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Aviation History
1929
1929 - 0864.PDF
34 TO FLIGHT APRIL 26, 1939 THE AIRCRAFT ENGINEER might expect, take the three examples quoted by Mr. Parkin- son, viz., a £-in. diameter bolt in material having/, = 30 tons/ sq. in. and/, = 25 tons/sq. in., and a f-in. diameter bolt in material having f, = 55 tons/sq. in. The results as found from the table are quoted as 13,194 lbs., 10,995 lbs., and 13,607 lbs. The corresponding values as deduced from the nomogram are 13,250 lbs., 11,000 lbs., and 13,750 lbs. respectively. This gives an error of the order of 1 per cent, in the worst case, which should satisfy the most fastidious of detail designers engaged on aircraft work. Although the nomogram is by no means a new method of plotting data it is, in the experience of the writer, regarded by the majority of aircraft draughtsmen as a mysterious affair requiring a highly developed mathematical knowledge for its construction. This is not a fact, and the attitude towards the nomogram is all the more peculiar, bearing in mind the general average facility with which draughtsmen manipulate the slide rule. Perhaps, under these circumstances it would not be out of place here to add a few general remarks on nomography, and to describe, in some detail, the construction of the nomogram accompanying these notes. Nomography was first introduced into this country by Ideut.-Col. R. K. Hezlet, R.A., in 1910, and three years later SlOO, he presented a short treatise on the subject, which" was published by the Royal Artillery Institution, Woolwich. For those readers who may evidence any further interest in the subject one can recommend a study of the text-book " Line Charts for Engineers," by Rose, and the pamphlet "Logarithmic Scales," by Newby, the latter issued by the Association of Engineering and Shipbuilding Draughts- men. Only one side of the nomogram herewith, that referring to shank properties, will be considered, as this diagram virtually consists of two nomogramfi—one on each side of the stress scale—the principles involved being the same for both sides. First it is necessary, from a knowledge of the variables which we wish to connect, to plan the layout of the nomo- gram, and this we must do with an eye to compactness and facility of operation. It is generally, but not necessarily so, an aid to operation to arrange for the scale for the derived quantity to lie between the two scales for the given quantities. In the case under consideration then, the load scale is em- braced by the stress scale and the bolt diameter scale. The spacing of these two latter scales is also a matter of choice and convenience, and their graduation is logarithmic, being taken direct from an ordinary standard 10-in. slide rule. The stress scale is based on a 10-in. logarithmic scale and bears a direct notation, i.e., the graduation marked 40 tons/sq. in. corresponds with the 4 graduation on scale D of the standard 10-in. slide rule, 80 tons/sq. in. with the 8 graduation, 15 tons/sq. in. with the 1-5 graduation, and so on. The bolt diameter scale is based on a 5-in. logarithmic scale and bears an indirect notation. It is graduated according to the full area of the bolt, but the notation is referred to the bolt diameter. Hence, the division marked \ in. corre- sponds with the 4-91 graduation on scale A of the standard 10-in. slide rule and not with the 2-5 graduation, the full sectional area of a J-in. diameter bolt being 0-0491 sq. ins. Again, the division marked \ in. corresponds with the 19-63 graduation on scale A of the slide rule and not with the 5 graduation, the full sectional area of a £-in. diameter bolt being 0-1963 sq. in. And so on. The arithmetical operation which we wish to perform is represented by the formula W = 2240/A where, W = the failing load of the bolt, in lbs. / = the stress, in tons/sq. in. A = the cross-sectional area of the bolt in sq. ins. However, the basic data given are usually the stress and the bolt diameter, hence, in constructing the nomogram we must use sectional area, but in using the nomogram wo employ bolt diameter. This accounts for the apparent complication in the bolt diameter scale. We now have to determine both the position and the graduation of the support, i.e., the load scale. First the position. This is fixed by what are known as the upper and lower datum points. Briefly, we have to determine two combinations of / and A giving a low value of W, and two other combinations giving a high value. Thus, (i) f-in. diam. with 10 tons/sq. in. gives W = 9,900 lbs. (ii) i-in. diam. with W = 9,900 lbs. givee / = 90 tons/sq. in. and (iii) 1-in. diam. with 40 tons/sq. in. gives W=70,368 lbs. (iv) |-in. diam. with W = 70,368 lbs. gives / = 71 • 11 tons. sq. in. The lower datum point is defined by (i) and (ii), and the upper datum point by (iii) and (iv). The application is illus- trated in Fig. 1. Actually it is sufficient to calculate one datum point only because it is proved mathematically that formula of the nature of the one with which we are dealing give nomograms comprising three parallel rectilinear scales. It would be in order, therefore, to determine one datum point and draw through it a straight line parallel to the other two scales. The determination of the second datum point, however, provides a useful check at this stage on the graduation of the other two scales, as any error therein will result in a support which is non-paralleL Now for graduation. It is required to fix two values on the load scale giving a reasonable range. It would be in order to use the two datum points previously calculated, but personally one prefers to use round figures. Taking the stress at 35 tons/sq. in., then, a 2 B.A. bolt will earn' 2,100 lbs., and a f bolt will carry 24,000 lbs. These two points are determined on the load scale, and their intercept thereon is referred to a master logarithmic scale to obtain the entire graduation of the load scale. This is accomplished as follows. Lay out from the slide rule the master scale, see Fig. 2, and at some convenient, distance from it, and parallel to it, draw a straight line as a support to bear the load scale. Transfer to any convenient position on this support the intercept from the nomogram, as previously determined. Connect, by straight lines, the limits of this intercept with the corresponding values on the master scale, and extend these lines beyond the support until they intersect in the origin 0. Straight lines drawn between the master scale and this origin will cut the support in a number of points, thus giving the appropriate reduction of the master logarithmic scale. This can finally be transferred to the load support of the nomogram. RG.2 338;
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