the aircraft engineer march 27, 1931

7/27/2019 The Aircraft Engineer March 27, 1931

1/5

ch 27, 1931 Supplement to FLIGHT

ENGINEERINGSECTIONEdited by C. M. POULSEN

March 27, 1931CONTENTS

PAGEA Graphical Method of Stressing Aeroplane S par s. By D . Williams.B.S c, A.M.I.Mech.E 17Technical Featu res of the Air Mail, By Frank Radcliffe, B.Sc.,A.M.I.A.E., A.R.Ae.S 21Technical Lite ratu re ... ... ... ... ... ... ... ... 23

A GRAPHICAL METHOD OF STRESSING AERO PLAN ESPARS.B y D . WILLIAMS, B .SC. , A.M.I.Mech.E.

[Some time ago Mr. H . B. Howard of the Air Ministrydeveloped a graphical method of stressing aeroplane spars, thetheory of the method being described in R.


2/5

18SUPPLEMENT TOF L I G H T MA RCH 27, 1931THE AIRCRAFT ENGINEER

and equal to MH (if Mi, had been nega tive 2m ]t would havebeen in the opposite direction) and similarly k,m k in thedirection A'A and equal to M A. A t mB and mA erectperpendiculars to B JB and A !A respectively, which cut eachother at X . W ith OX as diameter draw a, circular arcjn uXm A. By shading in the space between the two arcsthe bending moment diagram is obtained.Suppose the moment at x ins. from A is required. Thelinear mea suremen t a; is converted int o an angu lar measure-men t by m ultiplying by 57 -3 [A, giving 5 7-3 \ix. Draw thevector OR, so tha t D ROA 1 = 57-3 [xx degrees : the requiredmoment is given by the intercept r1J"2 between the twoarcs. Where the arc k^ 2 is below the arc mAw,B, the momentis -f w ; where the reverse is th e case it is ve .It is seen that the two arcs intersect at two points, C x an dC 8. Here obviously the bending moment is zero, and,therefore, these points represent points of contraflexure onthe beam. The variation of the bending mom ent as thebeam is traversed from A to B is obtained from the diagramby swinging the v ector OR from OA 1 to OB1. At OA1 (Aon the beam) the moment = k t wA = MA and + ve . I tdiminishes to zero at c,, reaches a maximum ve value atOX, becomes zero again at C 2, and finally reaches a + vevalue equal to k% m I( = MB at OB1 (B on the beam).The end load P affects the shear, aa well as the bendingmoment in the beam, and the true value of the shear canalso be read off the diagram . Fo r example, the shear a tx in. from A, i.e., at OR in the diagram, is obtained by

measuring the length of the line joining r 2 , the point ofintersection of OR and the arc m AmB, to X, on the bendingmoment scale, and then multiplying the result by y..The ease of the single bay with more complicated loadingwill not be dealt with at this juncture, as the correct pro-cedure is fully covered by the following treatment of thecontinuous beam . In this treatm ent it will be found that forany p articular bay two diagrams are drawn ; the first enablesthe bending moments at the supports to be found, and thesecond is the actual bending moment diagram for the baybased on the end moments and other quantities found bymeans of the first diagram. W hen, therefore, it is desired todraw the bending moment diagram for a single bay in whichthe end moments are known, the procedure is to draw thefirst diagram as if the bay formed part of a continuous beam,and as if the end moments were unknown ; then to draw theactual bending moment diagram based on the known endmom ents an d the dat a obtained by means of the firstdiagram.

cLet C, B, A, be three consecutive supports of a continuousbeam . As in the ordinary theorem of three moments, themethod depends on finding an expression for the slope at B,firstly in terms of the bend ing m oments at A and B andknown constants, and, secondly, of those at C and B andknown con stants for th at bay . Eq uatin g the two expres-sions so found gives a relation between M A, MB and MWhen dealing with bays AB and BC, it is convenient toreckon the directions from A to B and from C to B positive,i.e., directions towards the common point B are + re.Before e qua ting th e tw o expressions for th e slope *'B it will,therefore, be necessary to change the sign of one of them.Once the values of the bending moments at the supportsare obtained, the actual drawing of the bending momentdiagram is a simple matter, as nothing but straight lines andarcs of circles enter into the construction.Probably the clearest description of the procedure can begiven by dividing it into three parts dealing with

I. Changes of spar loading and concentrated loads.I I . Changes of m omen ts of inertia of spar section.III. Combination of I and II.The table of da ta below is first prep ared . Each sub-bayis marked with a number, and the numerical suffixes to thevarious tabulated quantities denote the values of thosequantities for the corresponding bays, e.g., a3 is the valueof


3/5

MARCH 27, 1931THE AIRCRAFT ENGINEER

SUPPLEMENT TOFLIGHT

for : ub-bay 1. In the table, a positive or upward concen-tra> -d load " W " is marked with an arrow pointing in thatdirection, while an upward or + vedistributed loading " w "is denoted by placing a wavy line underneath the horizontalline joining CBA ; e.g., W2 is a + ^e concentrated load, andws is a downward or negative distributed load. It is assumedthat wJii^wJy.^, and M)v/(x22>we/ 22-In the 5th line of the table the length " a " of a sub-bayhas been converted into an angular measurement, or sub-sector, by multiplying by a factor 57-3[A. It is this angularmeasurement " a " in the polar diagram that correspondsto the linear value " a " on the actual spar.

obviously negative : hjit is therefore directed towards thenegative branch of h%. At h2 erect the perpendicular h2h3 =Ws/ni to take account of the concentrated load, and as W,this time is a downward or negative load, h2h3 is drawn tothe left of its boundary line Ji^h. At h3 draw the fourth andlast locus line K4, parallel to ll3, to cut B2B in Z4. Measurethe angle 6 which this last locus line makes with BXB. (Note.When there is no change of moment of inertia, all the locuslines make the same angle with B1B, aa in this case).

It will have been noticed that at each boundary line ameasurement along the line takes account of the change of" w," and a measurement perpendicular to the line takes

Consider the bay AB and refer to Fig. 1. With OB hori-zontal, draw the angle AOB = (aj + aa + a3 +


4/5

SUPPLEMENT TOFLIGHTMARCH 27, 1931

TH E AIRCRAFT ENGINEERBay CB.The diagram for this bay and the resultingequations are given without further comment, except topoint out that the angle (i will this time be assumed to be>90.

convenient scale, which will be retained throughout taeremainder of the construction). If w is an up-load, the arc(contrary to what might have been expected) will be drawnin the negative sector; if a down load, in the + ve sector.

1 s t e q u a t i o n : -f- l-J,t ZSZ3 + mB) ton 6 =

I * B | X |2nd equation :PiB -f- SB = f- RB, where RB

is now calculated from the loading in bay CB.If there were another bay CD to the left of C, the pointsD , C, B, would be treated in exactly the same way as C, B, A,have been, the total number of equations being equal to thenumber of unknown bending moments.Assuming now that the values of MA and MB have beenfound by the above method, it remains to draw the bendingmoment diagrams. Bay AB will be taken as an example.

For convenience these arcs will be called " loading arcs "and are marked k^k^, kjcv kjcs and ktkt in the figure.Suppose mA + veand JB ve. Lay off OWA and 0iB alongthe + ve branch OA and the ve branch OB1 respectively.Draw perpendiculars at mk and mB to give locus lines Uxandi/4(l) respectively (a second ll4 marked 11^(2) will presentlybe obtained). Having located point lv the pointsZ2, Z8and lt are inserted in the same relative position, in so faras their order and distance apart are concerned, as in Fig. 1,thus avoiding a repetition of the construction there used.At these points draw locus lines U2,'ll3 and llt{2) all parallel tollx. The point of intersection of ZZ4(1) and llt(2) gives theapex X4. At X4 draw a ||' to h3h\. of Fig. 1 to cut llsin Xs. At X, draw a ||' to g^ji of Fig. 1 to cut llt inX,. At X, draw a ||' to / J i of Fig. 1 to cut llt in Xx.

Referring to Fig. 3, draw the boundary lines as for Fig. 1. With 0Xx, OX2, 0X3 and OX4 as diameters draw circular arcsWith 0 as centre, draw in each sub-bay an arc of radius in the sub-sectors 1, 2, 3 and 4, respectively. It will beequal to the value of ic/n! for the particular bay (choosing a found that an arc will sometimes cut both the + ve and the


5/5

KA RCH 27, 1931THE AIRCRAFT ENGINEER SUPPLEMENT ft)FLIGHT

_ ;, branch of a sub-sector. Fo r convenience of reference Th e following is a list of th e prese nt charge s per 10 gramm esca_ these " cuttin g " arcs. The space between the loading ($ oz.), in addition to the ordinary postage from France.ai: cutting arcs for any sub-sector is shaded as shown. If y r British dti, cutting arc is above the loading arc (" ab o v e " meaning _ ' 'fu/ther towards the + ve branch of the sector) the mom ent *

r a n c e- i

r a< l *is ve ; if below, it is ve . Thus at the radius 0r x in sub- " T ersia ... ... 4ststor 3, the moment m-jn2 is + ve , as also are the mom ents " " T j m ' " 7V,. R

mim t at the radius Or s in sub-sector 4, and m 6m e at radius " -J-nao-Onina and biam b0r3in sub-sector 1. To read the bending mom ent at any point In all the above cases, the B ritish G.P.O., with its minimumin a sub-bay, all th at is necessary is to convert the distance of of half-ounce letters, und ertakes to carry letters under thethe point from its nearest su b-bay boun dary in to ang ular existing air-mail service at an equal or slightly less expensemeasurement by multiplying by 57 - 3 ^ (if y. is variable its from Eng land. The ac tua l surcharges are indicated invalue for the pa rticular point is taken ), and then draw ing a brack ets, and the franc can be reckoned as twopence,radius. The intercep t on the radius made by the loading (2) Continental System, also with a con tract extendingand cutting arcs gives the bending mom ent to the scale chosen, over 30 years : the maximu m ann ual subsidy being 391,220.The true shear at any point is obtained by first drawing the (3) Western System, divided into two subdivisions : theradius corresponding to the point, and then joining the point South American section, operated by the Aeropostale, andof intersection of the radius and the cutting arc to the apex a new comp any for the African section. Both have contractsX for th at sub-sector. The length of this joining line multi- for 20 yea rs.plied by th e app ropriate [X gives th e shear. If, looking along In all th e thre e system s, a shar e in th e cap ital is held bythe + ve direction of the radius, the line is drawn to the the State . An interesting accou nt of the technical aspectsright to m eet the apex, th e shear is + ve , while if to the left, it f the Sou th Am erican system is to be found in a p ape r byis ve . The reactions at the suppo rts are found in th at M. Grima ult, published in the R.Ae.S. Jou rnal for Novem ber,way. As exam ples, we hav e 1930, from which th e following notes are tak en :Tv, ,n l,. , >-, , -v w ~~ A i . ^ v The Fren ch claim, for 1929, th at on the rou te operatin giru e shear at Or, = m,X 3 X Ui and is + ve since wiiX. , , -.T . , 1T > . . , . , X U J I Jis drawn to the right between Na tal and Buenos Aires, the percentage of scheduledTrue shear at Or - m X v n and k ,,? sinre m X departu res was 94, and the percentage of arrivals less tha n. , , , , , (. J 4 n 3 4 4.3 ij OU I.8 j a t e n a ( j D e e n 82. On the Toulou se-Dakar section,is drawn to the leit. ,, ,. - ,_ . __TV Dv, t- n v w A v the correspond ing figures were 100 and 90 per cen t.Iru e shear at Or, = m .X , x u, and is ve since % X i mi , , , 6 . , .,, , . , * ,s drawn to th 1 ft Atlan tic crossnig is made with boats at present, bu t(T b I ded ) - soon it can be expe cted th a t flying-boats will be in service ;then, Buenos Aires will be within five days of Paris.In FLIGHT, May 16, 1930, will be found a description ofthe L at 28-3 seaplane, which has been designed for theA tlan tic crossing. I t is a single-engined all-metal mo noplan e,fitted w ith a 600-h.p. Hispan o Suiza, and has an all-up weightTECHNICAL FEATURES OF THE AIR MAIL. of 11,044 lb. and an em pty weight of 5,720 lb. CruisingBy FBANK RADCUFFB, B . S C , A.M.I.A.E., A.R.Ae.S. speed = 1 3 2 m.p.h and range = 2,500 miles. This typ eor machine was exhibited at the recent Paris Aero bhow.(Concluded from p. 14). An other bigger typ e, the La t 38 0, fitted with two HispanoSouth America Suiza engines of 650 h. p. each , in tan de m , has been recen tly' produ ced with a rang e of 2,200 miles. This is a flying-boatThe development of air services in Sou th America has resembling, in man y ways, Dornier type s, as it has stubbeen rapid during the last three years, and two American w m rr floatsfirms Pan-American Airways and the " N y rb a" (New F^om t t e a b o v e b r i e f a o c o u n t it will be evident thatYork, Rio, and Buenos Aires Line) have now combined in Fra nce is alive to the possibilities of air mail,

an endeavour to capture as much of the South Americantrade as "possible from the ir ma ny com petito rs (see Map II ). Germany.There are no British air lines operating in South America Flying is done by the Luft Ha nsa , and very full detailsat the presen t tim e. Fulle r pa rticu lars of these 18,217 miles o f Germany's air developments are to be found in two papersof scheduled air routes, flying 80,868 miles weekly, will be b y M a j o r Wronsky, read before the R.Ae.S., and publishedfound in FLIGHT, Sep tem ber 19, 1930. This consolidation i n t n e J o u r n a i 8 f o r July, 1927, and October, 1930.of air lines is extremely interesting, and its developments in T h e p a s t y e a r h a s s e e n a condensing of the air lines inthe future a re worth y of careful notice. There is now a Germ any, and ma ny which were less imp orta nt have beenweekly air mail service to and from the principal U.S . cities deleted. The following ta ble ind icates w hat Germ any hasand Buenos Aires and Montevideo. been doing during the pa st few years :West Indies K g - 1 9 2 6 - 1 9 2 7 - 1 9 2 8 " 1 9 3 -Total mail carried 188,214 274,073 317,588 366,845Jamaica s first British Air Mail Service was inaugu rated T o t a j fre ight carried 258 ,464 641,186 1,023,206 1,198,790on Decem ber 10, 1930, and comp rises p ar t of a 33-hour air To tal km . flown 6,141,479 9,208,029 10,217,528 9,087,694mail service between Jam aica and Mo ntreal. Holland.Trance. ( /S ee M a p I n )There were four principal air-operating companies in T h e r e f tre t w Q s e c t i o n s o f t h e D u t c h a i r j ^ g . K .L .M. ,France : Air Union, Far ma n A ir Lines, Air-Orient and the o p e r ating from Holland as the base, and K.N.I.L.M., whichAeropostale. These have now been grouped into three sys- o p e r a t e s m the Dutc h-E ast Indies. A full account of thei/ems : activities of these two services are to be found in two articles(1) Eastern System, with a contract extending over 30 years , by Mr. M. Langley, appearing in FLIGHT for Jan ua ry 9 and 16,The subsidies to this com pany are, 1930 450,000 ; 1931 1931. The Du tch service to the Eas t Indies is proving a rival600,000, w ith gradu al reductions in subsequen t years, to the Fren ch line, which also goes to the Fa r Ea st. Fok kerAir lines exte nd from Marseilles to Ita ly , Greece, Syr ia, Ir aq , aircraft are used e xclusively, an d it is inter estin g t o n otePersia, K arach i, C alcutta, Burm a, Rangoo n, and on to th at they are all land 'planes. The Du tch air service is theSaigon in Ind o-C hina . most econom ically sound in Eu rop e, for its subsidy is onlyThe service Bag hdad -Bang kok -Saigo n is at present 3 francs per kilometre, as against Fra nce , 17 francs ; German y,' peratin g on a fo rtnig htly time -table , and is reserved for 14 francs ; U.S.A., abo ut 11 francs . British air lines receive. ostal traffic only. the highest subsidies, abo ut 20 francs on Europ ean Airways,

272*

the aircraft engineer march 27, 1931

Documents