01.05 Aerodynamics Weight & Balance

Aim

At the end of this lesson, you should be able to correctly:

• Terminology:
  • Aerofoil, angle of attack and relative airflow;
  • Centre of pressure and centre of gravity;
  • Lift, weight, thrust and drag;
• “Bernoulli’s principal”, “Coanda effect” and “Newton’s third law”;
• Basic weight and balance principles;
  • Empty weight;
  • Operating weight;
  • Maximum gross weight;
  • Arm, moment, datum, station and index unit;
  • Centre of gravity limits;
  • Loading limits.

Terminology

• Lift
• Weight
• Thrust
• Drag
• Relative Airflow
• Aerofoil
• Angle Of Attack
• Centre Of Pressure
• Centre Of Gravity

Forces

A basic question – What Exactly is a Force?

• A force is a push or pull upon an object resulting from the object’s interaction with another object.
• A force is a vector quantity – it has both magnitude and direction.
• It is common to represent a force by an arrow.
• Because forces are vectors, the effect of an individual force upon an object is often cancelled by the effect of another force.
• A force is represented diagrammatically as an ‘arrow’, the length of the arrow representing magnitude, and the direction the arrow points represents the direction of the force.

Resultant Force

A resultant force is the single force which represents the vector sum of two or more forces.

The ‘start’ of the second force needs to be moved to the ‘end’ of the first force, with the resultant going from the start of the first force directly to the end of the second force (as shown in the diagram).

A force acting on a point can be broken up into it’s horizontal (x) and vertical (y) components:

Principle of Moments

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.

When a system is in equilibrium, the TOTAL anticlockwise moment = TOTAL clockwise moment.

Consider the following system:

In this system, at this point in time, the system is in equilibrium!

Aerodynamic Forces

Distribution of Forces

The main forces acting on an aircraft in straight and level flight are lift and weight,which act in opposite directions,  but not necessarily from the same point on the aircraft.

For STRAIGHT and LEVEL Flight:

• L = W
• T = D

Lift

• Lift is an aerodynamic force
• Lift opposes weight
• Lift is a component of Total Reaction Force
• Lift acts through the Centre of Pressure
• Lift operates:
  • Perpendicular (90°) to Relative Air Flow
  • Perpendicular (90°) to lateral axis

Basic Aerofoil Shape

Aerodynamic Forces

The fluid on top of the wing is accelerated and the fluid on the bottom of the wind is slowed down compared to velocity of the aircraft itself because the wing geometry and angle narrows the flow area above the wing and widens the flow area below the wing. (Venturi Effect!)

Centre of Pressure

As the Airfoil angle of attack changes, the pressure field changes. Due to this, the centre of pressure changes with variation in the angle of attack. In the airplane’s normal range of flight attitudes, if the angle of attack is increased, the centre of pressure moves forward; and if decreased, it moves rearward.

Pressure Distribution

Types of Drag

Theories of Physics

Bernoulli’s Theorem

Relationship between Velocity & Pressure:

Total Pressure (H) = Dynamic Pressure (q) + Static Pressure (p)
H = q +p

Coanda Effect

Coanda effect is the tendency of a fluid jet to stay attached to a convex surface. It is named after Romanian inventor Henri Coandă, who described it as “the tendency of a jet of fluid emerging from an orifice to follow an adjacent flat or curved surface and to entrain fluid from the surroundings so that a region of lower pressure develops.”

Newton’s Third Law

When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.

Weight & Balance

Weight = Mass x Gravity

The Centre of Gravity (CoG) is the average location of the weight of the aircraft components in total.

• Empty weight – Airframe, engine and all fixed equipment necessary for flight. Includes unusable fuel and oil
• Operating weight – Empty weight plus pilot and fuel
• Gross weight – total weight of the aircraft at a given time
• Maximum gross weight (Maximum take-off weight) – heaviest weight allowed for the aircraft at Take-off
• Moment – Leverage of a force equal to size of the force and the moment arm
• Arm – distance the force is applied from the pivot point
• Datum – a point determined (usually by the manufacturer) from which measurements apply for CoG calculations
• Station – the distance in mm from the datum for a particular part of the aircraft
• Index unit – If calculations result in huge figures, you can use index units to factor measurements to allow easier representation
• Centre of gravity limits – forward and aft limits of the CoG that keep the aircraft controllable and able to manoeuvre safely
• Loading limits – Any limitations placed on size or location of weight added to the aircraft. Used to ensure the aircraft remains within permissible CoG limits.