details can be seen in the photograph , fig 4 . during the early part of the tests the rotors were run at 1,800 r.p.m , at which speed the radial acceleration was approximately 2,350 g , resulting in very high forces at the hub . the blades were provided with both flapping and drag hinges , the former being freely mounted on ball races and the latter having adjustable cork friction dampers . the blades were found to vary slightly in weight so provision was made for final balancing by means of small adjustable weights on screwed rods radiating from the hubs between the blades . these can be seen in the photograph , fig 4 . in order to avoid the possibility of resonance it was at first thought advisable to run the rotors with drag hinges locked . eventually however fatigue cracks were noticed in the roots of two of the blades and it was suspected that the lack of freedom in the drag hinges was the possible cause . later , after new blades had been fitted , it was thought better to run with drag hinges free and so reduce root stresses , experience having shown that the possibility of resonance was small . as a further precaution , to eliminate fatigue failure , the new blades of a modified design were run at a reduced top speed of 1200 r.p.m . this question of blade fatigue is more fully discussed in the appendix . 2.3 . equipment for measuring tracking of blades and flapping angle . the front rotor carried a commutator with a single brass segment contacting four carbon brushes mounted on a ring attached to the front rotor spindle housing . three of these brushes were approximately 120 &amp;deg; apart and the fourth diametrically opposite to one of the three . the brush contacts were used to trigger off a stroboscope lamp illuminating the blades whilst rotating . the three contacts at approximately 120 &amp;deg; spacings were set so that , with all three in circuit together , they were successively out of phase by about one chord length when the ends of the rotor blades were observed . by this method it could be seen if the blades were tracking correctly . the two diametrically opposed contacts were used to facilitate the observation of flapping angles . each contact had a switch in circuit and the timing adjusted so that the stroboscope flashed when a particular blade was parallel to the longitudinal body axis either in a fore or aft direction . the height of the blade tips in each position was measured by means of a travelling periscope projecting vertically downwards into the tunnel . the difference in height of the blade tips in these two positions gave a measure of flapping angle . the periscope was of the type used on midget submarines . the stroboscope lamp was mounted on gimbals and the direction of the light , shining through a thick perspex window , could be adjusted by the observer to illuminate the particular blade tip under observation . it was estimated that the accuracy of the measurements was of the order of one tenth of a degree . a photograph of the head of the periscope is shown in fig 6 from which can be seen one of the two vertical slides behind which is the measuring scale . as the periscope weighed about 60 lb it had to be counterweighted and the wires carrying these weights , passing over pulleys , can be seen in the photograph . 3 . safety precautions . due to the high value of centrifugal force on the rotors and the possibility of instability , resonance , or fatigue , it was thought expedient to protect the personnel by reinforcing the tunnel inside with sheet steel and outside with shutters . these shutters were of sandwich construction comprised of blocks of paper between 1/4 thick plywood , totalling about two inches in thickness . to minimise the possibility of stopping the rotors before the tunnel and thereby losing the stabilising effect of centrifugal force on the blades , an interlock was incorporated in the electrical circuits , with a time delay of about a quarter of a minute , to ensure that the rotors attained a reasonable speed before starting the tunnel and also that the tunnel speed had dropped sufficiently on shutting down . as the electrical supplies to the tunnel and rotors were separate there remained the danger arising from a failure of the current to the rotors but as that was thought to be very improbable , no attempt was made to cover that eventuality . 4 . method and scope of experiments . the model was suspended from the main roof balance by two struts spaced 22 1/2 apart . these struts carried at their ends a spindle mounted on ball races , passing through and fixed to the helicopter body 29 1/2 from the nose . this spindle being freely mounted acted as a pitching axis . a further support was provided towards the rear of the body , using a pair of V-wires attached to an overhead split-beam balance , see fig 2 . these wires were adjustable by means of a windlass carried on the balance , so that the attitude of the model could be varied . the earlier tests were made at 1800 r.p.m giving a tip speed of about 400 ft &amp;sol; sec . later the speed was reduced to 1200 r.p.m and a tip speed of 267 ft &amp;sol; sec . lift , drag , and pitching moments were measured at wind speeds of 40 , 80 , 120 , 160 and 180 ft &amp;sol; sec for the tests at a rotor speed of 1800 r.p.m giving approximate values of tip-speed ratio , m , of 0.1 , 0.2 , 0.3 , 0.4 and 0.45 . when the rotor speed was reduced to 1200 r.p.m the wind speeds used were 25 , 55 , 80 , 100 and 120 ft &amp;sol; sec giving values of m = 0.094 , 0.206 , 0.300 , 0.374 and 0.449 respectively . measurements were made for blade angles , th0 , of 4 &amp;deg; , 8 &amp;deg; and 12 &amp;deg; . the angles were set by a worm and wheel at the blade roots using a surface table and scribing blocks to measure the difference in heights at leading and trailing edges . flapping angles were also measured by the method described in para 2.3 . although it would have been desirable to make measurements at very low values of m , less than 0.1 , difficulty was experienced due to the flow induced by the rotors themselves , especially at the higher body angles . for example , without the tunnel motor running , a vane anemometer indicated a wind speed of about 15 ft &amp;sol; sec at th0 = 8 &amp;deg; and th = 20 &amp;deg; . as the flow was unreliable these tests were abandoned . table 1 gives a summary of all the tests on the various rotor combinations together with references to the tables giving the results . 5 . corrections . the tunnel measurements were converted to the coefficients ct and Cm where ct is the coefficient of the force normal to the longitudinal axis of the helicopter and Cm is the pitching moment coefficient about the axis shown in fig 3 . a further correction was made for the forces and moments on the body and rig , etc , by making the appropriate measurements with rotors removed and subtracting from the total . no account is therefore taken of forces due to the interference between rotors and body . as the final results were to be presented for constant values of tip speed ratio , m , and the wind speeds chosen did not give exact values and also as &amp;formula; , where th is the body angle , the correction varied with attitude of the model and so all the results had first to be plotted against m and then the values for m = 0.1 , 0.2 , 0.3 , 0.4 and 0.45 taken from the curves . corrections had also to be made to th due to tunnel interference and therefore the values corrected for m had then to be plotted against th and values read off at the chosen values of th viz , 0 &amp;deg; , 5 &amp;deg; , 10 &amp;deg; , 15 &amp;deg; , 20 &amp;deg; and 25 &amp;deg; . for convenience th has been taken to be positive with the nose of the model downwards which is opposite to the normal convention . for the 9 x 7 wind tunnel the correction to body angle ( th ) has been taken to be &amp;formula; where A is the total rotor disc area C is the cross-sectional area of the wind tunnel , cl is the overall lift coefficient based on total disc area . the correction is such that the effective inclination is less than the geometric inclination . it is felt that the above correction is not entirely satisfactory as it is based on fixed wing theory . it is hoped that at some future time a systematic series of experiments will be made to establish the order of wind tunnel corrections to be applied to helicopter model testing . the corrections to pitching moment due to flapping hinge offset are included in para 6 . 6 . results . 6.1 . effect of flapping hinge offset . in addition to the corrections mentioned in para 5 account had also to be taken of the effect of flapping hinge offset which , due to design difficulties , was of necessity rather large , about 6.275 % . the effect of flapping hinge offset on the characteristics of a rotor is dealt with in a report by Meyer and Falabella and the analysis given in that report has been used to estimate the theoretical values of rotor thrust and flapping angles and also the effect on overall pitching moment . 6.2 . thrust coefficient . assuming uniform distribution of induced velocity and neglecting blade tip losses the theoretical value of ct is given by equation ( 38 ) of Ref 3 . &amp;formula; . as there is no cyclic pitch B1 = 0 and the term involving a1 is small and may be neglected and therefore approximately &amp;formula; . for zero forward speed where m = 0 &amp;formula; . also &amp;formula; . in order to determine a the slope of the lift curve of the blade section ct was required for zero wind speed . as the tunnel was of the return flow type it was difficult to obtain a true zero wind speed due to the flow induced by the rotors . this was cut down to a minimum by closing the tunnel with a screen , but even so there was a circulation of air in the neighbourhood of the model , particularly at the larger blade angles . it was assumed that at zero tunnel speed the induced circulation at th0 = 4 &amp;deg; would be very small and the measured value of ct = 0.00142 was inserted in the equations ( 2 ) and ( 3 ) . this gave a value of a = 5.0 ( per rad ) which was subsequently used in equation ( 1a ) . a curve of static thrust coefficient using the above value of a is given in fig 7 . the theoretical values of ct using equation ( 1a ) for th0 = 4 &amp;deg; , 8 &amp;deg; and 12 &amp;deg; are included in figs 9 , 13 and 19 . it is of interest to note that the effect of flapping hinge offset on ct is negligible , particularly at the lower values of m . 6.3 . division of thrust . from a knowledge of the total thrust and the pitching moment about a defined axis the contribution of thrust due to each rotor has been calculated . it was assumed that the thrust of each rotor acted at the disc centre and normal to the body axis and also that the rotor drag force , parallel to the longitudinal axis , acted at the mean height of the two rotors . the pitching moments as measured in the experiments included a contribution due to the effect of the offset flapping hinges and therefore before the thrust due to each rotor could be calculated the pitching moments had to be corrected for offset . in the report by Meyer and Falabella an expression is given for pitching moment due to hinge offset ( My ) . this expression is &amp;formula; where &amp;formula; &amp;formula; . values of a0 , b1 , and a1 are obtained by solving three simultaneous equations ; these solutions are given in equations ( 27 ) , ( 28 ) and ( 29 ) in the report . as there is no cyclic pitch , i.e , B1 = 0 in the case of the model , these solutions become &amp;formula; . the value of l is given by the expression &amp;formula; and &amp;formula; &amp;formula; . using the wind tunnel values of ct , in equation ( 9 ) My has been calculated for various cases and it was found that the terms involving a0 and b1 were quite small compared with the a1 term . 