Payloads – Weight & Moments

The Four Forces and the Centre of Gravity

The four forces are represent a simplified model of our aircraft. There are actually many other forces at work!

A Moment is force that causes or tries to cause an object to rotate.

When a system is in equilibrium:

Total anticlockwise moment = Total clockwise moment

Consider the following system…

• The moment of a force is a measure of its tendency to cause a body to rotate about a specific point or axis.
• The magnitude of the moment of a force acting about a point or axis is directly proportional to the distance of the force from the point or axis. It is defined as the product of the force and the moment arm.
• The moment arm or lever arm is the perpendicular distance between the line of action of the force and the centre of moments.

The Basic Concept

In aviation, all forces that act on the aircraft will create a moment around the Centre of Gravity (C.o.G.), where:

Moment = Force x Distance

In this case, the force could also be a weight!

Horizontal Stabiliser and its Turning Moment

Most airplanes are designed so that the wing’s centre of lift (C.o.L.) is to the rear of the centre of gravity.

• We need a counter-acting force at the tail to balance out the moments!
• Adding more payload weight will change this balancing equation!

Applying simple physics principles, it can be seen that if a bar was suspended at point L with a heavy weight hanging on it at the CG, it would take some downward pressure at point T to keep the ‘lever’ in balance. 

There are two distinct points along the aircraft longitudinal axis:

• The Weight of the aircraft, applied at the Centre of Gravity (CG) of the aircraft;
• The Lift, applied at the Centre of Pressure (CP).

The CG is further forward than the CP for aircraft stability reasons. The more distant the two points, the bigger the pitch-down moment.

In order to well understand the impact of weight and balance on the stability and manoeuvrability of the aircraft, it is worth getting back to the forces that apply to the aircraft, and more specifically to focus on the vertical ones.

The distance between the CG and the CP induces a pitch down moment that needs to be compensated for, to keep the aircraft level.

• Compensation is done through the Trimmable Horizontal Stabilizer (THS) which exerts a downward force.
• This force is applied at the THS, a distance from the CG, therefore it creates a big pitch-up moment.
• This compensation force also increases the required overall lift to keep the aircraft level.