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The Aircraft Engineer: Tlesultant B.M

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91

DECEMBKK 26, 1930 SUPPLEMENT TO

THE AIRCRAFT ENGINEER


Equations to be Used
Sin 9K = sin 0A cos 67 9 sin < | > (1) A sin 67 9 MA cos 20-9 - T A sin 20-9 + MK cos 47 = 23,150 . . . .(2) MA sin 20-9 + T A cos 20-9 MK sin 47 + 1 17 Po = 27,550 (3)

FLIGHT

37-27 ' 51-27 Sin 6R, sin 0A. and sin A must be determined in terras of the bending moments and torsions. Before sin 0A and sin 6E may be estimated, approximate end loads in the members must be found. Assume TA = 0 From (2) Subst. (4) 0-934 M, + 0-682 MK = 23,150 M A = 24,800 - 0 - 7 3 0 MR.

0-5794 P o = 5.440 +

MA - M'A

MR

(4)

0-5794 Po = 5,440 + 665 0-0196 M + 0-0195 M = 6,105 Po 10,540 approximately applied loads at B are Along BF = + 2,000 430 = + 1,570 Along BE = - 4,390 + 8,570 = + 4,180 By the triangle of forces Po = 4,400 T and P = 0. For end loads due to the couple about the z axis, ignore 0-0188 TV The net couple is 30,980 10,540 X 2-312 cos 20'9 = 8,180 in lb. This must be taken entirely by the axle. The shear in the axle is 8,180/37-27 = 220 lb., and must be balanced at B by end loads. By a simple triangle of forces Po = 90 T and P = 230 C. Net loads are Po = 4,400 + 9 0 = 4,490 T. 220 = 220 C. Pu = To estimate dyjdx for the axle (2\ in. X 16 SWG x: T-2). P 4,490 - 0-000679 .-. [j. - 0-0261 6 m 30 x 10 x 0-2203 0-972
dy dx

Substituting in (3) and (4) 1-778 MA + 1 1 7 Po = 61,500 0 069 MA - 5-79 Po = 59,550 0-069 MA + 0-04 Po = 2,390 - 5 - 8 3 P o = -61,940 Po = 10,620 MA= 27.600 in Ib. TA = 4,490 in Ib. . M K = - 1,530 in Ib. The maximum bending moment in the axle at B will be the resultant of the bending moment just found and the bending moment due to C's. i.e., MA max. = v ^ G O O 2 + 8,1802 = 28,780 in Ib. The position of maximum stress is 6" inside B. To find the bending moment at this point 31-27 Vector perpendicular to plane = 8,180 X 37-27 + 4,490 x 0-0188 X = 6,870 in lb. 31-27 = 28,780 X 3 + 4,490 X 0-0569 X = 24,170 in lb. = v/24,170 2 + 6,870* ^ 25,130 in lb. = 1/2(25,130 + N/25 = 25,520 in lb. 25,520
0-2073 X 2,240 37-27 6 37-27

Vector in plane

tlesultant B.M.
The equivalent B.M.

4.4902)

Stress

0-0261MA x 1-50 4,490 X 1-125 M A - 0 - 0569 TA 1 37-27 :K 4,490 6 = 0-294 TA x 1 0 - " r-75M " A x 100 0261 x 0-056 9TA 4,490 x 1-125 + 5-97 MA x 1 0 - - 0-340 T,k X l 0 - " = - 1-78 MA x 10- B - 0-046 TA X 1 0 - 6
6

4,490 0-414 x 2,240 = 59-8 tons/sq. in. Note.The vertical lines in margin indicate work which applies to all cases of stressing, i.e., it is done once only for each undercarriage. TECHNICAL FEATURES OF THE AIR MAIL.
By FRANK RADCLIFFE, E . S C , A.M.I.A.E., A.R.Ae.S.

To estimate dyjdx for the radius rod (2" ojd x 17 SWG).

Ignoring the end load dy _ 51-27 x 2 MR


dx 6 x 30 x 10" x 0-1616 To estimate sin (JJA for the axle. 1-25 x T x 37-27 (j>A radians = 30 x 10" x 0-2691

3-52M R xl0- 6

5-76 TA x 1 0 - ' the values of =0 =23,150 = 27,550 = 54,400 (1) (2) (3) (4)

Re-writing the equations and substituting sin 0R, sin 8A, and sin < } > , A 0 - 6 7 0 M A - 5 - 3 1 T A - 3 - 5 2 MR 0-934 M A - 0 - 3 5 7 TA + 0 - 6 8 2 MR 0-357 MA + 0-934T A - 0-731 M R + 1-17 Po 0-268 MA - 0-015 TA + 0195M R - 5-79 Po From (1) MR = 0-190 MA - 1-51 TA From (2) 1 -064 MA - 1 -39 TA = 23,150 TA = 16,650 + 0-765 MA MR = + 25,170 - 0-966 MA

(Continued from p. 84.) Visitors to the Paris Aero Show, and readers of FLIGHT'S report on the Show, will, doubtless note the similarity between the retractable undercarriage used, on Mr. Radcliffes design this month and that fitted on, the Bleriot 111. Lest there should be any tendency to accuse Mr. Radcliffe of " copying," we think it is only fair to state that the design shown in Fig. V was in our hands before Mr. Radcliffe could possibly have known of the Bleriot machine, so that if there are points of resemblance, they are due to two designers thinking alike, arid not to wilful copying on the part of Mr. Radcliffe. In any case, we do not know what are the details of Mr. Radcliffe's retractable undercarriage design, and it will most probably be found that they are very different from those of the Bleriot monoplane retractable, undercarriage. While on the subject of the retractable undercarriage, it is of interest to note that Mr. Radcliffe comes to the conclusion that by fitting it, and slightly reducing the wing area, an increase in top speed of no less than 22 miles per hour is achieved, which corresponds to a redaction in petrol at cruising speed of 23 gallons, or put in another way, an increase in range from 750 miles to 860 miles. Or, if the saving in fuel were used to carry extra pay load, this would be increased from 1,000 Ib. to 1,1801b. V.Design for a Mail-plane. It was stated in the last article that a cruising speed of 150 m.p.h. was possible with an orthodox type of aeroplane

1484c

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