Patent Publication Number: US-7712677-B1

Title: Water heater and control

Description:
RELATED APPLICATIONS 
     The present application is a continuation-in-part of U.S. patent application Ser. No. 10/382,056, filed Mar. 5, 2003, for “Water Heater and Control,” which is assigned to the same assignee as the present application. 
     The present application is related to U.S. patent application Ser. No. 09/745,686, filed Jan. 3, 2000, entitled “Hot Water Heater Stacking Reduction Control,” which is assigned to the same assignee as the present application, and which is fully incorporated herein by reference. Further, the present application is related to concurrently filed, and commonly assigned, U.S. Patent Applications entitled “Method and Apparatus for Safety Switch” Ser. No. 10/424,257, “Method and Apparatus for Thermal Power Control” Ser. No. 10/382,050, and “Method and Apparatus for Power Management” Ser. No. 10/382,303, all of which are fully incorporated herein by reference. 
    
    
     BACKGROUND 
     1. Field of the Invention 
     The present invention relates to water heaters and more particularly to a water heater with an improved water-heater-controller assembly and an improved water-heater-control method. 
     2. Description of Related Art 
     Water heaters are used in homes, businesses and just about any establishment having the need to heat water. Water heaters heat water using the simple “heat rises” principle. In operation, water heaters heat cold or ambient temperature water entering at or near the bottom of the water heater to a desired temperature using a gas-fired burner, an electric heater or some other form of energy. During a heating cycle, the cold or ambient temperature water at the bottom of the water heater becomes hotter and begins to rise towards the top of the water heater. Denser water, once on top of the water being heated, falls toward the bottom of the water heater so that it can be heated to the desired temperature. After the temperature of the water at the bottom of the water heater reaches a certain desired temperature, the water heater stops heating the water. 
     When demand for hot water arises (e.g., someone turns on a faucet to run a shower), fresh, cold or ambient water enters the water heater and “pushes out” or supplies the hotter water at or near the top of the water heater. When a sufficient amount of the hotter water exits from the top of the water heater so that the fresh, cold or ambient water entering the bottom causes the temperature of the water at the bottom of the tank to drop below the desired temperature, the water heater repeats the heat cycling. 
     A conventional water heater typically has at least one heating element or “heater,” such as a gas-fired and/or electric burner. To take advantage of the “heat-rises” principle, the heater is located at or near the bottom of the water heater. Each water heater typically also has at least one thermostat or controller for controlling the heater. 
     To facilitate the heating of water, the controller receives signals related to the temperature of the water. When these signals indicate that the water temperature is below a predetermined threshold, for example, when the water temperature is below 120 degrees Fahrenheit, the controller turns on the heater and the water at or near the bottom of the water heater begins to heat. After some time, the temperature of the water at the bottom of the water heater increases to a second threshold, which, for example, may be about 140 degrees Fahrenheit. When receiving signals indicating that the water temperature at the bottom of the tank is greater than the second threshold, the controller causes the heater to reduce its heat output or, alternatively, causes the heater to turn off. The heat cycle begins again when the temperature of the water at the bottom of the water heater drops below the first threshold. 
     Unfortunately, the signals received by the controller only indicate the temperature of the water close to or at the water heater&#39;s bottom. Consequently, the water at the top of the water heater, i.e., the water supplied upon demand, may be at a different temperature from the water at the bottom. The water at the top is typically hotter than or close to the same temperature as the water at the water heater&#39;s bottom. Further, depending on demand for water, heat cycling, and heat loss, water temperature throughout the water heater might not equalize. Generally, in operation, the temperature of the water in the water heater does not equalize, but rather has one or more temperature gradients. That is, there may be hot and cold “spots” within the water heater, which can cause problems with outgoing temperature of the water. In some cases, these gradients may become substantial. 
     In one situation, when the demand for hot water from the water heaters is rapidly cycled on and off, the controller may follow in sequence. Cycling the controller on and off in turn cycles the heater on and off. Consequently, the water within the water heater may become layered by temperature. This phenomenon is known as temperature stacking or stratification. Because of temperature stratification, the temperature of the water at the top of the water heater during this multiple cycling might be within or close to the first and the second threshold. Thus, upon demand, delivered water may be hot or cold. In this situation, as well as others, the water heater may be energy inefficient, since the heater will needlessly cycle on when the water temperature at the top of the water heater is within an acceptable range. 
     Thus, it is desirable to provide a method and system to better control the delivered water temperature, and to control the temperature of the water in an energy-efficient manner. 
     SUMMARY 
     A water heater having the combination of a tank for holding water, a heater for heating the water, a controller having logic to regulate the heater, and first and second sensors. Each of the sensors detects the water temperature at different areas within the water heater. The sensors also provide the controller with signals corresponding to the detected water temperature. In response to these signals, the controller regulates the heater when at least one of the signals of the first and second sensors satisfies at least one predetermined state condition. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Exemplary embodiments of the invention are described below in conjunction with the appended figures, wherein like reference numerals refer to like elements in the various figures, and wherein: 
         FIG. 1  is cutaway view of a water heater according to an exemplary embodiment; 
         FIG. 2  is a second cutaway view of a water heater according to an exemplary embodiment; 
         FIG. 3A  is a state diagram illustrating a first of the processing states for the controller shown in  FIG. 2  according to an exemplary embodiment; 
         FIG. 3B  is a second state diagram illustrating a second of the operational states for the controller shown in  FIG. 2  according to an exemplary embodiment; 
         FIG. 3C  is a third state diagram illustrating a third of the operational states for the controller shown in  FIG. 2  according to an exemplary embodiment; 
         FIG. 3D  is a fourth state diagram illustrating a fourth of the operational states for the controller shown in  FIG. 2  according to an exemplary embodiment; 
         FIG. 4  is a first graph illustrating experimental results for the average temperature over a eight-hour period of a 24 hour simulated use test to determine the water heater&#39;s energy factor (EF) according to an exemplary embodiment; 
         FIG. 5  is a second graph illustrating a plurality of heater-control zones for controlling a water heater having a two-sensor heater control assembly according to an exemplary embodiment; 
         FIG. 6  is a third graph illustrating slow-water-draw control of a water heater having a two-sensor heater control assembly according to an exemplary embodiment; 
         FIG. 7  is a fourth graph illustrating fast-water-draw control of a water heater having a two-sensor heater control assembly according to an exemplary embodiment; 
         FIG. 8  is a fifth graph illustrating a plurality of heater-control zones for controlling a water heater having a two-sensor heater control assembly in accordance with another exemplary alternative embodiment; 
         FIG. 9  is a fifth state diagram illustrating a sixth of the operational states for the controller shown in  FIG. 2  in accordance with another exemplary embodiment; and 
         FIG. 10  is a sixth graph illustrating a plurality of heater-control zones for controlling a water heater having a two-sensor heater control assembly in accordance with another example. 
     
    
    
     DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     1. Exemplary Architecture 
       FIG. 1  is cutaway view of a water heater  100  of an exemplary embodiment. The water heater  100  includes a tank  102 , an insulating layer  104 , an external shell  106 , a heater  108 , and a controller assembly  110 . The tank  102  holds water that is to be heated and may be constructed of steel or other heat conducting material. The tank  102  has an inner surface  112 , an input supply tube or dip tube  114 , an output conduit or pipe  116 , a drainage valve  118 , a rust inhibiting liner  120 , and an outer surface  122 . 
     The insulating layer  104  may be located between the outer surface  122  of the tank and the external shell  106 . The insulating layer  104  limits or otherwise minimizes the heat loss of the heated water from passing from the tank  102  to the outside world. Bonded to the inside of the inner surface  112  is the rust inhibiting liner  120 . In addition, the tank  102  may have a sacrificial anode rod to keep the tank  102  from corroding. 
     The tank  102  also has a top surface  124  and bottom surface  126 . Passing through the top surface  124  are the dip tube  114  and the output pipe  116 . The output pipe  116  extends through the top surface  124  to a second predetermined distance from the bottom surface  126 . This second predetermined distance may be fairly close to the top surface  124 . Having the output pipe  116  close to the top surface  124  allows the hotter water, which may be the hottest water in the tank  102 , to exit the tanks upon demand. In operation, when the hot water is demanded, fresh water flows into the dip tube  114  to the bottom of the tank  102  and pushes or otherwise causes the hotter water at the top of the tank  102  to exit through the output pipe  116 . 
     Like the output pipe  116 , the dip tube  114  extends through the top surface  124  to a predetermined distance from the bottom surface  126 . This predetermined distance may be fairly close to the bottom surface  126 . Having the exit of the dip tube  114  close to the bottom surface allows the fresh, cold or ambient water to enter the tank near the bottom surface  126 . This prevents the cold or ambient water from mixing and cooling the hotter water near the top surface  124 . In practice, the dip tube  114  may be typically located about three quarters of the distance from the top surface  124  to the bottom surface  126 . Because the fresh water entering the tank  102  is denser than heated water, the fresh water sinks to the bottom of the tank  102 , where it may be heated. 
     The heater  108  heats the tank  102 , which in turn heats any water inside the tank  102 . The heater  108  may be a gas-fired heater, an electric heater, a plurality of gas-fired burners, a plurality of electric heaters, a combination of gas-fired and electric heaters or any other heat source. When called upon, the heater  108  may provide a small amount of heat, a large amount of heat, or no heat at all. 
     In the exemplary gas-fired water heater shown in  FIG. 1 , heater  108  may have a gas-flow valve (not shown), a burner  128  and an ignition source  130 . The gas-flow valve may be a solenoid-controlled valve, a linear actuated valve, a motor actuated valve, or any other valve capable of supplying gas to the burner  128 . The ignition source  130  may be a pilot light, a solid-state igniter, an electric heat element, or any other ignition source capable of igniting gas. 
     The heat output of the heater  108  may be controlled by burner orifice size, gas pressure, and/or time. To produce heat in the gas-fired water heater, gas flows into the burner  128  through the gas-flow valve, where the ignition source  130  ignites the gas. The gas will continue to burn until the supply of gas is terminated. 
     In an alternative water heater embodiment (not shown), the heat output may be controlled by an electric current flow through an electric heating element. To produce heat in an electric heater, the amount of current impressed on the electric heating element is regulated. In regulating the heat output, the more current impressed on the electric heating element, the more heat is produced. Conversely, less or no heat is produced if the current is reduced or turned off, respectively. 
       FIG. 2  illustrates a water heater  100  with a controller assembly  110 . For simplicity, hereinafter the controller assembly  110  is described in reference to an exemplary gas-fired water heater. Those skilled in the art will recognize that the controller assembly  110  is not limited to such an embodiment, and other controller assemblies, such as those used with electric water heaters, are possible as well. 
     The controller assembly  110  includes a logic unit  132 , a first sensor  134 , a second sensor  136 , and a gas-flow-valve actuator  138 . The logic unit  132  may include a set of relay logic modules, a processor, and programmable instructions for producing an output to actuate the gas-flow valve actuator  138 . As those skilled in the art will recognize, the logic unit  132  may have other alternative constructions as well. Details of an exemplary logic unit and controller are provided by another U.S. patent application filed concurrently with this document, and entitled “Method and Apparatus for Safety Switch” Ser. No. 10/424,257. 
     The logic unit  132  receives signals from the first and second sensors  134 ,  136 . Based on those signals, the logic unit  132  may produce an output to initiate a heat cycle. During the heat cycle, the logic unit  132  actuates the gas-flow-valve actuator  138 , which in turn opens the gas-flow valve to supply gas to burner  128 . When gas is supplied to the burner  128 , the logic unit  132  triggers the ignition source  130  to ignite the gas, if the ignition source  130  requires such trigger. 
     The burner  128  then burns the gas until the demand for heat ceases. Once the heat demand ceases, the logic unit  132  may produce a second output. This second output, in turn, deactivates the gas-flow-actuator  138 , thereby shutting off the gas supply and dampening the firing of the burner  128 . 
     The first sensor  134  may be a temperature sensor or another device capable of sensing water temperature at or near the top of the tank  102 . Thus, for example, a sensor capable of detecting a property of the water from which the water temperature may be derived (such as pressure) may also be used with the present system. While in an exemplary embodiment the first sensor  134  may be located towards the top surface  124  near the exit opening in the output pipe  116 , the sensor need not be physically located at the top of the water heater, provided that the temperature of the water at or near the top is detected by the sensor. In practice, the top sensor may be located from about 4 to about 8 inches from the top surface  124 . 
     The first sensor  134  may provide to the logic unit  132  signals related to the detected water temperature. Alternatively, first sensor  134  may also incorporate switches and logic modules so as to provide the logic unit  132  with switched signals that relate to the detected water temperature. For instance, in response to the first sensor  134  detecting a hot water temperature that is over a given threshold, one or more of such logic modules may cause one of the switches to open or close, thereby signaling the logic unit  132  that the hot water temperature is over the given threshold. Further, the logic modules may keep the switch in that position so long as the detected temperature is over the given threshold. 
     Like the first sensor  134 , the second sensor  136  may be a temperature sensor, or another device capable of sensing water temperature at or near the bottom of the tank  102 . In an exemplary embodiment, the second sensor  136  may be located towards the bottom surface  126  and towards the exit of the dip tube  114 . The second sensor  136 , however, need not be located in such position; rather all that is required is that the second sensor  136  may sense the water temperature at or near the bottom of the tank. Again, like the first sensor  134 , the second sensor  136  may provide to the logic unit  132  signals related to the detected water temperature. Alternatively, the second sensor  136  may also incorporate switches and logic modules so as to provide the logic unit  132  switched signals related to the detected water temperature. 
     The gas-flow-valve actuator  138  controls the amount of heat delivered by the heater  108 . In the exemplary embodiment shown in  FIG. 1 , the gas-flow-valve actuator  138  controls the opening and closing of the gas-flow valve. When heat is called for, the gas-flow-valve actuator  138  opens the gas-flow valve, which allows gas to flow into the burner  128 . When the logic unit  132  sends the gas-flow-valve actuator  138  an indication to stop the gas flow, it closes the gas-flow valve, thereby causing cessation of gas and, in turn, heat. 
     2. State Conditions for Water Heater Control 
       FIGS. 3A-3D  are a series of state diagrams showing operation of the controller in  FIG. 2 . Referring to  FIG. 3A , the logic unit  132  may initiate a heat cycle when at least two conditions are met, namely state  300  and state  302 . If the same conditions exist, but the heat cycle has already begun, the logic unit  132  maintains the heat cycle. Thus, when both state  300  and  302  are met, the logic unit  132  may send an indication to the gas-flow-valve actuator  138  to turn on or, at least, not to turn off. 
     The first of these two conditions or state  300  occurs when the first sensor  134  detects, measures, or otherwise determines that the water temperature at or near the top of the tank  102  is less than a maximum-temperature threshold  304 . “Less than” includes “less than and equal to” as well. 
     This maximum-temperature threshold  304  may be user selectable, fixed at a given temperature, and/or varied. The maximum-temperature threshold  304  may be chosen to control temperature stacking. Thus, the maximum-temperature threshold  304  may be a temperature just below a point where unacceptable temperature stacking occurs. 
     Alternatively, the maximum-temperature threshold  304  may be a first “cut-off” temperature threshold. The first cut-off temperature threshold may be a desired-setpoint temperature of the water exiting the pipe plus or minus a first differential temperature. The actual temperature of the water exiting the output pipe  116 , however, may be less than or greater than the first cut-off temperature. 
     The first differential temperature may be several degrees above or below the desired setpoint temperature. In practice, this first differential temperature assists in providing heat-hysteresis control and limits cycling the heater when the water temperature oscillates around the desired-setpoint temperature. 
     In another alternative embodiment, the maximum-temperature threshold  304  may be just below an overheat temperature threshold. This overheat temperature threshold may be the temperature at which the first and/or second sensors  134 ,  136  indicate to the logic unit  132  that the water heater may be malfunctioning. In response such indication by either sensor, the logic unit  132  or some other fail-safe circuitry may prevent the water heater from further operation until being serviced and/or reset. 
     The maximum-temperature threshold  304 , however, is not limited to these exemplary embodiments, but may be another temperature as well. For example, the maximum-temperature threshold  304  may be varied as a function of a temperature detected by the second sensor  136 . 
     The second of the two conditions or state  302  occurs when the second sensor  136  detects, measures, or otherwise determines that the water temperature at or near the bottom of the tank  102  is less than a first-setpoint-temperature threshold  306 . Hereinafter, “less than” includes “less than and equal to,” and “greater than” includes “greater than and equal to.” 
     This first-setpoint-temperature threshold  306  may be user selectable, fixed, and/or varied. In an exemplary embodiment, the first-setpoint-temperature threshold  306  may be chosen to limit the cycle rate. In another exemplary embodiment, the first-setpoint-temperature threshold  306  may be a first “turn-on” temperature threshold. This threshold may be the desired-setpoint temperature of the water exiting the pipe plus or minus a second-differential temperature. The actual temperature of the water exiting the output pipe  116 , however, may be less than or greater than the turn-on temperature threshold. 
     The second differential temperature may be several degrees above or below the desired setpoint temperature. In practice, this second differential temperature provides heat-hysteresis control and limits cycling the heater when the water temperature oscillates around the desired setpoint temperature. 
     The first-setpoint-temperature threshold  306 , however, is not limited to these exemplary embodiments, but may be another temperature as well. For instance, the first-setpoint-temperature threshold  306  may be varied as a function of a temperature detected by the first sensor  134 . 
     Referring now to  FIG. 3B , the logic unit  132  may terminate a heat cycle or prevent a heat cycle from occurring when at least one condition is met, namely state  308 . The state  308  occurs when the first sensor  134  detects, measures, or otherwise determines that the water temperature at or near the top of the tank  102  is greater than the maximum-temperature threshold  304 . When state  308  is met, the logic unit  132  may send an indication to the gas-flow-valve actuator  138  to turn off or, at least, not to turn on. 
     Referring now to  FIG. 3C , the logic unit  132  may terminate a heat cycle or prevent a heat cycle from occurring when state  310  is met. The state  310  occurs when the second sensor  136  detects, measures, or otherwise determines that the water temperature at or near the bottom of the tank  102  is greater than a second-setpoint-temperature threshold  314 . Thus, when state  310  is met, the logic unit  132  may send an indication to the gas-flow-valve actuator  138  to turn on or, at least, not to turn off. 
     This second-setpoint-temperature threshold  314  may be user selectable, fixed, and/or varied. In an exemplary embodiment, the second-setpoint-temperature threshold  314  may be a second cut-off temperature threshold. This second cut-off temperature threshold may be the desired-setpoint temperature of the water exiting the output pipe  116 . The actual temperature of the water exiting the output pipe  116 , however, may be less than or greater than the second cut-off temperature. 
     The second-setpoint-temperature threshold  314 , however, is not limited to these exemplary embodiments, but may be another temperature as well. Similar to the other thresholds, the second-setpoint-temperature threshold  314  may be varied as a function of a temperature detected by the first sensor  134 . 
     Referring now to  FIG. 3D , the logic unit  132  may maintain an ongoing heat cycle when at least two conditions are met, namely states  316  and  318 . Thus, when states  316  and  318  are met, the logic unit  132  may send an indication to the gas-flow-valve actuator  138  to maintain its current operation. 
     The state  316  occurs when the first sensor  134  detects, measures, or otherwise determines that the water temperature at or near the top of the tank  102  is less than the maximum-temperature threshold  304 . The state  318  occurs when the second sensor  136  detects, measures, or otherwise determines that the water temperature at or near the bottom of the tank  102  is less than the second-setpoint-temperature threshold  314 . 
     The following illustrates an exemplary operation of the water heater for the states illustrated in  FIGS. 3A-3D . For this example, assume that the water heater is full of water. Further, assume that the water heater has recently finished a heat cycle so that the water temperature detected by the second sensor  136  is close to the desired-setpoint temperature. In this example, the desired-setpoint temperature is approximately 135 degrees Fahrenheit. 
     Further, assume that the water temperature at the top of the tank  102  as detected by the first sensor is initially less than the maximum-temperature threshold  304 . The maximum-temperature threshold  304  may be approximately 142-degrees Fahrenheit (approximately 7 degrees Fahrenheit above the desired setpoint temperature). 
     As another initial condition, the maximum-temperature threshold  304  may be below the overheat temperature threshold. The overheat temperature threshold, for instance, may be approximately 5 degrees above the maximum-temperature threshold  304 . In this example, the overheat temperature may be approximately 147 degrees Fahrenheit. The overheat temperature threshold may be other temperatures as well. 
     When a demand for hot water occurs, fresh, cold or ambient temperature water flows into the tank  102  through dip tube  114  and exits at or near the bottom of the tank  102 . The second sensor  136  detects the inrush of cold or ambient water at or near the bottom of the tank  102 . As the cold or ambient water enters, the hotter water at the top of the tank exits through an inlet in the output pipe  116 . 
     The first sensor  134  detects the water temperature at or near the inlet of the output pipe  116 . If the water temperature detected by the first sensor  134  stays below the 142 degree temperature, then state  300  ( FIG. 3A ) is met. Alternatively, the state  300  may be met when the water temperature detected near the inlet of the output pipe  116  is just below the overheat temperature of 147 degrees Fahrenheit. 
     If a sufficient amount of fresh, cool or ambient temperature water flows into the bottom of the tank  102 , then the water temperature begins to drop at the bottom of the tank  102 . When the water temperature as detected by the second sensor  136  falls below the desired-setpoint temperature minus the first differential temperature (e.g., approximately 10 to 20 degrees Fahrenheit below the desired setpoint temperature), this improved two-sensor system may begin a heat cycle. 
     In the process, the logic unit  132  receives from the second sensor  136  signals indicating that the temperature at the bottom of the tank  102  is below the first-setpoint-temperature threshold  306 , thereby meeting the state  302  ( FIG. 3A ). The logic unit  132  also receives from the first sensor  134  signals indicating the water temperature at the top of the tank  102  is below the maximum-temperature threshold  304 . 
     In contrast, a legacy system with one sensor may initiate a heat cycle when the water temperature drops below the desired setpoint temperature minus a large differential amount (e.g., about 15 to 25 degrees Fahrenheit). In such a legacy system, its logic controller may cause its heater to heat the water even though the exiting water at the top of its tank may be above the maximum-temperature threshold  304 , thereby operating inefficiently. 
     In an alternative embodiment of the present two-sensor water heater, a heat cycle may be initiated when the second sensor  136  detects a rapid drop in water temperature. This may happen even if the detected temperature is not below the first-setpoint-temperature threshold  306 . A rapid drop in temperature may be defined by a change in cooling rate to approximately 1 to 5 degrees Fahrenheit per minute (deg. F./min.). The change in cooling rate, however, may be greater than or less than this exemplary range. 
     When both states  300  and  302  are met, the logic unit  132  may send to the gas-flow-valve actuator  138  a signal instructing it to open the gas-flow valve. If necessary, the logic unit  132  may send a signal to the ignition source  130  to light the gas. The ignition source  130  ignites the gas and the burner  128  heats the water in the tank  102 . 
     The heater  108  will maintain heating the water when states  316  and  318  ( FIG. 3D ) are met. Thus, when the water temperature at the top of the tank  102  is less than 142 degrees Fahrenheit (i.e., the maximum-temperature threshold  304 ) and when the water temperature at the bottom of the tank  102 , as sensed by the second sensor  136 , is below 135 degrees Fahrenheit (i.e., the second-setpoint temperature  314 ), the logic unit  132  may send the gas-flow-valve actuator  138  signals for keeping open the gas-flow valve. 
     If, however, the water temperature detected by the second sensor  136  stays below 135 degrees Fahrenheit, but the water temperature detected by the first sensor  134  rises above 142 degrees Fahrenheit, then the heat cycle may be terminated. To terminate the heat cycle, the logic unit  132  may send to the gas-flow-valve actuator  138  signals to turn off the gas-flow valve. This prevents needless heating when the exiting water is at or near the desired setpoint temperature, saving energy and reducing the operating cost as compared to legacy systems. 
     When the water temperature at the bottom of the tank, as measured by the second sensor  136 , rises above 135 degrees Fahrenheit or otherwise meets state  310  ( FIG. 3C ), the logic unit  132  may send the gas-flow-valve actuator  138  a signal for closing the gas-flow valve. Responsively, the gas-flow-valve actuator  138  closes the gas-flow valve and the flow of gas ceases, which in turn stops the burner  128  from continuing to heat the tank  102 . 
     In some situations, the water heater  100  may receive multiple sequential demands for hot water. These sequential demands may only be for small amounts of water as compared to the total volumetric capacity of the water heater  100 . For instance, a residential water heater may hold 40 gallons of water. Many of today&#39;s high efficiency appliances, such as dishwashers and clothes washers, only use about 5 to 15 gallon of hot water for a particular use (e.g., cleaning) cycle. When these appliances are operated simultaneously, the water heater may receive repeated demands for hot water in a relatively short amount of time. 
     In legacy water-heater systems, once the water temperature at the bottom of the tank drops below the setpoint, the heater cycle begins. Since the cold or ambient water entering the legacy water heater is approximately equal to the amount supplied for the demand, the heater may quickly heat the water at the bottom of the tank to the desired setpoint temperature and then shut off. With the repeated demands, temperature stacking can occur. The temperature stacking may be quite substantial and inefficient since the heater is cycled on and off when the temperature of the water at the top of the tank may be above the maximum-temperature threshold  304 . 
     Unlike the legacy systems, the water heater  100  may be prevented from cycling on when state  308  ( FIG. 3B ) is met. When the logic unit  132  receives a signal from the first sensor  134  indicating that the temperature is greater than 142 degrees Fahrenheit, it sends a signal to gas-flow-valve actuator  138  to turn off the gas-flow valve or otherwise prevent the burner  128  from heating the tank  102 . In addition to preventing the burner  128  from receiving gas, the logic unit  132  may also prevent the ignition source  130  from activating. 
     Cycling of the heater  108  may be prevented even if the logic unit  132  receives a signal from the second sensor  136  indicating that the water temperature at the bottom of the tank  102  is below the desired-setpoint temperature minus the differential temperature (i.e., state  302 ). Accordingly, temperature stacking and its resultant energy inefficiency may be reduced by employing the first sensor  134  and preventing needless heating when state  308  is met. 
     3. Experimental Results for a Water Heater with Two Sensor Control 
       FIG. 4  is a graph  400  illustrating experimental results for the average temperature over an eight hour period of a 24 hour simulated use test of two 40 gallon water heaters to determine the water heater&#39;s energy factor (EF) according to an exemplary embodiment. In  FIG. 4 , graph  400  includes a legacy system curve  402  that corresponds to the average temperature of a heater that uses a single-sensor-legacy-control system. 
     The average temperature shown by legacy system curve  402  is an average of water temperature of six temperature sensors vertically positioned in the tank  102 . Each of the six temperature sensors is located in the middle of each of six sections that represent one sixth of the height of the tank  102 . 
     Also illustrated in graph  400  is a two-sensor-control curve  404  that corresponds to the average temperature of six similarly mounted temperature sensors of the second of the two water heaters. The two-sensor-control curve  404  was produced using the two-sensor-control system as described above. 
     During part of period  406 , the temperature of water in each of the water heaters drops below the desired setpoint temperature (e.g., 135 degrees Fahrenheit) minus the differential temperature. Thereafter, each of the water heaters begins a heat cycle. After the heating cycle completes, the legacy system curve  402  indicates that the average water temperature may rise several degrees above the desired setpoint temperature. Conversely, two-sensor-control curve  404  indicates that the average water temperature is approximately a few degrees below the desired setpoint temperature after the heating cycle has completed. 
     Over time, the temperature of the water decreases due to heat transfer to the outside world. At period  408 , however, each water heater receives a demand for hot water. As the demand is fulfilled, a sufficient amount of cold or ambient temperature water rushes in, which causes each of the water heaters to begin a second heating cycle. While the two-sensor-control curve  404  indicates that the average water temperature is slightly lower the desired setpoint temperature, the water drawn from output pipe  116  will be at or slightly above the desired setpoint temperature. 
     4. Heater Control Zones 
       FIG. 5  is a graph  500  illustrating a plurality of heater-control zones for controlling a water heater having a two-sensor heater control assembly in accordance with an exemplary alternative embodiment. Included in the plurality of heater-control zones is an “ON” zone  510 ; a “COOLING-RATE-DEPENDENT-ON” zone  520 ; an “OFF” zone  530 ; and a “NO-CHANGE” zone  540 . 
     Each of the heater-control zones may delimit a group of water temperatures. When the water temperature of the water heater falls within this collective range of water temperatures, the first and/or second sensor  134 ,  136  may signal the heater control assembly  110  to drive the heater  108  to an on state, an off state, or alternatively, to maintain the current state of heater  108 . Further, the delimited boundaries of each of the heater-control zones may be defined by one or more temperature thresholds for the water temperature detected by the first and second sensors  134 ,  136 . 
     The temperature thresholds for the first sensor  134  may include a first-sensor-setpoint threshold  504 , a first-sensor-first threshold  514 , a first-sensor-second threshold  506 , and a first-sensor-cut-off threshold  518 . The temperature thresholds for the second sensor  136  may include a second-sensor-setpoint threshold  502 , a second-sensor-first threshold  512 , a second-sensor-second threshold  524 , a second-sensor-third threshold  526 , and a second-sensor-fourth threshold  528 . 
     The first-sensor-setpoint threshold  504  and the second-sensor-setpoint threshold  502  may be desired-setpoint thresholds for the first and second sensors  134 ,  136 , respectively. The desired-setpoint thresholds  502 ,  504  may be the same or different temperature. In an exemplary embodiment, both of the desired-setpoint thresholds  502 ,  504  may be, for example, a user selected threshold of about 135 degrees Fahrenheit. The desired-setpoint thresholds  502 ,  504 , however, may differ from this 135 degree Fahrenheit example. 
     Each of the other thresholds may be a function of the first-sensor and second-sensor setpoint thresholds  502 ,  504 . For example, each of the other thresholds may be equal to the first-sensor and the second-sensor setpoint thresholds  502 ,  504  plus or minus a differential temperature. Table 1 (below) illustrates such an example. 
     
       
         
           
               
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                   
                   
                   
                 Exemplary 
               
               
                   
                 Threshold 
                 Differen- 
                 Differential Value 
               
               
                 Threshold Name 
                 Label 
                 tial 
                 (Degrees Fahrenheit) 
               
               
                   
               
             
            
               
                 First-sensor-setpoint 
                 SP 
                 N/A 
                 135 
               
               
                 threshold 504 
               
               
                 First-sensor-first 
                 SP + HS1 
                 HS1 
                  5 to 10 
               
               
                 threshold 514 
               
               
                 First-sensor-second 
                 SP + HS2 
                 HS2 
                  0 to 1 
               
               
                 threshold 506 
               
               
                 First-sensor-cut-off 
                 SP + HS3 
                 HS3 
                  5 to 15 
               
               
                 threshold 518 
               
               
                 Second-sensor- 
                 SP 
                 N/A 
                 135 
               
               
                 setpoint threshold 
               
               
                 502 
               
               
                 Second-sensor-first 
                 SP − LS1 
                 −LS1 
                 10 to 20 
               
               
                 threshold 512 
               
               
                 Second-sensor- 
                 SP − LS2 
                 −LS2 
                  5 to 10 
               
               
                 second threshold 524 
               
               
                 Second-sensor-third 
                 SP − LS3 
                 −LS3 
                  0 to 3 
               
               
                 threshold 526 
               
               
                 Second-sensor-fourth 
                 SP − LS4 
                 −LS4 
                 10 to 12 
               
               
                 threshold 528 
               
               
                   
               
            
           
         
       
     
     The differential values for the thresholds listed in Table 1, however, are not limited to these exemplary embodiments, but may be other values as well. Moreover, the delimited boundaries of each of the heater-control zones may be defined as a function of the above-listed temperature thresholds. For example, boundary  532  may be based on an average of the second-sensor-third threshold  526  and the first-sensor-second threshold  506 . The average temperature is a constant on boundary  532 . 
     Also shown in  FIG. 5  is step boundary  534 . Step boundary  534  may be used to ensure that water drawn from the tank after a heating cycle is at or slightly above the desired setpoint temperature even though the average water temperature in the tank  102  is controlled at approximately the desired setpoint temperature. A lower average temperature may reduce heat loss to the ambient surroundings, and thus, improve energy efficiency. 
     In the exemplary embodiment shown in  FIG. 5 , the step boundary  534  is a horizontal section of the boundary delineated by first-sensor-second threshold  506  located between the second-sensor-third threshold  526  and the second-sensor-setpoint threshold  502 . The step boundary  534  may be set at a value to lower the average temperature boundary (e.g., boundary  532 ) a couple of degrees Fahrenheit below the desired setpoint temperature. This value may vary depending on the configuration and other physical attributes of the water heater. Preferably, the step boundary  534  is set approximately 0 to 3 degrees Fahrenheit wide. 
     During initial heating, the water temperatures detected by the first and second sensors  134 ,  136  closely track each other. These water temperatures will continue to rise up until the point at which the water heater enters the “OFF” zone  530  (e.g., the point at which the water temperatures exceed the second-sensor-setpoint threshold  502  and the first-sensor-second threshold  506 ). This control is illustrated in  FIG. 4  at point  412 , where the two-sensor-control curve  404  initially exceeds the preferred 135 degree Fahrenheit setpoint temperature. 
     After some water is drawn from the tank  102  and cooler water is drawn into the bottom of the tank, an upper to lower temperature differential may build. After each successive re-heating, the temperatures as detected by the first and second sensors  134 ,  136  may rise to just above the boundary  532 . Yet, the average temperature may be approximately 0 to 3 degrees Fahrenheit lower than the desired setpoint. In the exemplary embodiment shown in  FIG. 4 , this is represented by the difference  414 , which is preferably about 1.5 degrees Fahrenheit lower than the setpoint. The difference of the averages 410 of the legacy system curve  402  and two-sensor-control curve  404  demonstrates that the average water temperature using the legacy control is greater than the average water temperature using the present two-sensor-controlled water heater. The present two-sensor controlled water heater, nonetheless, maintains the average water temperature at just below the desired setpoint temperature, whereas the legacy water heater maintains the average temperature above the desired water temperature. Thus, given that the temperature as detected by sensor  134  and the supply of water from the output pipe  116  can be delivered at or slightly above the desired setpoint temperature, the current two-sensor-controlled water exhibits improved energy efficiency (e.g., less heat loss to the ambient environment) as compared with the legacy control. 
     A. ON Zone 
     When the first and second sensors  134 ,  136  detect a water temperature within the ON zone  510 , then the logic unit  132  may either initiate a heat cycle or maintain a previously initiated heat cycle. This may occur when (i) the second sensor  136  detects a water temperature that is less than the second-sensor-first threshold  512  and (ii) the first sensor  134  detects a water temperature that is less than the first-sensor-first threshold  514 . Point  501  is an example of such condition. 
     B. OFF Zone 
     When the first and/or second sensor  134 ,  136  detects a water temperature within the OFF zone  530 , then the logic unit  132  may halt any ongoing heat cycle or prevent a heat cycle from starting. Point  503  defines a coordinate within the OFF zone  530 . 
     C. NO-CHANGE Zone 
     When the first and second sensors  134 ,  136  detect a water temperature within the NO-CHANGE zone  540  after exiting from the OFF zone  530 , the logic unit  132  prevents the water heater from initiating a heat cycle. Preventing a heat cycle under these conditions may prevent needlessly heating water that may be at or above the desired setpoint temperature. This may be the case when the water temperature drops from point  503  to point  505 . At point  505 , the second sensor  136  detects a water temperature that is less than the second-sensor-fourth threshold  528 , and the first sensor  134  detects a water temperature that between the first-sensor-first threshold  514  and the first-sensor-cut-off threshold  518 . 
     Alternatively, when the first and second sensors  134 ,  136  detect a water temperature within the NO-CHANGE zone  540  after exiting the ON zone  510  or the COOLING-RATE-DEPENDENT-ON zone  520 , the logic unit  132  may maintain the previously initiated heat cycle. In this instance, the NO-CHANGE zone may provide heat-hysteresis control and limit cycling the heater when the water temperature oscillates around the desired-setpoint temperature. 
     Point  507  illustrates the condition where the first and second sensors  134 ,  136  detect a water temperature within the NO-CHANGE zone  540  after exiting from the COOLING-RATE-DEPENDENT-ON zone  520 . At point  507 , the second sensor  136  detects a water temperature that is less than the second-sensor-second threshold  524  and the first sensor  134  detects a water temperature that is between the first-sensor-first threshold  514  and the first-sensor-cut-off threshold  518 . 
     D. COOLING-RATE-DEPENDENT-ON Zone 
     When the first and second sensors  134 ,  136  detect a water temperature within the COOLING-RATE-DEPENDENT-ON zone  520  after exiting the OFF zone  530  or the NO-CHANGE zone  540 , the logic unit  132  may maintain the current off state of the heater  108 . Alternatively, the logic unit  132  may initiate a heat cycle when the water cools at a rate exceeding a cooling rate threshold. 
     The cooling rate threshold may be a threshold for comparing the rate of change of the average water temperature measured by the first and second sensors  134 ,  136  as the water in the tank  102  cools. In an exemplary embodiment, the cooling rate threshold may be approximately 2 degrees Fahrenheit per minute. The cooling rate threshold may be other rates as well. Further, the cooling rate threshold may be an asymmetric condition. The asymmetry may depend on whether the water heater enters the COOLING-RATE-DEPENDENT-ON zone  520  from the ON zone  510 , the OFF zone  530 , and/or the NO-CHANGE zone  520 . 
     The first of the asymmetric conditions occurs when the water heater enters the COOLING-RATE-DEPENDENT-ON zone  520  from the OFF zone  530  and/or the NO-CHANGE zone  540 . When entering from either of these zones, the water may be cooling, and thus, a cooling rate can be detected. The cooling rate threshold may be satisfied when the first and second sensors  134 ,  136  detect an average rate of change that is greater than the cooling rate threshold. 
     The following examples indicate how the cooling rate of change threshold may be implemented. These examples may be illustrated with reference to  FIGS. 6 and 7 .  FIG. 6  is a graph  600  illustrating slow-water-draw control of a water heater having a two-sensor heater control assembly according to an exemplary embodiment.  FIG. 7  is a graph  700  illustrating fast-water-draw control of a water heater having a two-sensor heater control assembly according to an exemplary embodiment. For exemplary purposes only, the cooling rate of change threshold is 2 deg. F./min. in the following examples. 
     (1) Example 1 
     Curve  610  illustrates a water temperature detected by the second sensor  136  over a period of approximately 0.6 hours or 36 minutes. Curve  612  represents the “ON” and/or “OFF” condition of the heater  108 , as measured from the open and/or closed state of the gas-flow-valve actuator  138 . During the period between t 1  and t fd , the heater  108  is off, and between t fd  and t 7 , the heater  108  is on. Curve  614  represents a slow water draw of about 0.5 gallons per minute. The curve  614  illustrates a condition that is indicative of one or more low rate and/or short duration demands for water. Curve  616  represents a fast water draw, which may be a condition that is indicative of one or more high rate and/or long duration demands for water. 
     As can be seen in  FIG. 6 , shortly after the initiation of the slow water draw at t sdi , the temperature near or at the bottom of the tank  102  (as may be detected by the second sensor  134 ) begins to fall. During this slow water draw, the temperature at or near the bottom of the tank  102  decays as illustrated by the downward sloping portion of the curve  610  between t sdi  and t sde . In this example, the decay pattern represents the average rate of change over the period between t sdi  and t sde  and is approximately 1.8 deg. F./min. The slow water draw may cause the water temperature to decay at different rates. In addition, the decay pattern may differ from that shown. 
     Conspicuously, the heater  108  remains off during the decay period between t sdi  and t sde , as illustrated by curve  612 . After the slow water draw completes, the decay of the water temperature ceases. Thereafter, the temperature of the water remains substantially constant until the large water draw occurs at t fd . The substantially constant portion of the curve  610  is illustrated by the horizontal portion of curve  610  between t sde  and t fd . 
     While the water temperature as detected by the second sensor  136  decayed from the desired setpoint temperature (e.g., 135 degrees Fahrenheit), the heater  108  did not cycle on until the large water draw caused the water temperature to drop below the second-sensor-first threshold  512 . (And, of course, the temperature at the top of the tank  102  also satisfies the conditions of ON zone  510 .) Thus, the average rate of change of the water temperature between t sdi  and t sde  did not exceed the cooling rate threshold. By not exceeding the cooling rate threshold, frequent operation of the gas-flow-valve actuator  138  and in turn firing the heater are prevented, thereby improving the efficiency of the water heater  100 . 
     In an alternative embodiment (not shown), when a large amount of low rate and short duration demands for water draw are called for, the water temperature as detected by the second sensor  136  may decay at a rate similar to the decay pattern shown in curve  610  between the period of t sdi  and t sde . The decay pattern may also include periods where the decay levels off. In this case, the average rate of change might not exceed the cooling rate threshold as well. Consequently, the logic unit  132  might not initiate a heat cycle, until entering the ON zone  510 . Given that the heating rate, which may be about 1 to 2 degrees Fahrenheit per minute, is generally the same or higher than the cooling rate, the supply of hot water should not be interrupted. 
     (2) Example 2 
     Referring now to  FIG. 7 , curve  710  illustrates a water temperature detected by the second sensor  136  over a period of approximately 0.1 hours or 6 minutes. Curve  712  represents the “ON” and/or “OFF” condition of the heater  108 , as measured from the open and/or closed state of the gas-flow-valve actuator  138  during the same period. During the period between t i  and t mvi , the heater  108  is off, and between t mvi  and t 7 , the heater  108  is on. Curve  714  represents a fast water draw, which may be a condition indicative of one or more high rate and/or long duration demands for water. 
     As can be seen in  FIG. 7 , a short time after the initiation of the fast water draw at t fd , the temperature near or at the bottom of the tank  102  as detected by the second sensor  136  begins to fall. During the fast water draw, the temperature at or near the bottom of the tank  102  decays rapidly as illustrated by the sharp downward sloping portion of the curve  710  between t fd  and t mvi  (or between t fd  and t 7 ). 
     In this example, the decay pattern or the average rate of change over the period between t fd  and t mvi  is approximately 13.8 deg. F./min., which is greater than the cooling rate of change threshold of approximately 2 deg. F./min. Thus, the average rate of change of the water temperature between t fd  and t mvi  exceeds the cooling rate of change threshold. By exceeding the cooling rate of change threshold under this high rate of change condition, the logic unit  132  may signal the gas-flow-valve actuator  138  to turn on. 
     Unlike the slow water draw condition, the heater  108  turns on at a temperature within the COOLING-RATE-DEPENDENT-ON zone  520  (e.g., 122 degrees Fahrenheit). In effect, the logic unit  132  anticipates that the water temperature as measured by the second sensor  136  will enter the ON zone  510  before the water temperature actually reaches the second-sensor-first threshold  512 . Responding to the large rate of change and initiating a heat cycle at t mvi  may increase the water heater&#39;s delivery capacity of hot water. 
     As noted, the cooling rate of change threshold may be an asymmetric condition that depends upon the zone from which the water heater enters the COOLING-RATE-DEPENDENT-ON zone  520 . When entering from ON zone, the water is being heated, so the cooling-rate dependent condition does not apply. When the first and second sensors  134 ,  136  detect a water temperature within the COOLING-RATE-DEPENDENT-ON zone  520  after exiting the ON zone  510 , the logic unit  132  may maintain the previously initiated heat cycle. As such, the logic unit  132  may signal the gas-flow-valve actuator  138  to remain on. This signal may remain until the water temperature enters the OFF zone  530 . 
       FIG. 8  is a graph  800  illustrating a plurality of heater-control zones for controlling a water heater having a two-sensor heater control assembly in accordance with another exemplary alternative embodiment. Included in the plurality of heater-control zones is the “ON” zone  510 ; a “TIME-DEPENDENT-ON” zone  820 ; the “OFF” zone  530 ; and the “NO-CHANGE” zone  540 . 
     The heater-control zones of  FIG. 8  are similar in most respects to the heater-control zones of  FIG. 5 , except as described herein. While the functions that define the boundaries of the TIME-DEPENDENT-ON zone  820  and the COOLING-RATE-DEPENDENT-ON zone  520  are similar or substantially the same, the TIME-DEPENDENT-ON zone  820  differs from the COOLING-RATE-DEPENDENT-ON zone  520  by the addition of another threshold, namely a time-dependent threshold. Like the cooling rate threshold, the time-dependent-threshold is an asymmetric threshold. The asymmetry may depend on the amount of time the water heater remains off. 
     For example, when entering the TIME-DEPENDENT-ON zone  820  from the ON zone  510 , the logic unit  132  may maintain the current heat cycle. If entering the TIME-DEPENDENT-ON zone  820  from the OFF zone  530  and/or the NO-CHANGE zone  540 , then the logic unit  132  may maintain the current off state if the off time is longer than the time-dependent threshold. Alternatively, when the heater  108  has been off for a period shorter than the time-dependent threshold, then the TIME-DEPENDENT-ON zone  820  may mimic or otherwise emulate the ON zone  510 . In practice, however, the TIME-DEPENDENT-ON zone  820  and the COOLING-RATE-DEPENDENT-ON zone  520  are different embodiments, which may or may not be used concurrently. 
     Like the COOLING-RATE-DEPENDENT-ON zone  520 , the thresholds of the TIME-DEPENDENT-ON zone  820  may be variable. For instance, the boundaries may be continually adjusted by varying the differential settings from a default value to another value (e.g., from LS 1  to LS 4 ) when there is no call for heat during a given period. For instance, one or more of the thresholds of the TIME-DEPENDENT-ON zone  820  may be adjusted incrementally by adding or subtracting a predetermined number of degrees per unit time (e.g., an hour) from the threshold. 
       FIG. 10  is a graph  1000  illustrating a plurality of heater-control zones for controlling a water heater having a two-sensor heater control assembly. In this example, a temperature control algorithm may be dynamically adjusted based on average water temperature, water draw time, and heat cycle time of the gas-flow-valve actuator  138 . The temperature control algorithm may also include a first setpoint differential (UT 1 ) adjustment based on the water draw time and a second setpoint differential (LT 1 ) adjustment based on water cycle time. 
     The temperature control algorithm may be implemented in software as part of the programmable instructions included in the logic unit  132 . The logic unit  132  may receive inputs from the first and second sensors  134 ,  136  and provide as an output a signal that controls the gas-flow-valve actuator  138 . The logic unit  132  may store the temperature data obtained from the first and second sensors  134 ,  136 . As a result, the logic unit  132  may have access to both current and historical temperature data received from the first and second sensors  134 ,  136 . With this data, the logic unit  132  may use temperature change rates to determine when a water draw occurs, and estimate a water draw rate and a water draw time. 
     In addition, the logic unit  132  may store the output signals used to control the gas-flow-valve actuator  138 . As a result, the logic unit  132  may be able to calculate on-time, off-time, and heat cycle time of the gas-flow-valve actuator  138 . The logic unit  132  may then process the temperature data and on-time and off-time of the gas-flow-valve actuator using the temperature control algorithm. The temperature control algorithm may be used for controlling the gas-flow-valve actuator  138  and adjusting the setpoint differentials (UT 1 , LT 1 ) as needed. 
     The temperature control algorithm may be more clearly explained with reference to  FIG. 10 . The graph  1000  depicts four heater-control zones. The heater-control zones include an “ON” zone  1002 , a “COOLING-RATE-DEPENDENT-ON” zone  1004 , a “NO-CHANGE” zone  1006 , and an “OFF” zone  1008 . Each of the heater-control zones may delimit a group of water temperatures. When the water temperature of the water heater, as sensed by temperature sensors  134  and  136 , falls within this collective range of water temperatures, the heater control assembly  110  may drive the heater  108  to an on state, an off state, or alternatively, to maintain the current state of heater  108 . Further, the delimited boundaries of each of the heater-control zones  1002 - 1008  may be defined by one or more temperature thresholds for the water temperatures detected by the first and second sensors  134 ,  136 . 
     The graph  1000  has a first axis (y-axis) in which the temperatures detected by the first sensor  134  are plotted and a second axis (x-axis) in which the temperatures detected by the second sensor  136  are plotted. The y-axis includes three temperature thresholds: a first-sensor setpoint threshold (“SP”)  1010 , a first-sensor-first threshold (“SP+UT 1 ”)  1012 , and a first-sensor-second threshold (“SP+UT 2 ”)  1014 . The x-axis includes six temperature thresholds: a second setpoint threshold (“SP”)  1016 , a second-sensor-first threshold (“SP-LT 1 ”)  1018 , a second-sensor-second threshold (“SP-LT 2 ”)  1020 , a second-sensor-third threshold (“SP- 2 *LT 2 -UT 1 ”)  1022 , a second-sensor-fourth threshold (“SP- 2 *LT 2 -UT 2 ”)  1024 , and a second-sensor-fifth threshold (“SP-LT 2 -UT 2 ”)  1026 . 
     The first-sensor and the second-sensor-setpoint thresholds  1010 ,  1016  may be desired setpoint thresholds for the first and second sensors  134 ,  136 , respectively. The first-sensor and the second-sensor-setpoint thresholds  1010 ,  1016  may be the same or different temperatures. For example, the first-sensor and the second-sensor-setpoint thresholds  1010 ,  1016  may be a user selected threshold of about 135 degrees Fahrenheit. However, the first-sensor and second-sensor-setpoint thresholds  1010 ,  1016  may differ from this 135 degree Fahrenheit example. 
     Each of the other thresholds may be a function of the first-sensor and the second-sensor-setpoint thresholds  1010 ,  1016 . For example, each of the other thresholds may be equal to the first-sensor and the second-sensor-setpoint thresholds  1010 ,  1016  plus or minus a differential temperature. Table 2 (below) illustrates such an example. 
                                 TABLE 2                           Example                   Differential                   Value           Threshold   Differen-   (Degrees       Threshold Name   Label   tial   Fahrenheit)                  First-sensor-setpoint   SP   N/A   135       threshold 1010       First-sensor-first   SP + UT1   UT1   0 to 8       threshold 1012       First-sensor-second   SP + UT2   UT2   0 to 6       threshold 1014       Second-sensor-   SP   N/A   135       setpoint threshold       1016       Second-sensor-first   SP − LT1   −LT1   7 to 20       threshold 1018       Second-sensor-   SP − LT2   −LT2   0 to 3       second threshold       1020       Second-sensor-third   SP − 2 *    −2 * LT2 − UT1   Calculate       threshold 1022   LT2 − UT1       from above       Second-sensor-fourth   SP − 2 *   −2 * LT2 − UT2   Calculate       threshold 1024   LT2 − UT2       from above       Second-sensor-fifth   SP − LT2 −   −LT2 − UT2   Calculate       threshold 1026   UT2       from above                    
The differential values for the thresholds listed in Table 2, however, are not limited to these examples, but may be other values as well.
 
     The UT1 differential may typically be set to a default value of eight degrees Fahrenheit. The UT2 differential may typically be set to approximately two degrees Fahrenheit less than the UT1 differential. The temperature control algorithm may adjust the value of the UT1 differential based on the water draw time. As the water draw time increases, the UT1 differential may be reduced to a minimum of zero degrees Fahrenheit. The UT2 differential may also be reduced to maintain the two degree Fahrenheit difference from the UT1 differential until the UT2 differential reaches zero degrees Fahrenheit. By adjusting the UT1 differential, the amount of temperature stacking allowed in the tank  102  may also be adjusted. 
     The LT1 differential may typically be set to a default value of twenty degrees Fahrenheit. If a maximum time between water draws is within a window of time, then the LT1 differential may be reduced. If the maximum time between water draws is not within this window of time, then the LT1 differential may remain at the default value. For example, the window of time may be five to ten hours between water draws. If the maximum time between water draws is within this window, the LT1 differential may be reduced from twenty degrees Fahrenheit to seven degrees Fahrenheit. Once the LT1 differential has been adjusted to the reduced value, the LT1 differential may remain there until the time between two consecutive water draws exceeds the maximum for the window—ten hours in this example. However, other windows of time and temperature differential values may be used. 
     The detection of water draws and consequential adjustment of LT1 differential improves the overall accuracy of the temperature control algorithm. In most cases the heater  108  is in idle for much of the night allowing the temperature in the tank  102  to slowly cool down to as low of a temperature as setpoint minus LT1 differential. By using the maximum time between water draws to reduce this value the outlet water temperature will be much closer to the desired setpoint and provide much better performance to the user. If the demand for water is lower and time between water draws is very long, then the LT1 differential is not adjusted and the tank  102  operates more efficiently. Boundaries of each of the heater-control zones may be defined as a function of the above-listed temperature thresholds. The boundaries include a first boundary  1028 , a second boundary  1030 , and a third boundary  1032 . The first boundary  1028  may be located between the ON zone  1002  and the COOLING RATE DEPENDENT ON zone  1004 . The first boundary  1028  may be a line that slopes from the first-sensor-setpoint threshold  1010  to the second-sensor-first threshold  1018 . 
     The second boundary  1030  may be located between the COOLING RATE DEPENDENT ON zone  1004  and both the NO CHANGE zone  1006  and the OFF zone  1008 . The second boundary  1030  may be a horizontal line located at the first-sensor-second threshold  1014  until the second boundary  1030  reaches the second-sensor-third threshold  1022 . At the second-sensor-third threshold  1022  and continuing to the second-sensor-setpoint threshold  1016 , the second boundary  1030  may be a line that slopes downwardly. The slope of the second boundary  1030  in this area may be approximately −1. When the second boundary  1030  reaches the second-sensor-setpoint threshold  1016 , the second boundary  1030  may be a vertical line. 
     The third boundary  1032  may be located between the NO CHANGE zone  1006  and the OFF zone  1008 . The third boundary  1032  may be a horizontal line located at the first-sensor-first threshold  1012  until the third boundary  1032  reaches the second-sensor-third threshold  1022 . At the second-sensor-third threshold  1022  and continuing to the second-sensor-fourth threshold  1024 , the third boundary  1032  may be a line that slopes downwardly. The slope of the third boundary  1032  in this area may be approximately −1. 
     When the third boundary  1032  reaches the second-sensor-fourth threshold  1024 , the third boundary  1032  may be a horizontal line located at the first-sensor-second threshold  1014  until the third boundary  1032  reaches the second-sensor-fifth threshold  1026 . At the second-sensor-fifth threshold  1026  and continuing to the second-sensor-second threshold  1020 , the third boundary  1032  may be a line that slopes downwardly. The slope of the third boundary  1032  in this area may be approximately −1. 
     When the third boundary  1032  reaches the second-sensor-second threshold  1020 , the third boundary  1032  may be a horizontal line located at the first-sensor-setpoint threshold  1010  until the third boundary  1032  reaches the second-sensor-setpoint threshold  1016 . When the third boundary  1032  reaches the second-sensor-setpoint threshold  1016 , the third boundary  1032  may be a vertical line. The two sloped line segments in the third boundary  1032 , which may be described as a double step down function, may further improve the efficiency of the water heater by further controlling the temperature stacking in the tank  102  while maintaining a fairly consistent average tank temperature. 
     When the first and second sensors  134 ,  136  detect a water temperature within the ON zone  1002 , then the logic unit  132  may either initiate a heat cycle or maintain a previously initiated heat cycle. When the first and/or second sensors  134 ,  136  detect a water temperature within the OFF zone  1008 , then the logic unit  132  may halt any ongoing heat cycle or prevent a heat cycle from starting. When the first and second sensors  134 ,  136  detect a water temperature within the NO-CHANGE zone  1006 , the logic unit  132  may maintain the water heater  100  in the previous state (i.e., maintains a previously initiated heat cycle or prevents a heat cycle from starting). 
     The temperature control algorithm may disable the COOLING-RATE-DEPENDENT-ON zone  1004  based on the average water temperature, the water draw time, and the heat cycle time. For example, the COOLING-RATE-DEPENDENT-ON zone  1004  may be enabled when initially applying power to the water heater  100 ; when the gas-flow-valve actuator  138  has been off for a long period of time, such as greater than five hours; when the gas-flow-valve actuator  138  has been off for less than a short period of time, such as thirty minutes; and when the average water temperature is low, such as fifteen degrees below the first-sensor and second-sensor-setpoint thresholds  1010 ,  1016 . 
     For example, the COOLING-RATE-DEPENDENT-ON zone  1004  may be enabled whenever the gas-flow-valve actuator  138  off time is less than thirty minutes or greater than five hours, and the average water temperature is fifteen degrees less than the first-sensor and second-sensor-setpoint thresholds  1010 ,  1016 . Otherwise, the COOLING-RATE-DEPENDENT-ON zone  1004  may be disabled. By disabling the COOLING-RATE-DEPENDENT-ON zone  1004  when not needed, the logic unit  132  may delay turning on the gas-flow-valve actuator  138 , which may improve efficiency of the water heater  100 . While improving efficiency, this feature maintains performance for frequent use periods (less than 30 minutes burner off time) and for long durations without usage (greater than 5 hours burner off time) by starting a heat cycle quickly to ensure faster recovery in such times. 
     When the COOLING-RATE-DEPENDENT-ON zone is enabled and the first and second sensors  134 ,  136  detect a water temperature within the COOLING-RATE-DEPENDENT-ON zone  1004  after exiting the NO-CHANGE zone  1006  or the OFF zone  1008 , the logic unit  132  may maintain the current off state of the heater  108 . Alternatively, the logic unit  132  may initiate a heat cycle when the water cools at a rate exceeding a cooling rate threshold. 
     The cooling rate threshold may be a threshold for comparing the rate of change of the average water temperature measured by the first and second sensors  134 ,  136  as the water in the tank  102  cools. The cooling rate threshold may be satisfied when the first and second sensors  134 ,  136  detect an average rate of change that is greater than the cooling rate threshold. For example, the cooling rate threshold may be approximately 2 degrees Fahrenheit per minute. However, the cooling rate threshold may be other rates as well. 
     When entering the COOLING-RATE-DEPENDENT-ON zone  1004  from ON zone  1002 , the water is being heated, so the cooling-rate dependent condition does not apply. When the first and second sensors  134 ,  136  detect a water temperature within the COOLING-RATE-DEPENDENT-ON zone  1004  after exiting the ON zone  1002 , the logic unit  132  may maintain the previously initiated heat cycle. As such, the logic unit  132  may signal the gas-flow-valve actuator  138  to remain on. This signal may remain until the water temperature enters the OFF zone  1008 . 
     As described, the temperature control algorithm may be modified to track how long a water draw lasts and adjust the UT1 differential to control the amount of temperature stacking allowed; adjust the LT1 differential based on a maximum time between water draws; modify the OFF zone boundary  1032  to have a double step down function; and disable the COOLING-RATE-DEPENDENT-ON zone  1004  based on water draw time, cycling time, and average water temperature. By modifying the temperature control algorithm in this manner, the water heater  100  may have improved efficiency with minimal impact to a user of the water heater  100 . 
     5. Thermal Cutout 
     In many legacy water heaters, single-shot and/or thermal cutout units or switches provide overheat protection when one or more elements of the legacy controller fail. This overheat condition may occur when the temperature of the water exceeds a preset overheat limit that is typically built into the thermal cutout units. 
     The logic unit  132  (or some other fail-safe circuitry of the controller assembly  110 ) in combination with the first and/or second sensors  134 ,  136  may replace the thermal cutout units. Alternatively, this combination may be redundant to the thermal cutout units. 
       FIG. 9  is a state diagram showing a thermal cutout operation of the controller assembly  110 . As noted above, the logic unit  132  will (i) stop the heater from initiating or maintaining a heat cycle, and (ii) prevent the water heater from further operation until being serviced and reset. The logic unit  132  may initiate this cutout protection when a cutout condition  910  is satisfied. 
     The cut-out condition  910  may be satisfied when the first sensor  134  detects, measures, or otherwise determines that the water temperature at or near the top of the tank  102  is greater than a predetermined-overheat state condition  912 . Alternatively, the cut-out condition  910  may be satisfied when the second sensor  136  detects, measures, or otherwise determines that the water temperature at or near the bottom of the tank  102  is greater than a predetermined-overheat state condition  912 . 
     The predetermined-overheat state condition  912  may be approximately 5 degrees above the predetermined-maximum temperature  304 . The predetermined-overheat state condition  912  may be other temperatures as well. 
     6. Conclusion 
     In view of the wide variety of embodiments to which the principles of the present invention can be applied, it should be understood that the illustrated embodiments are exemplary only, and should not be taken as limiting the scope of the present invention. For example, the method steps described may be taken in sequences other than those described, and more or fewer elements may be used in the block diagrams. Further, the claims should not be read as limited to the described order or elements unless stated to that effect. In addition, use of the term “means” in any claim is intended to invoke 35 U.S.C. §112, ¶6, and any claim without the word “means” is not so intended. Therefore, all embodiments that come within the scope and spirit of the following claims and equivalents thereto are claimed as the invention. 
     Preferred and alternative embodiments of the present invention have been illustrated and described. It will be understood, however, that changes and modifications may be made to the invention without deviating from its true spirit and scope, as defined by the following claims.