The Design and Perform ance of an A xial-Flow Fan AER-56-13 LIONEL S. MARKS1 a n d JOHN R. W ESKE,2 CAMBRIDGE, MASS. T h is paper d eals w ith th e d esig n a n d p erfo rm a n ce o f a n axial-flow fa n for co m p arativ ely h ig h p ressu res. T h e d esig n is based largely o n ex ten siv e in v estig a tio n s o f th e air flow th rou g h a fa n o f w ell-k n o w n d esig n w h ich y ield ed cer­ ta in co n sta n ts. T h e p roced ure in d esig n is sk etch ed very briefly— it in volves th e u se o f b o th a irfoil th eo ry an d circu latio n th eory. F u ll d eta ils are g iv en o f th e co m p leted fan . T h e p erform an ce o f th is fa n is sh o w n in a series o f graphs an d is com p ared w ith th a t o f th e fa n u sed for th e p relim inary in v estig a tio n s. T h e in flu en ce o f th e n u m b er and lo ca tio n o f g u id e v an es w as in v estig a ted . D iffu ser a ctio n is a lso d iscu ssed . T h e n o ise e m issio n w as m ea su red and w as fo u n d to be co n sid era b ly low er th a n th a t fro m th e origin al fa n . A rela tio n b etw e en n o ise a n d fa n p erform ­ an ce is p o in ted o u t. T HIS PAPER deals with the design and performance of an axial-flow fan for comparatively high pressures. It was hoped that some improvement in efficiency over values previously recorded might be obtained by giving careful sideration to the aerodynamic principles involved, including both airfoil theory and circulation theory. To analyze fully the operation of an axial-flow fan, it is neces­ sary to have knowledge of the pressure, direction, and velocity of the air in every part of the fan while in operation. To obtain these data a fan was built, following closely a design which has given good performance, and an extensive investigation was made of the air flow through this fan. The details of this in­ vestigation and its results would require too much space to be 1 Professor of M echanical E ngineering, H a rv a rd U niversity, C am ­ bridge, M ass. M em . A .S .M .E . Professor M arks w as b o rn in B ir­ m ingham , E ngland. H e received th e degree of B.Sc. from th e U ni­ versity of L ondon in 1892 and M .M .E . from C ornell U n iv ersity in 1894. H e w as w ith th e Am es Iro n W orks, Oswego, N . Y ., in 1894 and th en w ent to H a rv a rd U n iversity as in stru cto r in m echanical engineer­ ing. In 1900 he w as m ade a ssistan t professor and in 1909 w as ad­ vanced to his present position. Professor M ark s is a u th o r of “ S team T ables and D iagram s,” “ G as and Oil E n gines,” “ M echanical E ngi­ neers’ H an d book,” “ T he A irplane E n gine,” and has co n trib u ted num erous articles to th e technical press. 2 B ethlehem Shipbuilding C orporation, Q uincy, M ass. M r. W eske entered th e H an o v er In stitu te of T echnology in 1920 and in 1923 was g raduated w ith th e degree of D iplom Ingenieur in m echanical engineering. F rom 1924 u n til 1930 he w as engaged in m echanical engineering and design w ork w ith several in d u stria l concerns. T hese included D eutsche Schiffs u n d M aschinenbau A. G ., B rem en, G er­ m any; several firm s in D e tro it and San F rancisco; a n d th e tu rb in eengineering d ep artm en t, G eneral E lectric C om pany, Schenectady, N. Y. Since 1930 M r. W eske has been in te rm itte n tly w ith th e B ethlehem Shipbuilding C orp., Q uincy, M ass. F ro m 1931 to 1934 he has been engaged in g rad u ate studies and research a t th e H a rv ard E ngineering School, receiving in 1932 th e degree of M .S. and in 1934 th a t of S.D . C on trib u ted b y th e A eronautics D ivision for p re se n ta tio n a t th e A nnual M eeting, N ew Y ork, N . Y ., D ecem ber 3 to 7 , 1 9 3 4 , of T h e A m e r ic a n S o c ie t y of M e c h a n ic a l E n g in e e r s . D iscussion of this p ap er should be addressed to th e Secretary, A .S .M .E ., 29 W est 3 9th S treet, N ew Y ork, N . Y ., a n d will be ac­ cepted u n til Ja n u a ry 10, 1935, for p u b lication in a la te r issue of T ransactions. N o t e : S tatem en ts a n d opinions ad v an ced in p ap ers are to be u nderstood as individual expressions of th eir au th o rs, and n o t those of th e Society. included in this paper and it is expected that they will be pub­ lished elsewhere. Certain constants obtained from this preliminary investiga­ tion have been used in the new design and the fan developed on the basis of these researches has high efficiency. In addition, consideration was given throughout the design to the question of minimizing noise, and tests appear to show that in this respect also the fan performance shows improvement over previous designs. D e s ig n A consideration of the two-dimensional flow around a blade element in a fluid of infinite extent, with corrections for mutual blade interference and for finite blade length, leads to certain basic conclusions which after having been verified by test were applied to the design. The velocity diagram, Fig. 1, shows the conditions of flow at inlet and discharge in the usual manner and with the standard symbols for velocities and their components. It is drawn for an airfoil operating with a constant axial-velocity component. It is con­ apparent from Fig. 1 that an increase in the angle of attack, a, accompanies a diminution of the axial velocity and an increase F ig . 1 V e l o c it y D ia g r a m for I d eal F an in the discharge circumferential velocity. At the same time, it increases the lift and drag until the stalling angle is reached. The decrease in relative velocity of the air with respect to the blade corresponds to a static pressure difference across the wheel. The endeavor to obtain constant axial velocity leads, in the first approximation, to constant pitch or a pitch angle inversely proportional to the radius. The fan can be designed so that the same amount of work is done on each particle of air, at the flow conditions corresponding to the point of maximum efficiency. To accomplish this, varia­ tion in the angle of attack was utilized, but this procedure can­ not be effective through a large range of maximum to minimum radius of blade. Consequently a large hub diameter is necessary. Increase in hub size will increase the necessary diameter of the fan for a desired capacity. A compromise had to be reached and, for the present design, the hub diameter was made one-half the fan diameter. Choice was made of an airfoil profile with a straight front, for which the center of pressure difference across the blade is well toward the leading edge. With this profile, eddy formation at the trailing edge is reduced—a condition favorable to the minimizing of noise. A study of the lift and drag characteristics of such airfoils 807 TRANSACTIONS OF THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS 808 shows that thin profiles have their best lift-drag ratio at small the blade at an angle to the radius and of the leading edge of the angles of attack, while thicker profiles produce an optimum ratio guide vanes in the opposite direction had also for its purpose the at larger angles of attack and have also a large stalling angle. reduction of noise. The lift produced by these sections can be increased by increasing The guide vanes were designed on the basis of measurements the angle of attack above the value giving the best lift-drag ratio. of the air stream at discharge, and the varying direction and This increase in the angle of attack above the optimum was varied velocity of the air stream approaching the guide vanes was con­ from a negative quantity at the periphery to a maximum at the sidered when selecting a suitable profile. While the angle of hub and resulted in an increase of pitch along the radius from tip incidence was selected for best results at maximum efficiency, the to hub. Some decrease in the angle of attack is necessary as a thick profiles were intended to obtain good flow under other result of mutual blade interference. The angle of attack was operating conditions. The change of section of the guide vane selected so as to give constant pressure on each blade element. with radius is shown in Fig. 3. Diffuser action was obtained in a cylindrical casing by the tapering of the hub. Diffusers for moderate deceleration are F ig . 3 F ig . 2 S t r e a m l in e s a n d V e l o c it y ose o f H ub N C y l in d r ic a l S e c t io n s of G u id e V a n e s D is t r ib u t io n A r o u n d The theory of the individual blade element does not take into account the mutual interference of neighboring blades, or induc­ tion phenomena near the tip and the hub, or the effect of rota­ tional flow in the interval between two blades. The last is a rotation of the air relative to the blades and in a direction op­ posite to the direction of rotation of the fan and is due to the fact that the air enters without rotational motion. A more precise estimate of the pressure difference was obtained through application of the circulation theory. According to this theory, the circulation at the discharge side is equal to the sum of the circulations around the individual blades, provided that the circulation at the suction side is zero. Through Joukowsky’s theory, relating the circulation to the lift of an airfoil, the connection between airfoil theory and circulation theory is established. To investigate this relation, measurements were made of the rotational velocity at discharge from the fan, in the preliminary investigations. The results of these investigations were summarized in the computation of a mean-value coefficient, which is the ratio of the arithmetic average of measured circum­ ferential velocities and the circumferential velocity of the ideal fan. This coefficient has the value of 0.5 to 0.6 for a fan in which the chord of the blade section is approximately equal to the normal pitch at that section. This factor is not greatly altered for deviations from this ratio of chord to normal pitch. The principles of streamlining were observed throughout the design of the fan and adjoining air passages. The nose of the hub is shown in Fig. 2, which also gives the calculated flow lines for the case in which the air approaches the hub in an axial direc­ tion. It will be seen that this shape has the advantage of giving somewhat greater axial velocities in the vicinity of the hub. The number of guide vanes was chosen so as to avoid simul­ taneous encounters of the trailing edge of the wheel and the lead­ ing edge of a guide. This should tend to keep down the in­ tensity of sound emission. The tilting of the trailing edge of F ig . 5 A rrangem ent T h r e e -B laded P r o pel l e r C a s in g of in AERONAUTICAL ENGINEERING AER-56-13 809 fairly efficient—up to 85 per cent. For area ratios in excess of 1.22 with a conical diffuser and with laminar flow, back flow sets in and the efficiency drops. With a cylindrical casing and a tapering hub the inequality of decrease in velocity is counteracted and a good efficiency is possible. T e st in g A e r a n g e m e n t s The details of the fan design are given in the pattern drawing, Fig. 4; its arrangement in the casing, with its stationary stream­ line continuation, is shown in Fig. 5. The well-rounded entry to the casing is omitted from Fig. 5 but is indicated in Fig. 6, which shows the test set-up. The stationary streamline con­ tinuation of the fan hub was centered in the casing by a spider of five radial blades and it contained the ball bearings which support the shaft at the fan end. The guide vanes are located between the fan and the radial blades. As shown in the set-up for performance tests, Fig. 6, the fan dis­ charges directly into the atmosphere. The air enters through a calibrated nozzle and the resistance is controlled by screens and slats located 22 ft past the nozzle. The resistances are suc­ ceeded by a 12Va-ft length of square duct of about 50-in. side. The air enters the fan casing through a well-rounded bell mouth. The fan is driven by a long shaft which permitted the use of diffusers of any desired length and located the dynamometer at such distance as to offer no disturbance to the air flow. It had the disadvantage, however, of limiting the permissible speed of operation to about 3000 rpm. The volume of air passing through the fan was measured by an impact tube arranged on the center line of the nozzle, one-half of its diameter distant from its outlet. The total pressure is the difference between the impact pres­ sures at the inlet to the bell mouth and at discharge from the fan casing or diffuser. The velocity pressure at the bell mouth is too small to be measurable at any operating condition and conse­ quently a static-pressure measurement was substituted at the location indicated. As the velocity over the discharge area is variable, the discharge impact pressure was calculated from the static pressure (which is atmospheric) and the mean-velocity pressure computed from the air flow. This gives a smaller value than the actual pressure. Tests were made at 1800, 2400, 2700, and 3000 rpm and a stroboscopic device, consisting of a neon lamp and a disk with radial markings, rotating with the shaft, served to adjust the speed to within one rpm of the desired speed. The power input shown in the performance curves is the net input, i.e., the difference between the measured and the frictional horsepower. The latter was determined by tests in which a plain cylindrical hub was substituted for the fan. The test set-up differs in many ways from that of the Standard Test Code for Propeller Fans of the American Society of Heating and Ventilating Engineers. After the completion of the tests at Harvard University the fan was tested in another laboratory, following the methods of the Standard Test Code. The pres­ L o n <h F ig . 6 A rrangem ent of t u d /m a l F ig . 7 P e rfo rm a n c e C h a r a c te r is tic s o f T h re e -B la d e d P ro p e lle b F a n (Tests with ten guide vanes and diffuser; clearance, d = 1 in.) sures, volumes and efficiencies as determined by the Standard Test Code are greater than those recorded here. T est R esu lts The curves of Fig. 7 give the results of tests in which the fan was provided with 10 guide vanes and discharged through a conical diffuser, which increased in diameter from 20 in. to 38 in. in a length of 80 in. All the remaining tests described in this paper are with a cylindrical casing and no conical diffuser. The curves of static pressure, efficiency, and horsepower input are typical of propeller fans. The static pressure rises steadily with decreasing flow to a “no-flow” value which is 70 per cent of the spouting pressure corresponding to tip velocity, or equal to the velocity head of a particle rotating with the fan wheel 8 in. distant from the axis. At about 40 per cent of the flow giving best efficiency, there is a disturbance, noticeable by a bend in the curves and by a considerable increase in noise. Measurements of flow within the fan show that this is caused by secondary currents due to centrifugal effects. Peak efficiencies vary with the velocity as indicated by the measurements at different speeds, but at 2700 and 3000 rpm the maximum total efficiency has a constant value of about 80 per cent. s e c t / oa/ A x ia l - F l o w P r o p e l l e r F a n V ie w "A' fo r P erform a n ce T ests TRANSACTIONS OF THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS 810 The same phenomenon of variation of peak efficiency with rpm has been observed in propeller and centrifugal pump operation. As a considerable part of the loss incidental to the operation of axial-flow fans is due to conditions of flow in the discharge, an investigation of the interaction of guide vanes and fan blades was undertaken. Two factors were investigated: (1) the effect of the number of guide vanes upon fan performance and (2) the effect of the axial clearance between the trailing edge of the fan wheel and the leading edge of the guide vanes. G u id e V a n e s Efficiency tests were conducted with 10 and with 5 guide vanes installed and also without guide vanes. For these tests the axial clearance between the fan wheel and the guide vanes was maintained constant at a value of l 3/s in., which other tests had shown to be a favorable distance in respect to efficiency and noise. The five radial blades supporting the bearing hous- F ig . 8 S t a t ic P r e s s u r e , N e t H o r s e p o w e r I n p u t , T o t a l E f f ic ie n c y and (Stub outlet duct; ten guide vanes; clearance, d — l 3/s in.) F ig . 10 S t a t ic P r e s s u r e , N e t H o r s e p o w e r I n p u t , a n d T o t a l E f f ic ie n c y (Stub outlet duct; no guide vanes; clearance, d = l 3/s in.) F ig . 9 S ta tic P r e s s u re , N e t H o rs e p o w e r In p u t, a n d T o ta l E ffic ie n c y (Stub outlet duct; 5 guide vanes; clearance, d = l 3/s in.) ing presumably functioned in part as guide vanes during the operation which is designated as “without guide vanes.” The tests which were made cover the range of normal operating condi­ tions, but a few additional points were included down to the “no-flow” operation. The results obtained are given in Figs. 8, 9, and 10 which give static pressures, total efficiencies, and net horsepower inputs at 1800, 2400, 2700, and 3000 rpm. The following conclusions may be drawn from them. (1) The variation of number of guide vanes does not affect the quantity of air flow through the fan. (2) As the number of guide vanes is increased, the static pressure rises. The rise is 4 per cent for five guides and 13 per cent for ten guides, as compared with operation with no guides, in the region of best efficiency. (3) The gain from guide vanes is most clearly shown by the AERONAUTICAL ENGINEERING curves jf total efficiency. For no guides the total efficiency has a maximum of 70 per cent at 3000 rpm but diminishes slowly with change of volume flowing. With five guides the peak efficiency is brought up to 79 per cent at 3000 rpm but the ef­ ficiency curve is steeper. At large flows, the efficiency obtained with five guides is slightly less than with no guides, as the guides are not designed for this condition. For all other operating conditions the use of five guides yields higher efficiency than with no guides. With ten guide vanes the maximum efficiency in­ creases to 81 per cent but the efficiency curve becomes steeper still and a further moderate decrease of efficiency is indicated at largest flows. These tests seem to indicate that the optimum number of guide vanes for a fan of this type is between five and ten. E ffect of C learance B etw een F an and AER-56-13 811 pactness of the equipment is considered. The fan performance with greater diffuser action was determined by substituting the conical diffuser for the stub cylindrical duct. The dimensions of this diffuser are given earlier in connection with the discussion of Fig. 7. A comparison of the performance with the two degrees of diffuser action is presented in Fig. 15, which is for a speed of G u id e s Variation of the axial distance, d, between propeller and guides has a considerable influence upon the noisiness of the fan. In- F i g . 11 E f f i c i e n c y C u r v e s W ith A x ia l C le a r a n c e d = 3/ 8 I n . F i g . 13 E f f i c i e n c y C u r v e s W ith A x ia l C le a r a n c e d — I 3/* I n . F i g . 15 C o m p a riso n W ith a n d W ith o u t D if f u s e r (3000 rpm ; 10 guide vanes; clearance, d = 1 in.) F ig . 12 E f f i c i e n c y C u r v e s F i g . 14 P e a k V a l u e s o f T o t a l E f ­ fic ie n c ie s a t T h r e e S p eed s P l o tte d W ith A x ia l C le a r a n c e A g a in s t A x ia l C le a r a n c e , d d = 3/ t I n . crease of noise becomes noticeable as d is decreased below 1 in. It becomes a maximum when d is made very small. The effect of the axial distance d upon efficiency was in­ vestigated in the region of best efficiency. Tests were made at 3000, 2700, and 2400 rpm and in some cases at 1800 rpm. The results are shown in Figs. 11, 12, 13, and 14. The axial clearance was varied from 3/ s in. to l 3/ 4 in. The lower limit was deter­ mined by the increase of noise, while above l 3/ 4 in. changes in clearance did not influence the test results appreciably. In Fig. 14 peak efficiencies are plotted against the axial dis­ tance, d, for various speeds. It will be seen that highest ef­ ficiencies are obtained for a clearance of 1 in. A somewhat larger clearance was found desirable in order to reduce noise further and a compromise was made in the adoption of a clear­ ance of 13/ a in. At this clearance, the efficiency is only slightly lower than at 1-in. clearance. 3000 rpm and an axial distance between blades and guides of 1 in. The conical diffuser has too large an area ratio (1 to 3.6) for opti­ mum results. The static pressures are not increased except at large volumes but the net horsepower input is diminished, the computed diffuser efficiency is 70 per cent and the maximum total efficiency is decreased by about 1.5 per cent. C o m p a r a t iv e P e r f o r m a n c e For purposes of comparison, performance tests were made on the two-bladed propeller fan referred to in the second paragraph of this paper. The fan was built, as stated, for the research preliminary to undertaking the design of a fan. Its general features are shown in Fig. 16. The ratio of hub diameter to tip diameter is 0.3. During the tests the hub was provided with a well-rounded nose and a streamlined after-body. The blade surfaces are parallel over a cylindrical section, tapering off to a slightly rounded edge on both sides, as compared with the airfoil sections of the new design. In the cylindrical develop­ ment, the blade is a curved plate of constant thickness with the front or driving side convex as against the straight front shown in Fig. 4. The pitch is constant along a radius but increases in the axial direction, from inlet to outlet, as shown in Fig. 17. The ratio of pitch at the leading edge to that at the trailing edge is 0.68. This change in pitch is proportional to the axial depth D if f u s e r except in the region near the trailing edge where the pitch The cylindrical discharge casing of the fan, Fig. 5, gives remains constant. This has the effect of reducing the pressure probably as much diffuser action as is desirable when the com­ difference across the blade in this region. Both the leading 812 TRANSACTIONS OF THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS edge and the trailing edge are radial lines in an axial plane. In the new design the pitch is variable along a radius and is constant in the axial direction. Ten guide vanes of constant curvature along the radius and with an angle of incidence of 28 deg were installed for the perform­ ance tests. The test results with this fan are given in Fig. 18 and a com­ parison of the two fans is made in Table 1. The tabulation is TABLE 1 COM PARISON OF A TW O-BLADED AXIAL-FLOW FAN W ITH T H E NEW THREE-BLA D ED AXIAL-FLOW FAN TwoThreebladed bladed fan fan Tip diam, in........................................................................ 20 19.3 H ub diam, in...................................................................... 6 10 Axial depth, tip, in........................................................... 6 3.5 Axial depth, hub, in......................................................... 6 5.5 R pm ....... ............................................................................. 3000 3000 Tip velocity, ft per sec................................................... 262 252.5 Air volume at maximum efficiency, cfm ................... 6500 4650 Mean axial velocity at fan discharge plane, fps. . . . 54.2 51.6 Static pressure at maximum static efficiency, in. of w ater............................................................................... 2.40 Net horsepower input..................................................... 3.58 Maximum static efficiency, per cent........................... 68.5 Maximum total efficiency, per cent............................ 69.5 Volume coefficient, _ / axial velocity at discharge plane\ 0.207 0.205 \ tip velocity / Pressure coefficient, _____ static pressure \ 0.157 0.216 velocity head at tip speed/ Characteristic speed based on 1 in. of w ater........... 1580 1150 °W ith stub-discharge duct; all other figures with conical diffuser. N o is e U sed F i g . 17 tD e p t h for C o m p a r is o n W it h N e w T h r e e -B laded F a n High-speed axial-flow fans are noisy in operation as com­ pared with centrifugal fans. The problem of noise reduction was kept in mind throughout the design as indicated at several places in this paper. The completed fan was tested for noise and similar tests were made on the two-bladed fan and on* a centrifugal fan. In the noise tests of the axial-flow fans, the stub cylindrical discharge duct was used and the microphone was placed 2 ft from the end of the duct, near the edge of the air V a r ia t io n o f P it c h W it h A x ia l T w o - B l a d e d A x ia l - F l o w F a n in for 3000 rpm which is considerably below the optimum operating speed. The new design has a diameter slightly smaller than the two-bladed fan and conse­ quently has a lower tip speed. The F ig . 18 P e r f o r m a n c e C h a r a c t e r i s t i c s o f T w o - B l a d e d 2 0 - I n . P r o p e l l e r F a n smaller discharge volume of the new (3000 rpm ; 10 guide vanes and diffuser.) design results from the larger hub di­ ameter, the lower tip speed, the thicker blades, and the decrease flow, and was oriented at 45 deg to the axial direction. In the in pitch of the blades. The tests were made with the conical case of the centrifugal fan, the microphone was placed 2 ft away from the edge of the well-rounded inlet to the fan and was diffuser previously described. It will be noted that the pressure coefficient of the new fan is oriented at 45 deg. to the fan axis. The results of these tests are presented in Figs. 19, 20, and 21. 37.5 per cent greater than that of the two-bladed fan. This is in accordance with the original purpose of designing a fan for com­ For the axial-flow fans, observations were made at two speeds, 2400 and 3000 rpm, with one additional observation at 1800 rpm paratively high pressures. AERONAUTICAL ENGINEERING on the new fan. »The axial-flow fans had 10 guide vanes located 1 in. past the fan blades. For the centrifugal fan, obser­ vations were taken at one speed only. In each case the observations covered the usual operating range of capacity. The results obtained show an inter­ esting relation between fan performance and noise. It will be observed that, with the axial-flow fans, minimum noise coincides approximately with maximum efficiency and that noise increases rapidly from that point, with decrease in ca­ pacity, until a break-down point is reached where the noise intensity drops suddenly. This break-down point coincides with the inflection point in the static-pressure curve. With further decrease in capacity the noise increases again. A comparison of the two fans at 3000 rpm and at maximum efficiency shows a noise intensity of 84.3 db for the new fan and 92.3 db for the two-bladed fan. This represents a decrease in sound AER-56-13 813 F ig . 20 N o is e M e a s u r e m e n t s o f T w o -B l a d e d P r o p e l l e r F a n (2400 and 3000 rpm.) F ig . 21 N o ise M e a s u re m e n ts o f 38-In. TVID S tu r t e v a n t C e n tb ifu g a l F a n (720 rpm.) energy, for the new fan, to less than one-sixth of its value for the two-bladed fan. The same ratio holds approximately at a speed of 2400 rpm. The variation in noise with rpm, as shown by the broken curve in Fig. 19, is exceedingly rapid. It is obvious that the noise problem in axial-flow fans is not yet solved. The noise characteristics of the centrifugal fans are quite differ­ ent from those of the axial-flow fans. Minimum noise occurs at very low capacities and noise intensity increases regularly with capacity, except for a break-down point which again coincides with an inversion in curvature of the static-pressure curve. The actual sound intensities for a given volume and static pressure are much lower than with the axial-flow fans. A cknow ledgm ent F ig . 19 N o is e M e a s u r e m e n t s of N e w T h r e e -B la d e d F a n (2400 and 3000 rpm.) The authors desire to acknowledge the valuable assistance of Mr. Thomas Flint, graduate student in the Harvard Engi­ neering School, in carrying out tests on which this paper is based.