Patent Publication Number: US-11661206-B2

Title: Method, system, and graphical indicator for providing a lateral center of gravity of an aircraft

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application claims priority to U.S. Provisional Patent Application bearing Ser. No. 62/565,235 filed on Sep. 29, 2017, the contents of which are hereby incorporated by reference. 
    
    
     TECHNICAL FIELD 
     The present disclosure relates generally to aircraft instrumentation, and more specifically to a lateral center of gravity display and systems and methods for providing the lateral center of gravity of an aircraft on an aircraft display. 
     BACKGROUND OF THE ART 
     The location of the center of gravity of an aircraft can affect its stability. If the positioning of the center of gravity exceeds a certain threshold set by the aircraft manufacturer, the aircraft performance may be impacted. 
     The center of gravity of the aircraft may be specified in the longitudinal, lateral and vertical directions. The longitudinal center of gravity refers to the balance of the aircraft along the longitudinal or lengthwise axis (known as the pitch direction or forward and aft direction). The lateral center of gravity refers to the balance of the aircraft in the lateral direction (known as right to left direction). The vertical center of gravity refers to the positioning of the center of gravity of the aircraft in the vertical direction (known as the up and down direction). Aircraft manufacturers may set longitudinal, lateral and vertical center of gravity limits. 
     An imbalance in the lateral center of gravity has historically been considered less critical than an imbalance in the longitudinal center of gravity, as most of the mass of the aircraft is located close to its center. However, the lateral center of gravity of the aircraft can be affected by fuel stored in fuel tanks located inside the wings not being evenly distributed between both sides of the aircraft. Existing alerting systems of aircraft do not readily facilitate such lateral center of gravity imbalance to be remedied. 
     SUMMARY 
     The present disclosure provides methods and system for providing a lateral center of gravity of an aircraft on an aircraft display. A fuel distribution in the aircraft fuel tanks is determined. A lateral center of gravity of the aircraft is determined based on the fuel distribution. The lateral center of gravity is sent to the aircraft display. The present disclosure further provides a graphical indicator for an aircraft display for displaying the lateral center of gravity of an aircraft. 
     In accordance with a broad aspect, there is provided a method for providing a lateral center of gravity of an aircraft on an aircraft display. The method comprises determining a fuel distribution in fuel tanks of a first wing and a second wing of the aircraft, determining a lateral center of gravity of the aircraft based at least in part on the fuel distribution, and sending a signal indicative of the lateral center of gravity to the aircraft display. 
     In some embodiments, the first wing comprises a first tank that is an inboard tank and a second tank that is an outboard tank, and the second wing comprises a third tank that is an inboard tank and a fourth tank that is an outboard tank. 
     In some embodiments, determining the fuel distribution comprises determining a first mass of fuel in the first tank from fuel density and fuel volume measurements in the first tank, determining a second mass of fuel in the second tank from fuel density and fuel volume measurements in the second tank, determining a third mass of fuel in the third tank from fuel density and fuel volume measurements in the third tank, determining a fourth mass of fuel in the fourth tank from fuel density and fuel volume measurements in the fourth tank, and determining the fuel distribution based on the first mass of fuel, the second mass of fuel, the third mass of fuel, the fourth mass of fuel and a configuration of the first tank, the second tank, the third tank and the fourth tank. 
     In some embodiments, determining the lateral center of gravity of the aircraft comprises determining a first moment arm based on the first mass of fuel and a first distance between a first tank center of mass and a substantially centered longitudinal axis of the aircraft, determining a second moment arm based on the second mass of fuel and a second distance between a second tank center of mass and the substantially centered longitudinal axis of the aircraft, determining a third moment arm based on the third mass of fuel and a third distance between a third tank center of mass and the substantially centered longitudinal axis of the aircraft, determining a fourth moment arm based on the fourth mass of fuel and a fourth distance between a fourth tank center of mass and the substantially centered longitudinal axis of the aircraft, and determining the lateral center of gravity using the first moment arm, the second moment arm, the third moment arm and the fourth moment arm. 
     In some embodiments, the method further comprises displaying the lateral center of gravity on the display with respect to at least one threshold. 
     In some embodiments, the method further comprises displacing a pointer indicative of the lateral center of gravity on the display with respect to the at least one threshold when the lateral center of gravity of the aircraft changes. 
     In some embodiments, the at least one threshold comprises at least one on ground threshold for use when the aircraft is on ground and at least one inflight threshold for use when the aircraft is in flight. 
     In some embodiments, the method further comprises determining the at least one threshold as a function of a total fuel mass. 
     In some embodiments, the method further comprises triggering a rebalancing of fuel between at least some of the first tank, the second tank, the third tank, and the fourth tank when the lateral center of gravity exceeds a first one of the at least one threshold. 
     In some embodiments, the method further comprises triggering an alert when the lateral center of gravity exceeds a second one of the at least one threshold. 
     According to another broad aspect, there is provided a system for providing a lateral center of gravity of an aircraft on an aircraft display. The system comprises a processing unit and a non-transitory computer-readable memory having stored thereon program instructions. The program instructions are executable by the processing unit for determining a fuel distribution in fuel tanks of a first wing and a second wing of the aircraft, determining a lateral center of gravity of the aircraft based at least in part on the fuel distribution, and sending a signal indicative of the lateral center of gravity to the aircraft display. 
     In some embodiments, the first wing comprises a first tank that is an inboard tank and a second tank that is an outboard tank, and the second wing comprises a third tank that is an inboard tank and a fourth tank that is an outboard tank. 
     In some embodiments, determining the fuel distribution comprises determining a first mass of fuel in the first tank from fuel density and fuel volume measurements in the first tank, determining a second mass of fuel in the second tank from fuel density and fuel volume measurements in the second tank, determining a third mass of fuel in the third tank from fuel density and fuel volume measurements in the third tank, determining a fourth mass of fuel in the fourth tank from fuel density and fuel volume measurements in the fourth tank, and determining the fuel distribution based on the first mass of fuel, the second mass of fuel, the third mass of fuel, the fourth mass of fuel and a configuration of the first tank, the second tank, the third tank and the fourth tank. 
     In some embodiments, determining the lateral center of gravity of the aircraft comprises determining a first moment arm based on the first mass of fuel and a first distance between a first tank center of mass and a substantially centered longitudinal axis of the aircraft, determining a second moment arm based on the second mass of fuel and a second distance between a second tank center of mass and the substantially centered longitudinal axis of the aircraft, determining a third moment arm based on the third mass of fuel and a third distance between a third tank center of mass and the substantially centered longitudinal axis of the aircraft, determining a fourth moment arm based on the fourth mass of fuel and a fourth distance between a fourth tank center of mass and the substantially centered longitudinal axis of the aircraft, and determining the lateral center of gravity using the first moment arm, the second moment arm, the third moment arm and the fourth moment arm. 
     In some embodiments, the program instructions are further executable by the processing unit for displaying the lateral center of gravity on the display with respect to at least one threshold. 
     In some embodiments, the program instructions are further executable by the processing unit for displacing a pointer indicative of the lateral center of gravity on the display with respect to the at least one threshold when the lateral center of gravity of the aircraft changes. 
     In some embodiments, the at least one threshold comprises at least one on ground threshold for use when the aircraft is on ground and at least one inflight threshold for use when the aircraft is in flight. 
     In some embodiments, the program instructions are further executable by the processing unit for determining the at least one threshold as a function of a total fuel mass. 
     In some embodiments, the program instructions are further executable by the processing unit for triggering a rebalancing of fuel between at least some of the first tank, the second tank, the third tank, and the fourth tank when the lateral center of gravity exceeds a first one of the at least one threshold. 
     In some embodiments, the program instructions are further executable by the processing unit for triggering an alert when the lateral center of gravity exceeds a second one of the at least one threshold. 
     According to another broad aspect, there is provided a graphical indicator for an aircraft display. The graphical indicator comprises a first segment extending from a first end to a second end, a central marker substantially centered between the first end and the second end of the first segment to represent a balanced lateral center of gravity, and a pointer displaceable along the first segment between the first end and the second end, a position of the pointer along the first segment being indicative of one of a balanced lateral center of gravity, a left wing imbalance, and a right wing imbalance as a function of a relative position of the pointer with the central marker. 
     In some embodiments, the graphical indicator further comprises a first pair of threshold markers positioned along the first segment, wherein each threshold marker of the first pair of threshold markers is spaced equidistantly from the center marker towards a respective one of the first end and the second end. 
     In some embodiments, the graphical indicator further comprises a second pair of threshold markers positioned along the first segment, wherein each threshold marker of the second pair of threshold markers is spaced equidistantly from a respective threshold marker of the first pair of threshold markers towards a respective one of the first end and the second end. 
     In some embodiments, the graphical indicator further comprises a second segment extending from a third end to a fourth end, wherein the first segment is for use when the aircraft is in flight and the second segment is for use when the aircraft is on ground. 
     In some embodiments, the first segment and the second segment are positioned one above the other, and wherein the pointer is positioned between the first segment and the second segment. 
     In some embodiments, the central marker is substantially centered between the third end and the fourth end of the second segment. 
     In some embodiments, a visual element of the graphical indicator indicates usage of one of the first segment and the second segment as a function of an aircraft status. 
     In some embodiments, the graphical indicator further comprises a third pair of threshold markers positioned along the second segment, wherein each threshold marker of the third pair of threshold markers is spaced equidistantly from the center marker towards a respective one of the third end and the fourth end. 
     In some embodiments, the graphical indicator further comprises a fourth pair of threshold markers positioned along the second segment, wherein each threshold marker of the fourth pair of threshold markers is spaced equidistantly from a respective threshold marker of the first third of threshold markers towards a respective one of the third end and the fourth end. 
     In some embodiments, the first segment and the second segment display the lateral center of gravity of the aircraft using a same scale. 
     Features of the systems, devices, and methods described herein may be used in various combinations, and may also be used for the system and computer-readable storage medium in various combinations. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Further features and advantages of embodiments described herein may become apparent from the following detailed description, taken in combination with the appended drawings, in which: 
         FIG.  1 A  is a diagram of an example aircraft; 
         FIG.  1 B  is a diagram of a partial top view of the aircraft of  FIG.  1 A ; 
         FIG.  1 C  is a diagram of a cross sectional forward/aft view of the aircraft of  FIG.  1 A  taken through wings of the aircraft; 
         FIG.  2    is a flowchart of a method for providing a lateral center of gravity of an aircraft in accordance with an embodiment; 
         FIG.  3 A  is a flowchart illustrating an example embodiment for determining a fuel distribution in fuel tanks; 
         FIG.  3 B  is a flowchart illustrating an example embodiment for determining a lateral center of gravity of an aircraft; 
         FIG.  3 C  is a flowchart illustrating another example embodiment for determining a fuel distribution; 
         FIG.  3 D  is a flowchart illustrating an example embodiment for determining a fuel distribution in two tanks; 
         FIG.  3 E  is a flowchart illustrating another example embodiment for determining a lateral center of gravity of an aircraft; 
         FIG.  4 A  is an example of a lateral center of gravity display illustrating a substantially balanced lateral center of gravity of an aircraft; 
         FIG.  4 B  is an example of a lateral center of gravity display illustrating a right wing lateral center of gravity imbalance; 
         FIG.  4 C  is an example of a lateral center of gravity display illustrating a left wing lateral center of gravity imbalance; 
         FIG.  5 A  is a flowchart illustrating example embodiments for displaying a lateral center of gravity of an aircraft; 
         FIG.  5 B  is an example graphical representation of fuel rebalancing thresholds and catastrophic imbalance thresholds; 
         FIG.  6    is a block diagram of an example lateral center of gravity system; and 
         FIG.  7    is a block diagram of an example computing device. 
     
    
    
     It will be noted that throughout the appended drawings, like features are identified by like reference numerals. 
     DETAILED DESCRIPTION 
     Methods and systems for providing a lateral center of gravity of an aircraft on an aircraft display are described herein. The lateral center of gravity is determined based on distribution of fuel in the fuel tanks of the aircraft. The present disclosure further provides a graphical indicator for displaying the lateral center of gravity of an aircraft. 
     With reference to  FIG.  1 A , an exemplary aircraft  10  is shown. The aircraft  10  may be any type of aircraft such as a propeller plane, jet plane, turbojet plane, turbo-propeller plane, and the like. For example, the aircraft  10  may be a narrow-body, twin-engine jet airliner. The aircraft  10  may be a fixed-wing aircraft. The aircraft  10  may comprise flight control components  16 , wings  31 ,  32 , fuselage  18 , engines  20  and empennage  22  of known or other type. In the embodiment illustrated, a single engine  20  is mounted under each of the wings  31 ,  32 . However, two or more engines  20  may be mounted to one or more of wings  31 ,  32 . Alternatively, or in addition, one or more engines  20  may be mounted to fuselage  18  or be installed on the aircraft  10  in any suitable manner. A cockpit  12  may be positioned at any suitable location on the aircraft  10 , for example at a front portion of the fuselage  18 . The cockpit  12  is configured for accommodating one or more pilots who control the operation of the aircraft  10  by way of one or more operator controls. 
     With reference to  FIG.  1 B , the aircraft  10  comprises a first wing  31  and a second wing  32 . The first wing  31  comprises a first tank  41  and a second tank  42 . The second wing  32  comprises a third tank  43  and a fourth tank  44 . The tanks  41 ,  42 ,  43 ,  44  are for holding fuel for the aircraft  10 . The tanks  41 ,  42 ,  43 ,  44  may have various volumetric shapes and may be positioned inside the wings  31 ,  32  in any suitable manner. In the illustrated embodiment, the first tank  41  and the third tank  43  are inboard tanks, the second tank  42  and the fourth tank  44  are outboard tanks. For the purposes of the present disclosure, the first wing  31  is referred to as a right wing on a right side of the aircraft  10  and the second wing  32  is referred to as a left wing on a left side of the aircraft  10 . A longitudinal axis  50  is defined along the fuselage  18 . Each of the tanks  41 ,  42 ,  43 ,  44  has a configuration corresponding to a volumetric shape and a position in one of the wings  31 ,  32 . The volumetric shape of a tank refers to the form of the tank such as the size, position, height, width and length of various surfaces that define the tank. The position of a tank refers to the location of the tank in one of the wings  31 ,  32  of the aircraft  10 . The configuration of each of the tanks  41 ,  42 ,  43 ,  44 , i.e. the volumetric shape and position, may vary from one tank to another. The amount of fuel in each of the tanks  41 ,  42 ,  43 ,  44  and the configuration of each of the tanks  41 ,  42 ,  43 ,  44  are used to determine the lateral center of gravity of the aircraft  10 . 
     In some embodiments, the aircraft  10  comprises one or more additional tanks for holding fuel. The one or more additional tanks may be positioned in the wings  31 ,  32  or the fuselage  18 . By way of a specific and non-limiting example, the aircraft  10  may comprises a rear fuselage tank. In some embodiments, the amount of fuel in each of the tanks  41 ,  42 ,  43 ,  44  and the one or more additional tanks and the configuration of each of the tanks  41 ,  42 ,  43 ,  44  and the one or more additional tanks are used to determine the lateral center of gravity of the aircraft  10 . 
     Referring to  FIG.  1 C , each of the tanks  41 ,  42 ,  43 ,  44  has a corresponding mass of fuel m 1 , m 2 , m 3 , m 4 . Each mass of fuel m 1 , m 2 , m 3 , m 4  has a corresponding center of mass c 1 , c 2 , c 3 , c 4 . The position of each center of mass c 1 , c 2 , c 3 , c 4  may be represented by a lateral distance from the longitudinal axis  50  of the aircraft  10 , substantially centered within the fuselage  18 . More specifically, a lateral distance d 1  exemplifies the position of the center of mass c 1  of the mass of fuel m 1  of the first tank  41 , a lateral distance d 2  exemplifies the position of the center of mass c 2  of the mass of fuel m 2  of the second tank  42 , a lateral distance d 3  exemplifies the position of the center of mass c 3  of the mass of fuel m 3  of the third tank  43 , a lateral distance d 4  exemplifies the position of the center of mass c 4  of the mass of fuel m 4  of the fourth tank  44 . In some embodiments, the lateral distances d 1 , d 2 , d 3 , d 4  and the masses of fuel m 1 , m 2 , m 3 , m 4  are used to determine the lateral center of gravity of the aircraft  10 . 
     With reference to  FIG.  2   , there is illustrated a flowchart of an example method  200  for providing a lateral center of gravity of an aircraft on an aircraft display, such as the aircraft  10  of  FIGS.  1 A,  1 B and  1 C . While the method  200  is described herein with reference to the aircraft  10 , the method  200  may be applied to other types of aircraft. 
     At step  202 , a fuel distribution in the fuel tanks of the aircraft  10  is determined. For example, in an embodiment where there are four fuel tanks such as the first tank  41 , the second tank  42 , the third tank  43  and the fourth tank  44 , the fuel distribution is determined across the fuel tanks  41 ,  42 ,  43  and  44 . If more than four fuel tanks are present on aircraft  10 , the fuel distribution may be determined across all of the fuel tanks in the aircraft  10 . 
     The fuel distribution may be determined in various manners depending on practical implementations. For example, determining the fuel distribution may comprise determining each mass of fuel m 1 , m 2 , m 3 , m 4  and the position of each center of mass c 1 , c 2 , c 3 , c 4 . If more than four tanks are present, determining the fuel distribution may comprise determining a mass of fuel in each tank and position of a center of mass for each tank. By way of another example, fuel density and fuel volume measurements of tanks  41 ,  42 ,  43  and  44  may be used to determine the fuel distribution. 
     At step  206 , a lateral center of gravity of the aircraft  10  is determined based on the fuel distribution. For example, the lateral center of gravity of the aircraft  10  is determined based on the distribution of fuel in the tanks  41 ,  42 ,  43 ,  44  of the wings  31 ,  32  of the aircraft  10 . 
     At step  208 , a signal indicative of the lateral center of gravity is sent to the aircraft display. The signal indicative of the lateral center of gravity may be sent directly to the aircraft display or via another aircraft component. The signal indicative of the lateral center of gravity may be sent via wireless or wired means, depending on the practical implementations of a communication system of the aircraft. 
     At step  210 , optionally, the lateral center of gravity is displayed on the aircraft display. The lateral center of gravity may be displayed on the aircraft display in any suitable manner, including via a numerical value, a textual indication, a visual icon or a graphical indicator, an embodiment of which will be described in more detail below. At step  211 , optionally, a remedial action is triggered when the lateral center of gravity exceeds at least one threshold, as will be explained in more detail below. 
     With reference to  FIG.  3 A , there is illustrated an example embodiment for determining the fuel distribution, as per step  202  of  FIG.  2   , when there are two tanks present on each aircraft wing. At step  302 , the mass m 1  in the first tank  41  is determined, the mass m 2  in the second tank  42  is determined, the mass m 3  in the third tank  43  is determined and the mass m 4  in the fourth tank  44  is determined. 
     The masses m 1 , m 2 , m 3 , m 4  may be determined from fuel density and fuel volume measurements of the tanks  41 ,  42 ,  43 ,  44 . The masses m 1 , m 2 , m 3 , m 4  may be determined by the product of fuel volume and fuel density and represented by the following equations:
 
 m   1   =V   1   p   1 ,  (1)
 
 m   2   =V   2   p   2 ,  (2)
 
 m   3   =V   3   p   3 ,  (3)
 
 m   4   =V   4   p   4 ,  (4)
 
where V 1 , V 2 , V 3 , V 4  correspond to fuel volume in the first tank  41 , the second tank  42 , the third tank  43 , and the fourth tank  44 , respectively, and p 1 , p 2 , p 3 , p 4  correspond to fuel density in the first tank  41 , the second tank  42 , the third tank  43  and the fourth tank  44 , respectively.
 
     Fuel density in the tanks may be determined in any suitable manner. For example, fuel density may be measured by a fuel density measuring device comprising one or more sensors for measuring density of fuel. In some embodiments, the fuel density measuring device comprises a hydrometer configured to determine density of a liquid. Other manners for determining fuel density in the tanks are contemplated, including via one or more look-up table(s) or schedule(s), among other possibilities. In some embodiments, an analytical fuel density is used, which may depend on one or more of fuel type, temperature and pressure. 
     Fuel volume in the tanks may be determined in any suitable manner. For example, fuel volume may be measured by a fuel volume measuring device comprising one or more sensors. In some embodiments, the fuel volume measuring device comprises one or more pressure sensors. In some embodiments, the fuel volume measuring device comprises one or more fuel level sensors. The fuel volume may then be determined depending on the volumetric shape of the tank. One or more of equation(s), look-up table(s), schedule(s) and the like may be used to determine fuel volume from the fuel level and/or the pressure in the fuel tanks. The equation(s), the look-up table(s), and/or the schedule(s) may be predetermined based on the volumetric shape of the tank. Other manners for determining fuel volume are contemplated. 
     The fuel density and fuel volume determinations may be actively retrieved, or may be passively received. The fuel density and fuel volume determinations of the tanks may be retrieved and/or received from a control system or aircraft computer. In some embodiments, step  302  comprise triggering determination of the fuel density and/or fuel volume of the tanks whenever method  200  is initiated. 
     At step  306 , the fuel distribution is determined based on the mass of fuel m 1  in the first tank  41 , the mass of fuel m 2  in the second tank  42 , the mass m 3  in the third tank  43 , the mass m 4  in the fourth tank  44  and a configuration of the first tank  41 , the second tank  42 , the third tank  43  and the fourth tank  44 . In some embodiments, determining the first fuel distribution comprises determining the position of the center of mass c 1  in the first tank  41 , determining the position of the center of mass c 2  in the second tank  42 , determining the position of the center of mass c 3  in the third tank  43  and determining the position of the center of mass c 4  in the fourth tank  44 . In some embodiments, determining the position of the center of mass c 1  comprises determining the lateral distance d 1  between the center of mass c 1  and the longitudinal axis  50 . Similarly, in some embodiments, determining the position of the center of mass c 2  comprises determining the lateral distance d 2  between the center of mass c 2  and the longitudinal axis  50 . In some embodiments, determining the position of the center of mass c 3  comprises determining the lateral distance d 3  between the center of mass c 3  and the longitudinal axis  50 . In some embodiments, determining the position of the center of mass c 4  comprises determining the lateral distance d 4  between the center of mass c 4  and the longitudinal axis  50 . 
     The positions of the center of masses may be determined in any suitable manner. For example, the position of the center of mass in the fuel tank may be determined based on the fuel density and fuel volume of the tank and the configuration of the tank. One or more of equation(s), look-up table(s), schedule(s) and the like may be used to determine the position of the center of mass in the fuel tank from the fuel density and fuel volume measurements of the tank. The equation(s), look-up table(s) and/or schedule(s) may be predetermined based on the configuration of the tank. Other manners for determining the positions of the center of masses are contemplated. 
     In some embodiments, the lateral distances d 1 , d 2  correspond to positive values and the lateral distances d 3 , d 4  correspond to negative values. In other words, a positive value for a lateral distance from a center of mass to the substantially centered longitudinal axis  50  indicates a position on the right side of the aircraft  10  and a negative value for a lateral distance from a center of mass to the substantially centered longitudinal axis  50  indicates a position on the left side of the aircraft  10 . 
     The lateral center of gravity of the aircraft may be determined based on moment arms of each of the fuel tanks in the aircraft, such as fuel tanks  41 ,  42 ,  43 ,  44  in the wings  31 ,  32 . With reference to  FIG.  3 B , there is illustrated an example embodiment for determining the lateral center of gravity of the aircraft  10 , as per step  206  of  FIG.  2   . At step  322 , a moment arm is determined for each tank  41 ,  42 ,  43 ,  44 . Each lateral distance d 1 , d 2 , d 3 , d 4  may be referred to as an “arm”. Each moment arm may be determined from the fuel distribution. A moment for each fuel tank  41 ,  42 ,  43 ,  44  may be determined by multiplying each mass m 1 , m 2 , m 3 , m 4  by its corresponding arm d 1 , d 2 , d 3 , d 4 . At step  326 , the lateral center of gravity may be determined from the moment arms and a sum of the masses of fuel. The lateral center of gravity may be determined from the sum of the moment arms divided by the sum of the masses of fuel. Accordingly, the determination of the lateral center of gravity CG may be determined on a moment arm basis and may be represented by the following equation: 
     
       
         
           
             
               
                 
                   
                     
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     If more than four tanks are present, the lateral center of gravity CG may be determined in a similar manner based on the fuel masses and center of masses of all tanks in the aircraft. 
     With reference to  FIG.  3 C , there is illustrated another example embodiment for determining the fuel distribution, as per step  202  of  FIG.  2   . At step  332 , a first fuel distribution between fuel tanks of the first wing  31  of the aircraft  10  is determined. At step  334 , a second fuel distribution between fuel tanks of the second wing  32  of the aircraft  10  is determined. For example, in an embodiment where there are two fuel tanks on the first wing  31  such as the first tank  41  and the second tank  42 , the first fuel distribution is determined across fuel tanks  41  and  42 . Similarly, for example, in an embodiment where there are two fuel tanks on the second wing  32  such as the third tank  43  and the fourth tank  44 , the second fuel distribution is determined across fuel tanks  43  and  44 . If more than two fuel tanks are present on the first wing, the first fuel distribution is determined across all of the fuel tanks on the first wing. Similarly, if more than two fuel tanks are present on the second wing, the second fuel distribution is determined across all of the fuel tanks in the second wing. 
     With reference to  FIG.  3 D , there is illustrated an example embodiment for determining the first fuel distribution, as per step  332  of  FIG.  3 C , when there are two tanks present on an aircraft wing. At step  352 , the mass m 1  in the first tank  41  is determined. At step  354 , the mass m 2  in the second tank  42  is determined. At step  356 , the first fuel distribution is determined based on the mass of fuel m 1  in the first tank  41 , the mass of fuel m 2  in the second tank  42 , and a configuration of the first tank  41 , the second tank  42 . The first fuel distribution may be determined in various manners depending on practical implementations. For example, determining the first fuel distribution may comprise determining a total mass of fuel in the first wing  31  and a position of a center of mass of the total mass of fuel in the first wing  31 . The total mass of fuel in the first wing  31  and the position of the center of mass of the total mass of fuel in the first wing  31  may be determined from the masses of fuel m 1 , m 2  and the positions of the center of masses c 1 , c 2 . In some embodiments, determining the first fuel distribution comprises determining the position of the center of mass c 1  and the position of the center of mass c 2 . In some embodiments, determining the position of the center of mass c 1  comprises determining the lateral distance d 1  and determining the position of the center of mass c 2  comprises determining the lateral distance d 2 . By way of another example, fuel density and fuel volume measurements of the first tank  41  and the second tank  42  may be used to determine the total mass of fuel in the first wing  31  and the position of the center of mass of the total mass of fuel in the first wing  31 . The second fuel distribution may be determined in various manners depending on practical implementations. The second fuel distribution may be determined in a similar manner as the first fuel distribution or differently therefrom. Note that the number of fuel tanks on the first wing  31  may differ from the number of fuel tanks on the second wing  32 . 
     In some embodiments, determining the second fuel distribution comprises determining the masses of fuel m 3 , m 4 , the position of the center of mass c 3  and the position of the center of mass c 4 . In some embodiments, determining the position of the center of mass c 3  comprises determining the lateral distance d 3  and determining the position of the center of mass c 4  comprises determining the lateral distance d 4 . 
     With reference to  FIG.  3 E , there is illustrated another example embodiment for determining the lateral center of gravity of the aircraft  10 , as per step  206  of  FIG.  2   . At step  362 , a first center of gravity is determined from the first fuel distribution. The first center of gravity is a center of gravity of the first wing  31 . In some embodiments, the first center of gravity is determined based on the masses m 1 , m 2  and the lateral distances d 1 , d 2 . By way of a specific and non-limiting example, equation (6) may be used to determine the first center of gravity CG 1 . It is noted that the sum of the masses m 1 , m 2  is a total mass of fuel in the first wing  31 . 
     
       
         
           
             
               
                 
                   
                     
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                   6 
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     At step  364 , a second center of gravity is determined from the second fuel distribution. The second center of gravity may be determined in a similar manner as the first center of gravity, for example based on the masses of fuel m 3 , m 4  and the lateral distances d 3 , d 4 . The second center of gravity CG 2  may be represented by the following equation: 
     
       
         
           
             
               
                 
                   
                     
                       C 
                       ⁢ 
                       
                         G 
                         2 
                       
                     
                     = 
                     
                       
                         
                           
                             d 
                             3 
                           
                           ⁢ 
                           
                             m 
                             3 
                           
                         
                         + 
                         
                           
                             d 
                             4 
                           
                           ⁢ 
                           
                             m 
                             4 
                           
                         
                       
                       
                         
                           m 
                           3 
                         
                         + 
                         
                           m 
                           4 
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     It is noted that the sum of the masses of fuel m 3 , m 4  is a total mass of fuel in the second wing  31 . 
     At step  366 , the lateral center of gravity is determined from the first center of gravity CG 1  and the second center of gravity CG 2 . For example, equation (8) may be used to obtain the lateral center of gravity CG of the aircraft. It is noted that the sum of the masses of fuel m 1 , m 2 , m 3 , m 4  corresponds to a total fuel mass in the first wing  31  and the second wing  32 . 
     
       
         
           
             
               
                 
                   
                     
                       C 
                       ⁢ 
                       G 
                     
                     = 
                     
                       
                         
                           
                             ( 
                             
                               
                                 m 
                                 1 
                               
                               + 
                               
                                 m 
                                 2 
                               
                             
                             ) 
                           
                           ⁢ 
                           C 
                           ⁢ 
                           
                             G 
                             1 
                           
                         
                         + 
                         
                           
                             ( 
                             
                               
                                 m 
                                 3 
                               
                               + 
                               
                                 m 
                                 4 
                               
                             
                             ) 
                           
                           ⁢ 
                           C 
                           ⁢ 
                           
                             G 
                             2 
                           
                         
                       
                       
                         
                           m 
                           1 
                         
                         + 
                         
                           m 
                           2 
                         
                         + 
                         
                           m 
                           3 
                         
                         + 
                         
                           m 
                           4 
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   8 
                   ) 
                 
               
             
           
         
       
     
     In some embodiments, the fuel distribution may be determined based on fuel volume measurements without fuel density measurements. For example, fuel density may be estimated or approximated for the purposes of determine the masses of fuel m 1 , m 2 , m 3 , m 4  and the positions of the center of masses c 1 , c 2 , c 3 , c 4 . 
       FIG.  4 A  is a specific and non-limiting example of an aircraft display  400  for displaying the lateral center of gravity of the aircraft. As illustrated, the aircraft display  400  comprises a graphical indicator  407 . The graphical indicator  407  includes a segment  408  that extends from a first end  401  to a second end  402 . A central marker  405  is substantially centered between the first end  401  and the second end  402  to represent a balanced lateral center of gravity of the aircraft  10 . A pointer  450  is displaceable along the segment  408  between the first end  401  and the second end  402 . The pointer  450  is indicative of a position of the lateral center of gravity of the aircraft  10 . A position of the pointer  450  along the segment  408  is indicative of one of a balanced lateral center of gravity, a left wing imbalance, and a right wing imbalance as a function of a relative position of the pointer  450  with the central marker  405 . A right wing imbalance refers to the lateral center of gravity of the aircraft  10  being offset from the longitudinal axis  50  towards the right wing  31 . A left wing imbalance refers to the lateral center of gravity of the aircraft  10  being offset from the longitudinal axis  50  towards the left wing  32 . 
     Note that while the pointer  450  is illustrated as a circle, various other shapes may also be used. In addition, the pointer  450  may be represented by a line, an icon, a letter, a number, or any other graphical element. Its position on the graphical indicator  407  may also vary. For example, it may be displayed above or below the segment  408 , instead of overlaid thereon as illustrated. In yet another embodiment, the pointer  450  is represented by a change in color of a portion of the segment  408 , as a function of the position of the pointer  450 . Other embodiments will be readily understood by those skilled in the art. 
     A left wing imbalance is displayed when the pointer  450  is between the central marker  405  and the second end  402 . A right wing imbalance is displayed when the pointer  450  is between the central marker  405  and the first end  401 . A balanced lateral center of gravity is displayed when the pointer  450  is aligned with the central marker  405 . As the pointer  450  gets closer to the first end  401 , the right wing imbalance increases. As the pointer  450  gets closer to the second end  402 , the left wing imbalance increases. In some embodiments, numerical values may be presented on the graphical indicator  407  for indicating a degree of lateral center of gravity imbalance. 
     In some embodiments, a first threshold marker  412  and a second threshold marker  413  are provided along the segment  408 . Each threshold marker  412 ,  413  is spaced equidistantly from the center marker  405  towards a respective one of the first end  401  and the second end  402 . In some embodiments, the threshold markers  412 ,  413  correspond to a fuel rebalancing threshold for each aircraft wing. For example, if the pointer  450  exceeds the first threshold marker  412  towards the first end  401 , then this is indicative of a need for rebalancing of fuel between at least some of the fuel tanks in the aircraft due to a right wing imbalance of the lateral center of gravity. Similarly, if the pointer  450  exceeds the second threshold marker  413  towards the second end  402 , then this is indicative of a need for rebalancing of fuel between at least some of the fuel tanks due to a left wing imbalance of the lateral center of gravity. In each case, the direction of imbalance, i.e. a left wing imbalance or a right wing imbalance, will inform the decision on how to rebalance the fuel in order to achieve a balanced later center of gravity for the aircraft. Note that the rebalancing may be performed automatically or manually. 
     In some embodiments, a third threshold marker  414  and a fourth threshold marker  415  are provided along the segment  408 . The third threshold marker  414  is spaced from the first threshold marker  412  towards the first end  401 . The fourth threshold marker  415  is spaced from the second threshold marker  413  towards the second end. The threshold markers  414 ,  415  may be used to represent another level of imbalance, beyond the need for rebalancing of fuel. For example, the threshold markers  414 ,  415  may correspond to a crew alert system (CAS) imbalance threshold. When the pointer  450  exceeds threshold marker  414  towards the first end  401  or threshold marker  415  towards the second end  402 , this is indicative of a need to alert the crew as the imbalance of the lateral center of gravity has reached a significant level. 
     With reference to  FIG.  4 B , there is illustrated another embodiment for the aircraft display  400 . In this example, the graphical indicator  407  comprises first segment  410  and second segment  420 . As illustrated, the first and second segments  410 ,  420  are positioned one above the other and the pointer  450  is positioned therebetween. Alternatively, a pointer  450  may be displayed on each segment  410 ,  420 , or on an active one of the segments  410 ,  420  as a function of the status of the aircraft. The first segment  410  may be used when the aircraft  10  is in flight and the second segment  420  may be used when the aircraft  10  is on the ground. The first segment  410  extends from the first end  401  to the second end  402  and the threshold markers  412 ,  413 ,  414 ,  415  are associated with the first segment  410 . The second segment  420  extends from a third end  403  to a fourth end  404  and has threshold markers  422 ,  423 ,  424 ,  425  associated therewith. Note that threshold markers  412 ,  413 ,  414 ,  415  may be visually aligned with threshold markers  422 ,  423 ,  424 ,  425  but segments  410 ,  420  may use different scales. Alternatively, and as illustrated, the same scale is used for both the first segment  410  and the second segment  420 , and the position of each threshold marker is adapted as a function of the appropriate threshold for an inflight imbalance and a ground imbalance, respectively. 
     One or more of the threshold markers  412 ,  413 ,  414 ,  415 ,  422 ,  423 ,  424 ,  425  may correspond to remedial action threshold markers. That is, if the pointer  450  exceeds one of the threshold markers  412 ,  413 ,  414 ,  415 ,  422 ,  423 ,  424 ,  425 , then this is indicative that a remedial action is occurring or needs to occur. The remedial action may be rebalancing of fuel between at least some of the tanks  41 ,  42 ,  43 ,  44 , causing an alert indicating that the lateral center of gravity of the aircraft is at dangerous level, and the like. 
     In some embodiments, a visual element of the graphical indicator  407  is used to identity one of the two segments  410 ,  420  as active, as a function of the aircraft status. For example, only one of the two segments  410 ,  420  may be displayed at any one time. In another example, one of the two segments  410 ,  420  is illuminated while the other of the two segments  410 ,  420  is darkened. In yet another example, the active segment is displayed in a first color, such as green, while the inactive segment is displayed in a second color, such as red. Other embodiments for visually indicating the active segment are also contemplated. Note that the aircraft status may be determined using any known means, such as using a weight-off wheels conditions of the aircraft  10  or an altitude measurement. The aircraft status may be obtained from various aircraft systems, such as an aircraft computer, an engine computer, and the like. 
     With reference to  FIG.  4 C , there is illustrated another embodiment of the graphical indicator  407  having two segments  410 ,  420 . In this example, the first and second segments  410 ,  420  are positioned side by side. The pointer  450  is positioned above the active segment. In alternative embodiments, the pointer  450  is overlaid on the active segment, or a pointer  450  is provided for each segment  410 ,  420 , while other visual indicators are used to designate the active segment. 
     The variants with respect to the pointer  450 , the nature, position, and size of the threshold markers  412 ,  413 ,  414 ,  415 ,  422 ,  423 ,  424 ,  425 , and any other elements associated with the graphical indicator  407  are applicable to any of the embodiments illustrated in  FIGS.  4 A- 4 C . 
     With reference to  FIG.  5 A , there is illustrated an example embodiment for displaying the lateral center of gravity on an aircraft display, as per step  210  of  FIG.  2   . While  FIG.  5 A  is described with reference to the graphical indicator  407  of  FIG.  4 B , other embodiments may also apply. 
     At step  502  the lateral center of gravity is displayed on the aircraft display  400  with respect to at least one threshold marker, which may be any one of threshold markers  412 ,  413 ,  414 ,  415 ,  422 ,  423 ,  424 ,  425 . The lateral center of gravity may be displayed by use of the pointer  450 . At step  504 , the pointer  450  is displaced on the display with respect to the at least one threshold marker when the lateral center of gravity of the aircraft  10  changes. 
     In some embodiments, the method  200  comprises determining the threshold markers as a function of the total fuel mass and displaying the threshold markers on the graphical indicator of the aircraft display. With additional reference to  FIG.  5 B , a graphical representation illustrates various thresholds that vary as a function of the total fuel mass. In particular, a first threshold  512 , a second threshold  514 , a third threshold  522  and a fourth threshold  524  are illustrated. In this example, the first threshold  512  corresponds to the first threshold marker  412  of the first segment  410  and the second threshold  514  corresponds to the third threshold marker  414  of the first segment  410 . The third threshold  522  corresponds to the first threshold marker  422  of the second segment  420  and the fourth threshold  524  corresponds to the third threshold marker  424  of the second segment  420 . Also in this example, the first and third thresholds  512 ,  522  are fuel rebalancing thresholds and the second and fourth thresholds  514  and  524  are CAS imbalance thresholds. 
     The total mass of fuel may be used to determine a value for setting a corresponding one of the threshold markers  412 ,  414 ,  422 ,  424 . For example, a marker  550  illustrates a value from the third threshold  522  for a given total fuel mass and the value may be used to set the third threshold marker  422  of the second segment  420 .  FIG.  5 B  illustrates example thresholds  512 ,  514 ,  522 ,  524  for use when there is a right wing imbalance. Similar thresholds maybe be used for a left wing imbalance. 
     As per step  211 , in some embodiments, the method  200  comprises triggering a remedial action when the lateral center of gravity exceeds at least one threshold. In some embodiments, step  211  comprises comparing the lateral center of gravity to at least one of the thresholds  512 ,  514 ,  522 ,  524  to determine if the lateral center of gravity exceeds at least one threshold. If so, then a remedial action may be triggered. 
     The remedial action may vary depending on practical implementations. For example, when the lateral center of gravity exceeds the first threshold  512  or the third threshold  522 , then a rebalancing of fuel between at least some of the tanks  41 ,  42 ,  43 ,  44  is triggered. The aircraft  10  may comprise one or more pumps for transferring fuel between one or more of the tanks  41 ,  42 ,  43 ,  44 . Each of the tanks  41 ,  42 ,  43 ,  44  may comprise one or more controllable valves used for transferring fuel to and/or from the tanks  41 ,  42 ,  43 ,  44  for fuel rebalancing. In another example, when the lateral center of gravity exceeds the second or fourth thresholds  522 ,  524 , an alert is triggered. The alert may convey that the lateral center of gravity of the aircraft is at a dangerous position. The remedial action may be triggered automatically and performed by one or more control systems of the aircraft. Alternatively, the remedial action may be performed upon input from the pilot or another crew member. 
     In some embodiments, each of the wings  31 ,  32 , comprises more than two tanks. For example, each of the wings  31 ,  32  may comprise three tanks, four tanks, five tanks or more than five tanks. In some embodiments, one or more of the tanks  41 ,  42 ,  43 ,  44  comprises more than one sub-compartment. Accordingly, the method  200  may be implemented in a similar manner as described herein but adapted according to the number of fuel tanks and/or sub-compartments. 
     With reference to  FIG.  6   , the method  200  may be implemented by a system  600  comprising a computing device  710 . In some embodiments, the system  600  comprises one or more sensors  602  and/or an aircraft display  400 . The one or more sensors  602  may comprise one or more fuel density sensor operatively coupled to computing device  710  for measuring fuel density in any given tank  41 ,  42 ,  43 ,  44  of the aircraft  10 . The one or more sensors  602  may comprise one or more fuel volume sensors operatively coupled to computing device  710  for measuring fuel volume in any given tank  41 ,  42 ,  43 ,  44  of the aircraft  10 . The one or more sensors  602  may comprise one or more pressure sensors operatively coupled to computing device  710  for measuring fuel pressure in any given tank  41 ,  42 ,  43 ,  44  of the aircraft  10 . The one or more sensors  602  may comprise one or more fuel level sensors operatively coupled to computing device  710  for measuring fuel level in any given tank  41 ,  42 ,  43 ,  44  of the aircraft  10 . The one or more sensors  602  may comprise any other suitable sensors used to measure any suitable parameters relating to the fuel in any given tank  41 ,  42 ,  43 ,  44  of the aircraft  10 . In some embodiments, the sensors  602  are separate from the system  600  and/or may be existing parts of the aircraft  10 . In some embodiments, data described herein as coming from the sensors  602  are provided by one or more other aircraft computing device or control system. 
     With additional reference to  FIG.  7   , the computing device  710  comprises a processing unit  712  and a memory  714  which has stored therein computer-executable instructions  716 . The processing unit  712  may comprise any suitable devices configured to implement the method  200  such that instructions  716 , when executed by the computing device  710  or other programmable apparatus, may cause the functions/acts/steps performed as part of the method  200  as described herein to be executed. The processing unit  712  may comprise, for example, any type of general-purpose microprocessor or microcontroller, a digital signal processing (DSP) processor, a central processing unit (CPU), an integrated circuit, a field programmable gate array (FPGA), a reconfigurable processor, other suitably programmed or programmable logic circuits, or any combination thereof. 
     The memory  714  may comprise any suitable known or other machine-readable storage medium. The memory  714  may comprise non-transitory computer readable storage medium, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. The memory  714  may include a suitable combination of any type of computer memory that is located either internally or externally to device, for example random-access memory (RAM), read-only memory (ROM), compact disc read-only memory (CDROM), electro-optical memory, magneto-optical memory, erasable programmable read-only memory (EPROM), and electrically-erasable programmable read-only memory (EEPROM), Ferroelectric RAM (FRAM) or the like. Memory  714  may comprise any storage means (e.g., devices) suitable for retrievably storing machine-readable instructions  716  executable by processing unit  712 . 
     The methods and systems for providing a lateral center of gravity of an aircraft described herein may be implemented in a high level procedural or object oriented programming or scripting language, or a combination thereof, to communicate with or assist in the operation of a computer system, for example the computing device  710 . Alternatively, the methods and systems for providing a lateral center of gravity of an aircraft may be implemented in assembly or machine language. The language may be a compiled or interpreted language. Program code for implementing the methods and systems for providing a lateral center of gravity of an aircraft may be stored on a storage media or a device, for example a ROM, a magnetic disk, an optical disc, a flash drive, or any other suitable storage media or device. The program code may be readable by a general or special-purpose programmable computer for configuring and operating the computer when the storage media or device is read by the computer to perform the procedures described herein. Embodiments of the methods and systems for providing a lateral center of gravity of an aircraft may also be considered to be implemented by way of a non-transitory computer-readable storage medium having a computer program stored thereon. The computer program may comprise computer-readable instructions which cause a computer, or more specifically the processing unit  712  of the computing device  710 , to operate in a specific and predefined manner to perform the functions described herein, for example those described in the method  200 . Computer-executable instructions may be in many forms, including program modules, executed by one or more computers or other devices. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform particular tasks or implement particular abstract data types. Typically the functionality of the program modules may be combined or distributed as desired in various embodiments. 
     The aircraft display  400  may comprise any kind of display such as an LCD (liquid crystal display), an LED (light emitting diode) display, a CRT (cathode ray tube) display, a HUD (Heads-up Display), a PFD (primary flight display) and/or any other suitable display device. A HUD is any transparent display that presents data in the pilot or co-pilot&#39;s field of vision without obstructing the view. A PFD is an aircraft instrument dedicated to flight information. The aircraft display  400  may display the lateral center of gravity of an aircraft as calculated by the computing device  710 . Accordingly, the computing device  710  may cause a GUI (graphical user interface) to display the lateral center of gravity of the aircraft on the aircraft display  400 . In some embodiments, the aircraft display  400  is separate from the system  600  and/or may be an existing part of the aircraft  10 . The aircraft display  400  may be operably coupled to the computing device  710  by one or more data buses such that the computing device  710  may provide the lateral center of gravity and/or other suitable parameters to the aircraft display  400 . 
     Computer simulation, modeling, engineering simulators and/or processing may be used to determine the various equations, look-up tables, and/or schedules described herein. By way of a specific and non-limiting example, computer simulation and modeling is used to determine an equation for each of the tanks  41 ,  42 ,  43 ,  44 , where each equation is a function of at least one of fuel volume and fuel density and can be used to determine fuel mass and/or a corresponding center of mass. The equations, look-up tables, and/or schedules may be determined in real-time during takeoff, may be pre-determined in advance to takeoff, and/or may be determined at regular intervals. 
     Computer simulation, modeling, engineering simulators and/or processing may be used to determine the thresholds  512 ,  514 ,  522 ,  524  that vary as function of total fuel mass. Computer simulation, modeling, engineering simulators and/or processing may be used to determine the thresholds  512 ,  514 ,  522 ,  524  based on one or more of configurations of the tanks  41 ,  42 ,  43 ,  44  and a fuel burn sequence. The fuel burn sequence (also known as fuel burn scheduling) corresponds to ordering and amount in which fuel is obtained and burned from the tanks  41 ,  42 ,  43 ,  44  to keep the longitudinal CG within acceptable limits. The fuel burn sequence may depend on the configuration of tanks  41 ,  42 ,  43 ,  44 . The thresholds may be determined in real-time during takeoff, may be pre-determined in advance to takeoff, and/or may be determined at regular intervals. 
     The above description is meant to be exemplary only, and one skilled in the art will recognize that changes may be made to the embodiments described without departing from the scope of the invention disclosed. Still other modifications which fall within the scope of the present invention will be apparent to those skilled in the art, in light of a review of this disclosure. 
     Various aspects of the methods and systems for providing a lateral center of gravity of an aircraft may be used alone, in combination, or in a variety of arrangements not specifically discussed in the embodiments described in the foregoing and is therefore not limited in its application to the details and arrangement of components set forth in the foregoing description or illustrated in the drawings. For example, aspects described in one embodiment may be combined in any manner with aspects described in other embodiments. Although particular embodiments have been shown and described, it will be obvious to those skilled in the art that changes and modifications may be made without departing from this invention in its broader aspects. The scope of the following claims should not be limited by the embodiments set forth in the examples, but should be given the broadest reasonable interpretation consistent with the description as a whole.