Abstract:
A thermal control system for a space body uses an active control means to prevent laser beam radiation damage to a heat radiator. A conventional louver and louver actuator are coupled to an active overdrive actuator that closes the louver when hostile laser radiation is present. An extended bimetallic coil spring with a heater therein rotates opposite to the louver actuator in an increasing temperature environment. A cam of the overdrive actuator engages a louver arm when hostile laser radiation is present, otherwise, the louver can move freely within the cam.

Description:
STATEMENT OF GOVERNMENT INTEREST 
     The invention described herein may be manufactured and used by or for the Government for governmental purposes without the payment of any royalty thereon. 
    
    
     BACKGROUND OF THE INVENTION 
     This invention relates generally to space vehicles and, in greater particularity, relates to a device and method of protecting selected surfaces on the space vehicle from external incident radiant energy. 
     Many satellite components require temperature control within a narrow band to assure long life and correct operation. One temperature control method is to enclose the instrument either singly or in a group inside a chamber which is designed to have good internal thermal coupling so as to give near uniform internal temperature. One side of the chamber is a radiator: a good conductor which is thermally coupled to heat sources inside the chamber and which has a high emissivity surface facing dark space. Finally, this radiator is covered by louver blades arranged so they can be opened or closed, exposing or covering the radiator. Rectangular blades in a venetian blind like arrangement are illustrated in  FIGS. 1 and 2 . A pinwheel arrangement has also been used. In either case, a bimetallic coil spring, thermally coupled to the radiator senses the temperature of the radiator, opening the louver when the radiator is warm and closing it when the radiator is cool with respect to the control range, and generally finding an intermediate position to maintain the specified temperature. This thermo-mechanical mode of operation is called the “passive mode.” 
     More precise control of the radiator temperature is accomplished by adding an electronic device to sense the radiator temperature and to control an electric current to a heater which is bonded onto the bimetallic coil. This “active mode” gives greater rotation of the louver per unit temperature change due to its amplification and accomplishes quicker, more precise temperature control; solar and earth albedo energy are prevented from entering the louver by three methods:
         (1) keeping the radiator surface always directed toward dark space,   (2) providing a thermal fence to shield the radiator, and   (3) coating the radiator and louver blades with a material which gives a low solar absorptivity while still giving high emissivity.       

     If hostile high energy radiation such as a laser beam is directed at the louver, it presents a dual threat:
         (1) the energy may be absorbed into the exposed surface materials, heating them until they are destroyed, and   (2) as the radiant energy heats the exposed surfaces, that heat is conducted to the bimetallic coil springs causing the coil springs to open the louver completely exposing the radiator and admitting even more radiation. Then, the thermal control louver is rendered inoperative and more radiant energy is admitted directly into the radiator.       

     Existing louvered radiator designs are extremely vulnerable to laser attack because of the light weight materials generally used, the sensitivity of their performance to the radiative characteristics of their surface, and in some cases, the fundamental conflict between radiative characteristics desirable for their normal function and those desirable for rejecting laser radiation. 
     These drawbacks have motivated the search for alternative devices which can prevent laser damage to radiators in space. 
     SUMMARY OF THE INVENTION 
     A conventional bimetallic temperature sensitive actuator controls the movement of a louver used to control heat from a radiator. If satellite components to be protected reach an excessive operating temperature, the actuator, being thermally coupled to the radiator, opens the louver thus permitting excess heat to be radiated into space. When the components cool, the actuator closes the louver to retain heat within the system. 
     In the case of hostile high energy radiation, (i.e. a laser beam) directed in the direction of the louver, the energy may be absorbed into the exposed surface materials heating them until they are destroyed. This heat is conducted to the actuator which opens the louver and further exposes the internal components to excess radiation which would not have been admitted if the louver remained closed. 
     In order to counter this destructive radiation that is incident on the louver, a combination of steps are taken. Firstly, the louver surface is coated with a protective coating to prevent the absorption of incident radiation. Secondly, a bimetalic overdrive actuator positioned opposite to the louver actuator, acting through a cam and pin assembly, drives the radiator louver in the opposite direction than that of the louver actuator. A shield attached to the overdrive actuator, normally in the open position, allows the incident radiation to heat a bimetallic coil. This coil turns counter to the radiator actuator bimetallic coil forcing the louver radiator to close. 
     The cam and pin arrangement allows the louver actuator to rotate without interference from the overdrive actuator unless excessive heat is received by the overdrive actuator. Thus, in the presence of excessive thermal radiation, the louver and the shield are closed. 
     An electronic sensor is attached to the thermal control system so that a more rapid response is produced than by just the bimetallic coils of the overdrive actuator alone. 
     It is therefore an object of the present invention to provide for a laser hardened thermal control system for a satellite or other space object; 
     It is another object of the present invention to provide for a protective coating to the materials used in the thermal control system; 
     It is another object of the present invention to provide for an overdrive actuator that closes a louvered radiator upon receiving laser radiation; 
     It is another object of the present invention to provide for an active overdrive actuator rather than passive. 
     These and many other objects and advantages of the present invention will be readily apparent to one skilled in the pertinent art from the following detailed description of a preferred embodiment of the invention and the related drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a plan view of the louvered thermal control system of the present invention. 
         FIG. 2  is a cross section taken through one louver assembly of  FIG. 1  of the present invention; 
         FIGS. 3A ,  3 B, and  3 C shows the operation of the cam and pin arrangement of the present invention and is taken along lines IIIA-IIIA of  FIG. 2 ; 
         FIG. 4  is a functional block schematic of an active thermal control used on the thermal control system of the present invention; and 
         FIG. 5  is a cross-section of the materials applied to protect the surfaces. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     Referring to  FIG. 1 , a thermal control system  10  is shown. Louvers  12  control heat flow from a radiator  14 , shown in FIG.  2 . Conventional louver actuators  16  sense the temperature of radiator  14  and cause louvers  12  to rotate to an open position to allow the flow of heat to space. Actuators  16  have therein bimetallic coil springs with heaters thereon so that when heated, louvers  12  rotate open. Overdrive actuators  18  upon receiving a high temperature rise indication cause louvers  12  to be placed in the closed position, shown in  FIGS. 2 and 3A , even when louver actuators  16  desire to rotate open louvers  12 . Details to be provided herein below. 
     Specific requirements of louvered temperature-control radiator  14  vary substantially from one spacecraft to another, and within any one spacecraft, depending on (a) area available; (b) internal heat loads—average power, peak power, and duty cycles; (c) temperature-control-range requirements; (d) the size, location, and thermal characteristics of other parts of the spacecraft that are within the hemispheric field of view of the radiating surface; and (e) the ranges and variations of normal and abnormal directions of view of the surface normal with respect to the sun, the earth (with sunlit and dark as essential distinctions) and space. This variety tends to make it impossible to define a general set of radiator functional requirements as a baseline for laser hardening; however, the task becomes more reasonable when looked at from the viewpoint of how dominant the laser-resistance requirements are, and in recognition of the basic design choice that is always available, that of the size of radiator  14  that is most appropriate to meeting its functional requirements. 
     Although a battery radiator is used for purposes of explaining the invention, other types of radiators are functionally equivalent. In this case radiator  14  is a wall of a battery, not further shown. 
     Battery radiator  14  has three attributes: First, the radiator surface itself has excellent heat-sinking capabilities; it is the solid aluminim base of the battery itself. Second, to accommodate the high worst-case heat loads generated by internal dissipation in the battery, an unlouvered passive “bias” radiator is incorporated, in addition to the actively controlled louvered radiator. Third, the sun never directly impinges on the main radiator in normal mission attitude (a thermal fence  20 —a rudimentary sunshade—is provided in order to preserve this condition for small sun angles on the “wrong” side of the orbit plane). The absorptivities and emissivities of the louver-blade coatings and radiator coatings have been selected to take advantage of the fact of no solar illmination; in particular, high emissivities can be chosen for the radiator surface and low emissivities for the lower blade surface without regard to the absolute solar absorptivity or the α/ε ratio—radiators in spacecraft locations that do see the sun must take α/ε into account. The impact of relative solar orientation results in a substantial variety of surface-finish choices and combinations for louver blades and inner radiator surfaces in radiators for various functions on the spacecraft, of which the battery radiator is only one. 
     In spite of the range of design parameters that will consequently characterize different radiators for the infinite variety of spacecraft applications, it should be noted that the detailed requirements of battery radiator  14  used have not resulted in a hardening solution that is peculiar to the specific application. The same invention is applicable to louvered radiators with substantially different load-dumping, temperature, and radiant-interface requirements; the area of radiator  14  and the temperature set-point and gain of a control loop would be the principal design parameters that would be adjusted to adapt to differing applications. 
     Since Denton silver has both a low absolute emissivity and a relatively favorable α/ε ratio for sun rejection, it can be used on both sun-exposed and sun-shaded louvers  12 . The Z93 white paint has excellent emissivity and a very good α/ε ratio, so it can be substituted for second-surface teflon in sun-exposed radiator applications with little or no compromise in performance. 
     The threat to thermal control system  10  is hypotheized to be a laser pulse of 100 seconds total duration, of 1 watt per square centimeter intensity at onset and at termination, of 10 watts per square centimeter intensity at peak, following a cosine-squared law for the intensity variation with time, depositing 550 joules per square centimeter total energy, and generated by a carbon dioxide laser at 10.6 centimeters wavelength. 
     No amelioriation has been allocated to partial shielding by other spacecraft parts or to non-normal incidence. In addition, it has been postulated for conservatism that the full threat could be (transiently) incident on the inner surfaces of louvers  12 ; these surfaces have also been made hard against direct exposure, by coating them, also, with Denton silver. Analytic consideration has been given to the effects of changing these inner-surface finishes, for the eventuality that the assumption of direct exposure turns out to be unnecessarily pessimistic. Blackened inner surfaces, rather than Denton-silvered, would raise the maximum attained temperature of the radiator  14  proper somewhat, while substantially lowering that of the louver blade. Both choices lead to acceptable attained temperature limits for both components, and so a change from Denton silver would be dictated by factors that are presently not operative, such as higher threat levels, different time profiles, or weight limitations that call for consideration of blade materials lighter than Kovar. 
     The solution to the above problems is: (1) the use of protective coatings to exposed surfaces to prevent the absorption of the incident hostile laser energy, and (2) overdrive actuator  18  having a laser beam sensor  22 . 
     Referring to  FIG. 5 , a Denton silver coating  26 , is applied to the top of overdrive shield  24 , to radiator louver  12 , both sides preferrably, and to other exposed parts such as a louver arm  28 . 
     The principal characteristics of Denton silver coating  26  are given in Table 1. 
     
       
         
               
             
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                 Principal characteristics of Denton-silver coating 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 a. 
                 Process 
               
               
                   
                 Substrate - Mirror finish, flat or slightly 
               
               
                   
                 curved, metal or glass (also tapes and films 
               
               
                   
                 attached to solid substrates for coating purposes) 
               
               
                   
                 Primer film - Approximately 500 Angstroms (Å) 
               
               
                   
                 Inconel   
               
               
                   
                 Silver film - Approximately 100 Å, purity 99.8% 
               
               
                   
                 Protective interface film - Approximately 1300 Å 
               
               
                   
                 reagent grade Al 2 O 3   
               
               
                   
                 Protective surface film - Approximately 1300 Å 
               
               
                   
                 reagent grade SiO 2   
               
               
                 b. 
                 Finished Coating 
               
               
                   
                 Reflectance - More than 98% at any wavelength 
               
               
                   
                 from 0.5 to 50 micrometers 
               
               
                   
               
             
          
         
       
     
     In particular, suitable substrate materials may be aluminum, nickel, stainless steel, glass or tape. Surfaces to be coated shall have mirror finish and surfaces to be coated shall preferentially be flat or slightly curved whereby the angle of deviation shall not exceed 30°. 
     When faces join in an angle greater than 30°, the respective faces shall be coated separately with the alternate face masked. The radius of edges and corners shall be as small as possible so as to minimize areas of marginal coating quality such as optical imperfection and low adhesion. Surface steps shall be avoided. 
     The coating process starts with an Inconel primer film  32  made from reagent grade Inconel. The Inconel film shall be deposited from a tungsten resistance heater to a thickness of approximately 500 Angstrom in 5×10−5 torr vacuum in accordance with U.S. Pat. No. 3,687,713 . 
     Next, a silver film  34  of a purity greater than 99.8% is deposited. Silver film  34  shall be deposited from a tungsten resistance heater to a thickness of approximately 1,000 Angstrom in 5×10−5 torr vacuum in accordance with U.S. Pat. No. 3,687,713. 
     Although Denton silver was used as protective coating  26  against a CO 2  laser beam, other types of coatings are clearly feasible and are applied in a similar manner as described above where different types of lasers are used. 
     In order to protect radiator  14  against a laser beam  40 ,  FIG. 2 , radiator louver  12  must be rapidly closed against the normal opening tendency supplied by convential louver actuator  16 . 
     Referring to  FIG. 1 , thermal control system  10  has two louvers  12  shown. Additional louvers  12  are possible depending on heat transfer requirements. As shown, louver actuators  16  and overdrive actuators  18  are at opposite ends of louvers  12 . Although this placement is preferred because of present devices, the placement at one end of these actuators  16  and  18  is also possible and the principles of this invention are still applicable even though the mechanical design would be complicated to a greater degree. 
     In order to describe the operation of this invention a partial cross section,  FIG. 2 , is taken through the longitudinal axis along lines II-II of FIG.  1 . 
     In  FIG. 2 , convention louver actuator  16  having a bimetallic coil spring therein with attached heater, not shown, is connected to louver  12  by an arm  44 . The heater in actuator  16  receives driving current in response to a temperature radiator sensor  42 . The current is controlled by means of a circuit shown in  FIG. 4  where temperature sensor  42  sends data to a temperature control device  48  that in turn sends current to a heater  50  such that a higher temperature causes actuator  16  to open louver  12  to allow heat radiation. 
     Louver  12  is further connected to a pin arm  52  that rotates in overdrive actuator  18 . The opening of louver  12  allows heat to flow from radiator  14  through an aperature  54 . Pin arm  52  turns on an axle  56  which is mounted in a cam  58  of overdrive actuator  18 A. A bearing  60  allows for minimum friction between axle  56  and cam  58 . Cam  58  is mounted in a drive support  62  with a bearing  96 . Attached to cam  58  is a drive shaft  64 . Drive shaft  64  is mounted to a center support  66  with a bearing  68  and to a end support  70  with a bearing  72 . Further attached to cam  58  is overdrive shield  24 . On the other end of shaft  64 , a shield support  74  is mounted to both shaft  64  and shield  24 . A counter balance  75  minimizes the amount of torque needed to move shield  24  and louver  12 . 
     A bimetallic overdrive assembly  76 , only one shown in detail, is mounted to support  62  and shaft  64 . The purpose of an extended bimetallic coil spring  78  is to expose as much as possible of coil  78  to incoming laser radiation beam  40  so that the heating provided causes spring  78  to counter rotate to the bimetallic coil spring mounted in louver actuator  16 . If so required, additional bimetallic coils  78  can be mounted to shaft  64  to provide the necessary torque and heating surface to close louver  12  to laser radiation  40 . 
     In addition to or in the alternative, a heater  80 , shown in outline on spring  78 , can heat bimetallic coil spring  78  to provide the necessary torque in a much quicker manner. This is preferable since a quicker closing of louver  12  can be obtained without possible damage to radiator  14 . The presence of laser radiation  40  is detected by a sensor  22  which sends data to a temperature control  82 . The circuit provided would be similar to that shown in FIG.  4 . Sensor  22  is shown as being flat but a more omni-directional sensor  22  will be used to detect laser radiaton  40  at different angles. 
     To better understand the interaction between cam  58  and a pin  84  of pin-arm  28  a cross section along lines III A-III A is shown in FIG.  3 A. 
       FIG. 3A  shows shield  24  in a closed position resting against a stop  86  when laser radiation  40  is received and responded to.  FIG. 3C  shows cam  58  in the normally open position with shield  24  resting against a stop  88 . The symbols shown in  FIG. 3C  are hereafter used in an analysis of the interaction between bimetallic overdrive assembly  76  and pin  84  of pin-arm  28  that is attached to louver  12 . An intermediate position is shown in  FIG. 3B  where cam  58  has not engaged pin  84 . 
     In normal operation pin  84  can move through a 90° angle. Upon the receipt of laser radiation  40 , bimetallic overdrive assembly  76  causes cam  58  to move in a counter-clock wise direction. If sufficient energy is received, pin  84  is engaged and turned to the position shown in  FIG. 3A  where both shield  24  and louver  12  are in the closed position. Referring to  FIG. 3A , cam  58  has a counter balance  90  mounted opposite shield  24 . Shield  24  is mounted to an arm  92  that has therein a pin engagement slot  94 . As shown in  FIG. 3C , when cam  58  is in the fully open position, pin  84  can rotate through a full 90 degree angle without contacting slot  94 . In the fully closed position,  FIG. 3A , slot  94  forces pin  84  into a vertical position thus closing louver  12 . 
     In the following analysis, heater  80  is not considered attached to bimetallic coil spring  78 . This is named the “passive mode” and provides a minimum response to the intended threat assumed by the present invention. 
     The following nomenclature is used throughout the analysis presented:
         T=temperature, °C.   T o =set point temperature   ΔT=temperature change, °C.   P=Coupling load, in. -lb   α=bimetallic spring angular thermal expansion coefficient, degrees/°C.   k=bimetallic spring angular spring rate, in.-lb/deg.   θ=angular positions, degrees, see  FIG. 3C     A=allowable angular travel between louver and shield, degrees=90°.   Subscripts:
           L=louver   S=shields   o=initial condition   
               

     For each of the bimetallic springs which drive louver  12  as well as shield  24 , the following relationship exists between the spring angular position and temperature change, i.e.
 
θ=θ o +α T   ΔT    (1) 
 
     When overdrive spring  78  is coupled (i.e. contacted) with the louver spring, not shown, a constraining force will be developed and Equation (1) is no longer valid. A general coupling equation is derived which will relate the angular position of louver  12  and shield  24  for arbitrary initial angular position and for any temperature changes for louver  12  and for shield  24 . 
     Assume that at certain temperature changes, ΔT L  and ΔT S , louver  12  and shield  24  are coupled as shown in FIG.  3 C. Louver  12  rotates through an angle θ L  and shield  24  rotates an angle θ S  and their final positions are designated as θ L  and θ S , respectively. When the coupling load between them is P, the compatibility condition is:
 
θ L +θ S   =A    (2)
 
     But the angles are individually given by: 
               θ   L     =       Δ   ⁢           ⁢     T   L     ⁢     α   L       -     P     K   L       +     θ   OL               (   3   )                 θ   S     =       Δ   ⁢           ⁢     T   S     ⁢     α   S       -     P     K   S       +     θ   OS               (   4   )             
 
     The first term on the righthand side of Equations 3 and 4 gives the amount of unrestrained rotation for a given temperature rise and the second term represents the reduction of rotation due to the coupling load. The third terms are the initial locations. 
     Substituting Equations 3 and 4 into Equation 2 and solving for P gives:
 
P=X/Y   (5)
 
where: 
             X   =       Δ   ⁢           ⁢     T   L     ⁢     α   L       +     Δ   ⁢           ⁢     T   S     ⁢     α   S       +     θ   OL     +     θ   OS     -   A             (   6   )               Y   =       1     K   S       +     1     K   L                 (   7   )             
 
Substituting Equation 5 into Equation 3 gives: 
               θ   L     =       Δ   ⁢           ⁢     T   L     ⁢     α   L       -     X       K   L     ⁢   Y       +     θ   OL               (   8   )             
 
where:
 
ΔT L   =T   L   −T   OL    (9)
 
ΔT S   =T   S   −T   OS    (10)
 
and X, Y are given in Equations 6 and 7.
 
     Equation 8 is the general coupling equation which allows arbitrary louver  12  and overdrive spring  76  characteristics and initial locations. For the configuration shown on  FIG. 3C , all bimetallic springs are identical, so that α S =α L =α, and k s =2k L =2k. For this case Equation 8 can be reduced to: 
               θ   L     =       Δ   ⁢           ⁢     T   L     ⁢   α     -       2   3     ⁡     [       (       Δ   ⁢           ⁢     T   L       +     Δ   ⁢           ⁢     T   S         )     +   α   +     θ   OL     +     θ   OS     -   A     ]       +     θ   OL               (   11   )             
 
     Since in Equation 5 we define the coupling load as P = X/Y, the temperature rise required for coupling to start can be found by setting P=0 or X=0. 
     Thus, Equation 6 becomes: 
             X   =         Δ   ⁢           ⁢     T   L     ⁢   α     +     Δ   ⁢           ⁢     T   S     ⁢   α     +     θ   OL     +     θ   OS     -   A     =   0             (   12   )             
 
     Now substituting Equation 9 and Equation 10 into Equation 12 gives:
 
(T L   −T   OL )α+( T   S    −T   OS )α+θ OL +θ OS   −A= 0   (13)
 
     For the special case of T L =T S =T, the above equation leads to: 
             T   =       A   -     θ   OL     -     θ   OS     +     α   ⁡     (       T   OL     +     T   OS       )           2   ⁢           ⁢   α               (   14   )             
 
     The temperature rise required to close louver  12  can be determined by setting θ L =0 in Equation 8, or 
                 α   L     ⁢   Δ   ⁢           ⁢     T   L       =       x       K   L     ⁢   Y       -     θ   OL                             
 
     Another special case of interest is when only one of the overdrive springs  78  is heated. For this case, K S =K L =K, then Equation 7 leads to K L Y =2, and for θ L =0, Equation 8 becomes: 
               αΔ   ⁢           ⁢     T   L       =       X   2     -     θ   OL               (   17   )             
 
     Substituting the definition of X from 6, Equation 17 is simplified to: 
                 Δ   ⁢           ⁢     T   S       -     Δ   ⁢           ⁢     T   L         =       A   -     θ   OS     +     θ   OL       α             (   18   )             
 
     The Chace 6650 bimetallic spring  78  angular rotation-temperature relationship can be described by the following linear equation: 
             θ   =       θ   o     +       α   T     ⁢   Δ   ⁢           ⁢   T               (   19   )             
 
where: θ o =initial angular position for ΔT=o, degrees
         αT =bimetallic spring angular thermal expansion coefficient degrees/degree °C.       

     Since the overdrive springs  78  are elongated from an ordinary spring, a Tenney chamber test was performed to determine α T . The average α T  was computed to be 10.6 degrees/°C., by using a least square straight line fit technique. In the subsequent calculations, a nominal value of:
 
α T =9 Degrees/°C.=5 Degrees/=°F.   (20)
 
is used. This is the design value for this particular spring which was calculated from the Chace design manual.
 
     It is informative to do some additional analysis of the laser test conditions. Using the overdrive spring  78  characteristics and equation 18 for only one overdrive spring heated, it is estimated that the temperature of the overdrive spring  76  is at louver  12  closing, i.e. 
                 Δ   ⁢           ⁢     T   S       -     Δ   ⁢           ⁢     T   L         =         A   -     θ   OS     +     θ   OL         α   T       =           90   ⁢   °     -     5   ⁢   °     +     15   ⁢   °       5     =     20   ⁢   °   ⁢           ⁢     F   .                   (   21   )             or                             (       T   S     -     T   OS       )     -     (       T   L     -     T   OL       )       =     20   ⁢   °   ⁢           ⁢     F   .               (   22   )             then                           T   S     =         T   OS     +     (       T   L     -     T   OL       )     +   20     =       77   +   12   +   20     =     109   ⁢   °   ⁢           ⁢     F   .                   (   23   )             
 
     For the case where both overdrive springs  78  are heated by laser radiation  40 , the temperature T S  at louver  12  closing can be calculated using Equation 8 by letting θ L =0 and K L Y= 3/2, and use Equation 6 for x, i.e. 
             0   =       Δ   ⁢           ⁢     T   L     ⁢   α     -       2   3     ⁢     (       Δ   ⁢           ⁢     T   L     ⁢   α     +     Δ   ⁢           ⁢     T   S     ⁢   α     +     θ   OL     +     θ   OS     -   A     )       +     θ   OL               (   24   )             
 
     which can be simplified to: 
                 2   ⁢           ⁢   Δ   ⁢           ⁢     T   S       -     Δ   ⁢           ⁢     T   L         =         2   ⁢           ⁢   A     +     θ   OL     -     2   ⁢     θ   OS         α             (   25   )                 T   S     =       T   OS     +       1   2     ⁢       (       Δ   ⁢           ⁢     T   L     ⁢   α     +     2   ⁢           ⁢   a     +     θ   OL     -     2   ⁢     θ   OS         )     α                 (   26   )             
 
From the tests it was determined that 
         T   S     =       77   +       1   2     ⁢       (       12   ×   5     +     2   ×   90     +   15   -     2   ×   5       )     5         =     101.5   ⁢   °   ⁢       ⁢     F   .             
 
     Assuming the overdrive spring  78  temperature rises linearly, then, from the test data, the rate of temperature rise is 
             =         107   -   75     34     =     1   ⁢   °   ⁢       ⁢     F./second                 (   27   )             
 
Then, if both springs are illuminated by the laser, the final temperature T S =100° F. can be reached 9 seconds sooner, or it would take 25 seconds to close the louver if both the overdrive springs  78  are heated, instead of 34 seconds.
 
     Although the invention has been described with reference to a particular embodiment, it will be understood to those skilled in the art that the invention is capable of a variety of alternative embodiments within the spirit and scope of the appended claims.