Abstract:
A process for determining a center of gravity of a vehicle having a sprung portion and an unsprung portion on the basis of selective variation of a lateral and a longitudinal orientation of the sprung portion relative to the unsprung portion.

Description:
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OF DEVELOPMENT 
       [0001]    This invention was made and funded in part by the U.S. Government, specifically by the U.S. Army Tank-Automotive &amp; Armaments Co. under Contract W56HZV-05-9-0002. The U.S. Government has certain rights in the invention. 
     
    
     FIELD OF THE INVENTION 
       [0002]    The present invention relates generally to the field of vehicles, and, more particularly, to determination of the center of gravity of the vehicle. 
       BACKGROUND OF THE INVENTION 
       [0003]    A loaded vehicle traveling over sloping terrain is susceptible to turning over, creating a hazard for the vehicle, the vehicle load, and the operating personnel. Problems arise, even on level terrain, when loads may become asymmetric or when the vehicle acquires a side-to-side swaying motion. 
         [0004]    If the location of the center of gravity of a loaded vehicle were available to an active stability control system and/or a roll over warning system, measures might be taken to preserve the vehicle stability. When road conditions and driving operations cause vehicle orientation to approach the boundary of stable operation beyond which the center of gravity of the loaded vehicle falls outside of the perimeter associated with the wheelbase and the track of the vehicle, the vehicle light he slowed or the turning angle reduced to prevent the vehicle from tipping over. 
         [0005]    Although the location of the center of gravity of the vehicle when empty may be known, the center of gravity of a vehicle holding cargo is generally unknown. Moreover, being dependent on the configuration of the vehicle, for example, on the amount and distribution of fuel, cargo, and passengers, the center of gravity often changes. As cargo is loaded onto vehicle, it would be helpful to know the vehicle center of gravity on an ongoing basis. Knowing the center of gravity of the vehicle and the weight per axle is valued information to those individuals responsible for loading the vehicles onto other means of transportation. Such information would allow those loading the vehicle to adjust the load to assure that the center of gravity remains within the range specified by the manufacturer of the vehicle during vehicle travel over expected terrain at anticipated speeds, thereby assuring safe operation of the vehicle. The real time output of the center of gravity of the loaded vehicle could be used to allow those loading the vehicle to adjust the load to assure that the center of gravity is within the manufacturer&#39;s specified range to assure safe operation of the vehicle. If the vehicle is also equipped with an active stability control system and/or a roll-over warning system, the true center of gravity would be an important input into those systems. 
         [0006]    What is needed is a method and system for determining the center of gravity of a vehicle quickly and accurately in the field when the vehicle is carrying cargo and is resting on level or on non-level terrain. Information regarding the location of the center of gravity may be used to guide loading of the vehicle in anticipation of expected terrain. 
       SUMMARY OF THE INVENTION 
       [0007]    The needs of the invention set forth above as well as further and other needs and advantages of the present invention are achieved by the embodiments of the invention described herein below. 
         [0008]    According to one aspect of die invention, a method for determining a center of gravity of a vehicle having a sprung portion and an unsprung portion includes determining at least one unraised tilt angle by determining an unraised longitudinal tilt angle and an unraised lateral tilt angle, determining at least one unraised sprung weight determining an unraised longitudinal sprung weight and an unraised lateral sprung weight, raising a side of the sprung portion, determining a raised tilt angle, determining a raised sprung weight, lowering the side of the sprung portion, raising another side of the sprung portion, determining another raised tilt angle, determining another raised sprung weight, lowering the other side of the vehicle, determining a sprung portion center of gravity position, and determining the vehicle center of gravity position based upon the above determinations. 
         [0009]    In certain embodiments according to the present invention, determining an unraised longitudinal tilt angle may include determining a terrain-induced front-to-back tilt angle and determining an unraised lateral tilt angle may include determining a terrain-induced right-to-left tilt angle. 
         [0010]    In other embodiments according to the present invention, determining an unraised longitudinal sprung weight and an unraised lateral sprung weight may include determining a terrain-induced sprung weight over a rear-left wheel, determining a terrain-induced sprung weight over a rear-right wheel, determining the unraised longitudinal sprung weight by summing the terrain-induced sprung weight over a rear-left wheel and the terrain-induced sprung weight over a rear-right wheel, determining a terrain-induced sprung weight over a front-left wheel, and determining the unraised lateral sprung weight by summing the terrain-induced sprung weight over a front-left wheel and the terrain-induced sprung weight over a rear-left wheel. 
         [0011]    In further embodiments according to the present invention, raising a side of the sprung portion may include raising a longitudinal side of the sprung portion and determining a raised tilt angle may include determining a raised longitudinal tilt angle. Raising a longitudinal side of the sprung portion may include expanding a rear-left wheel adjustable support and a rear-right adjustable support. Determining a raised longitudinal tilt angle may include measuring a raised front-to-rear tilt angle. Determining a raised longitudinal tilt angle may include determining a height of an adjustable support, the adjustable support being at a lateral position, determining a height of another adjustable support, the other adjustable support being at the lateral position, and determining the raised longitudinal tilt angle as a difference between the height of the adjustable support and the height of the other adjustable support divided by a wheel base of the vehicle. The adjustable support may be at a maximum expansion and the other adjustable support may be at a minimum expansion. 
         [0012]    Determining a raised sprung weight may include determining a raised longitudinal sprung weight. Determining a raised sprung weight may include determining a raised-sprung weight over a rear-left wheel, determining a raised-sprung weight over a rear-right wheel, and determining the longitudinal raised sprung weight as the sum of the raised-sprung weight over the rear-left wheel and the raised-sprung weight over the rear-right wheel. 
         [0013]    In additional embodiments according to the present invention, raising another side of the vehicle may include raising a lateral side of the vehicle and determining another raised tilt angle may include determining a raised lateral tilt angle. Raising the lateral side of the vehicle may include expanding a front-left wheel adjustable support and a rear left-wheel adjustable support. Determining a raised lateral tilt angle may include measuring a raised left-to-right tilt angle. Determining a raised lateral tilt angle may include determining a height of an adjustable support, the adjustable support being at a longitudinal position, determining a height of another adjustable support, the other front adjustable support being at the longitudinal position, and determining the raised lateral tilt angle as a difference between the height of the adjustable support and the height of the other adjustable support divided by a wheel base of the vehicle. The adjustable support may be at a maximum expansion and the other adjustable support may be at a minimum expansion. 
         [0014]    Determining another raised sprung weight may include determining a raised lateral sprung weight. Determining a raised lateral sprung weight may include determining a raised-sprung weight over a front-left wheel, determining a raised-sprung weight over a rear-left wheel, and determining the raised lateral sprung weight as the sum of the raised-sprung weight over the front-left wheel and the raised-sprung weight over the rear-left wheel. 
         [0015]    In still further embodiments according to the present invention, determining a sprung portion center of gravity position may include determining a lateral angle of a sprung portion center of gravity relative to a line connecting a center of a front-right wheel and a center of a rear-right wheel, determining a lateral position of the sprung portion center of gravity relative to the line connecting the center of the front-right wheel and the center of the rear-right wheel, determining a longitudinal angle of the sprung portion center of gravity perpendicular to the line connecting the center of a front-left wheel and center of the front-right wheel, determining a longitudinal position of the sprung portion center of gravity perpendicular to the line connecting the center of the front-left wheel and the center of the front-right wheel, and determining a height of the sprung portion center of gravity relative to the sprung portion. 
         [0016]    Determining a longitudinal angle of a sprung portion center of gravity perpendicular to the line connecting the center of the front-left wheel and center of the front-right wheel may include evaluating 
         [0000]        A′= tan −1 ((( B   1 )(cos β′)−( B   2 )(cos α′))/(( B   1 )(sin β′)−( B   2 )(sin α′))); 
         [0000]    wherein A′ is the longitudinal angle of the sprung portion center of gravity, B 1  is an unraised longitudinal sprung weight, B 2  is a raised longitudinal sprung weight, α′ is an unraised longitudinal tilt angle, and β′ is a raised longitudinal tilt angle. Determining a longitudinal position of the sprung portion center of gravity perpendicular to the line connecting the center of the front-left wheel and the center of the front-right wheel may include evaluating 
         [0000]        Y   S =(( B   1 )( WB )(cos  A′ ))/(( W   S )(cos ( A′+α′ ))); 
         [0000]    wherein Y S  is the longitudinal position of the sprung portion center of gravity perpendicular to the line connecting the center of the front-left wheel and the center of the front-right wheel, WB is the wheelbase of the vehicle, and W S  is the sprung weight of the vehicle. Determining the height of the sprung portion center of gravity relative to the unsprung portion may include evaluating 
         [0000]        H   S =( Y   S )(tan  A′ ); 
         [0000]    wherein H S  is the height of the sprung portion center of gravity relative to a plane of the unsprung portion, said plane of the unsprung portion including wheel centers. Determining a lateral angle of a sprung portion center of gravity relative to a line connecting a center of the front-right wheel and a center of the rear-right wheel may include evaluating 
         [0000]        A =tan −1 ((( L   1 i)(cos β)−( L   2 )(cos α))/(( L   1 )(sin β)−( L   2 )(sin α))); 
         [0000]    wherein A is a lateral angle of the sprung portion center of gravity relative to a line connecting a center of the front-right wheel and a center of the rear-right wheel, L 1  is an unraised lateral sprung weight, L 2  is an raised lateral sprung weight, α is an unraised lateral tilt angle, and β is a raised lateral tilt angle. Determining a lateral position of the sprung portion center of gravity relative to the line connecting the center of the front-right wheel and the center of the rear-right wheel may include evaluating 
         [0000]        X   S =(( L   1 )( T )(cos  A ))/(( W   S )(cos( A+α ))); 
         [0000]    wherein X S  is the lateral position of the sprung portion center of gravity relative to the line connecting the center of the front-right wheel and the center of the rear-right wheel, T is the track width of the vehicle, and W S  is the sprung weight of the vehicle. 
         [0017]    In still additional embodiments according to the present invention, determining the vehicle center of gravity position may include determining a lateral position of the vehicle center of gravity relative to the line connecting the center of a front-right wheel and the center of a rear-right wheel, determining a longitudinal position of the vehicle center of gravity perpendicular to the line connecting the center of a front-left wheel and the center of the front-right wheel, and determining a height of the vehicle center of gravity relative to a terrain. 
         [0018]    Determining a lateral position of the vehicle center of gravity relative to the line connecting the center of the front-right wheel and the center of the rear-right wheel may include evaluating 
         [0000]        X   T =(( W   S )( X   S )+( W   U )( T/ 2))/( W   T ); 
         [0000]    wherein X T  is the lateral position of the vehicle center of gravity relative to the line connecting the center of the front-right wheel and the center of the rear-right wheel, W S  is a total sprung weight, X S  is a lateral position of the sprung portion center of gravity relative to the line connecting the center of the front-right wheel and the center of the rear-tight wheel, W U  is a weight of the unsprung portion, T is a track width, and W T  is the total weight of the vehicle, the sum of W S  and W U . Determining a longitudinal position of the vehicle center of gravity perpendicular to the line connecting the center of the front-left wheel and the center of the front-right wheel may include evaluating 
         [0000]        Y   T =(( W   S )( Y   S )+( W   U )( WB/ 2))/( W   T ); 
         [0000]    wherein Y T  is the longitudinal position of the vehicle center of gravity perpendicular to the line connecting the center of the front-left wheel and the center of the front-right wheel, Y S  is a longitudinal position of the sprung portion center of gravity relative to the line connecting the center of the front-left wheel and the center of the front-right wheel, and WB is a wheel base of the vehicle, and determining the height of the vehicle center of gravity relative to the terrain may include evaluating 
         [0000]        H   T =(( W   S )( H   S   +R   U )+( W   U )( R   U ))/( W   T ); 
         [0000]    wherein H T  is the height of the vehicle center of gravity relative to the terrain, H S  is a height of the sprung portion center of gravity relative to a plane of the unsprung portion, said plane of the unsprung portion including wheel centers, and R U  is a height of the center of gravity of an unsprung portion. 
         [0019]    For a better understanding of the present invention, together with other and further aspects thereof, reference is made to the accompanying drawings and detailed description and its scope will be pointed out in the appended claims. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS  
         [0020]    For a better understanding of the present invention, reference is made to the figures, in which: 
           [0021]      FIG. 1A  is a cross-sectional side schematic illustration of a prior art vehicle having a sprung portion capable of being elevated relative to the centers of the wheels by adjustable supports; 
           [0022]      FIG. 1B  is a top view schematic illustration of a prior art vehicle having a sprung portion capable of being elevated relative to the centers of the wheels by adjustable supports; 
           [0023]      FIG. 1C  is a front view schematic illustration of a prior art vehicle having a sprung portion capable of being elevated relative to the centers of the wheels by adjustable supports; 
           [0024]      FIG. 2  is a cross-sectional side schematic illustration of a vehicle having a sprung portion capable of being raised and containing a pressure sensor for each adjustable support, longitudinal and lateral tilt sensors, and a controller, according to an embodiment of the present invention; 
           [0025]      FIG. 3  is a schematic illustration of a vehicle, according to an embodiment of the present invention, having a sprung portion capable of being raised and resting on a sloping terrain; 
           [0026]      FIGS. 4A and 4B  is a flowchart, according to an embodiment of the present invention, for a method for calculation of the location of the center of gravity of the vehicle; 
           [0027]      FIG. 5A  is a schematic illustration of a vehicle, according to an embodiment of the present invention, showing a side view of the vehicle on sloping terrain in an unraised condition; 
           [0028]      FIG. 5B  is a schematic illustration of a vehicle, according to an embodiment of the present invention, showing a side view of the vehicle on sloping terrain in a raised conditions where the rear is raised relative to the front; 
           [0029]      FIG. 6A  is a schematic illustration of a vehicle according to an embodiment of the present invention, showing a front view of the vehicle on sloping terrain in an unraised condition; 
           [0030]      FIG. 6B  is a schematic illustration of a vehicle, according to an embodiment of the present invention, showing a front view of the vehicle on sloping terrain in a raised condition where the left side of the vehicle (as viewed by an operator of the vehicle) is raised relative to the right side; 
           [0031]      FIG. 7  is a flowchart for a method according to an embodiment of the present invention for calculation of the sprung portion center of gravity; 
           [0032]      FIG. 8  is a flowchart for a method according to an embodiment of the present invention for calculation of the vehicle center of gravity, including the sprung and unsprung portions of the vehicle; and 
           [0033]      FIG. 9  is a schematic illustration of vehicle, according to an embodiment of the present invention, having a sprung portion capable of being raised and resting on a sloping terrain, further illustrating a relationship between the center of gravity of the sprung portion and the vehicle center of gravity. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0034]      FIG. 1A  includes a cross-sectional side view schematic illustration of a prior art vehicle  100  having the capability of raising its chassis  105  to varying amounts.  FIG. 1B  is the related top view schematic illustration of the prior art vehicle  100  and  FIG. 1C  is the related front view schematic illustration of the prior art vehicle  100 . In addition to the adjustable supports  110  associated with each wheel  125  is a compressor  115  to furnish pressurized fluid such as air or hydraulic fluid and valves  120  to selectively allow inflation or deflation of the adjustable supports  110 . Examples of adjustable supports  110  are air springs or air bags and hydraulic struts, which may take the place of springs. 
         [0035]    Vehicles for use offroad benefit from an ability to raise he clearance between their chassis or cargo-carrying section and the ground, thereby becoming less endangered by high water levels or debris in their path. One means to gain this clearance is to mount an adjustable support  110  proximate to each wheel  125  and positioned between the chassis  105  and a support fixture  130  associated with each wheel  175 . As the adjustable supports  110  are pressurized, the height of the chassis  105  increases to a variable and controllable degree. Deflation of the adjustable supports  110  results in a lowering of the chassis  105 . The portion of the vehicle  100  raised by the adjustable supports  110  is the sprung portion or chassis  105 , and that portion remaining in fixed height relation with the ground or terrain  150  is the unsprung portion  135 . The unsprung portion  135  may include, for example, the wheels  125 , including tires  126  and wheel ends  127 , and a portion of the suspension components, such as support fixture  130 , axles  140 , and drive train  145 , dependent upon the specific vehicle design in use. 
         [0036]      FIG. 2  is a cross-sectional plan view schematic illustration of a vehicle  200  according to an embodiment of the present invention. In addition to the adjustable support  110  for each wheel  125  and a valve  120  for each adjustable support  110 , the vehicle includes a controller  205 , tilt sensors  210 O, and pressure sensors  215 . A lateral tilt sensor  211  may provide the lateral tilt, for example, in the right-to-left direction, of a plane  220  of the sprung portion  105  in the form of a signal to a controller  205 , and a longitudinal tilt sensor  212  may provide the longitudinal tilt, for example, in the front-to-rear direction, of the sprung portion  105  in the form of another signal to the controller  205 . Of course, the lateral tilt sensor  211  may also provide the left-to-right tilt angle and the longitudinal tilt sensor  212  may also provide the rear-to-front tilt angle. The pressure sensor  215  coupled to each adjustable support  110  may provide the pressure within each adjustable support  110  to the controller  205 . The controller  205 , upon receiving tilt sensor  210  and adjustable support pressure sensor  215  signals, may determine the position of vehicle center of gravity  240 , in a manner to be described. 
         [0037]      FIG. 3  is a schematic illustration of the vehicle  200 , according to an embodiment of the present invention, resting on a sloping terrain  150 . The distribution of a load  305  carried by the sprung portion  105  has much to do with the stability of the vehicle  200  during transit. There may be a need for arranging the load  305  to minimize the likelihood of the vehicle  200  rolling over. Although the distribution of the weight of the vehicle  200  without load  305  is determined at the time of manufacture, the overall stability of the vehicle  200 , as influenced by both the vehicle  200  and its load  305 , depends upon the positioning of the load  305 . 
         [0038]    The vehicle center of gravity  240  may be calculated for a distribution of the load  305  as shown in  FIG. 3 . If the center  315  of each wheel  125  is vertically projected onto a horizontal plane  375  lying beneath the vehicle  200 , and if points of intersection  372  on the horizontal plane  375  are interconnected, the result is a perimeter  370  lying on the horizontal plane  375 . If a vertical projection  365  of the vehicle center of gravity  240  onto the horizontal plane  375  falls within the perimeter  370  associated with the vertical projections  367  of the wheel centers  315  onto a horizontal plane  375 , the vehicle  200  remains stable. However, if the vehicle center of gravity  240  falls beyond the perimeter  370 , the vehicle  200  is liable to roll over. 
         [0039]    The vehicle center of gravity  240  of the vehicle  200  without load  305  may be determined from data supplied by the vehicle manufacturer. However, the vehicle center of gravity  240  may change in the field in connection with loading of the vehicle  200 . Often, such loading is done on sloping ground or terrain  150   
         [0040]    In the embodiments according to the present invention shown in  FIG. 2  and in  FIG. 3 , the vehicle  200  includes the sprung portion  105  and the unsprung portion  135 . The unsprung portion  135  includes the part of the vehicle positioned on the ground  150 . Examples of the components of the unsprung portion  135  include, but are not limited to, the wheels  125 , including tires  126  and wheel ends  127 , and a portion of the suspension components, such as support fixture  130 , axles  140 , and drive train  145 , dependent upon the specific vehicle design in use. Proximate to each wheel  125  is a separately inflatable adjustable support  110 . 
         [0041]    The controller  205  monitors pressures within the adjustable supports  110  and controls the amount of air injected into or released from the adjustable supports  110 . The controller  205  also monitors the sensors  210  measuring the tilt of the sprung portion, both longitudinally  212 , with respect to the front  320  and rear  325  of the vehicle  200 , and laterally  211 , with respect to the left  330  and the right sides  335  of the vehicle  200 , where left and right are as viewed from the rear  325  of the vehicle  200 . Ordinarily, the adjustable supports  110  over each wheel  125  are inflated equally, resulting in the plane  220  of the sprung portion  105 , substantially coinciding with a bottom  222  of the sprung portion  105 , being parallel to the plane  225  of the unsprung portion  135 , containing the centers  315  of the wheels  125 , and to the plane  230  of the terrain  235  as presented in  FIG. 2  and in  FIG. 3 . However, equal inflation is not considered a limitation to the invention since the adjustable supports  110  may be inflated unequally as well. 
         [0042]      FIG. 4  contains a flowchart for a method  400  according to an embodiment of the present invention for determining the vehicle center of gravity  240  when the vehicle  200  carrying load  305  resides on sloping terrain  150 . The position of the vehicle center of gravity  240  is related to the results of measurements performed when the vehicle  200  is in three orientations—the sprung portion  105  parallel to the terrain  150 , the sprung portion  105  deliberately tilted front-to-rear relative to the terrain  150 , and the sprung portion  105  deliberately tilted left-to-right relative to the terrain  150 . For each orientation, measurements of the angle of the plane  220  of the sprung portion  105  relative to the horizontal plane  375  are taken, as well as measurements of the pressures in the adjustable supports  110  supporting the sprung portion  105  above each wheel  125 . From the pressure measurements and from the areas of the adjustable supports  110  elevating the sprung portion  105  above each wheel  125 , the weights carried by each adjustable support  110  is determined. As the orientation of the vehicle  200  is changed, the weights carried by the adjustable supports  110  change also as weight shifts away from the elevated adjustable supports  110  to the depressed adjustable supports  110 . From the measured angles and the shifting weights, the location of the vehicle center of gravity is determined. Although the plane  220  of the sprung portion  105  is taken to be initially parallel to the plane  225  of the unsprung portion  135  and to the plane  230  of the terrain  150 , this need not be the case and equations may be adjusted to reflect a non-parallel initial relationship between the plane  220  of the sprung portion  105  and the plane  225  of the unsprung portion  135  and the plane  230  of the terrain  150 . In practice, determination of the center of gravity  240  of the vehicle  200  using the method  400  may take between 5 and 15 seconds. 
         [0043]    Initially, the longitudinal tilt and lateral tilt of the terrain  150  and the adjustable support pressures for the sprung portion  105  in an unraised position, that is, where the sprung portion  105  is parallel to the unsprung portion  135  and to the terrain  150 , are measured. However, the sprung portion  105  need not he originally parallel to the unsprung portion. In step  410 , the right-to-left unraised tilt angle  605  (α), corresponding to an unraised lateral tilt angle, and the front-to-rear unraised tilt angle  505  (α′), corresponding to an unraised longitudinal tilt angle, both arising from the tilt of the terrain  150  as shown in  FIG. 5A  and  FIG. 6A , are measured. 
         [0044]    In step  418 , the weights W carried by each of the adjustable supports  110  when the vehicle  200  is in an unraised position is determined from a measurement of the pressure within the adjustable supports  110  and from the area of the adjustable support  110  supporting the sprung portion  105  at that point. Pressure relates directly to the force exerted by the adjustable supports  110 . The relationship between pressure within the adjustable support  110  and the force exerted by the adjustable support  110  on the sprung portion  105  may be supplied by the manufacturer of the adjustable support  110 . The rear-right unraised or terrain-induced sprung weight over the rear right wheel  380  (W RRU ), the rear-left unraised or terrain-induced sprung weight over the rear left wheel  381  (W RLU ), the front-right unraised or terrain-induced sprung weight over the front right wheel  382  (W FRU ), and front-left unraised or terrain-induced sprung weight over the front left wheel  383  (W FLU ) unraised or terrain-induced sprung weights are determined from measurements of the pressures in the rear-right  385 , rear-left  386 , front-right  387 , and front-left  388  adjustable supports in step  415 . 
         [0045]    In step  420 , the total sprung weight W S (=W RRU +W RLU +W FRU +W FLU ), the unraised rear sprung weight B 1 (=W RRU +W RLU ), corresponding to an unraised longitudinal sprung weight, and the unraised left side sprung weight L 1 (=W RLU +W FLU ), corresponding to an unraised lateral sprung weight, are determined, with the suspension geometry taken into account. In each case, it is assumed that the sprung weights act through the center points  315  of the particular wheels  125 . 
         [0046]    Since all calculations are based on dimensions assessed from the centers of the wheels, the specific geometries of the actual suspension in use must be taken into consideration. The moment arm from the adjustable support  110 , that is, air bag, mounting point to the wheel center  315  would be an element of the calculations used in determining individual sprung weights over individual wheels  125  in the situations where the sprung weights do not act through the center points  315  of the particular wheels  125 . 
         [0047]    In step  425 , the vehicle  200  is raised longitudinally, that is, the rear end  325  of the vehicle  200  is elevated.  FIG. 5A  and  FIG. 5B  are schematic illustrations of the vehicle  200  shown on sloping terrain  150  in  FIG. 3 .  FIG. 5A  and  FIG. 5B  include side views of the vehicle  200  according to an embodiment of the present invention and illustrate adjustable support inflation or expansion resulting in a front-to-back tilt of the vehicle  200 . Adjustable support pressure sensors  215  and the front-to-back tilt sensor  212  provide the controller  205  with signals indicative of the pressures within the adjustable supports  110  and the tilt of the sprung portion  105 . 
         [0048]    In  FIG. 5A , the sprung portion  105  is parallel to the unsprung portion  135  and to the ground or terrain  150  having a slope α′. When the rear-right adjustable support  385  and the rear-left adjustable support  386  ( FIG. 3 ) are further inflated, the sprung portion  105  is given an additional tilt from the front to the rear of the vehicle  200 . It is also possible to maintain the pressure in the rear-right  385  and rear-left  386  adjustable supports and to additionally inflate the front-right adjustable support  387  and the front-left adjustable support  388  ( FIG. 3 ). The greater the tilt provided by inflation of the adjustable supports  110 , the more accurate is measurement of the tilt by tilt sensor  210  ( FIG. 2 ). In fact, theoretically, any change in tilt, no matter how small, may be adequate. The example and the subsequent equations reflect the vehicle  100  pointing down a slope. The equations may be modified in a straightforward manner to accommodate the vehicle  100  pointing up a slope. 
         [0049]    As shown in  FIG. 5B , a longitudinal side of the sprung portion, in this case, the rear end or rear side  510  is raised by further expanding the rear-left  386  and rear-right  385  adjustable supports ( FIG. 3 ). A raised longitudinal tilt angle, in this case the raised front-to-rear tilt angle β′, is measured in step  430  and the rear-right and rear-left adjustable support pressures are measured in step  435  and used to determine the raised rear-right and raised rear-left raised sprung weights (W RRR  and W RLR ). In step  40 , a raised longitudinal sprung weight, in this case, the raised rear sprung weight B 2 (=W RRR +W RLR ), is determined. Once the controller  205  captures the measurements, the rear-left adjustable support  386  and the rear-right adjustable support  385  are deflated, and the rear side  510  of the sprung portion  105  returns to an unraised position. 
         [0050]    After the rear side  510  of the sprung portion  105  is lowered so that the sprung portion  105  once again is parallel to the unsprung portion  135  and to he terrain  150  (step  445 ), the sprung portion  105  is raised laterally (step  450 ).  FIG. 6A  and  FIG. 6B  are schematic illustrations of the vehicle  200  shown on sloping terrain  150  in  FIG. 3 , from the point of view of the front  320  of the vehicle  200 . In embodiments according to the present invention, the adjustable supports  110  are inflated differentially to cause an addition to the tilt of the vehicle  200  beyond the tilt provided by the terrain  150 . 
         [0051]    In  FIG. 6A , the sprung portion  105  is parallel to the unsprung portion  135  and to the ground or terrain  150 . When the front-left adjustable support  388  and the rear-left  386  adjustable support are further inflated, the sprung portion  105  is given an additional tilt from the right side to the left side. Of course, it is also possible to maintain the pressure in the rear-left  386  and front-left adjustable supports  388  and to additionally inflate the front-right adjustable support  387  and the rear-right adjustable support  385 . 
         [0052]    As shown in  FIG. 6B , a lateral side, in this case, the left side  330  of the sprung portion  105 , is raised relative to the right side  335  of the sprung portion  105  by initiating a front-left wheel adjustable support  388  and a rear-left adjustable support  386 . Once the left side  330  of the sprung portion  105  is raised, a raised lateral tilt angle, in this case, the right-to-left raised tilt angle  610  (β), is measured in step  455  and the rear-left and front-left adjustable support pressures are measured in step  460  and used to determine the raised rear-left and raised front-left sprung weights (W RLR  and W FLR ) in step  462 . In step  465 , the raised lateral sprung weight, in this case, the left-side sprung weight L 2 (×W RLR +W FLR ), is calculated. In step  470 , the left-side  330  of the sprung portion  105  is lowered so that the sprung portion  105  is parallel to the unsprung portion  135  and the underlying terrain  150 . 
         [0053]    The sprung portion center of gravity  310  is determined in step  475 . (Step  475  addresses the complete calculation of the sprung portion center of gravity, shown in detail in  FIG. 7 .)  FIG. 7  includes a flowchart of a method according to an embodiment of the present invention for determining the sprung portion center of gravity  310 . A longitudinal angle of the center of gravity of the sprung portion  105  with respect to the front axle  140  or a line between the centers  315  of the front-right wheel  382  and front-left wheel  383 , A′  340 , as shown in  FIG. 3 , is determined in step  710  as: 
         [0000]        A′= tan −1 ((( B   1 )(cos β′)−( B   2 )(cos α′))/(( B   1 )(sin β′)−( B   2 )(sin α′))). 
         [0054]    (Step  475  of  FIG. 4  includes all the steps of  FIG. 7 .) 
         [0055]    A lateral angle of the center of gravity of the sprung portion  310  with respect to a line connecting the centers  315  of the front-right wheel  382  and the rear-right wheel  380 , A  345 , as shown in  FIG. 3  is determined in step  725  as: 
         [0000]        A =tan −1 ((( L   1 )(cos β)−( L   2 )(cos α))/((L 1 )(sin β)−( L   2 )(sin α))). 
         [0056]    A longitudinal position of the center of gravity of the sprung portion  310  relative to the front axle  140  of the vehicle  200  or a line between the centers  315  of the front-right  382  and front-left  383  wheels, Y S    350 , is determined in step  715  as: 
         [0000]        Y   S =(( B   1 )( WB )(cos  A′ ))/(( W   S )(cos ( A′+α′)));   
         [0000]    where WB is the wheelbase of the vehicle  200 , that is, the distance or separation between the centers  315  of the front-right wheel  382  and the rear-right wheel  381 . 
         [0057]    The lateral position of the center of gravity of the sprung portion  310  relative to a line between the centers  315  of the front-right wheel  382  and the rear-right wheel  380 , X S    355 , is determined in step  730  as: 
         [0000]        X   S =(( L   1 )( T )(cos  A ))/(( W   S )(cos( A+α ))); 
         [0000]    where T is the track of the vehicle, that is, the separation between the centers of the front-right wheel  382  and the front-left wheel  383 . The calculation assumes that T is also the separation between the centers of the rear-right wheel  380  and the rear-left wheel  381 , that is, that there is even track width front and rear. If the separation between the front wheel centers differs from the separation between the rear wheel centers, that difference needs to be taken into account in the calculation. In determining X S    355 , the effects of the particular suspension in use is to he taken into consideration. In certain suspension designs, for example, independent suspensions, the track width T may change as the suspension goes through its range of travel. The effects of the roll center of the vehicle and the potential change in track width (T) as a function of suspension travel are to be accounted for. 
         [0058]    The height of the sprung portion center of gravity  310  above the plane containing the wheel centers  315 , that is, the plane of the unsprung portion  225  ( FIG. 2 ), is calculated in step  720  as: 
         [0000]        H   S =( Y   S )(tan  A′ ) 
         [0059]    For the other orientations, for example, raising the right side  335  instead of the left side  330  or raising the front  320  rather that the rear  325 , alternative versions of the above equations apply. 
         [0060]      FIG. 8  contains flow chart of a method according to an embodiment of the present invention for determining the location of the vehicle center-of-gravity  315 , including both the sprung  105  and the unsprung  135  portions, W U  is the weight of the unsprung portion  135 . R U  is the height of the center of gravity of the unsprung portion  135 , taken to be at the wheel centers  315 . Both W U  and R U  are manufacturer&#39;s constants. 
         [0061]    Y T    905  ( FIG. 9 ) is the longitudinal location of the vehicle center of gravity  240  relative to the center  915  of the front-right wheel  382 , determined in step  810  as: 
         [0000]        Y   T =(( W   S )( Y   S )+( W   U )( WB/ 2))/( W   T ). 
         [0062]    X T    910  is the lateral location of the vehicle center-of-gravity  315  relative to the center  915  of the front-right wheel  382 , determined in step  815  as: 
         [0000]        X   T =(( W   S )( X   S )+( W   U )( T/ 2))/( W   T ). 
         [0063]    H T    915  is the height of the vehicle center of gravity  240  above the terrain  150 , determined in step  820  as: 
         [0000]        H   T =(( W   S )( H   S   +R   U )+( W   U )( R   U ))/( W   T ). 
         [0000]    The vehicle weight or total weight W T  may be determined as: 
         [0000]        W   T   =W   S   +W   U . 
         [0064]    Although the preceding discussion was directed to measurement of the center of gravity  240  on uneven terrain, measurement of the center of gravity is also achievable on level terrain, that is, when the right-to-left unraised tilt angle α and front-to-rear unraised tilt angle α′ are substantially zero. In this case, the right-to-left raised tilt angle β and the front-to-rear raised tilt angle β may also be determined by the tilt sensor  210 . However, the right-to-left raised tilt angle β and the front-to-rear raised tilt angle β may be also be determined by ride height sensors (rear-right  245 , rear-left  246 , front-right  247 , and front-left  248 ), placed on the rear-right  385 , rear-left  381 , front-right  387 , and front-left  388  adjustable supports and generating signals indicative of the separation between the rear-right  385 , rear-left  386 , front-right  387 , and front-left  388  adjustable supports and the chassis  105  above the center  315  of each wheel  125 . 
         [0065]    The front-to-rear raised tilt angle β may be the difference in height between the chassis  105  raised above the rear-left adjustable support  381  and the chassis above the front-left adjustable support  388  divided by the wheel base WB or the difference in height between the chassis  105  raised above the rear-right adjustable support  385  and the chassis  105  above the front-right adjustable support  387  divided by the wheel base WB. 
         [0066]    The right-to-left raised tilt angle β may be the difference in height between the chassis  105  raised above the front-left adjustable support  388  and the chassis  105  above the front-right adjustable support  387  or the difference in height between the chassis  105  raised above the rear-right support  385  and the chassis  105  above the rear-left adjustable support  386  divided by the track width T. 
         [0067]    With information from the manufacturer, the right-to-left raised tilt angle β and the front-to-rear raised tilt angle β may be obtained without a tilt sensor  210  or a height sensors  245 ,  246 ,  247 , and  248 . If the difference in heights of the adjustable supports  110  driven to two predetermined settings, e.g. at minimum inflation and at maximum inflation, is known, then the right-to-left raised tilt angle β may be determined as the difference in height between the chassis  105  raised above the front-left adjustable support  388  and the chassis  105  above the front-right adjustable support  387  divided by the track width T or the difference in height between the chassis  105  raised above the rear-left adjustable support  386  and the chassis  105  above the rear-right adjustable support  385  divided by the track width T. 
         [0068]    The front-to-rear raised tilt angle β may be determined as the difference in height between the chassis  105  raised above the rear-left adjustable support  386  and the chassis  105  above the front-left adjustable support  388  divided by the wheelbase WB or the difference in height between the chassis  105  raised above the rear-right adjustable support  385  and the chassis  105  above the front-right adjustable support  387  divided by the wheelbase WB. 
         [0069]    Although the invention has been described with respect to various embodiments, it should be realized that this invention is also capable of a wide variety of further and other embodiments within the spirit and the scope of the appended claims.