Wind Tunnel Tests on Seven AerovanesDaniel A. Mazzarella Citation: Review of Scientific Instruments 25, 63 (1954); doi: 10.1063/1.1770886 View online: http://dx.doi.org/10.1063/1.1770886 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/25/1?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Dereverberation of a closed test section of a wind tunnel with a mult imicrophones cesptral method J. Acoust. Soc. Am. 133, 3394 (2013); 10.1121/1.4805894 Micromachined reconfigurable microphone array for wind tunnel testing. J. Acoust. Soc. Am. 129, 2674 (2011); 10.1121/1.3588960 Tone injected nacelle for aeroacoustic wind tunnel testing J. Acoust. Soc. Am. 88, 2050 (1990); 10.1121/1.400169 Ultrasonic method for flow field measurement in wind tunnel tests J. Acoust. Soc. Am. 71, 42 (1982); 10.1121/1.387276 Application of a Blowdown Wind Tunnel for Large Scale Acoustic Environmental Testing J. Acoust. Soc. Am. 33, 846 (1961); 10.1121/1.1936861

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions.

Downloaded to IP: 141.212.109.170 On: Tue, 09 Dec 2014 12:46:49

THE REVIEW OF SCIENTIFIC INSTRUMENTS VOLUME 25. NUMBER 1 JANUARY. 1954

Wind Tunnel Tests on Seven Aerovanes*

DANIEL A. MAZZARELLA

Brookhaven National Laboratory, Upton, New York (Received April 10, 1953)

Each of the Aerovanes used on the 420-ft meteorology tower at Brookhaven has been tested in one or more wind tunnels. An equation of motion is defined. Comparisons are offered in terms of the period of each in­strument and its damping coefficient. Other comparisons include starting speeds, stopping speeds, and the effects of aging and unbalance on the performance of Aerovane propellers.

The effect of yaw on the readings of windmill-type anemometers has been investigated further. An ex­pression is given for the relationship between true speed, indicated speed, and angular displacement.

The recovery time of an Aerovane propeller from rest can be expressed as a hyperbolic function of speed.

INTRODUCTION

EACH of the eight Aerovanes at Brookhaven has been in use on the 420-ft meteorology tower for

approximately three years. Routine calibration checks through each transmitter and recorder have been con­ducted quarterly by the removal of the propeller and the turning of the tachometer shaft at predetermined speeds with a synchronous motor. At least once a year each transmitter is removed for a complete servicing and lubrication check.

The tower exposure subjects the Aerovanes to severe conditions. For example, on November 25, 1951, the instruments sustained gusts to 147 ft secl (100 mph). A single transmitter was damaged; the welded joint between vane and vertical support of the uppermost unit was sheared. A similar break had occurred pre­viously on another transmitter when a blade of the plastic rotor snapped at its root. Troublesome welded joints of all the vanes on the tower have been rein­forced with rivets.

In performance the Aerovanes have satisfied all initial requirements for ruggedness, a continuous record of wind velocity with a linear response to wind speed. Secondary requirements, arising from research in tur­bulence, have made more demands on the equipment. Therefore, each instrument in use has been tested for its vane and propeller response characteristics in one or more of the three wind tunnels. From time to time, similar tests have also been made on the tower.

A single transmitter was tested for speeds ranging from 3 ft secl to 16 ft secl in the 12X8 ft return flow section of the Gust Tunnel at Langley Field, Virginia. The same transmitter and seven others were tested at speeds from 10 ft secl to 16 ft secl at the low speed wind tunnel of the Engineering Division, New York University. At a later date, three of the Aerovanes were re-examined in the range from 10 ft secl to 54 ft secl at the larger 7XlO ft tunnel of New York University. A typical testing installation is shown (Fig. 1).

* Research carried out at Brookhaven National Laboratory under the auspices of the Atomic Energy Commission.

63

VANE CHARACTERISTICS

The procedure used for determining a vane's response characteristics has been described for the Dines vanel

as well as for the Brookhaven National Laboratory Bivane2• In the tests herein reported, the vane was deflected at angles from 10 to 60 deg for each of several wind speeds. A sudden release was effected at each position, thus permitting the vane and the Esterline­Angus recorder to describe an oscillation of decreasing amplitude.

Following the experiments on an anemoscope, made at the National Physical Laboratory in England,

FIG. 1.

1 M. A. Giblett, Met. Off. Geo. Phys. Mem. 54, 20-34 (1932). 2 D. A. Mazzarella, Bull. Am. Meteorol. Soc. 33, No.2, 60-66

(1952).

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions.

Downloaded to IP: 141.212.109.170 On: Tue, 09 Dec 2014 12:46:49

64 DANIEL A. MAZZARELLA

'0 1& ILl I/) 14 I-!!;. 12

C ~ 10 Q. I/) 8

C Z 6 i

• 4 :j

18

U 16 I.LI Vl 14 U:i Z 12

~ 1.1.. 10 o o 8 o ir 6 UJ 0.. ...... 4

,/"

/x /~

JC

/

DAMPING COEFFICIENT AEROVANE NO.1

><=.038 AT I FTSEC-I >< N.Y.U. LOW SPEED

." TUNNEL

.1 .2 .5 .4 .S .,

i\, DAMPING COEFFICIENT( tk-t,l (a)

~/ /

/

J( PERIOD OF AERO-VANE NO.1

/

-1' • NAC:= ~UST TUNNEL )( N.Y.U. LOW SPEED

0/0 TUNNEL

/ ,­, , . 3 .4 .5 .6

I ( I ) WIND SPEED, u Tr'SEC- 1

(b)

FIG. 2.

GiblettI reported that the motion of a Dines vane can be expressed as a damped oscillation. The equation used by the British is of a standard form; it has been used herein with two modifications. A cosine function has been substituted for a sine function, and the phase displacement term has been eliminated:

O=Ooo-Xt cos (2;t ), (1)

where 00 is the initial angular displacement, 0 the dis­place~ent after t seconds, A the damping coefficient, and T the period in seconds.

The response of the Aerovane is one of periodic motion. With regard to wind speed, the period is in­versely related, whereas the damping coefficient is directly proportional. This is shown in the graphs of T and A for a sample Aerovane (Fig. 2). There is reason-

TABLE I. Period.and damping coefficient of Aerovanes.

No. of Aerovane

Period (T), sec 41.0

Damping coeff. (X) 0.038

2 3 4 5 6 8

42.0 39.5 41.0 44.0 39.0 39.0

0.042 0.041 0.044 0.037 0.042 0.042

able agreement from one instrument to another in the computed values of the period and the damping coeffi­cient, In Table I the figures have been reduced to a wind speed of 1 ft secl • The mean value of the period for the seven vanes tested is 40.3 sec; for the damping coefficient the mean is 0.042. With reference to Eq. (1), the dynamic characteristics of the Aerovane are given by:

0=00e-·042ut cos(27rU t). (2) 40.3

A convenient graph can be constructed by plotting period against time (Fig. 3). The zone of resonance, or region of free period, is shown by a double dashed line. No attempt has been made in this investigation to de­fine the limits of this area. Very recently, however, R. McCormick, of the United States Weather Bureau at Brookhaven, has shown in a mathematical analysis that the width of the zone increases at lower wind speeds.3 In general, good agreement was found with Fig. 3 which was constructed from experimental data.

Records of the free atmosphere depict the zone by a rapid succession of oscillations, representing resonance. The response curve presents an easy method for deter­mining the limitations of a given set of measurements . For example, at a wind speed of 10 ft sect, only those eddies with periods greater than 4 sec can be recorded in their full amplitude .

The literature on vane motion contains many terms describing the aerodynamic characteristics discussed heretofore. In an effort to clarify the terminology with respect to the Aerovane, the following definitions and comparisons are offered:

(1) The dampingfactor is a nondimensional, numerical expression, representing the decay of an oscillation. It is here defined as the absolute magnitude of the ratio of two successive amplitudes.

k= 100/01 1, 10/02 1" ·IOn/On+ll. (3)

The experimental data indicate that k is a constant with a value of 2.2 for displacements less than approximately 30 deg. Also, it is independent of wind speed.

(2) The logarithmic decrement is the natural logarithm of the damping factor. For this case, In2.2=0.788. This figure has been treated variously as the ratio of a full period or a half-period.4

(3) The damping co4ficient is defined by the value of A in Eq. (1). It was obtained from the experimental data by solving,

A= 1/tlnk. (4)

Using the notations given heretofore, this is derived from

(5) 3 Personal communication. 4 H. Bateman, Partial Differential Equations of Mathematical

Physics (Cambridge University Press, Cambridge, 1932), p. 49.

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions.

Downloaded to IP: 141.212.109.170 On: Tue, 09 Dec 2014 12:46:49

WIND TUNNEL TESTS ON SEVEN AEROVANES 65

By taking the logarithm of each side,

Xt=lnk,

which is identical to Eq. (4).

(6)

(4) Critical damping is said to exist in a moving system when the mass comes to equilibrium in a minimum time after a displacement. It is the transition zone between underdamping and overdamping. Using the equation

n= 1/[rl (lnk)2+ 1Jl, (7)

as given by Behar,5 the Aerovane is found to be 28 percent critically damped. This is in good agreement with a separate analysis made by the National Advisory Committee for Aeronautics6 in which it was reported that the Aerovane is 27-percent critically damped.

(5) The period, or the periodic time, is the time required for a vane to describe a full cycle, 211". In the case of the Aerovane, the value of the period is given by:

T=41/u, (8)

where u is the wind speed in ft secI.

TABLE II. Starting speeds of Aerovane.

No. of Aerovane 2 3 4 5 6 8

Starting speed 3.3 2.6 2.3 2.6 4.6 1.6 (ft sec-I)

PROPELLER AND TACHOMETER CHARACTERISTICS

It is evident from the several tests conducted in wind tunnels and from the experience associated with using Aerovanes on a high tower that the sources of error in a tachometer system are twofold: mechanical and elec­trical. Mechanical errors can usually be traced to excessive friction because of either a lack of proper lubrication or unnecessary pressure at the brushes. Few electrical errors have been found outside of a less-than­standard voltage output. In the three cases witnessed, this was the result of a loss of flux in a magnet which had been affected by a lightning strike on the tower.

The starting speed of an Aerovane is the product of tachometer and propeller characteristics. Each of the starting values listed in Table II was determined in the low-speed tunnel of New York University. These are averages for several trials. They were obtained by slowly increasing the tunnel flow, until the propeller started to turn. Meanwhile, the changing tunnel speed was read to 0.001 of an inch of alcohol on a sensitive manometer. Aerovane No.6, it should be noted, had the highest starting speed. In the tests on vane motion reported earlier, it alone produced extreme values. In some re­spects this is a satisfying disclosure, for in several analysis of tower data the No.6 Aerovane on the 300-ft

~ M. F. Behar, The Handbook of Measurement and Control (Instruments Publishing Company, Pittsburgh, 1951), pp. 32-33.

• Nat. Advisory Comm. Aeronaut. Tech. Mem. L52L29b (1952).

TABLE III. The response of different propellers on the same transmitter.

Propeller Vel. (ft sec-I) Approximate time in use

A B C D E F

15.1 15.1 15.1 15.4 15.1 15.1

2 years 6 months 3 years 2 years (segment replaced) New 6 months

level gave anomalous results. The stopping speed of this instrument was determined as 3.6 ft secI. All other stopping speeds have been omitted. This was a difficult determination to make, and the reliability of the data was considered doubtful.

In an installation where comparative readings are made from many transmitters, it is conceivabie that different propellers on the same Aerovane might produce varying results. The probability of this conclusion's being true is enhanced when one is dealing with pro­pellers which have been exposed to the weather for different periods of time. To test this possibility, six standard propellers were installed in sequence on a single transmitter. The tunnel speed was unchanged during the trials. With only one exception (Table III), the recorded velocity for each propeller was identical. Propeller D, the single variant, was damaged while in use on the tower. An attempt was made to replace one of the molded blades; presumably, the repair resulted in an unbalanced unit.

Occasionally, the nose caps have been found missing on the Aerovanes at the tower. In the majority of cases this can be ascribed to negligence. Nonetheless the magnitude of the error which results from such an occurrence was the object of another series of tests. At selected speeds between 5 and 16 ft secr, several trials were made with a nose cap on and off. There was no perceptible difference in the recorded velocity. This does not imply that similar results would be ob­tained in a gusty wind.

If a mean be taken of the starting speeds listed in Table II, excluding Aerovane No.6, we obtain the figure 2.5 ft seci • This is in good agreement with ob­servations made of instruments in use on the tower. It

FIG. 3. Response curve for Aerovane.

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions.

Downloaded to IP: 141.212.109.170 On: Tue, 09 Dec 2014 12:46:49

66 DANIEL A. MAZZARELLA

LO

• Vi

Vi 6

2 •

... ,Q,EROVANE N01,98FfSEc-' (NACA GUST TUIllNEL)

• TOWER TEST, 16.1 FTSEC-I

• AEROVANE NO 2,14,1FT.so;of t1"IOFT, N.Y.U, TUNNEL}

_ lCOS812

o 90 eo 10 EO 50 40 30 20 10- + 10 20 30 40 50 60 70 BO 90 ANGLE or OEFUCTION

FIG. 4. The effect of yaw on the Aerovane. " .& Aerovane No.1, 98 ft sect (NACA gust tunnel)." Should read".& Aerovane No.1, 9.8 it secl (NACA gust tunnel)."

differs somewhat from the starting speed of about 1.7 ft sec! given for a new transmitter.7 The validity of either figure is questionable for instances when the vane is not pointed directly into the wind. Many cases have been observed when lightweight, conical-cup anemometers have responded to the onset of a wind sooner than the Aerovane.

In writing on the theory of vane anemometers, Owers has shown that the speed of rotation of a given set of vanes is determined by the pitch of the blades, the wind speed, and the friction inherent in the system. For the ideal case, where friction is absent, he has indicated:

u=vtana. (9)

Where u is the vane speed, v is the wind speed, and a is the angle at which the blades are mounted within the anemometer. In the Aerovane the helicoidal blades produce a calibration curve which follows the above relationship i the curve is near linear once the region of starting friction has been exceeded.

Until recently the effect of yaw on an anemometer was reported only for relatively small angles. The error was expressed as a percentage of the wind velocity when no deflection was present. Conover9 found the indicated readings to be 0.5 percent low at 5 deg and 2.5 percent low at 10 deg. The National Bureau of Standards, as reported by L. E. Wood,!O has now in­vestigated the error through 20 deg. Although it is true that an angle of yaw greater than 30 deg is infrequent in the natural wind, this report includes data through 90 deg. These have been plotted (Fig. 4) as fractions Vi/Vt. The results show that the indicated velocity, Vi, can be expressed as a product of the true velocity, Vt, and the cos2 of the angle of yaw:

Vi= Vt (cos2(J). (10)

7 L. E .. Wood, Bull. Am. Meteorol. Soc. 26, 361-370 (1945). 8 E. Ower, The Measurc1tlenl of Air Flow (Chapman and Hall,

Ltd., London, 1949), third edition, pp. 157-162. 9 J. H. Conover, personal communication (1950). 10 See reference 7, p. 368.

If, instead of yaw, one applies pitch to an Aerovane transmitter, it can be shown that Eq. (10) is satisfied for angles up to 45 deg. The implications of this rela­tionship for measurements in the natural wind are significant. It has been shown heretofore that the Aerovane is underdamped. If it be assumed that a vane can be constructed which would faithfully follow hori­zontal changes, then the speed measured by the rotor can be an indication of the magnitude of the three­dimensional wind vector. On a typical gusty day, for example, the speed trace of an Aerovane shows large amplitude changes. In part, this results from the angle of attack of the wind with respect to the rotor blades. The combined use of an Aerovane and a bi-vane in close proximity provides a means for obtaining the three­dimensional wind vector.l1

The speed of response of a velocity-indicating system has been examined heretofore.'2-14 Fergusson, with respect to cup anemometers, and Conover, with respect to the Aerovane, have written concerning the "sensi­tivity" of a wind-measuring system. In each case they tabulated the total time and the number of rotations for an anemometer to reach a steady state. Spilhaus16

has indicated that the manner in which an anemometer approaches equilibrium is of an exponential nature. Evidence has been found in the experimental data to support this supposition.

The speed of response, as herein given, is defined for a given wind speed i it is the interval in which a trans­mitter and its accompanying recorder indicate 0.63u, that is, the time required to reduce the difference be­tween an instantaneous value and an equilibrium value to e-l of its initial figure. Several typical propeller curves are shown (Fig. 5), as are the graphs from which the response time was determined. The graphs are solutions to the relationship:

Vi-VI ---=e-, (11)

VI T

where V. is the velocity at time t, VI is the final, or equilibrium, velocity, and T is the coefficient which describes the speed or response.

The value of tau varies in relation to the equilibrium wind speed. A plot of this variable for the experimental data from 9 to 54 ft sec-t, gives the curve shown (Fig. 6).

11 H. A. Panofsky and I. A. Singer, "Annual Progress Report, A.E.C.-Air Pollution Project, Meteorological Phase, New York University," N.Y.D. No. 1559 (1951).

12 G. E. W. Hartley, "Symposium of Papers on Electrical Meteorological Instruments" (The Institution of Electrical Engineers, London 5, 1951).

13 S. P. Fergusson, "Experimental Studies of Anemometers," Harvard Meteorological Studies No.4 (Harvard University Press, Cambridge, Mass .• 1939), pp. 65-77.

14 J. H. Conover, Bull. Am. Meteorol. Soc. 21,523-531 (1946). 16 A. F. Spilhaus, Bull. Am. Meteorol. Soc. 16,301-303 (1935).

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded

to IP: 141.212.109.170 On: Tue, 09 Dec 2014 12:46:49

WIND TUNNEL TESTS ON SEVEN AEROVANES 67

<Ii C1J > ....

" u >, .... <l)

-.t,\,: > 0 u C1J .... ....

.s; OJ §-....

I"-< u; <.!i ~

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded

to IP: 141.212.109.170 On: Tue, 09 Dec 2014 12:46:49

68 DANIEL A. MAZZARELLA

-~ S 0

"' "' :l; 0 ~ !l ~.

70

60

50

40

30

\" \\ -:z AEROVANE 7,10 TUNNEL,NYU \ \ • 8 AEROVANE ACE TOWER \ \ • :7 AEROVANE 7, 10 TUNNEL,N~U \ • 8 AEROVANE 7, 10 TUNNEL N ~U

+ \ \ ' "I AEROVANE NACA GUST TUNNEL \ '\ r FERGUSSON'S DATA FOIl 'TOTAl TIME CFJ \., 'I 3-CUP ANEMCMETER

" " :a: FERGUSSON'S DtlTA FOR • TOTAL TIME OF " '- 4 - ru> ANEMOMETER

ZO

'- "-" " , , ...... ' ...

to

0~----~----~Z~----~3------~4------J T ,RESPONSE (SEC.)

FIG. 6. Aerovane prop ell or response curve.

In its simplest form, this is a hyperbola defined by

K T=­,

U (12)

where T is the time in seconds, u is the velocity in ft secI, and K is a constant whose dimensions are those of length 24.6 ft. It is interesting to note that a plot of the data on log-log paper produces a straight line of slope -1. As a matter of further interest, Fergusson's data13 for three and four cup anemometers have been plotted with the Aerovane data in Fig. 6. There is good agreement in the shapes of the curves even though Fergusson determined the total time from rest to equilibrium.

The effect of a fluctuating wind speed could not be tested in this investigation. It can be assumed, how-

ever, that the findings of Ower8 for rotor-type anemom­eters are applicable. He has shown that the error in indica ted speed is proportional to the square of the amplitude of the fluctuations. Unless the amplitude of the fluctuations is large, the error is negligible; it has been given as under 1 percent for a wind fluctuating ± 14 percent.

CONCLUSION

The several investigations reported herein indicate the usefulness of the Aerovane as an instrument for research in a wide range of investigations as well as for general weather station observations. All of the equip­ment tested had been used under severe conditions for long periods of time; nevertheless there was good agree­ment in the vane and propeller response characteristics for nearly all of the transmitters.

ACKNOWLEDGMENTS

The findings of this report were made possible through the cooperation of the National Advisory Committee for Aeronautics and New York University with Brook­haven. The generous assistance of Mr. James K. Thompson at Langley Field is acknowledged, as is that of Professor G. Strom and his associates at New York University. The help of Professor Panofsky, formerly of New York University, now at Pennsylvania State College, has been invaluable.

Gratitude is expressed to G. Mitchell for technical assistance, to P. H. Lowry and I. A. Singer for their assistance with mathe~atics, and to M. E. Smith for a continued interest in seeing the project performed.

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions.

Downloaded to IP: 141.212.109.170 On: Tue, 09 Dec 2014 12:46:49