Calculated Thermal Behavior of Ventilated High Precision Radio Telescopes

A. Greve and M. Bremer

Institut de Radioastronomie Millimetrique (IRAM) 300 rue de la Piscine, 38 406 8t. Marin d'Heres, France

E-mail: greve@iram.fr

Abstract

Radio telescopes that operate at millimeter and sub-millimeter wavelengths need a reflector-surface precision of a few tens of microns and a pointing accuracy of a few arcseconds. When built in a conventional way from steel and aluminum, as in the case of larger-diameter telescopes, thermal control must be applied to reduce temperature-induced deformations, in particular of the reflector backup structure. We illustrate that it is possible to make model calculations - for instance, during the design phase - that simulate the thermal behavior and the operation of a telescope when servo-loop-controlled ventilation or climatization (air-conditioned ventilation) of the backup structure is applied. We explain the technique of model calculations, and present as an example the calculated thermal behavior of a ventilated 64-m-diameter telescope and of the climatized 30-m IRAM telescope. It is explained that the thermal control of a telescope mount is Jess demanding if frequent pointing corrections can be made.

Keywords: Radio astronomy; thermal factors; thermal variables control; millimeter wave antennas; submillimeter wave antennas; servo systems; temperature control

1. Introduction

In this decade, several radio telescopes will be commissioned for observations, either exclusively at millimeter and sub-millimeter

wavelengths (�1 rom to 0.3 mrn, i.e., -250 GHz to 1000 GHz), or with observations at 3 mrn (100 GHz) wavelengths as the shortest

wavelength of operation (�3 rnm, i.e., -100 GHz). The telescopes are, for instance, the IO-m South Pole telescope [1], the IO-m ASTE telescope ofNRO (Chile) [2}, the 12-m telescopes of APEX [3] and ALMA (Chile) [4, 5], the 40-m telescope at Yebes (Spain) [6], the 50-m Large Millimeter Telescope (LMT, Mexico, USA) [7], the 64-m Sardinia Radio Telescope (SRT, Italy) [8], and the 100-m Green Bank Radio Telescope (GBT, USA) [9]. At the wavelength (A) of operation, these telescopes require a high reflector-surface precision with a root-mean-square value a 5; A./I 5 "" 0.02 - 0.2 mm, a small focus variation of

M � ,1/10 "" 0.03-0.2 mm, and a high pointing accuracy of

!10.s; 0/10 .s; 1 arcsec, where e "" 1 .2 A/ D "" 10 arcsec is the beam­

width. A high mechanical stability must therefore be guaranteed under envirorunental thermal loads (and wind loads), in particular if the telescope, or a part of the telescope, is built in a conventional way from steel and aluminum. In order to reduce the thermal load, passive thermal protection of the reflector backup structure (BUS), the telescope mount (fork, alidade, yoke), and the subreflector sup­ports is obtained from the application of white paint, insulation, radiation shields, and low-thermal-expansion material (for instance, CFRP, or carbon-fiber-reinforced plastic) orland from active thermal protection by ventilation or climatization (ventila­tion with heated or cooled air). In addition to thermal protection�

IEEE Antennas and Propagation Magazine, Vol. 48, No.3, June 2006

metrology is foreseen on some telescopes in order to correct a large part of the temperature- (and wind-) induced deformations. The metrology may consist of regular temperature measurements en of many parts of the telescope structure and real-time analysis from look-up tables or finite-element calculations [lO-13]; or of laser ranging (L) of the instantaneous deformations of many parts of the telescope structure [14]; or of a combination of both. Some oper­ating and prospective telescopes are listed in Table 1.

Obviously, it is important to evaluate the thermal behavior of a telescope during the design. This has been done for a long time by finite-element model (FEM) calculations of structural deforma­tions under static thermal loads, such as, for instance, a thermal gradient through the telescope structure, or a random temperature distribution throughout the telescope components. However, we have emphasized earlier [17] that it is possible to be more realistic, and to simulate with good precision the time-dependent dynamic thennal behavior of a radio telescope under the influence of the time-variable environment, and to use these data in a FEM calcu­lation. Here, we explain the possibility of also predicting from model calculations the thermal behavior of a servo-loop-controlled ventilatedlclimatized telescope structure with sufficient accuracy for design and operational purposes. We exclude telescopes in a radome: for these, see [18].

Calculations of the thennal behavior of a telescope may indi­cate that passive protection is insufficient to fulfill the performance specifications, so that, in addition, ventilation or c1imatization must be applied. For this purpose, the BUS must be covered by rear-side cladding or insulation, in order to create an air volume that can be

ISSN 1045-924312006/$20 ©2006 IEEE 9

Table 1. Operating and prospective telescopes with ventilation/climatization and/or metrology.

Telescope Diameter Tbermal Protection Ventilation Thermal Control Metrology [ml ofBUS of BUS of Mount

O�erating ASTE (Chile) 10 CFRP, Paint, Insulation yes APEX (Chile) 12 CFRP, Paint no Focus Cabin ALMA-J (USA) 12 CFRP, Paint, Insulation yes ('1) SEST (Chile) [151 15 CFRP no Fork !RAM (Spain) 30 Paint, Insulation yes Tower T NRO (Japan) [16] 45 Paint, Insulation yes T GBT(USA) 100 Paint no 'I{£)

Pro�ective Yebes (Spain) 40 Paint, Insulation

LMT (MEX-USA) 50 Paint, Insulation

SRT (Italy) 64 Paint, Insulation

ventilated or climatized. To illustrate this situation, we present as examples the calculated effect of(l) ventilation applied to the BUS of a 64-m diameter telescope, similar to the telescope on Sardinia [8, 19], and of (2) c1imatization applied to the BUS of the !RAM 30-m telescope on Pica Veleta [10,20]. The examples demonstrate the possibility of determining, for instance, the efficiency of the ventilation from thermal model calculations, i.e., the requited heat-

transfer coefficient, h [ W / m2 K J, between the ventilating air and

the tube network of the BUS (Equation (I)); the amount of ventila­tion, i.e., the volume of air to be moved or circulated per hour

[m3/ h]; the amount of climatization, i.e., the heating or cooling to

be applied through the ventilated air [kW]; and other parameters. The results of such calculations determine the layout and operation

of the ventilation or climatization system (for instance, the number of fans, heaters, and coolers), and the investment and operating costs.

There ex ists a difference between the effect of thermal defor­mations of the BUS and of the telescope mount. Thermal deforma­tions of the BUS primarily affect the beam shape and the gain; thermal deformations of the mount primarily affect the pointing. Thermal defOlmations of the reflector surface - which are noteas­ity measured in real time unless many temperature sensors are installed in the BUS [11] - are today controlled by passive/active thermal protection of the BUS, rather than by an active reflector surface. On the other hand, pointing errors - in part due to thermal defonnations of the mount - can easily be measured and corrected in quasi-real time. The thermal control of the mount is therefore less demanding if frequent pointing is possible.

2. Dynamic Thermal Model Calculations

The time-dependent thennal behavior of a telescope, or part of a telescope (for instance, the BUS or mount), can be predicted with good precision from model calculations. In these calculations, the telescope is divided into a large number, N (up to a few hun­

dred), of significant thermal components, Ii] (thermal n odes), specified by their location in the telescope's structure, their mate­rial, and their thennal properties (steel, aluminum, CFRP; heat capacity, heat conductivity, etc.), their masses and surfaces, their thermal interactions, and their exposure to the thermal environ-

10

yes T yes (£,7) no T

ment. As illustrated in Figure 1, the heat transfer between the indi­

vidual thermal components of the telescope, [i) 4 [j], depends on

conduction (heat transfer through contact), convection (heat trans­fer by intervening air or fluiq), and radiation. Likewise, the com­

ponents Ii] are connected tOI the time-variable (t) components of

the thermal environment in which the telescope resides: i.e., the

ambient air of temperature TA{t) , the wind of speed v(t) (convec-

Conduction

60 (T2 -;- T,)/(d/kA)

Convection

�o hA(T2 - T,)

I T,

60

{3,

Figure 1. An illustration of beat transfer tbrough conduction, convection, and radiation, between two bodies of temperatures 1\ < T2 (see [22, 23]). A, AI' A2: surface areas; k: heat

conductivity; d: representative distance; h: convective beat­transfer coefficient; [; : radiation emissivity; a : Stefan­

Boltzmann constant.

IEEE Antennas and Propag�tion Magazine, Vol. 48, No.3, June 2006

Environment Telescope

Components

SUN Irradiation

"- [ S(t)

Radiation SKY "- Conduction

<. /\ Ts(t)

- i'---Convection j

AIR " V

TA(t) Conduction

> Convection v

Radiation

k

GROUND Radiation /L J-.

TG(t) v

Figure 2. A thermal model of heat transfer among the telescope

components [i], Ij] , I k], .. " and between the telescope and the

timeMvariable thermal environment.

tion), the cool sky and the wann ground of temperature s Ts (t)

and To(t), and the heat input from solar radiation, S(t). Such a

thennal model is shown schematically in Figure 2. The model of

the telescope and the environment results in :.. (2 -6) N coupled

time-dependent differential equations of the node temperatures,

1/ (t ) , which can be solved by a network pro gram, for instance the

ESACAP program [21] used by us. The results of the calculations are the temperatures, 1/(t), of the components [1}=1,2, .. ,N as

functions of time and of the external and internal variable thermal conditions.

The relations for heat transfer and the thennal properties of materials are available from textbooks, for instance, Chapman [22]

and Bejan [23J. Thermal-model calculations of a similar kind have been made for radio-telescope structures [24, 10], radio-antenna radomes [IS], and optical telescopes [for instance, 25, 26, 27].

It is important to note that a thermal model is not a structural FEM applied to a thermal·load case. The FEM of a telescope, which may consist of several hundreds of thousands of nodes, is used to calculate deformations of the structure under the forces of gravity, temperature, and wind. These forces are static load cases. A thermal model, which may consist of several hundred nodes, allows the calculation of the time-dependent temperatures of sig­nificant components of the telescope's structure. These calculated temperatures, as function of time, may then be used in the FEM to calculate the corresponding structural deformations, as functions of time. In this paper, the example of the ventilated 64-m BUS struc-

IEEE Antennas and Propagation Magazine, Vol. 48. No.3, June 2006

ture presents a pure thermal model calculation; the example of the

c1imatized IRAM 30-m telescope presents a thermal model calcu­lation of which the results are used in a FEM calculation to predict the change of the reflector's surface shape, and to predict in a sub­sequent diffraction calculation the associated change of the beam pattern.

In order to visualize the scale of active thermal control of a BUS, Table 2 sununarizes the ventilationlclimatization system of several operating and prospective telescopes. For the examples dis­cussed here, Table 3 summarizes the number of thermal nodes con-

.... sidered in the model calculations, their average masses, and their heat capacities. When noting the large masses of the telescope structures and the relatively small number of thermal nodes, it seems pretentious to predict temperatures from model calculations. However, the agreement between calculations and the temperatures measured on several large telescope structures gives confidence in the method [10, 17]; for radomes, see [IS]. Whenever we have made a design calculation we have tried to test the thermal model on a similar telescope for which measured temperatures have been published.

3. Formalism of Ventilation and Climatization

Although rather inefficient, the simplest method for ventila­tion is natural convection, in which warm air at a lower level moves (under the influence of gravity) into cooler air at a higher level. To some extent, natural ventilation can be exploited and controlled by louvers. Here, we are dealing with forced ventila­

tionlclimatization, in which air of temperature Tv (t) is actively

moved in order to produce temperature homogeneity of the BUS. The ventilating air may either be the air inside the BUS, or outside ambient air, or a mixture of both. The ventilating air may be cooled to remove excess heat from solar radiation and internal heat sources, or it may be heated to counterbalance radiative heat loss towards the cool sky. The ventilation/c\imatization may be con­tinuously running or used as a servo-loop-controlled system. In addition, ventilation in a circular direction seems to be more effec­tive than radial ventilation [2S].

In the heat-transfer equation, the heat, AQ;, transferred by the

ventilating air moving along the surface A [m2J of the thermal

component [i] (a pipe, a bar, a plate, a box, the BUS, etc.) is

proportional to the coefficient h [W/m2KJ, i.e.,

(I)

The coefficient h is a complicated function of the geometry of the structural element [i] and of the air flow, being lam inar or

turbulent [22, 23). The value of h is also dependent on the altitude of the observatory through the density of the air [29). In order to investigate the influence of ventilation, in the model calculation of the 64-m telescope, the value h was varied until the specified ther­mal state of the telescope was obtained. Certainly, the obtained

solution, h·, must have a technical realization for the geometry of the telescope components and for the commercially available ven-

tilation/air-conditioning systems. In essence, the value h· defines the volume of the air to be moved [m3h]. In the example of the 30-m telescope, the ventilation is continuously running, and the

11

12

Table 2. Backup structure (BUS) ventilation and climatization systems.

ASTE lO-m Telescope Back-structure enclosed air volume (Vss) Number of ventilators Air moved per ventilator Total moved air Circulation of air volume VBS Ventilation speed Flow direction Heating/cooling of enclosed air IRAM 30-m Telescope Back-structure enclosed air volume (Vss ) Number of ventilators Air moved per ventilator Total moved air Circulation of air volume VBS Ventilation speed Flow direction Heating_capacity of enclosed air (max) Cooling c�pacity of enclosed air (max)

Yebes 40-m Telescope Back-structure enclosed air volume (VlJS ) Number of ventilators Air moved per ventilator Total moved air Circulation of air volume VBS Ventilation speed Flow direction Heating/cooling of enclosed air NRO 45-m Telesc�e Back-structure enclosed air volume (Ves ) Number of ventilators Air moved per ventilator Total moved air Circulation of air volume VBS Ventilation speed Flow direction Heating/cooling of enclosed air LMT 50-m Telescope Back-structure enclosed air volume (VBS) Number of ventilators Air moved per ventilator Total moved air Circulation of air volume VBS Ventilation speed Flow direction HeatinglcoolinK of enclosed air

BUS Ventilation fu(lIie!fr 65 m3

10

780-3600 m3/h = 0.2-1.0 m3Js 32400 m3/h = 9 m3/s

500 times/hour

2.2 mls Circular

none BUS c1imatization J.applied)

1800 m3

5 12600 m31h = 3.5 m3!s

63000 m31h = 17.5 m3!s 35 timeslhour

�3 mls Circular

6 kW (ventilator 4 kW/ventilator

BUS Ventllation (prospective) 4154 m3

20

1440-5760 m31h = 0.4-1.6 m3/s 91000 m31h = 25 m3/s

22 timeslhour

-3 mls ,

Circular Intake ambient air

BUS Ventilation (applie<ll. 3000 m3

45 + 10 359100 m3/h = 100 m3/s

7140-3780 m3Jh = 2-1.1 m3/s 120 timeslhour

-1-2 mls Circular

none ,

BUS Ventilation M()Sllectiv� 7000 m3

6xl8

12600 m31h = 8 m3/s1 180000 m31h = 50 m3(s

25 timeslhour

-3 mls To be defined I

none ,

IEEE Antennas and Propagation Magazine, Vol. 48, No.3, June 2006

Table 3. Thermal components, nodes, average mass, and beat capacity per node.

Thermal Component Nodes Mass per Node Total Mass Heat Capacity per Node

(Elements) Environment

Ambient air (TA ) 1

Sky (Ts) 1

Ground (TG) 1

Solar radiation Set) 1

64-mBUS Central hub 8 Steel of BUS (inner ring) 4 Steel of BUS (middle ring) 8 Steel of BUS (outer ring) 16 Air in BUS 28 Panels(front & rear sid� 56 Insulation BUS rear 32 (Insulation behind panels) (56) Total number of Nodes 152 (208) JRAM 30-m BUS

Steel of BUS 12 Air in BUS 12 Panels (front & rear side) 24 Insulation behind �anels 24 Air gap behind panels 12 Insulation BUS rear 24 Membrane 8 Steel plates yoke 28 Air in yoke 2 Insulation yoke 28 Total number of nodes 186

adopted value was h:d [W/m2K]. It is important to consider in the calculations the fact that a part of the power of the fans (�IO-20%) is dissipated as heat, often remaining inside the BUS.

The example of the 64-m telescope illustrates a servo-loop­controlled ventilation system. This system has only fans. Whenever a temperature homogeneity of the BUS of, say, 3°C or better is obtained, the ventilation is switched off. The switched-off condi­tion was simulated in the calculation by using a small value, h = 0.2 [W/m2KJ, which expressed a negligible heat transfer by ventilation, Whenever temperature homogeneity is not obtained -for instance, because of asymmetric solar illumination, as dis­cussed below - the ventilation is switched on. The switched-on condition was simulated in the calculations by using a high heat­transfer coefficient, h '" 3 -10 [W/m2K], depending on the effi­ciency of the ventilation. In the model calculations, the temperature homogeneity and corresponding switch on-off condition were checked and controlled by if statements.

The example of the 30-m telescope illustrates a servo-loop controlled climatization system. This system has fans, air coolers, and air heaters. In this system, the ventilation is always running. Whenever the temperature of the BUS exceeds the temperature of the yoke by more than -1°C, the air inside the BUS is cooled; in the opposite situation, the air inside the BUS is heated. While Equation (1) described the process of ventilation, the heating and cooling in a climatization system is simulated by supplying or extracting a certain amount of heat from the ventilating air, when

IEEE Antennas and Propagation Magazine, Vol. 48, No.3, June 2006

(ton) -.Lton) J1000JIK)

infinite

infinite

infinite

'.

2 16 1000 44 176 21000 28 224 13000 5.5 88 2600 0.5 15 500 1.2 70 900 0.5 15 320

0.25 15 250 -620

8 100 3800 0.2 2 170

0.35 10 270 0.075 2 75 0.003 0.04 2.7 0.10 3 110 0.25 2 1000 6.5 180 3100

0.03 0.06 30 0.1 4 100

�330

necessary. In the model calculations, this perfonnance condition was checked and controlled by if statements. We mention that the 30-m telescope contains an independent servo-loop-controlled ventilation plus heating system to control the temperature homoge­neity of the yoke [II].

4. Examples of Thermal Model Calculations

4.1 Ventilation of a 64·m Telescope

This example explains design calculations of the BUS ventilation of a 64-m diameter radio telescope, similar in scale to the Sardinia telescope currently under construction [8], Although the final construction of the Sardinia telescope deviates from the model used here. the presented results nevertheless illustrate the potential o/such design calculaiions.

Among others, in the design study [19J the question was investigated for which insulation and ventilation a temperature

homogeneity of the BUS of, say, fj.T RL = TN - TL $; 3" C could be

achieved for an extreme case of solar illumination, for instance, when the telescope is tracking in such a way that the sun is con­stantly shining onto the right half (R) of the reflector, while the left

13

half (L) remains in shadow, as illustrated in Figure 3. As summa­rized in Table 3, the BUS was divided into 28 sectors of steel tubes and corresponding internal air volumes, with corresponding sec­

tions of the panels (front and rear side), insulation (partial or full, Figure 3), and a central hub (focus cabin). The model assumed that the ventilation used the air inside the BUS and 5-10% outside ambient air (through leaks). The calculations were made for a

summer day at Sardinia (geographic latitude qJ '" 40·) and air and

ground temperatures of the Mediterranean coastal area.

Figure 4 shows the calculated temperature difference, tJ.T RL , between the right side and the left side of the BUS throughout a day, under the conditions of no ventilation (h '" 0.2 "" 0), and venti­lation of efficiencies h = 3,6, and 10 [W/m2K]. In the calculations,

the ventilation was switched off whenever the performance specifi­

cation tJ.T RL S 3° C was fulfilled. The figure illustrates that in order

to fulfill the specification for partial insulation of the BUS, it was necessary to install a powerful ventilation of efficiency h "" 10 [W/m2K]. For a fully insulated BUS, only a moderate ventilation, of efficiency h "" 3 [W/m2K], was required, since the insulation behind the panels reduced the transfer of solar energy into the BUS. However, this may lead to higher panel temperatures, and perhaps to thermal-panel buckling [30]. It is not necessary that the ventilation runs all the time to fulfill the specification. For a BUS with rear-side cladding only and a ventilation efficiency of h = 10 [W/m2K], the servo-loop-controlled ventilation was running between 9 and 23 hours. For a BUS with insulation also behind the panels and ventilation efficiency h = 3 [W/m2KJ, the servo-loop­controlled ventilation was running between 9 and 19 hours. The amount of ventilation was 150,000 to 200,000 m3(h.

Figure 5 shows the calculated temperature of the steel of the 64'm BUS. In this figure, the panel labeled "SUN' was the solar illumination during one day (at 3 h intervals); the right side of the reflector was illuminated and the left side was in shadow. The panel labeled "NO(part.)" shows the temperature distribution of the 28 BUS segments for the partially insulated BUS, under the condi­tion of no ventilation. For comparison, the panel "NO(full)" shows the temperature distribution for the fully insulated BUS (Figure 3), again for no ventilation. The panel" h = 6 (part.)" shows the influ­ence of ventilation of efficiency h = 6 [W/m2K] for the partially insulated BUS. The temperature distributions shown in this figure can be used in an FEM calculation to predict the reflector-surface shape, the beam pattern, and part of the pointing error.

4.2. Climatization of the IRAM 30-m Telescope

The layout and operation of the thermal control of the IRAM 30-m telescope has been described earlier [10, 20]. A picture of the telescope and the c1imatization system is shown in [10, 11]; the capacity of the climatization is summarized in Table 2. We recall that the telescope is fully insulated and that the average tempera­ture of the BUS (Te) is slaved by the climatization system against

the reference temperature of the heavy yoke (Ty). Measurements

have shown that temperature homogeneity between the conditioned air and the steel of the BUS occurs within -30 minutes. The c1ima­tization uses the air inside the BUS and an -5% contribution within -30 minutes. The climatization uses the air inside the BUS and an

-5% contribution of outside ambient air. Under nonnal operating conditions, the thermal specification of the telescope of

Panels Ventilation

Climotizatian

DD Alidade/Fork

Figure 3. An extreme case of solar illumination is illustrated, in which throughout the day the right half of the reflector is con· stantly illuminated, while the left half remains in shadow. The BUS may be partially covered by insulation (rear side only), or fully covered by inSUlation (including insulation behind the panels). TR and TL are representative temperatures of the

right side and left side of the BUS.

� ()

0 '-' --'

I-

'" I-

-' '" I-<J

10

5

0

10

5

WITH Panel Insulation

0

10 20 Time of day (hour)

30

Figure 4. The temperature homogeneity of a 64·m telescope; the temperature difference, f"T RL' between the right side (illuminated) and the left side (in shadow) of the BUS is shown. The shaded area is the performance condition tJ.T RL :S 3" C. The parameter on the curves is the heaHransfer coefficient of the ventilation, h [W/m2KJ.

I

IEEE Antennas and Propagation Magazine, Vol. 48, No.3, June 2006

Sun h = 6(part.) NO(full)

12

10

8

6

4

2

o

-2

Figure 5. The solar illumination and calculated temperature distrihution of a 64-m telescope BUS, consisting of 28 sections (top left). Panel "Sun" is the solar illumination; panel NO(part.) gives the deviations from the average BUS tempera­ture for partial insulation and no ventilation; panel NO(full) gives the deviations for fuJI insulation and no ventilation; panel h = 6 (part.) gives the deviations for partial insulation and

ventilation of efficiency h = 6 [W/m2KJ. The temperature scale (0C) is on the right-band side; the bour of the day is indicated on the left side panels.

IEEE Antennas and Propagation Magazine, Vol. 48, No.3, June 2006

Ventilation Climatizotion

-10 0 10 -20 0 20 Diometer (m) 6 (ore.ee)

Figure 9. The calculated thermal bebavior of the lRAM 30-m telescope reflector surface with ventilation operating (no heat­ing and cooling of the air inside the BUS) and cIimatization (beating and cooling applied). The respective left panels show the best-fit reflector-surface shape predicted from the thermal calculations of Figures 6b and 6c, and used in the finite-ele­ment model. The respective right panels show the correspond. ing beam pattern at 230 GHz. The surface contours are in steps of 0.03 mm for ventilation, and in steps of 0.01 mm for climati­zation. The beam patterns have levels at -3 dB (full-width half­power), -10 dB, -20 dB, and -30 dB. The bour of the day is indicated.

15

(2a)

and

(2b)

is fulfilled. Heating of the inside air is required to counterbalance radiative cooling towards the sky (mainly at nighttime); cooling is required to counterbalance solar irradiation and dissipation of power from the fans.

The thermal model of the 30-m telescope (Table 3) contains the reflector surface panels, the air gap between the panels and the insulation covering the BUS, the rear-side insulation of the BUS, the steel network of the BUS and the air inside the BUS, the steel membrane between the BUS and the yoke, the yoke, the counter­weights, the insulation of the yoke, and the air inside the yoke. In the model, the BUS and the reflector are divided into four inner sections and a ring of eight outer sections, of approximately equal reflector surface area and mass. The FEM of the telescope was explained in [11]: it contained the BUS and the yoke. As found from holography measurements [11], this model allowed the cal­culation of thermal reflector-surface deformations with a precision of -0.005-0.01 0 mm. As also explained in [11], the incomplete FEM did not allow a full determination of temperature-induced pointing errors.

Using actual temperature measurements and model calcula­tions, the following illustrated that ventilation was not sufficient to fulfill the performance specification, Equation (2), of the 30-m telescope, and that climatization with heating and cooling were required. Temperature measurements of the BUS and yoke when operating only with ventilation (no heating and cooling; June, 1987) are shown in Figure 6a. We observed that for certain time

intervals, the performance specification I1TBy:;; 1" C was not ful­

filled. An example of temperature homogeneity of the BUS for operation with full c1imatization (June, 2004) is shown in Figure 7, with the arrangement of the corresponding temperature sensors

inside the BUS indicated in Figure 8. For this case, the perform­ance specification was fulfiUed.

The result of thermal-model calculations that corresponded to the conditions of ventilation and c1imatization and a realistic ther­mal environment are shovm in Figures 6b and 6c, respectively. The calculated temperatures of the BUS and yoke were then used in the FEM to derive the corresponding thermal deformation of the reflector surface and the corresponding beam pattern at 230 GHz (1.3 mm), as shown in Figure 9. The figure indicates (as was also verified by actual observations) that the reflector had an astigmatic shape in the case where onl y vent ilation was applied, and that the performance specification Equation 2 was not always fulfilled. However, when climatization with servo-loop-controlled heating and cooling of the ventilating air was applied, temperature homo­geneity between the BUS and the yoke was achieved, the reflector surface had small deformations, and the beam was clean. The cor­responding dependence of the focal length, l1F, and the accuracy,

crT (rms), of the reflector surface is shown in Figure 10. Without c1imatization, frequent focusing would be necessary to keep the focus stable to within M':>: AflO ,., 1.3 mm/IO = 0.15 nun . Since

the surface accuracy of the 30-m telescope is (5a .. 0.06mm, the

thermal surface error of (5T "" 0.06 mm, when operating only with

ventilation, would lead to a total surface accuracy of

(5 = )0'; + O'f "" 0.08mm, and a loss in gain of �25% at 230 GHz

16

(Ruze equation, [32]). Similar calculations, associated with tem­perature measurements, led to an improVed thermal control of the yoke [11].

Finally, we illustrate how thermal-model calculations allow defining the c1imatization system of a telescope. During the design of the 30-m telescope, we had to specify the cooling capacity of the control system that counterbalances the energy input from solar radiation. For this, we calculated the temperature difference between the BUS and the yoke (I1TBy) for full solar illumination

when tracking the sun throughout a day. Figure 11 shows the tem­perature difference predicted for different cooling capacities. It was evident that only a total Cooling capacity of at least -15 kW, as

actually installed, was sufficient to keep the BUS within the per­formance specification. A similar calculation was made of the heating capacity that counterbalances nighttime radiative cooling toward the sky.

15 -0 � (l> 10 .3 2 5 '" � E OJ f- a

E

15

:':: 10 .3 0 '- 5 '" 0.. f '" 0 ;,-

� 15 u � � 10 .3 � '" 5 0.. E '" 0 f-

Meosurement / Venti lotion only

,,'

llTSY . . -----.. -�.-�-._._--

0

B.Y

2 .Time (doys)

.'

Climotiza\ion

3

(0)

(b)

(c)

4

Figure 6. Data for the IRAM 30-m telescope: (a) The measured thermal behavior when operating with ventilation only (no heating and cooling of the BUS); (b) tbe results of model cal­culations for ventilation only; (c) the results of model calcula­tions for c1imatization (with beating and cooling). Curve B is the average temperature of. tbe BUS; curve Y is the tempera­ture of the yoke; curve A is the temperature of the ambient air.

The curve I1TBy is the measured or calculated temperature dif·

ference between the BUS and the yoke. Tbe gray band is the

performance specification /4TBY/S, I" C.

IEEE 'Antennas and Propagation Magazine, VOl. 48. No.3, June 2006

5. Telescope Mount

Thennal defonnations of the telescope mount primarily affect the pointing. The classical moun! (ali dade) - as, for instance, used on the Effelsberg, GBT, and Nobeyama telescopes - consists of large box and tube structures, occasionally being insulated. Venti­lation of the air inside the box and tube structures is technically complicated and inefficient, and experiments resulted in only some success. However, temperature sensors and inclinometers, together with FEM predictions of the alidades, seem to have given encour­aging results [ 12, 13; T. Pisanu, private communication] . The yoke mount of the IRAM 30-m telescope is insulated and ventilated; however, the necessity of ventilation was only recognized after 1 5 years of operation [1 1 J .

The smaller mm - and sub-rom-wavelength telescopes use a fork mount, which is prone to the thermal differences between the

A A. D

V' � v --e:/��� 14 ��������������4-�

o

_ 20 u !.., 18 ... 16

14 _ 20 " !.., 18 ... 16

14 _ 20 u !...... 18

-

16 14

o

5

5

10 15 UT [b'>u",,]

10 15 UT [hours]

20

J �

K -.

L --

.., j 20

Figure 7. The measured temperatures of the BUS and yoke of the IRAM 30-m telescope, with c1imatization in operation. For identification of the sectors A-H of the BUS, see Figure 8 and [31]. Plots J, K, and L are both arms and the top of the yoke. The heavy line is the reference temperature of lhe yoke used in the servo-loop climatization system.

IEE£3 Antennas and Propagation Magazine, Vol. 48, No. 3, June 2006

A

G

E

Figure 8. The distribution of .temperature sensors (black squares) in the BUS of the IRAM 30-m telescope. For each sec­tor, there are sensors at the front side (panel side) and the rear side.

---. E 0 . 5 E

LL 0 <l (/) � v - 0 . 5 0

LL

0 . 0 6 ,.......,

U) E '- 0 . 0 4 .......

.--." E E 0 . 0 2

... b

0 0 1 0 20

Time (hour)

Figure 10. The calculated thermal behavior of the IRAM 30-m telescope reflector surface for the case of ventilation (open cir­cles), and cIimatization (solid dots), predicted from the thermal calculations of Figures 6b and 6c, and used in tbe finite-ele­ment model. Shown are (a) the temperature-induced focus variation, t!.F , of the reflector, and (b) tbe reflector-surface degradation, eFT (rms value).

1 7

4 /""'. U 0 '-' 2 >-CD �

0

0 2 3 4 Time (days)

Figure 11. The determination of tbe cooling capacity of tbe c1imatization system for tbe IRAM 30-m telescope. 6.TBy is the temperature difference between the BUS and the yoke, calcu­lated for several total cooling capacities, as indicated (in kW). Tbe telescope tracked tbe sun, and on tbe second day the cool­ing system was switched on. The gray band is tbe temperature specification.

52 53 54 55 Ti m e (day)

56 57

Figure 12. The measured temperature of the. lRAM 15-m tele­scope fork mount. TL and TR are the average temperatures of the left and right fork arms; TR - TL is the corresponding tem­perature difference. TA is the ambient air temperatnre. Tbe sky was clear; the telescope was used for observations.

fork anus, mainly due to asymmetric solar i llumination. Insulation, in particular of a sophisticated design as applied on the IRAMlSEST 1 5-m telescopes [ 1 7}, results in a temperature homo­geneity and differential temperature stability between the fork arms

of -2°C under most environmental conditions, as illustrated in Figure 1 2. For the dimensions of the 1 5-m telescope fork (a height

'" 4 m, separation of arms "" 6 m) a temperature instability of 2°C results in an elevation-dependent (E) pointing error of approxi­

mately 4 cos (E) arcsec. Thermal-model calculations indicated that

it was possible to improve the thermal homogeneity of the individ­ual fork arms by ventilation; however, the same model calculations also indicated that it was difficult to improve the thermal differen­tial stability between the fork arms by ventilation. This is due to the fact that the fork arms are well-separated structures, allowing only little communication and exchange of the inside air. A com­plex servo-loop-controlled climatization system may provide improvement, however, a sophisticated thermal fayade (like an air­cooled fayade [ 1 7]) provides an easier and effective solution. Fre­quent pointing (which may, however, be inconvenient) can elimi­nate a large part of the thermal effects of the mount.

1 8

6. Summary

In a recent textbook on the construction of radio telescopes [33], Levy writes with respect to thermal considerations that "an accurate and practical analytical procedure that can incorporate thermal conductivity, convection, radiation, and reradiation appears to be beyond current technology because of overwhelming complexity, uncertainty in physical parameters, and requirements

for computer resources." We agree that it is rather difficult to use a structural finite-element model (FEM) to calculate the time­dependent thennal behavior Of a telescope for realistic environ­mental conditions. However" it is possible to predict the time­dependent thermal behavior of a telescope from a dynamic thermal model, and to use the data in the FEM to evaluate the radio per­formance. We have shown earlier [ 1 7] that this strategy was suc­cessful for telescopes that were thermally protected in a conven­tional way (paint, insulation). Here, we have shown that it is as well possible to use this strategy for the more-complex structures of ventilated and climatized telescopes. The (commercial) avail­ability of powerful (electric-circuit) network programs for calcula­tion ofthe thermal behavior allows this approach.

7. Acknowledgement

We are thankful for the information about the ASTE tele­scope and the 45-m Nobeyama telescope received from N. Ukita (NRO, Japan); of the Yebes 40-m telescope from J. Lopez-Perez (OAN, Spain); of the 50-m LMT telescope from R. D. Smith (USA, Mexico); and of the 64-m Sardinia telescope received from T. Pisanu (CNR, Italy). Part of the data of the 64-m telescope shown here were obtained while participating (A. G.) in the ther­mal-design study of the 64-m SRT, led by S . Busetti (VertexRSI, USA). The data of the IRAM 30-m and 1 5 -m telescopes were col­

lected in collaboration with J. Pefialver (IRAM, Spain) and M. Dan and P. Chaudet (IRAM, France). We thank the referees for their comments, and the Editor, R, Stone, for dealing with this paper, and its authors.

8. References

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2 . N. Ukita,. R . Kawabe, M. Ishiguro, H . Ezawa, Y . Sekimoto, T. Hasegawa, S . Yamamoto, LMSA Antenna Working Group, K. Miyawaki, and S. Marsumoto, "NRQ lOom submillimeter tele­scope," SPIE, 4015, 2000, p. 1 77.

3 . http://www .mpifr-bonn.mpg.de/APEX.

4. A. Wootten, "Atacama Large Millimeter Array," SPIE, 4837, 2003, p. 1 1 0.

5. N. Ukita, M. Saito, H. Ezawa, B. Ikenoue, H. Ishizaki, H. Iwashita, N. Yamaguchi, T. Hauakawa, and ATF-J Team, "Design and Performance of the ALMA-J Prototype Antenna," SPIE, 5489, 2004.

6. J. A. Lopez-Perez (OAN, Spain), private communication.

IEEE Antennas and Propagation Magazine. Vol. 48, No. 3, June 2006

7. F. P. Schloerb and L. Carrasco, "The Large Millimeter Tele­

scope," SPIE, 5489, p. 754, 2004 (also http://www.lmtgtm.org).

8. G. Grueff, G. Alvita, R. Ambrosini et aI., "Sardinia Radio Tele­scope: The New Italian Project," SPIE, 5489, 2004, p. 773.

9. P. R. Jewell and R. M. Prestage, "The Green Bank Telescope," SPIE, 5489, 2004, p. 3 1 2 (also http://www.nrao.eduJGBT).

1 0 . J. W. M. Baars, A. Greve, B. G. Hooghoudt, J. Peilalver, "Thermal Control of the JRAM 30-m Millimeter Radio Tele­scope," Astron. Astrophys. , 195, 1 988, p. 364.

1 1 . A. Greve, M. Bremer, J. Pefialver, P. Raffin, D. Morris, "Improvement of the IRAM 30-m Telescope from Temperature Measurements and Finite Element Calculations," IEEE Transac­tions on Antennas and Propagation, AP-53, 2005, p. 8S 1 .

12. R. Ambrosini, G. Grueff, Morsiani, G. Maccaferri, P. Zacchiroli, A. Orfei, "Analysis of the Alidade Temperature Behaviour of the Medicina VLBI Radio Telescope," Astrophys. Space Sci. , 239, 1 996, p. 247.

13. A. M. Bayley, R. 1. Davis, J. S. Haggis, and H. Karcher, "Thermal Effects on the Pointing of the 32-m MERLIN Radio Telescope at Cambridge," Astron. Astrophys. , 238, 1 994, p. l OS 1 .

1 4. R . M . Prestage, K. T . Constantikes, D . S . Balser, and J. J . Con­don, "The GBT Precision Telescope Control System," SPIE, 5489, 2004, p. 1 029.

15 . K. Akabane, "A Large Millimeter Wave Antenna," Intern. J. of Infrared and MM Waves, 4, 1 983, p. 793 .

1 6 . R . S . Booth, G . Delgado, M . Hagstrom, et al., ''The Swedish­

ESO Submillimeter Telescope (SEST)," Astron. Astrophys. , 2 1 6, 1 989, p. 3 1S .

1 7 . A . Greve, M. Dan, and J . Peftalver, "Thermal Behavior o f Mil­limeter Wavelength Radio Telescopes," IEEE Transactions on Antennas and Propagation, AP-40, 1 992, p. 1 375.

1 8 . A. Greve and G. MacLeod, "Thennal Model Calculations of Enclosures for Millimeter Wavelength Radio Telescopes," Radio Science, 36, 200 I , p. 1 1 1 1 .

1 9. A. Greve, "64-m SRT Thennal Design Study," VertexRSI, Santa Clara, CA, USA, 2000.

20. J. W. M. Baars, A. Greve, H. Hein, D. Morris, J. Peiialver, and C. Thurn, "Design Parameters and Perfonnance of the IRAM 30-m Millimeter Radio Telescope," Proc. IEEE, 82, 1 994, p. 687.

2 1 . P. Stangerup, "ESACAP, a Minicomputer-Oriented Network Analysis Program," ESA J. , 6, 1 982, p. 301 (and IEEE Circuits and Devices Magazine, 4, 1 988, p. 20).

22. A. Chapman, Heat Transfer, New York, MacMillan, 1 974, 1 996.

23. A. Bejan, Heat Transfer, New York, John Wiley & Sons Inc., 1 993.

IEEE Antennas and Propagation Magazine, Vol. 48, No. 3, June 2006

24. J. D. Bregman and J. L. Casse, "A Simulation of the Thennal Behaviour of the UK-NL mm Wave Telescope," Intern. J. of Infra­

red and MM Waves, 6, 1985, p. 2S.

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26. W. A. Siegmund, "Design of the Apache Point Observatory 3.5 m Telescope: V. Telescope Enclosure Thennal Modeling," SPIE, 1236, 1 990.

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29. 1. Cheng, "Forced Air Cooling at High Altitude," MMA Memo, 203, NRAO, USA, 1 998 (httpJlwww.nrao.eduiALMA)

3 0. A. Greve and D. Morris, "Repetitive Radio Reflector Surface Deformations," IEEE Transactions on Antennas and Propagation, AP-53, 200S, p. 2 1 23.

3 1 . M. Bremer and 1. Pefialver, "FE Model Based Interpretation of Telescope Temperature Variations," Proc. SPIE, 4757, 2002, p. 1 86.

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33. R. Levy, Structural Engineering of Microwave Antennas, New York, IEEE Press, 1 996. @J

Correction

Two equations in B. Polat, "Remarks on the Fundamental Postulates on Field SingUlarities in Electromagnetic Theory", IEEE Antennas and Propagation Magazine, 47, 5, October 2005, pp. 47-54, should have appeared as follows:

- aB -m curIE + - = -)s

at ( l a)

The following equation was at the end of Section 7.2 , on page 52:

1 9