Abstract:
This is a novel shock absorber based on an oil-gas emulsion air shock design with both shock damping and suspension spring properties. The design&#39;s underlying purpose is the capability to extend beyond twice its compressed length—a quality inherently unobtainable by current shock absorbers. This capability is derived from a design possessing multiple stages whereby each stage refers to a paired working tube and shaft, and operates independently of and in series with other stages—in effect a shock within a shock. This shock is specifically created to exploit the extreme travel capacity associated with the opposed triangulated 4-link suspension system; and, is suitable for use with other high-articulation suspension systems that can be installed on street-driven four wheel drive (4WD) vehicles.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application represents a novel air shock specifically designed to operate in conjunction with the opposed triangulated 4-link suspension system. This novel suspension system is covered in U.S. patent application Ser. No. 13/586,458. 
       STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
       [0002]    Not Applicable 
       REFERENCE TO SEQUENCE LISTING, A TABLE, OR A COMPUTER PROGRAM LISTING COMPACT DISC APPENDIX 
       [0003]    Not Applicable 
       BACKGROUND OF THE INVENTION 
       [0004]    An automobile is built with a suspension system based on a spring arrangement. The suspension system disconnects the automobile&#39;s chassis from road obstructions like bumps, ruts, and holes. The springs react to road obstructions with a simple up/down movement, referred to as compression and extension, respectively. The spring&#39;s motion leaves the chassis relatively isolated from the sudden jarring effect of the road obstruction. However, the springs will continue to undergo an oscillatory compression/extension motion even as the automobile has passed over the road obstruction. In effect, the road obstruction causes part of the kinetic energy associated with the automobile&#39;s momentum to be transferred to the springs, in turn causing them to compress and extend, converting kinetic energy to potential energy. The springs continue to oscillate converting kinetic energy to potential energy and then back again until the kinetic energy is dissipated to other parts of the automobile. 
         [0005]    The most common method to control the spring&#39;s oscillation is with a shock absorber. The shock acts to resist or dampen the spring&#39;s oscillation by absorbing the kinetic energy from the spring as thermal energy that heats up the oil. A shock consists of two main parts: a working tube and a shaft. A piston, called a working piston, is attached to one end of the shaft which is then inserted into the working tube. The tube contains oil and the piston contains tiny holes and slots, called orifices. The shock is attached to the automobile such that as the suspension springs react to a road obstruction, the shaft moves into/out of the working tube. In order for the shaft to move, the oil in the working tube must pass through the orifices in the working piston. Thin shims and washers, called valves, are used to govern the flow of oil through these orifices. The nature of the orifices and valves regulate the flow of oil across the working piston which dampens the spring&#39;s reaction to road obstructions and eliminates its oscillatory tendency. The net result is an automobile that delivers good handling and a smooth ride. 
       Shock Type And Properties 
       [0006]    In the never-ending quest for better handling and ride characteristics, engineers have designed the shock absorber with a variety of properties. These properties all serve to more precisely regulate the flow of oil across the working piston and improve the shock&#39;s damping capability. Some of the more important properties are listed below: 
         [0007]    1. High-pressure gas-charging: An inert gas is added to pressurize the working tube to inhibit cavitation. 
         [0008]    2. Valves and Shims: Thin washer shaped disks with different sizes and shapes of holes are added to the working piston in order to change the damping properties by altering the flow of oil through the working piston. 
         [0009]    3. Dividing piston: A free-floating solid disk is inserted into the working tube. This piston is used in conjunction with gas-charging and divides the working tube into two chambers with the gas in one chamber and oil in the other, thereby preventing the mixing of gas and oil. 
         [0010]    4. Position sensitive Damping (PSD): Tapered grooves are machined on the inside walls of the working tube allowing oil to bypass the working piston. 
         [0011]    5. Acceleration Sensitive Damping (ASD): A special compression valve is added to the working piston. The valve is a closed loop system that enables bypass of oil during road impacts. 
         [0012]    6. Mono-tube: A gas-charged single-tube shock that comprises a mixture of oil and gas. It commonly utilizes a dividing piston. 
         [0013]    7. Reservoir: A type of mono-tube shock that houses the dividing piston, gas, and excess oil in an external reservoir. 
         [0014]    A variant of the gas-charged mono-tube shock is the air shock. Perhaps its defining characteristic, the air shock&#39;s shaft is more than twice the diameter of that in comparable regular (non-air) shocks. In particular, a stroke of the air shock&#39;s shaft causes a definite change in the volume occupied by the oil-gas mixture. The change in volume leads to a likewise definite change in the pressure of the gas. This pressure change gives the air shock a unique property—the buildup of gas pressure sufficient to support the weight of the vehicle. Thus, the air shock possesses the dual property of behaving as both a damping shock and a suspension spring. 
         [0015]    An air shock is a type of emulsion shock. This emulsion results from the mixing of its confined gas and oil. The gas and oil are immiscible and occupy the same space within the working tube. Although employing the same damping techniques used by other shocks, e.g., special orifices and valves to regulate the flow of oil through its working piston, an air shock&#39;s damping property is defined by the emulsion of its gas and oil. Yet, the exact nature of the emulsion remains elusive. As discussed in Section 1: Properties in the Appendix, reports in the relevant literature suggest that the emulsion may change form and exist either as an immiscible mixture of the oil and gas or as a foamy mixture of oil and gas bubbles. It seems likely that the immiscible mixture offers predictable damping, whereas the foamy mixture does not. 
         [0016]    An air shock is also a type of suspension spring. The gas charge in an air shock ranges between 10-500 psi, and its shaft stroke displaces over four times the volume of that by regular shocks. As mentioned above, the change in gas pressure due to a change in volume gives the air shock the unique ability to support the weight of an automobile. This gas pressure refers to the air shock&#39;s spring rate. Like the air shock itself, the spring rate is also unique among other suspension springs. As discussed in Section 1: Properties in the Appendix, reports in the relevant literature suggest that in general, the spring rate increases slightly for the first two-thirds or so of shaft compression and then increases rapidly during the last one-third of shaft compression. The reverse process also occurs during shaft extension. 
       Shock Travel 
       [0017]    As discussed in Section 3: Extended Length in the Appendix, one feature common to virtually all shocks is that the extended length is less than twice the compressed length. This feature results from the inherent design of a shock, namely, a single shaft that travels into/out of a single working tube. The length of the shaft defines the shock&#39;s travel; henceforth referred to as travel capacity. A common rule of thumb suggests that if a vehicle&#39;s suspension system has the capacity to travel 10″, then select a shock consisting of at least a 10″ shaft. This way, the travel capacity of the shock meets that of the suspension system. For a vehicle driven on the street, this rule of thumb does fine. The type of road obstacles a vehicle encounters on the street ordinarily are not large enough to require a suspension system nor a shock to have more than 10″ of travel capacity. Given that shocks with 12″ or so of travel capacity are readily available, a shock that extends no more than twice its compressed length is adequate for vehicles driven on the street. 
         [0018]    In contrast, for vehicles requiring long travel capacity, such as four wheel drive (4WD) vehicles, current shock travel capacity can be a problem. In the off-road environment, a 4WD vehicle routinely encounters trail (i.e., road) obstacles that exceed the limit of suspension travel. To contend with such obstacles, suspension manufacturers offer high articulation suspension systems for 4WD vehicles. In order to utilize the capacity of high articulation suspension systems, engineers have designed shocks with 16″, 18″ or more of travel. These shocks require a working tube length at least equal to their travel capacity. To account for the size of the working piston and shock mounting eyelets, the compressed length of these shocks are several inches longer than their travel capacity—at least 20″ or more at compressed length. Shocks with such a long compressed length do not present an issue for customized, purpose-built off-road vehicles because compressed (as well as extended) shock length is incorporated into the design of the vehicle. 
         [0019]    However for street-driven/non-lifted 4WD vehicles, the installation, of shocks whose compressed length is 20″ or more do present issues. Typical methods of dealing with long travel shock issues include allowing the upper portion of the shock to protrude through the hood of the vehicle (for front shocks), or to protrude into the bed or cargo area of the vehicle (for rear shocks). Although this is an effective method of installation, it&#39;s not an aesthetically pleasing one. 
         [0020]    The best technique for resolving long travel shock issues would involve a shock with a relatively short compressed length and a relatively long travel length. Conceptually, this technique would require a shock that could extend several times greater than just twice its compressed length. Such extreme shock travel capacity is impossible for shocks of current configurations: literally, it involves a shaft that would push down completely into a working tube of the same length thus giving a fully compressed shock; and, then push out of and seemingly grow several times greater than the working tube thus giving a fully extended shock whose length is several times greater than its compressed length. 
       New Shock Design 
       [0021]    In principle, a shock whose shaft was segmented like a simple telescope or spyglass could extend many times beyond its original compressed length. Consider a shock design that consists of many independent shock-units operating in series where the shaft for one shock-unit served as the working tube for the next smaller shock-unit, and so on. This design would have one shock-unit pushing down into the next larger one, and so on, so that the shock&#39;s compressed length is defined by the length of just one (the largest) working tube; and then extend to a length representative of the number of shock-units used in its construction—e.g., three shock-units could extend to three times compressed length, four shock units could extend to four times compressed length, and so on—in effect, a shock within a shock. 
         [0022]    A shock of this design would consist of three types of main parts—a working tube at one end, a shaft at the other end, and one or more working tubes and shafts in-between. Henceforth, a shaft is “paired” to the working tube that it slides into and out of, and a paired working tube and shaft is referred to as a stage. The working tube at one end of the shock is paired to a shaft and refers to the first stage in the shock; whereas, the shaft at the other end of the shock is paired to a working tube and refers to the last stage in the shock. An in-between stage is one where a shaft is paired to a working tube for one stage while at the same time serves as a working tube that is paired to a shaft for another stage. An in-between stage is a critical component of this type of shock because it serves a dual role—it acts as an independent shock consisting of both a working tube and a shaft, while it&#39;s working tube and shaft act as shaft and working tube in other stages, respectively. Each in-between stage must serve as a shaft and be small enough to fit inside the working tube of the next larger stage; yet, be large enough to serve as a working tube and accommodate a shaft, working piston, oil, and gas where that shaft serves as the working tube for the next smaller stage. Stage diameter is very important: an in-between shaft must possess a diameter such that (1) the space between itself and the paired working tube holds enough oil for effective damping properties for the stage, and (2) the space inside itself is sufficient to accommodate the paired shaft, working, piston, oil, and gas for the next smaller stage. 
         [0023]    This design suggests that for any given stage, the shaft&#39;s diameter will be only slightly smaller than is the paired working tube&#39;s diameter. When the stage undergoes compression or extension, the shaft will definitely cause a change in volume within the paired working tube. A meaningful change in volume during shaft stroke is a unique property among shock absorbers. When inspecting other types of known shocks, the only type that undergoes a meaningful change in volume when the shaft is stroked is an air shock. This observation strongly indicates that this shock design is a type of air shock. This shock design also serves as the basis for the present invention. Thus, the shock design of the present invention is a type of air shock—a segmented air shock. 
         [0024]    The segmented air shock refers to a multiple-stage air shock. An air shock that consists of two or more stages, where each stage acts independently of and is connected in series with other stages—in effect, a shock within a shock. The design of the segmented air shock is based on the properties of a known air shock and how those properties apply to a stage. In particular, how those properties facilitate the integration of two or more stages leading to a single multiple-stage air shock. Since the design of a multiple-stage air shock is novel, virtually all of the concepts derived in the shock&#39;s development are fundamental and theoretical. While such information is vital to understanding the nature of a multiple-stage air shock, it applies to all multiple-stage air shocks rather than to just one specific type of multiple-stage air shock. Therefore, this theoretical information is not disclosed in this specification, rather it is redirected to an Appendix that accompanies this specification. The Appendix consists of the following documents: (1) Section 1: Properties, (2) Section 2: Spring Rate, (3) Section 3: Extended Length, (4) Section 4: Loading, (5) Section 5: Temperature, and (6) Section 6: Math Concept. This information is drawn upon as needed in order to design an example (a specific type) of a multiple-stage air shock. This example is a four-stage air shock, and is discussed below in the section Detailed Description of the Invention; whereby, reference to information in the Appendix is cited as appropriate. 
       BRIEF SUMMARY OF THE INVENTION 
       [0025]    The present invention offers a novel shock absorber intended for use with the opposed triangulated 4-link suspension system. This novel shock absorber is the segmented air shock. The segmentation refers to multiple stages where each stage refers to an independent shock-unit consisting of a paired working tube and shaft. The stages operate in series such that the shaft for one stage may serve as the working tube for another stage—in effect a shock within a shock. 
         [0026]    The present invention also offers a shock absorber that: 
         [0000]    is designed by selecting a compressed length, and then adding larger stages one stage at a time to the shock.
 
can be designed so that for a given compressed length, the extended length reaches a maximum value at a specific number of stages, and then decreases as more stages are added to the shock.
 
is uniquely capable of extending beyond twice its compressed length; therefore, is specifically designed for use with the high-articulation suspension systems that can be installed on street-driven/non-lifted 4WD vehicles.
 
is an emulsion shock consisting of a mixture of oil and gas. Dampening is governed by the flow of oil through the working piston, where the flow is controlled by valves and shims.
 
is an air shock and acts as a suspension spring capable of supporting the weight of the vehicle.
 
has a spring rate which is a function of gas pressure, and can be analyzed with the ideal gas law.
 
enables each stage to be independently charged with gas; i.e., to be charged to a specific gas pressure such that the response of its shaft stroke is different from that of the other stages.
 
makes independent gas charging useful because (1) one stage can be charged to a low gas pressure while another is charged to a high gas pressure, thereby the one stage will be nearly fully compressed before another stage begins to compress, (2) one stage with low charging will respond to small road obstacles and then “bottom out” due to a large road obstacle while another stage with high charging won&#39;t be affected by small road obstacles but will respond to large road obstacles, and (3) one stage can be charged to operate in its working zone (the last 50% of shaft stroke) for a specific road condition while the other stages have only slightly begun to compress, thereby maintaining significant shock travel capacity.
 
possesses highly refined tuning capability because each stage can be set up with a different dampening property and charged to a different gas pressure; thereby, providing the shock with the capability to respond to a variety of road conditions and obstacles.
 
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING 
     List of Reference Numerals Utilized in the Drawings 
       [0027]    Note: Some items are labeled two different ways: one way refers to a stage after it&#39;s been added to the shock—regular text; while the other way refers to a stage at the time the stage is added to the shock—{text placed in here}. For an explanation, see the part Design Criteria in Section 3: Extended Length in the Appendix.
     10 —(EL) shock extended length     11 —(L TO ) first working tube overall length {overall length of the fourth working tube of the fourth stage added to the shock}     12 —(L WT1 ) first working tube length {length of the fourth working tube of the fourth stage added to the shock}     13 —(L WT2 ) second working tube length {length of the third working tube of the third stage added to the shock}     14 —(L WT3 ) third working tube length {length of the second working tube of the second stage added to the shock}     15 —(L WT4 ) fourth working tube length {length of the first working tube of the first stage added to the shock}     16 —(L SO1 ) first shaft overall length {overall length of the fourth shaft of the fourth stage added to the shock}     17 —(L SO2 ) second shaft overall length {overall length of the third shaft of the third stage added to the shock}     18 —(L SO3 ) third shaft overall length {overall length of the second shaft of the second stage added to the shock}     19 —(L SO4 ) fourth shaft overall length {overall length of the first shaft of the first stage added to the shock}     20 —(L S1 ) first shaft length {length of the fourth shaft of the fourth stage added to the shock}     21 —(L S2 ) second shaft length {length of the third shaft of the third stage added to the shock}     22 —(L S3 ) third shaft length {length of the second shaft of the second stage added to the shock}     23 —(L S4 ) fourth shaft length {length of the first shaft of the first stage added to the shock}     24 —(D WT1 ) diameter of first working tube {diameter of the fourth working tube of the fourth stage added to the shock}     25 —(D S1W2 ) diameter of first shaft/second working tube {diameter of the fourth shaft/third working tube of the third stage added to the shock}     26 —(D S2W3 ) diameter of second shaft/third working, tube {diameter of the third shaft/second working tube of the second stage added to the shock}     27 —(D S3W4 ) diameter of third shaft/fourth working tube {diameter of the second shaft/first working tube of the first stage added to the shock}     28 —(D S4 ) diameter of fourth shaft {diameter of the first shaft of the first stage added to the shock}     29 —(me) mounting eyelet     30 —(wp) thickness of working piston     31 —(ss) thickness of shaft shoulder     32 —(ec) thickness of end cap, also refers to shaft mounting eyelet     33 —(CL) shock compressed length   
 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0052]      FIG. 1  is a side plan view of the four-stage air shock at full extension; 
           [0053]      FIG. 2  is a side plan view of the four-stage air shock at full compression; 
           [0054]      FIG. 3  is a side plan view of the four-stage air shock at static ride height. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0055]    Discussed herein is the design of a four-stage air shock. This shock represents an example of a multiple-stage air shock, otherwise defined as a segmented air shock. As disclosed under Section 3: Extended Length in the Appendix, the number of stages that can be added to a segmented air shock is, in principle, unlimited. The selection of four stages in the present case is arbitrary, made to demonstrate the utility of the technology in designing a segmented air shock appropriate for installation on a 4WD vehicle. This example is based on the application of the techniques covered in the Appendix, which accompanies this specification. 
         [0056]    This four-stage air shock is designed to have an 11 inch compressed length, and to be installed on a 6000 lb vehicle; each shock will be subjected to a load of 1500 lbs. The diameters will be selected such that all stages have 0.5 inch difference between their working tubes and shafts, beginning with the fourth, smallest, stage having a 2.0 inch diameter shaft. As described in Section 4: Loading in the Appendix, static ride height can be set at a given shaft stroke of the stages in the shock. In the present case, the vehicle&#39;s static ride height will be established on a percentage basis in which the first, second, third, and fourth stages will be set at 90%, 70%, 40%, and 30% of their shaft lengths, respectively. As discussed in Section 5: Temperature in the Appendix, an air shock is known to be sensitive to temperature. Included below is a description of the effects of temperature on the (initial) ride height calculated for this four-stage air shock. This description will be based on the ride height ratio factor discussed in the part Ride Height Ratio Factor under Section 5: Temperature in the Appendix. 
       I. Design Process 
       [0057]    The methodology outlined below is followed in the design of the four-stage air shock:
       1. Diagrams are used to illustrate the type of shock and the dimensions involved in the design process. These diagrams are shown on pages 1/2 and 2/2.   2. Terms are used to define the characteristics of the shock, including the dimensions or conditions of the shock. These terms are listed above under the section Brief Description of the Several Views of the Drawing.   3. Derived Terms are used to describe the dimensions or conditions of the shock that require mathematical calculation. These terms are listed below.   4. Ride Height refers to the method of determining the shock&#39;s static ride height. This method refers to the application of the techniques discussed in the Appendix, in particular Section 4: Loading. The techniques utilize the terms and derived terms mentioned above, where selected dimensions are chosen values while derived dimensions are calculated values. The values for most terms are compiled in tables. Ride Height is discussed below.   5. Temperature Effects refer to a change in ride height due to a change in temperature. This method refers to the application of the techniques discussed in the Appendix, in particular Section 5: Temperature. This method draws upon the results obtained in the part Ride Height above, and is applied to each stage in the four-stage air shock. Temperature Effects are discussed below.   6. Conclusions refer to a summary of the results obtained in the design process and their relevance to the segmented air shock. Conclusions are discussed below.       
 
       II. Derived Terms 
       [0064]    Note: Many of the terms listed above under the section Brief Description of the Several Views of the Drawing are used below in calculations. Terms that refer to lengths, diameters, volumes, etc for a given stage are not associated with a subscript because the calculation is the same for a given dimension for each stage. Calculations involving gas law formulas use numbers defined in metric units, and then later the results are converted to English units—see items 15 and 17 below: 
         [0065]    1. CL: Shock Compressed Length. This is a chosen value. This term is based on equation 11 from the part Dimensions of a Stage under Section 1: Properties in the Appendix. In this case, it is used to calculate the working tube overall length of a four-stage shock: 
         [0000]        CL=L   TO Σ( ec   n )  (eq 1)
 
         [0000]        L   TO   CL −Σ( ec   n )  (eq 2)
 
         [0000]    where ec n  refers to the thicknesses of the end caps for all stages in the shock. 
         [0066]    2. EL: Shock Extended Length. This term is calculated with equation 9 from the part Derived Terms under Section 3: Extended Length in the Appendix. 
         [0000]        EL=L   TO   +ΣL   S   (eq 3)
 
         [0000]    where: L TO  refers to TOL 
         [0067]    3. L WT1 : length of the first working tube. This term is calculated with equation 4 from the part Dimensions of a Stage under Section 1: Properties in the Appendix. 
         [0000]        L   WT1   =L   TO   −me   (eq 4)
 
         [0068]    4. L WTn : length of the second, third, and fourth working tubes. This term is based on equation 4 in the part Derived Terms under Section Extended Length in the Appendix. 
         [0000]        L   WTn   =L   WTn-1   −wp−ss+ec   (eq 5)
 
         [0000]    where n≡2, 3, 4 and L WT  refers to TWL. 
         [0069]    5. L SO : shaft overall length. This term is calculated with equation 5 from the part Dimensions of a Stage under Section 1: Properties in the Appendix. 
         [0000]        L   SO   =L   WT   +ec   (eq 6)
 
         [0070]    6. L S : shaft length. This term refers to the shaft stroke and initial shaft stroke, L E . It is used to calculate the volume of the shaft. This term is calculated with equation 6 from the part Dimensions of a Stage under Section 1: Properties in the Appendix. 
         [0000]        L   S   =L   SO −( wp+ss+ec )  (eq 7)
 
         [0071]    7. L TC : Travel Capacity. This term is calculated with equation 7 in the part Derived Terms under Section 3: Extended Length in the Appendix. 
         [0000]        L   TC   =ΣL   S −Σ( ec   n )  (eq 8)
 
         [0000]    where: L S  refers to ESL 
         [0072]    8. V WT : volume of the working tube. This term is calculated with equation 2 from the part Dimensions of a Stage under Section 1: Properties in the Appendix: 
         [0000]        V   WT =π(½ D   WT ) 2   ·L   WT   (eq 9)
 
         [0073]    9. V S : volume of the shaft. This term is calculated with equation 3 from the part Dimensions of a Stage under Section 1: Properties in the Appendix: 
         [0000]        V   S =π(½ D   S ) 2   *L   S   (eq 10)
 
         [0074]    10. V O : volume of the working tube occupied by the oil. This term is calculated with equation 8 from the part Dimensions of a Stage under Section 1: Properties in the Appendix: 
         [0000]        V   O   =V   WT   −V   S   (eq 11)
 
         [0075]    11. V G : volume of the working tube occupied by the gas. This term refers to the initial volume of the gas (V E ), and is calculated with equation 9 from the part. Dimensions of a Stage under Section 1: Properties in the Appendix. 
         [0000]        V   G   =V   S   (eq 12)
 
         [0076]    12. V F : volume of the gas when the shaft is at selected length of stroke—static ride height. It is calculated with equation 18 in the part Derived Terms under Section 4: Loading in the Appendix: 
         [0000]        V   F =π(½ D   S ) 2   ·L   F   (eq 13)
 
         [0077]    13. A: cross-sectional surface area of shaft, where the diameter refers to the diameter of the shaft. This surface area is calculated from equation 19 in the part Derived Terms under Section 4: Loading in the Appendix: 
         [0000]        A=π·r   2 =π·(½ D   S ) 2   (eq 14)
 
         [0078]    14. P E : refers to the initial gas charge of the air shock. It is calculated from equation 5 in the part Initial Gas Charge At Static Ride Height under Section 4: Loading in the Appendix: 
         [0000]        P   E =( F   W   /A )·( V   F   /V   E )  (eq 15)
 
         [0000]    where F≡F W : force of external weight exerted on shock. 
         [0079]    15. c: the constant in Boyle&#39;s law. It is calculated with equation 13 in the part Derived Terms under Section 2: Spring Rate in the Appendix: 
         [0000]        c=P   E   V   E   (eq 16)
 
         [0080]    16. ΔV: change in volume of the gas, and occurs when the shaft is stroked. It is calculated with equation 14 in the part Derived Terms under Section 2: Spring Rate in the Appendix. The values for ΔL are selected: 
         [0000]      Δ V =π(½ D   S ) 2   ·ΔL   (eq 17)
 
         [0081]    17. AP: change in pressure of the gas. It is calculated with equation 15 in the part Derived Terms under Section 2: Spring Rate in the Appendix: 
         [0000]      Δ P=c ·(1/ΔV)  (eq 18)
 
         [0082]    18. F G : force associated with the gas pressure. It is calculated using equation 24 in the part Derived Terms under Section 4: Loading in the Appendix: 
         [0000]        F   G   =ΔP·A   (eq 19)
 
         [0083]    19. RH: temperature induced change in ride height. It is calculated with equation 11 in the part Ride Height Ratio Factor under Section 5: Temperature in the Appendix. 
         [0000]        RH=R   H   ·L   f   (eq 20)
 
         [0000]    where: 
         [0084]    L F ≡initial ride height, where L F  refers to L SI    
         [0085]    RH F ≡ride height ratio factor (defined as per 10° F.) 
         [0086]    20. ΔL n : change in initial ride height. It is calculated using equation 10 in the part Derived Terms under Section 5: Temperature in the Appendix: 
         [0000]      Δ L   n   =RH·ΔT   (eq 21)
 
       III. Ride Height 
       [0087]    A. Conversion Factors:
       1 atm=14.7 psi   1 liter=61 in 3      1 in 3 =16.39 cubic centimeters (cc)       
 
         [0091]    B. Selected Dimensions
       Shock Compressed Length—CL (in): 11   Working Tube mounting eyelet—me (in): 1.5       
 
         [0000]    
       
         
               
               
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                   
                 D WT   
                 D S   
                 wp 
                 ss 
                 ec 
               
               
                   
                 Stage 
                 (in) 
                 (in) 
                 (in) 
                 (in) 
                 (in) 
               
               
                   
                   
               
             
             
               
                   
                 1 
                 4.0 
                 3.5 
                 0.875 
                 0.5 
                 0.5 
               
               
                   
                 2 
                 3.5 
                 3.0 
                 0.750 
                 0.5 
                 0.5 
               
               
                   
                 3 
                 3.0 
                 2.5 
                 0.625 
                 0.5 
                 0.5 
               
               
                   
                 4 
                 2.5 
                 2.0 
                 0.500 
                 0.5 
                 0.5 
               
               
                   
                   
               
             
          
         
       
     
         [0094]    C. Derived Dimensions 
         [0000]    
       
         
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                   
                 L WT   
                 L SO   
                 L S   
               
               
                   
                 Stage 
                 (in) 
                 (in) 
                 (in) 
               
               
                   
                   
               
             
             
               
                   
                 1 
                 7.5 
                 8.0 
                 6.13 
               
               
                   
                 2 
                 6.6 
                 7.1 
                 5.38 
               
               
                   
                 3 
                 5.9 
                 6.4 
                 4.75 
               
               
                   
                 4 
                 5.3 
                 5.8 
                 4.25 
               
               
                   
                   
               
             
          
         
       
       
         
           
             Working Tube Overall Length—L TO  (in): 9 
             Travel Capacity—L TC  (in): 18.5 
             Shock Extended Length—EL (in): 29.5 
           
         
       
     
         [0098]    D. Calculation of Static Ride Height 
         [0099]    Steps To Determine Static Ride Height
       1. Select the percentage that each shaft length will be adjusted to (%).   2. Observe the shaft length for each stage (L S ) that was calculated in item C. Derived Dimensions above.   3. Calculate the shaft stroke of each stage at ride height (L F ) as the percent shaft length for each stage: i.e., L F =%·L 5 .   4. Calculate the travel capacity at ride height (L TCF ):       
 
         [0000]        L   TCF   =ΣL   F   −Σec   n   (eq 22)
 
         [0104]    5. Calculate the initial gas pressure charges (P E ) for each stage at % L S  with the equation 13 in the Derived Terms above.
       Note1: The shock length at static ride height can be calculated from the difference between the shock extended length and the percent travel capacity as follows:       
 
         [0000]        SL   F   =EL−ΣL   F   (eq 23)
 
         [0000]    
       
         
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                   
                 L S   
                   
                 L F   
               
               
                   
                 Stage 
                 (in) 
                 % 
                 (in) 
               
               
                   
                   
               
             
             
               
                   
                 1 
                 6.13 
                 90.0 
                 5.51 
               
               
                   
                 2 
                 5.38 
                 70.0 
                 3.76 
               
               
                   
                 3 
                 4.75 
                 40.0 
                 1.90 
               
               
                   
                 4 
                 4.25 
                 30.0 
                 1.28 
               
               
                   
                   
               
             
          
         
       
       
         
           
             Travel Capacity at Ride Height—L TCF  (in): 10.5 
             Shock Length at Ride Height—SL F  (in): 21.5 
           
         
       
     
         [0108]    E. Derived Volumes 
         [0000]    
       
         
               
               
               
               
               
             
           
               
                   
               
               
                   
                 V WT   
                 V S (V G ) 
                 V O   
                 V O   
               
               
                 Stage 
                 (in 3 ) 
                 (in 3 ) 
                 (in 3 ) 
                 (cc) 
               
               
                   
               
             
             
               
                 1 
                 94.26 
                 58.94 
                 35.32 
                 578.6 
               
               
                 2 
                 63.75 
                 38.00 
                 25.75 
                 421.8 
               
               
                 3 
                 41.53 
                 23.32 
                 18.21 
                 298.3 
               
               
                 4 
                 25.77 
                 13.35 
                 12.42 
                 203.5 
               
               
                   
               
             
          
         
       
     
         [0109]    F. Conditions Of Stage (Initial &amp; Final Conditions) 
         [0000]    
       
         
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                   
               
               
                   
                 L F   
                 A 
                 V F   
                 F W   
                 P E   
                 P E   
                   
               
               
                 Stage  
                 (in)  
                 (in 2 ) 
                 (in 3 ) 
                 (lbs) 
                 (psi) 
                 (atm) 
                 c 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 5.51 
                 9.62  
                 53.04 
                 1500  
                 140.30 
                 9.54 
                 9.22 
               
               
                 2 
                 3.76 
                 7.07  
                 26.60 
                 1500 
                 148.53 
                 10.10 
                 6.29 
               
               
                 3 
                 1.90 
                 4.91  
                 9.33  
                 1500  
                 122.22 
                 8.31 
                 3.18 
               
               
                 4 
                 1.28 
                 3.14 
                 4.01  
                 1500 
                 143.22 
                 9.74 
                 2.13 
               
               
                   
               
             
          
         
       
     
         [0110]    G. Changes in Volume, Pressure, and Force 
         [0000]    
       
         
               
               
               
               
               
               
               
               
             
               
             
               
               
               
               
               
               
               
               
             
               
             
               
               
               
               
               
               
               
               
             
               
             
               
               
               
               
               
               
               
               
             
               
             
               
               
               
               
               
               
               
               
             
           
               
                   
               
               
                 ΔL 
                 ΔV 
                 ΔV 
                 ΔP 
                 ΔP 
                 F G   
                 %  
                 % 
               
               
                 (in) 
                 (in 3 ) 
                 (L) 
                 (atm) 
                 (psi) 
                 (lbs) 
                 ΔL 
                 ΔP 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 Stage 1 
               
             
          
           
               
                 6.13 
                 58.94 
                 0.97 
                 9.54 
                 140.30 
                 1350.0 
                 — 
                 — 
               
               
                 6.0 
                 57.73 
                 0.95 
                 9.74  
                 143.22 
                 1378.1 
                  2 
                 2 
               
               
                 5.51 
                 53.04 
                 0.87 
                 10.60 
                 155.89  
                 1500.0 
                 10 
                 11 
               
               
                 5.0 
                 48.11 
                 0.79 
                 11..69  
                 171.87  
                 1653.8 
                 18 
                 23 
               
               
                 4.9 
                 47.15 
                 0.77 
                 11.93 
                 175.37 
                 1687.5 
                 20 
                 25 
               
               
                 4.5 
                 43.30 
                 0.71 
                 12.99 
                 190.96 
                 1837.5 
                 27 
                 36 
               
               
                 4.0 
                 38.49 
                 0.63 
                 14.61 
                 214.83 
                 2067.2 
                 35 
                 53 
               
               
                 3.5 
                 33.68 
                 0.55 
                 16.70 
                 245.52 
                 2362.5 
                 43 
                 75 
               
               
                 3.1 
                 29.47 
                 0.48 
                 19.09 
                 280.60 
                 2700.0 
                 50 
                 100 
               
               
                 3.0 
                 28.87 
                 0.47 
                 19.49 
                 286.44 
                 2756.3 
                 51 
                 104 
               
               
                 2.5 
                 24.06 
                 0.39 
                 23.38 
                 343.73 
                 3307.5 
                 59 
                 145 
               
               
                 2.0 
                 19.24 
                 0.32 
                 29.23 
                 429.66 
                 4134.4 
                 67 
                 206 
               
               
                 1.5 
                 14.43 
                 0.24 
                 38.97 
                 572.88 
                 5512.5 
                 76 
                 308 
               
               
                 1.2 
                 11.79 
                 0.19 
                 47.72 
                 701.49 
                 6750.0 
                 80 
                 400 
               
               
                 1.0 
                 9.62 
                 0.16 
                 58.46 
                 859.33  
                 8268.8 
                 84 
                 513 
               
               
                 0.5 
                 4.81 
                 0.08 
                 116.92 
                 1718.65 
                 16537.5 
                 92 
                 1125 
               
             
          
           
               
                 Stage 2 
               
             
          
           
               
                 5.38 
                 38.00 
                 0.62 
                 10.10 
                 148.53  
                 1050.0 
                 — 
                 — 
               
               
                 5.0 
                 35.35 
                 0.58 
                 10.86 
                 159.66  
                 1128.8 
                  7 
                 8 
               
               
                 4.5 
                 31.81 
                 0.52 
                 12.07 
                 177.41  
                 1254.2 
                 16 
                 19 
               
               
                 4.3 
                 30.40 
                 0.50 
                 12.63 
                 185.66  
                 1312.5 
                 20 
                 25 
               
               
                 4.0 
                 28.28 
                 0.46 
                 13.58 
                 199.58  
                 1410.9 
                 26 
                 34 
               
               
                 3.76 
                 26.60 
                 0.44 
                 14.43 
                 212.18  
                 1500.0 
                 30 
                 43 
               
               
                 3.5 
                 24.74 
                 0.41 
                 15.52 
                 228.09  
                 1612.5 
                 35 
                 54 
               
               
                 3.0 
                 21.21 
                 0.35 
                 18.10 
                 266.11 
                 1881.3 
                 44 
                 79 
               
               
                 2.7 
                 19.00 
                 0.31 
                 20.21 
                 297.05 
                 2100.0 
                 50 
                 100 
               
               
                 2.5 
                 17.67 
                 0.29 
                 21.72 
                 319.33 
                 2257.5 
                 53 
                 115 
               
               
                 2.0 
                 14.14 
                 0.23 
                 27.15 
                 399.16 
                 2821.9 
                 63 
                 169 
               
               
                 1.5 
                 10.60 
                 0.17 
                 36.21 
                 532.22 
                 3762.5 
                 72 
                 258 
               
               
                 1.1 
                 7.60 
                 0.12 
                 50.52 
                 742.63  
                 5250.0 
                 80 
                 400 
               
               
                 1.0 
                 7.07 
                 0.12 
                 54.31 
                 798.32  
                 5643.8 
                 81 
                 438 
               
               
                 0.5 
                 3.53 
                 0.06 
                 108.62 
                 1596.65 
                 11287.5 
                 91 
                 975 
               
             
          
           
               
                 Stage 3 
               
             
          
           
               
                 4.75 
                 23.32 
                 0.38 
                 8.31 
                 122.22 
                 600.0 
                 — 
                 — 
               
               
                 4.5 
                 22.09 
                 0.36 
                 8.78 
                 129.00 
                 633.3 
                  5 
                 6 
               
               
                 4.0 
                 19.64 
                 0.32 
                 9.87 
                 145.13 
                 712.5 
                 16 
                 19 
               
               
                 3.8 
                 18.66 
                 0.31 
                 10.39 
                 152.77 
                 750.0 
                 20 
                 25 
               
               
                 3.5 
                 17.18 
                 0.28 
                 11.28 
                 165.86 
                 814.3 
                 26 
                 36 
               
               
                 3.0 
                 14.73  
                 0.24 
                 13.16  
                 193.51 
                 950.0 
                 37 
                 58 
               
               
                 2.5 
                 12.27  
                 0.20 
                 15.80  
                 232.21 
                 1140.0 
                 47 
                 90 
               
               
                 2.4 
                 11.66  
                 0.19 
                 16.63  
                 244.43 
                 1200.0  
                 50 
                 100 
               
               
                 2.0 
                 9.82 
                 0.16 
                 19.75  
                 290.26 
                 1425.0  
                 58 
                 138 
               
               
                 1.90 
                 9.33 
                 0.15 
                 20.78 
                 305.54 
                 1500.0  
                 60 
                 150 
               
               
                 1.5 
                 7.36 
                 0.12 
                 26.33  
                 387.01 
                 1900.0  
                 68 
                 217 
               
               
                 1.0 
                 4.91 
                 0.08 
                 39.49  
                 580.52 
                 2850.0  
                 79 
                 375 
               
               
                 1.0 
                 4.66 
                 0.08  
                 41.57  
                 611.08 
                 3000.0  
                 80 
                 400 
               
               
                 0.5 
                 2.45 
                 0.04  
                 78.98 
                 1161.04 
                 5700.0  
                 89 
                 850 
               
             
          
           
               
                 Stage 4 
               
             
          
           
               
                 4.25  
                 13.35 
                 0.22  
                 9.74 
                 143.22 
                 450.0 
                 — 
                 — 
               
               
                 4.0 
                 12.57 
                 0.21  
                 10.35 
                 152.17 
                 478.1 
                  6 
                 6 
               
               
                 3.5 
                 11.00 
                 0.18  
                 11.83 
                 173.91 
                 546.4 
                 18 
                 21 
               
               
                 3.4 
                 10.68 
                 0.18 
                 12.18 
                 179.03 
                 562.5 
                 20 
                 25 
               
               
                 3.0 
                 9.43 
                 0.15  
                 13.80  
                 202.90 
                 637.5 
                 29 
                 42 
               
               
                 2.5 
                 7.86 
                 0.13  
                 16.56  
                 243.48 
                 765.0 
                 41 
                 70 
               
               
                 2.1 
                 6.68 
                 0.11  
                 19.49  
                 286.44 
                 900.0 
                 50 
                 100 
               
               
                 2.0 
                 6.28 
                 0.10  
                 20.70  
                 304.34 
                 956.3 
                 53 
                 113 
               
               
                 1.5 
                 4.71 
                 0.08 
                 27.60  
                 405.79 
                 1275.0 
                 65 
                 183 
               
               
                 1.28 
                 4.01 
                 0.07 
                 32.48 
                 477.40 
                 1500.0  
                 70 
                 233 
               
               
                 1.0 
                 3.14 
                 0.05  
                 41.41  
                 608.69 
                 1912.5  
                 76 
                 325 
               
               
                 0.9 
                 2.67 
                 0.04  
                 48.71  
                 716.10 
                 2250.0  
                 80 
                 400 
               
               
                 0.5 
                 1.57 
                 0.03 
                 82.81 
                 1217.38 
                 3825.0 
                 88 
                 750 
               
               
                   
               
             
          
         
       
     
       IV. Temperature Effects 
       [0111]    A. Ride Height Ratio Factor:
       RH F =0.02 in/10° F.       
 
         [0113]    B. Ride Height Ratio
       L F : shaft stroke at initial ride height   RH: ride height ratio; see equation 20 in Derived Terms above       
 
         [0000]    
       
         
               
               
               
             
           
               
                   
               
               
                   
                 L F   
                 RH 
               
               
                 Stage 
                 (in) 
                 (in/10° F.) 
               
               
                   
               
             
             
               
                 1 
                 5.51 
                 0.10 
               
               
                 2 
                 3.76 
                 0.07 
               
               
                 3 
                 1.90 
                 0.04 
               
               
                 4 
                 1.28 
                 0.02 
               
               
                   
               
             
          
         
       
     
         [0116]    C. Change in Static Ride Height
       ΔT: selected change in temperature   ΔL n : change in ride height for nth stage; see equation 21 in Derived Terms above.   ΔL TOT : change in shock ride height; i.e., ΣΔL n         
 
         [0000]    
       
         
               
               
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 ΔT 
                 ΔL 1   
                 ΔL 2   
                 ΔL 3   
                 ΔL 4   
                 ΔL TOT   
               
               
                   
                 (° F.) 
                 (in) 
                 (in) 
                 (in) 
                 (in) 
                 (in) 
               
               
                   
                   
               
             
             
               
                   
                 10 
                 0.10 
                 0.07 
                 0.04 
                 0.02 
                 0.24 
               
               
                   
                 20 
                 0.21 
                 0.14 
                 0.07 
                 0.05 
                 0.47 
               
               
                   
                 30 
                 0.31 
                 0.21 
                 0.11 
                 0.07 
                 0.71 
               
               
                   
                 40 
                 0.42 
                 0.28 
                 0.14 
                 0.10 
                 0.94 
               
               
                   
                 50 
                 0.52 
                 0.36 
                 0.18 
                 0.12 
                 1.18 
               
               
                   
                   
               
             
          
         
       
     
       V. Conclusions on Four-Stage Air Shock 
       [0120]    Outlined below are the characteristics of the four-stage air shock: 
         [0121]    A. Spring Rate 
         [0122]    1. For each of the four stages, the pressure of the gas increases 25%, 100%, and 400% as the length of the shaft stroke decreases 20%, 50%, and 80%, respectively. As discussed in Section 2: Spring Rate in the Appendix, this trend is fundamental to all (ideal) gases. 
         [0123]    2. For each of the four stages, the pressure of the gas increases 100% as the length of the shaft stroke decreases the first 50%; whereas, the pressure of the gas increases 300% as the length of the shaft stroke decreases from 50% to 20%. As discussed in Section 3: Spring Rate in the Appendix, this trend is fundamental to all (ideal) gases, and confirms that gas pressure undergoes small changes due to small changes in length when the volume has not decreased much; whereas, gas pressure undergoes large changes due to small changes in length when the volume has decreased significantly. 
         [0124]    B. Length 
         [0125]    1. Summary of Length Properties 
         [0000]    
       
         
               
               
               
               
             
               
               
               
               
             
           
               
                   
               
               
                 Label 
                 Dimension 
                 Value 
                 Valuation Method 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 CL 
                 shock compressed length 
                 11 
                 selected value 
               
               
                 L TO   
                 working tube overall length 
                 9 
                 eq 2, Derived Terms 
               
               
                 L TC   
                 travel capacity 
                 18.5 
                 eq 8, Derived Terms 
               
               
                 EL 
                 shock extended length 
                 29.5 
                 eq 3, Derived Terms 
               
               
                 L TCF   
                 travel capacity at ride height 
                 10.5 
                 eq 22, Ride Height 
               
               
                 SL F   
                 shock length at ride height 
                 21.5 
                 eq 23, Ride Height 
               
               
                   
               
             
          
         
       
     
         [0126]    2. This shock has an extended length that is 2.7 times greater than is the compressed length (29.5/11). This feature satisfies the fundamental purpose behind designing this shock, and improves upon the extended length/compressed length ratio of any known shock. 
         [0127]    3. Achieves 18.5 inches of travel capacity via the combined shaft strokes of four stages, each operating independently and in series, where the shaft strokes range from a maximum of 6.13 inches to a minimum of 4.25 inches. 
         [0128]    C. Static Ride Height 
         [0129]    1. Achieves a static ride height in which the two largest stages are just beginning to compress (90%, 70% stroke remaining) and the two smallest stages are mainly compressed (40%, 30% stroke remaining). 
         [0130]    2. Static ride height is set at an external weight/load of 1500 lbs, thereby representing a vehicle weighing 6000 lbs, at a relatively modest initial gas pressure charge in the neighborhood of 122-449 psi per stage. 
         [0131]    3. At static ride height the shock has the ability to compress 10.5 inches (L TCF =10.5″) and to extend 8.0 inches (18.5-10.5). 
         [0132]    D. Temperature 
         [0133]    1. The static ride height is expected to change clue to a change in temperature The temperature effects can be analyzed with the ideal gas law, in particular the Charles-Gay-Lussac Law. In the present case, each stage&#39;s sensitivity to a change in temperature is reflected in the ride height ratio (RH); which is 0.10, 0.07, 0.04, and 0.02 inches/10° F. for stages one, two, three, and four, respectively. The ride height ratio can be used to predict the change in ride height for a given change in temperature. For example, if the temperature increases 50° F., the ride height will increase about 0.52, 0.36, 0.18, and 0.12 for stages one, two, three, and four, respectively; thereby giving an increase in the shock&#39;s ride height of 1.18 inches. 
         [0134]    E. Relevant Principles 
         [0135]    In principle, this four-stage air shock: 
         [0136]    1. Represents a long-stroke air shock with relatively short-stroke stages such that each stage is able to reach the “working zone” faster and operate in that zone longer than a comparable single shaft long-stroke air shock. 
         [0137]    2. Possesses the capability of setting up each stage with its own properties (gas pressure charge, volume of oil, type of working piston, valving and shims) to operate in a specific type of terrain. This capability allows the shock to operate at an optimum level in different conditions or terrains. 
         [0138]    3. Requires the following amounts of gas and oil to operate properly at about 60% static ride height: 140.3, 148.53, 122.22, and 143.22 psi; and, 578.6, 421.8, 298.3, and 203.5 cc in stages one, two, three, and four, respectively. Addition of gas and oil is performed step-wise, first add oil, and then gas. The oil should fill each stage when it&#39;s fully compressed and the gas should set the vehicle at static ride height (see discussion in the part Initial Volumes of Oil and Gas under Section 1: Properties in the Appendix). 
         [0139]    While the invention has been illustrated and described as embodied in a shock absorbing device for a vehicle suspension system, it is not intended to be limited to the details shown, since it will be understood that various omissions, modifications, substitutions and changes in the forms and details of the device illustrated and in its operation can be made by those skilled on the art without departing in any way from the scope and spirit of the present invention.