So far we have considered the aeroplane as flying straight and level. Obvi-ously this is not always so, and since we have already said that we wish to consider it as a free body at rest under the influence of the system of bal-anced loads and reactions, we need a system for recognising the forces which accompany a manoeuvre, which is the name for any disturbance of straight and level flight.
Firstly, we must be convinced that a manoeuvre always involves accel-eration. Imagine, for instance, an aircraft flying due north which then turns 90° and heads due east. Before the turn the aircraft had no speed towards the east but after making the turn it has some speed towards the east, therefore between the two conditions it must have received an accelera-tion. To achieve this acceleration a force was applied to the aircraft which Fig. 4.5 Distribution of lift.
had to be resisted by the structure. A phenomenon which is familiar to all of us illustrates a method of introducing these accelerating forces into the free stationary body idea. Imagine being in a passenger lift or elevator;
just by eye we cannot tell whether or not the elevator is moving. In fact, if it is moving at a steady speed, it is difficult for us to tell from the load in our legs whether the elevator is going up or down. It is only when the elevator stops or starts that the positive or negative acceleration appears to change our weight and and the load in our legs is altered. If the eleva-tor is accelerating upwards the load in our legs is greater because the inertia forces in our body act in a downwards direction. (Inertia is the resistance of a body to any change in its motion. If the body is standing still, it requires some external effort to move it; if it is moving, it will con-tinue to move in a straight line and will resist the force needed to stop it or change its direction.) This is just another instance of the action and opposite reaction rule. In this case, acceleration or accelerating force acts one way and inertia the opposite way.
The analogy with the elevator is easy to understand when acceleration is up and down, and because we cannot see outside the elevator it is easy to accept the free stationary body idea. When the acceleration is hori-zontal, finding an analogy is more difficult. While travelling at a steady speed on a smooth road in a motor car, it may be difficult to admit that the loads acting on our body are exactly the same as if the car was sta-tionary, but they are. The loads only change during acceleration away from a stop (positive or forward acceleration); during deceleration by braking (which is negative acceleration or the same as rearward acceleration); or during sideways acceleration when turning a corner. Again the ‘accelera-tion one way, inertia the other way’ rule applies, so that, if the car turns to the left, some force (the action of the front-wheel tyres) has acted to the left and accelerated the car the same way, but the passenger has to restrain himself from being thrown to the right.
The essential point in the above discussion is that when the elevator or the car either stops or starts or changes direction (that is, manoeuvres), the passenger’s weight appears to increase in the opposite direction to the force directing the acceleration. This is always so. Do not be confused by the apparent contradiction of this truth when the passenger lift starts to descend. The situation then is that the acceleration in the downwards direction is small and although the passenger’s weight does increase in the upwards direction the increase is not enough to completely overcome his normal weight due to gravity. If the acceleration downwards became great enough, the occupant of the lift would need to push upwards on the roof to keep his feet on the floor and the greater the acceleration the harder the push would have to be. In an aircraft the same situations apply, and structural engineers deal with them by saying that during a manoeuvre the apparent weight of everything in the aircraft is increased by a factor (n) of the weight due to gravity (g). In some cases the factor n is deter-mined by calculation but usually a figure is specified by government
legislation working through its own Airworthiness Authority. (See the note in Fig. 4.6 for the various names given to n.)
4.2.1 Using V–n diagrams
The presentation of the Airworthiness Requirement for the inertia factor or load factor is usually by the V–n diagram, which is in a form shown in Fig. 4.6. Working from the European Aviation Safety Agency (EASA) Certification Specification 25 paragraph 337 (CS-25.337) for aeroplanes with a maximum take-off weight of 5700 kg (12 500 lb) or greater, for an aircraft weighing 22 690 kg (50 000 lb) or more n is 2.5 and for an aircraft weighing 6350 kg (14 000 lb) n is 3.1. Figure 4.6 describes a manoeuvring envelope and particular combinations of speed and load within the lope are called Cases. A similar V–n diagram, which describes a gust enve-lope, is used to present Airworthiness Requirements of the effect of air currents likely to be met by the aircraft. The air currents, or gusts, have an accelerating effect and increase apparent weights in exactly the same way as ordinary manoeuvres; they may also operate in any direction and in general they become more and more severe with higher speeds.
Fig. 4.6 V–n diagram (the manoeuvring envelope).
4.2.2 Emergency alighting loads
Another group of load factors specified by Airworthiness Authorities are the crash loads or emergency alighting loads. In the current issue of the EASA CS-25 for large aeroplanes these are required to be from nine (9) times g forward to 1.5 g rearwards, 6 g downwards to 3 g upwards and 3 g sideways. Helicopters and light aeroplanes have somewhat different sets of inertia requirements quoted in the appropriate certification specifi-cation. This method of specifying the loads along three axes mutually at right angles raises a further interesting point. Inertias are not always so conveniently applied and the section of the now obsolete British Civil Airworthiness Requirements which dealt with emergency alighting insisted that the prescribed loads should be taken as acting together, although the combined load need not exceed 9 g. Bearing in mind the random nature of emergency landings (such as ‘wheels up’ in a ploughed field) and the consequent random directions of the imposed loads, the BCAR principle does not seem too ridiculous. It is sometimes asked why a particular figure (such as 9 g) is set, the arguments being that the normal passenger travelling in an aircraft would be unable to withstand the effects of a 9 g deceleration and therefore the requirement should be set at a lower figure; or alternatively that by increasing the requirement to 12 g and ensuring a stronger structure, more passengers would survive a crash.
These arguments might well be true, but a figure must be set somewhere and the Airworthiness Authorities consider carefully the statistics avail-able and apply their expertise before fixing a factor at a certain level. Like most aspects of aircraft design, there is an element of compromise involved. It would be easy to set a figure which produced a very strong, safe aeroplane that was too heavy to fly, and the figure chosen is a balance of careful thought with the bias, no doubt, on the side of passenger safety.
Some of the arguments used in choosing a figure are set out in Tye’s Handbook of Aeronautics.
In case this question of load factors is not absolutely clear, we will con-sider the specific example of a piece of equipment bolted down to the floor of an aircraft and subjected to the emergency alighting conditions men-tioned above. If the piece of equipment is a rectangular box of 10 lb weight, to satisfy the requirement of 4.5 g downwards the floor will have to be strong enough to support 45 lbf (read forty-five pounds force) pushing down, i.e. 10 ¥ 4.5 g. (Note that 4.5 g is just a factor with no dimen-sions but it does alter a weight to a force.) Similarly, the 9 g forwards requirement means that the attachments must resist 90 lbf parallel to the floor. If we are working in SI units the arithmetic is slightly more compli-cated. A weight of 1 kg at an acceleration of 1 g produces 1 kgf (read one kilogramme force) but since the unit of force in SI units is the newton, we must convert. (The conversion factor is 1 kgf = 9.81 N.) So
therefore
7kg at 2.25 g=15 75. kgf
For a quick and rough calculation use a factor of 10 and say:
(Another useful conversion factor is 1 lbf = 4.45 N.)