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In this essay two key parameters that influence the design of turbofan powered transport aircraft: the thrust to weight ratio and the wing loading, will be considered. The author will briefly explain what these parameters are and what major factors determine the values. By way of assimilating the evidence into a tangible example, the author will discuss in detail the effects of thrust to weight ratio and wing loading in the design of the Boeing 767.
An aircraft has four forces acting upon it in flight: lift, weight, thrust, and drag, each having both magnitude and direction. The motion of an aircraft during flight is dependent upon the relative magnitude and direction of these forces. An aeroplane's weight is determined by its size, the materials used in its construction, and on the payload and fuel that it carries. Thrust is established by the size and type of propulsion system employed, as well as the amount of 'throttle' being used by the pilot. Weight, by virtue of gravity, acts directly towards the centre of the earth whilst thrust generally acts forward along the centre line of the aircraft. Lift and drag, although not predominantly being discussed in this essay, are aerodynamic forces and are dependent upon the shape and size of the aeroplane and the flying conditions. Lift is directed perpendicular to drag, which is directed along the flight path. It is widely understood that aerodynamic efficiency is dependent upon a favourable lift to drag ratio. It is equally accurate to state that the efficiency of aircraft propulsion depends on the ratio between thrust and weight.
Derived from Newton's second law of motion for constant mass, force is equal to mass times acceleration. Considering thrust as force, and mass as weight divided by gravity, it can be determined that the thrust to weight ratio (T/W) is directly proportional to the acceleration of the aircraft. T/W is often quoted as the powerplant sea level static thrust (the maximum thrust the engine will produce) divided by the aircraft gross weight (the maximum weight of the aircraft). It will, in fact, vary throughout the flight as thrust varies with throttle setting, speed, altitude and temperature and weight changes with fuel burn and changes of payload.
Wing loading (W/S) is described as an aeroplane's gross weight (W) divided by the gross wing area (S). Again weight, and therefore wing loading will vary throughout the flight . Wing loading reflects the aircraft's lift-to-mass ratio, which will influence its rate of climb performance, its load-carrying ability, and its turn performance.
In simplistic terms, lift is generated from the to the motion of air over a wing surface. The larger the wing, the greater the movement of air. Therefore, an aeroplane with a large wing area relative to its mass i.e. low wing loading, will have a greater amount of lift at any given speed. It can therefore be stated that an aircraft with a lower wing loading should be capable of taking off and landing at lower speeds or be capable of taking off with a greater payload. Its rate of climb figures will also be superior than those of a higher wing loading aircraft because less additional forward speed will be required to generate the additional lift. Cruising performance should also be good as less thrust would be required to maintain lift during sustained flight.
Manoeuvring performance of an aircraft is also largely determined by the wing loading. In order to turn, an aeroplane must roll in the direction of the turn, increasing its bank angle. When banking a wing becomes less effective at producing lift and the aircraft nose moves downwards, inciting a rudder input to keep the nose level and increasing drag as a consequence. Also, to maintain height during a turn, there is an increased wing angle of attack which creates even more drag. The harder the turn that is attempted, the greater the drag on the aircraft. This in turn necessitates the addition of greater thrust in order to overcome the increased drag. The maximum rate of turn possible for any given aicraft design is therefore limited by its wing size and the thrust available from its engines. Aircraft with a low wing loading tend to have better sustained turn performance because they are able to generate more lift from a given amount of thrust, however there is a trade-off insofar as a large, lightly loaded wing will have greater inertia and mass and will create more drag during banking. A small, highly loaded wing will have greater instantaneous turn performance, but will lack the ability to sustain a tight turn. It can therefore be deduced that a larger wing, which will also be thicker, will generate more drag than a smaller one, and drag reduces aircraft acceleration, especially at supersonic speeds. Conversley a small thin wing will be better suited for high speed flight because it will have less drag, however, as discussed it will have the penalty of higher take-off speeds and reduced turning performance.
Gust response is also a characteristic affected by wing loading, a large lightly loaded wing may be susceptible to a rough punishing ride compared to the smooth ride offered by a small highly loaded wing which would be less effected by turbulence. This is however is not a critical concern where the wing loading is above 340kg/m sq.
The introduction of any new airliner is only ever borne of necessity, and in most cases that necessity is financial. In 1982 the twin-engine Boeing 767-200 was introduced as a new-generation replacement for the ageing Boeing 707, primarily for flights of medium and short-range stage lengths although maximum range is much greater and in extended range (ER) guise. The 'ER' is now the dominant airliner on North-Atlantic routes, making more flights between North America and Europe than any other airliner. The design of the aircraft incorporated improved fuel efficiency and careful matching of range and payload capabilities. Fuel efficiency of the 767 and the low cost-per-seat-mile is mainly attributable to the use of 2 high by-pass (ratios between 4.5 and 5) turbofan engines, although careful aerodynamic design, as would be expected after some 25,000 hours of wind-tunnel time, also has a significant impact on fuel efficiency.
From table 1 it can be seen that the thrust to weight ratio of the 767-200 was increased for the ER following the introduction of higher powered engines, thus fitted with two Pratt & Whitney PW4062 turbofans, each producing 281.6 kN the thrust to weight ratio became:
MAX THRUST /GROSS WEIGHT = 3.14 N/kg
This compares favourably to the four engine 707-320B which, when fitted with Pratt & Whitney JT3D turbofans, each producing 80.1 kN has a thrust to weight ratio of 2.1 N/kg.
767-200 Short/med Range
767-200 Extended Range
280 m sq
283.35 m sq
283.35 m sq
152 400 kg
142 881 kg
179 170 kg
4 x 80.1 kN = 320.4 kN
2 x 213.5 kN = 417kN
2 x 281.6 kN = 563.2 kN
12 223 Km
544.3 Kg/m sq
504.3 Kg/m sq
627.9 Kg/m sq
From table 1 it can also be seen that the wing areas of the 707 and 767 are almost identical, however, with its higher gross weight, the 767 has a greater wing loading than the 707. Further extensions to the 767 family have pushed up the gross weight further and on the later 767-300 and 400 ER models the wing loading is significantly greater, although new wing tip designs have served to alleviate the problem by creating a greater surface area and a subsequent reduction in wing loading.
Extending the range of the aircraft does sacrifice the passenger capacity in favour of fuel contents, with the 767-200ER having room for 255 (max) in its passenger cabin whilst its non-ER stable mate has a max capacity of 290 on board. However, these both eclipse the less fuel-efficient 707, which has a maximum passenger capacity of 189. The performance characteristics of the 767 are, not surprisingly, a vast improvement to the older aircraft. The 767-200 with similar wing loading, but far superior thrust to weight ratio has significantly shorter takeoff and landing field lengths than the 707 enabling it to utilise smaller provisional airports. The aerodynamic configuration of the newer 767, particularly the ER leads to slower cruise speeds than its older relative, but the sacrifice in speed is more than compensated by the savings in fuel consumption. On short to medium haul flights, a minor decrease in speed is of no discernable difference.
It can be extrapolated, therefore, that the 767 was initially designed to haul lots of passengers on short to medium range domestic routes, in contrast to it's predecessor, the 707, which was almost identical in size and weight but was designated as a long-range airliner. The ER progression of the 767 retained many of its original attributes, but at the expense of passenger capacity, until that is, the inception of the 300 and 400 ER series.
Advancement in technology has enabled aircraft and engine manufacturers to produce far more efficient aircraft. The thrust produced by modern turbofan engines and the improvements in aerodynamic design serve to make it an uneven playing field when comparing the old to the new. However the parameters of thrust to weight ratio and wing loading can still clearly be seen in the design process, and the continual development of the 767 series. High thrust to weight ratio and relatively low wing loadings give the required take-off, landing and cruise characteristics. Extending the range capability of the 767 has resulted in heavier aircraft and necessitated the need for more powerful engines to maintain the thrust to weight ratio and to compensate for the increase in wing loading. This will have some adverse effect on the turning characteristics of the ERs, but with improved aerodynamic design and restricted flight parameters they are maintained within acceptable limits.