Next to a good preflight plan and current weather report is a thorough Weight & Balance calculation. This is a matter of serious concern to all pilots as well as many other people involved in the flight.
To understand what is going on with these calculations we need to establish some definitions. This way we all speak the same language and there will be no confusion. We therefore have compiled a list of the most common terms used in calculations and documentation.
The total weight of the aircraft at any particular time. Thus Basic Empty Weight plus Pilot, Crew and their baggage and payload (passengers and cargo) in addition to the fuel load. Gross Weight may not exceed the maximum weight permissible for any given maneuver at any time.
Snippets from Wikipedia: "In the physical sciences, weight is a measurement of the gravitational force acting on an object. Near the surface of the Earth, the acceleration due to gravity is approximately constant; this means that an object's weight is roughly proportional to its mass. In modern scientific usage, weight and mass are fundamentally different quantities: mass is an intrinsic property of matter, whereas weight is a force that results from the action of gravity on matter: it measures how strongly gravity pulls on that matter."
To convert between weight (force) and mass we use Newton's second law, F = m x a (force = mass × acceleration). Here, F is the force (weight) due to gravity, m is the mass of the object in question, and a is the acceleration due to gravity, on Earth approximately 9.8 m/s2 or 32.2 ft/s2. In this context the same equation is often written as W = m x g, with W standing for weight, and g for the acceleration due to gravity.
An imaginary vertical line, specified by the designer of the aircraft, from which all horizontal C of G measurement are made. In most cases, the datum is located near the aircraft nose. It is usually the firewall. Some experimental aircraft have the datum set at the leading edge of the wing. The datum for a particular aircraft is stated in the Pilot Operating Handbook or the Aircraft Flight Manual.
This is the horizontal distance from the datum to the 'C of G' of the aircraft or any item in the aircraft. A positive sign indicates measurement aft of the datum. You will find these values in the Aircraft Flight Manual or Pilots Operating Handbook of the aircraft and they can be expressed in inches, centimeters or meters.
To define the distance from the datum to a station the following syntax is used: STA 1000 is 1000mm (or inch) from the datum. A position in front of the datum would look like this: STA -200. And any weight at STA -200 would give a negative moment.
Based on Newton's second law: F = m x a. The mass of an item multiplied by the arm of its position. A moment is a turning effect about a given point depending on two factors: the distance from the datum, arm and its force.
This is the turning effect about a given point and it depends on two things: the magnitude of the force (weight) and its distance (arm). If the force is measured in kilograms and the arm in meters then the moment is expressed in kilogram/meters. It can also be expressed in kilograms/mm, or lbs/in of lbs/foot.
Remember that in aircraft center of gravity calculations all moments that tend to result in a nose-up rotation about the selected datum are positive and vice versa.
This is the point about which an aircraft would balance if suspended on this point. It is the sum of all moments in the W & B calculations or put another way: the pivotal point about which the nose heavy and the tail heavy moments are of equal magnitude.
Very important: these are the forward and aft limits in which the 'C of G' must fall if the aircraft is to be operated safely and in stable controlled flight. You will need to shift or add weight (ballast) to make sure the C of G is within its limits. These points are specified in the limitations section of the Aircraft Flight Manual or Pilots Operating Handbook of the aircraft and are determined by the designer of the aircraft. Recalculation is normally done when equipment is installed or changed.