Center of gravity and moment of inertia
Some models for optimizing the loading of aircraft already existed and took into account the importance of the center of gravity. In an aircraft, the weight should be distributed in such a way that the center of gravity, which is located near the wings, is respected. Otherwise the aircraft will simply not take off. “There is zone pre-defined by the aircraft constructor in which the loadmaster has some leeway. The more the center of gravity is positioned towards the rear of the plane within the zone, the less fuel it will use. For example, if the point of gravity is positioned 5% closer the rear of the aircraft, a fully-loaded Boeing 777 could burn around 1% less fuel which represents 1,000 liters for a 10,000 kilometer long flight, equivalent to the distance between Liège and Shanghai”, explains Sabine Limbourg, a physicist who specializes in management science.
These older models did not, however, take into account a whole series of constraints that already exist in practice. The physicist adds. “In reality they had another aim. They made it possible to select the ULDs to be placed in the aircraft from the premise that the latter was always full at the moment of take-off”. Professor Schyns continues, “Out of every 100 ULDs for 80 spaces on the aircraft, these models determined which ULDs were to be transported but then 20 of them remained on the tarmac and were not taken into account. However, in reality, such a situation would lead to unsatisfied customers and things don’t work like that in reality.” Indeed it is quite rare for an aircraft to be completely full on take-off. Aircraft are generally filled to about 60% of their full capacity and the model designed in Liége offers much better management of partially-loaded aircraft.
By taking account of this reality and incorporating it into the model, it became necessary from this point on to take account of another parameter that needed to be minimized for an optimally comfortable flight, the moment of inertia. The moment of inertia is rarely taken into account in a fully-loaded aircraft. In reality it is a brake on rotation generated by distribution of the weight that is too spread out. The computer scientist explains, “for example, if you want an object to turn on itself, you will use more energy if the weight is closer to the extremities than to the center. And in accordance with the same principle of physics, a figure skater will pull her arms and legs as close to her body as possible in order to turn faster. In this way she will minimize her moment of inertia. It is the same principle we are dealing with when an aircraft is being loaded.” The priority is to have a compact load, as is done in practice, for different operational reasons. The moment of inertia is the solution offered by the Liége model when there is only partial-loading. The operators do not think in terms of the moment of inertia and, in reality, do not think very much about maneuverability. The aim of the model by the team from Liège through the use of the moment of inertia is to make the load as compact as possible so that it is not distributed throughout the whole aircraft. The advantage is that this approach by means of the moment of inertia increases maneuverability, even though this was not the main aim of the exercise.
The aim of optimal loading for an aircraft that will not be fully filled is to respect the center of gravity in the first instance, and then to place the ULDs around this point without distributing them throughout the aircraft and without leaving spaces between them. A minimized moment of inertia will allow the aircraft to use fewer forces during changes in altitude or trajectory, which will result in greater maneuverability by the pilot as well as economizing on fuel. It will also reduce the risk of damage to the aircraft. The physicist explains, “If, in fact, we place the entire cargo at the two extremities of the aircraft while leaving the middle empty, the center of gravity is respected. However, the aircraft risks bending like a banana and in a worst-case scenario could break up.” Therefore, between two solutions involving the center of gravity, it would be preferable to choose that where the ULDs are the most concentrated, packed around this point.
