standard empty weight plus any accessories your airplane might have added

Licensed empty weight — An older term than “standard empty weight,” which does not include engine oil

Maximum ramp weight — Total loaded aircraft weight only published for some airplanes. This will be a few pounds heavier than maximum takeoff weight because it assumes you will burn some for taxi and run-up.

Maximum takeoff weight — Maximum weight you can take off with.

Maximum landing weight — Maximum weight you can land with. This is not always published, or it may be published as equal to takeoff weight. Larger aircraft have landing weights much less than takeoff weights since they are designed to burn hundreds (or thousands) of pounds of fuel during flight.

Maximum zero fuel weight — The loaded aircraft weight with everything except fuel. Only published for some aircraft. This is a loading figure to reduce stress on the wings.

Payload — A common term for the maximum weight an airplane can carry of things that can pay the bill—passengers or cargo. 

Useful load — A common term for what an airplane can carry that the pilot loads aboard—pilot, passengers, cargo, and fuel. It is found by taking the maximum takeoff weight and subtracting out the aircraft’s basic empty weight.

Datum — A reference point chosen by the manufacturer from which all arms are measured. Where it doesn’t matter, but it is usually located at the tip of the propeller spinner or the engine firewall.

Arm — The distance measured fore or aft of the datum. Every location a pilot can load an object will have an arm distance listed in the AFM (Aircraft Flight Manual). If an arm is located forward of the datum, it will be a negative number.

Station — A location in the airplane where you can load something. Examples of stations include front seats, rear seats, main baggage area, nose baggage area, fuel tanks, etc.

CG — The center of gravity measured in inches aft of the datum. The airplane will have a minimum and maximum CG location for every available weight.

Moment — A measurement of the force that an item places on the airplane. A 100-pound object will produce more force the farther away from the datum that it is located. In other words, a 100-pound bag will affect your CG location more the farther back in the airplane it is located. Moments are measured in inch-pounds.

Moment index — Moments are usually long numbers, so many AFMs index them to simplify the math. This simply means they divide them by either 100 or 1,000. So 224,537.0 in-lbs becomes 2,245.37 or 224.537. 

Finding the Weight and Balance with the Calculation Method

Make Your Table

To calculate weight and balance, create a blank table for each item, filling in columns “weights,” “arm,” and “moments.” Write the weight and balance formula at the top for reminder. Schools and FBOs (Fixed-base operator) often provide a planning sheet.

Weight x Arm = Moments

The usual line items will be as follows. The list will depend on the available stations for loading in your aircraft. The first line will always be the empty weight of the airplane.

Step 1: Find the Aircraft’s Empty Weight

To complete the table for an airplane, ensure you know the airplane’s AFM, where is written the last time a mechanic physically weighed the aircraft. Use this record to obtain the empty weight and total moments, and add them to the first row of your table.

Step 2: Weight Your Gear and Passengers

In a small airplane, use exact numbers for weight calculations. Ask passengers about their weight and use a scale if they don’t know. Include heavy jackets and boots for winter. Multiply the gallons of fuel by 6 to calculate avgas weight. Include all non-bolted items, such as flight bags, spare parts, oil, and baggage items. Remember to include everything not bolted down, such as flight bags, spare parts, and oil.

Step 3: Do the multiplication for each row to calculate the moment.

Step 4: Find Total Weight

Se hai superato il peso massimo al decollo, potresti dover lasciare alcuni oggetti (o persone!) dietro. Oppure potresti prendere in considerazione l’idea di partire con meno carburante se è sicuro farlo

Step 5 – Find Total Moment and CG

Your AFM will provide a way to find whether or not the airplane is in balance. It will provide the answer using the total moments, total arm (CG), total weight. The CG (Center of Gravity) is calculated as total moment divided by the total weight. Usually a graph method is used, by means you can verify if Total Weight and CG are within the “safety area” (delimited by closed lines, see figure below).

As well as the CG of airplane with Zero Fuel has to be calculate. The Zero Fuel indicated by blue dot in figure above, can be considered conservatively as landing phase of aircraft.

The “safety area” delimited by closed lines reported above, is provided by the AFM. The “safety area” is determined by a table (in the tool below is named as “CG Envelope Table”).

Below the tool to calculated the Weight and Balance (click on “N172XX Cessna 172M Example” or “ADD NEW AIRCRAFT PROFILE” if you want to change also the “CG Envelope Table”/”Safety area”).