PLANNING

Fuel Weight

The calculation of fuel requirements is one of the most important aspects of a good pre-flight. Also calculating the weight of the fuel is important to keep the aircraft within its limits.

Fuel and weight calculations:

Specific weight: (SW) This is a statement in word, i.e. 1USG = 6lbs
In South Africa we refuel in litres, so it is important to know that 1USG = 3.785L and 1kg = 2.205lbs

Fuel and weight calculations:

Specific gravity: (SG) This is a ratio. It compares the weight of a volume of liquid with an equal volume of water. The SG of water is therefore 1, 1L of water weighs 1kg. 1L of avgas weighs around 0.74kg (temperature dependant), therefore the SG of avgas is 0.74.
Volume x SG = Weight
Always convert units to litre and kilograms first.
If the fuel flow (F/F) of an aircraft is known, i.e.the amount of fuel burn in an hour, along with the ground speed of the aircraft. Then the amount of fuel for a certain distance can be calculated.
E.g. Distance to fly is 205nm, ground speed 122kts, F/F 8.0 Gph, a reserve of 45min required. What is the amount of fuel to be loaded?

 Answer: Flying time is 1hr 41 min + 45min reserve = 2.43 hrs v2.43 hrs x 8USG = 19.44 USG required for the flight.

Calculate endurance: (Amount of flying time with a certain amount of fuel)

E.g. Fuel on board is 40USG, F/F is 8.6Gph. Determine the endurance.

 Answer: 40 / 8,6 = 4.65hrs or 4hrs 40min

Mass and Balance

Weight: The effect of excessive weight may be:

Higher take-off speed
Longer take-off run
Reduction in rate of climb
Greater fuel consumption
Higher stall speed
Higher landing speed
Longer landing distance

Balance: This refers to the final location of the centre of gravity (CG). The CG is the point about which the total weight of the aircraft is assumed to be concentrated.

Datum:

A point along the longitudinal axis (centre line) of the aeroplane (or its extension) designated by the manufacturer as the zero or reference point from which all balance arms (distances) begin. By taking moments about the datum the CG position of the aircraft can be determined. For the purposes of this phase of study the lateral displacement of the CG from the longitudinal axis is assumed to be zero.

Arm:

This is the horizontal distance, usually in inches, from the Datum to each position where weight is to be loaded. •

Moment:

This is the product of the weight of an item multiplied by its arm. It is the effect of gravitational force that the weight of an item would have as a result of its distance from the Datum.

Weight x Arm = Moment

Basic principles of mass and balance: What we are looking for is the CG, the distance from the Datum of the aircraft. To see if the CG is within limits for stable flight.

All units of measurement must be the same!

Calculation of the Basic Empty Mass and CG Position

In order to determine the Basic Empty Mass and CG position of an aeroplane the aircraft must first be prepared to the basic empty mass standard which entails removing all special equipment and usable fuel and oils.

The aircraft is placed such that its main wheels and the nose (or tail) wheels rest on the individual weighing scales which have been calibrated and zeroed. The readings on the scales are recorded as shown:

The Basic Empty Mass of the aeroplane is 4500 lb and the CG is 24.4 inches behind the datum (as shown by the positive sign).

The Basic Empty Mass is found by adding together the readings on the scales.

To find the CG position we need to take moments about the datum. In Mass & Balance terms a moment is a mass multiplied by a balance arm. Remember that arms (distances) forward of the datum are negative and a negative multiplied by a positive gives a negative value (see the nose wheel line above).

Notice in the example that each of the three entries above the line consist of a mass multiplied by an arm to give a moment. The entry below the line consists of a mass and a moment but no balance arm. The missing arm is the CG position.

To find the CG position the total moment is divided by the total mass. If the CG value is negative then the CG is in front of the datum otherwise it is behind the datum.

It is important to distinguish between mass and weight. Mass is the amount of matter in a body in kilograms and weight is the force that the matter exerts on the earth’s surface, in Newtons.

If the readings on the weighing scales are given in Newtons but the question asks for the BEM and CG position then it is necessary to convert the weight into mass to arrive at the right answer.

Example: Pilot 75kg, passengers 80kg and 50kg, 40USG of fuel and SW 6lbs per USG, baggage 15kg.

Total loaded aeroplane arm is our CG from the Datum, now we must enter it into the CG envelope of the aircraft to see if it is within limits.