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Aviation History
1949
1949 - 1470.PDF
234 FLIGHT AUGUST 25TH, 1949 Joy Through Strength A Simple Treatment of the Use of Load Factors in Aircraft Design By S/L F. S. BLOOMFIELD, M.A., A.M.I.O.E. WHILST ignorance might not be actually blissful, itis frequently comfortable in the sense that know-ledge may make one somewhat uneasy. Pilots who, with care-free elan, chase about the sky in all manner of curious evolutions, generally have but a hazy notion of the forces imposed on their aircraft during such manoeuvres; which is, perhaps, as well for their peace of mind. Never- theless, for those who occasionally do pause to consider how strong an aircraft has to be, some broad considerations of load factors may well be of interest. During manoeuvres such as turning, looping, pulling out of a dive and so on, the wing lift is considerably greater than that in normal horizontal flight. In point of fact, when an aircraft is pulled out of a dive, the lift might well be five times that experienced in straight and level progress As a consequence, the loads on the various members of the airframe will be considerably increased, and allowance is made for this increase during the design stages. For the purpose, what are known as load factors are employed. The principle is essentially simple. Considering an aircraft of 1,200 1b all-up weight pulling out of a dive at 300 m.p.h. and so flying along an arc the vertical radius of which is 1,500ft, the laws of centrifugal force show that there must be a net force of lb acting through the aircraft towards the centre of the arc, where w == weight of aircraft, lb v = speed, ft/sec r = radius of arc, ftg = acceleration due to gravity = 32.3ft/sec/sec This force toward the centre of the arc is translated as increased lift by the wings which, in addition, must also support the weight of the aircraft, .Mift = =r? I2OO X = 1200 + 60 32.2 x 1500= 1200 -j- 4810 = 6010 lb It is thus seen that, during pull-out from this dive, the apparent weight of the aircraft has increased some five times. It should, however, be noted that the acceleration toward the centre of the arc is actually qg, as the true weight of the aircraft is, of course, essentially constant due to the pull of-gravity. Method of Calculation To allow for such increased loads on the airframe members, the designer first determines the loads the members will have to carry in normal flight—i.e., with lift equal to weight—these being termed the basic loads. The basic loads are then multiplied by 5 to cater for such a manoeuvre as described, and then are further multiplied by 2 to provide a factor of safety, i.e., x 10 in all. The component, if a tension member, is then designed to a stress equal to the ultimate tensile stress of the material. Referring back to our example, the load of 6,010 lb would be termed the design load for this manoeuvre, and the factor 10 is the ultimate load factor, thus the design load = basic load x ultimate load factor. The factor of safety of 2 is introduced to cover possi- bilities such as material not being up to specification, defective workmanship, unauthorized manoeuvres and so forth, and although at first sight it may be thought that this is an unduly high allowance, it should be remembered that a usual factor of safety in general engineering is 4— but in special cases even higher. To use such a factor of safety as 2 is, figuratively speaking, skating on rather thin ice, and is made possible only by the imposition of a very strict system of inspection, both of materials and workmanship. The ultimate load factor may be defined as the ratio of a component's breaking load to the load in normal hori- zontal flight. Once again, example may clarify the situation. It can be assumed that in pulling out of a dive, the lift on the wings is equivalent to 7 times the normal all-up weight of the aircraft. It may also be assumed that the basic load on a particular bracing wire is 200 lb, whilst the ultimate tensile strength of the material is 60 tons sq in. It is required to calculate the minimum cross-sectional area of the wire : Ultimate load factor = 7 x 2 = 14 Design load = 200 x 14 = 2,800 lb breaking loadCross-sectional area = ultiniate tensile stress 2800 sq in2240 x 60 = 0.0208 sq in It is, however, not sufficient to limit the calculations to a determination of the minimum size of wire to avoid fracture. Consideration must also be given to the possi- bility of the wire becoming permanently stretched due to the yield stress or proof stress of the material being exceeded. This introduces the proof load factor. Redesigning' a wire In the last example, the actual load on the wire during the manoeuvre would have been 200 times 7 lb and the 1400 stress lb/sq in = 30 tons/sq in. If the yield stress or 0.1 per cent proof stress of the material were less than 30 tons/sq in—say 25 tons/sq in—it follows that the wire would be permanently stretched as a result of this man- oeuvre, and the airframe thus become distorted. Such permanent stretching is dangerous as it imposes extra loads on other members of the airframe. In order to preclude this sort of thing occurring, the wire is re-designed as follows : Actual load on wire '— 200 x 7 — 1,400 lb Factor of safety = 1$ , . actual load x il Area of wire = -c • proof stress 1400 X \\ sq in 2240 x 25 = 0.0375 sq in The second factor of safety of \\ is employed to cater for the possibility of the aircraft being called upon to carry out unauthorized manoeuvres—a not uncommon occurrence in war-time. In the second calculation, the proof load factor (10 J) was obtained by multiplying first by 7 and then by ij. Since the second factor of safety (1 \) is \ of the first factor of safety (2), it follows that the proof load factor = \ of the ultimate load factor. Had the yield stress or proof stress of the material been f of the ultimate tensile strength (i.e., § of 60 = 45 tons/sq in), both calculations would have produced the same result, viz., 0.0208 sq in. If the yield stress had, however, been greater than f of the ultimate tensile stress, the design would necessarily have been dependent on the ultimate tensile strength. Calculations may further be simplified if the proportion between yield stress and ultimate tensile stress is first determined, for it is then necessary only to do one calculation. A moment's consideration will make it clear that certain B 28
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