two prototypes were built and tested , one provided with a coil external to the cylinder as in fig1 and using water as fluid , the other with an internal helical path shaped in the piston itself as shown in fig2 and using hydraulic fluid . fig1 illustrates an example of a force - controlling hydraulic device 1 according to the present invention . the device 1 comprises a cylinder 2 , a piston 3 movable within the cylinder , and a liquid 4 within the cylinder . the device further comprises a helical tube 5 located outside the cylinder creating a sealed path for the liquid to flow out and back into the cylinder via two orifices ( 6 , 7 ). movement of the piston 3 causes liquid 4 to flow through helical tube 5 which generates an inertial force due to the moving mass of the liquid . the cylinder may include one terminal , and the piston may include another terminal . as will be explained below , the inertial force due to a moving mass of liquid caused by relative movement between the terminals controls the mechanical forces at the terminals such that they are substantially proportional to the relative acceleration between the terminals . the motion of the piston 3 may be restricted by devices such as spring buffers 90 . such means may provide a useful safety feature to protect the device if large forces or velocities were generated at the limits of travel of the piston . the device of fig1 is implemented using a through - rod 8 . alternatives using a single rod with a floating piston or a double tube or other similar arrangements are equally feasible . means to pressurize the fluid ( not shown ) are envisaged . fig2 illustrates another example of a force - controlling hydraulic device 11 according to the present invention . the device 11 comprises a cylinder 12 , a piston 13 movable within the cylinder , and a liquid 14 within the cylinder . the outer surface of the piston 13 has a helical channel , such that , when inserted inside the cylinder , a helical path 16 is formed between the piston and the cylinder . movement of the piston 13 causes liquid 14 to flow through helical path 16 which generates an inertial force due to the moving mass of the liquid inside the cylinder . in the example of fig2 the helical path 16 has a cross - section which is a semi - disc which is convenient for machining other cross - sectional shapes may also be employed with advantage to control the damping characteristics of the device . the example of fig2 is implemented using a through - rod 15 . in the example shown in fig1 , the characteristic parameters of device 1 , namely the constant of proportionality with which the applied force at the terminals is related to the relative acceleration between the terminals , can be varied by altering values such as the radii of the piston , cylinder , and helical tube , the length of the cylinder , and liquid density . the effect of such parameters will be detailed below . consider the arrangement shown in fig1 , where r 1 is the radius of the through - rod , r 2 is the inner radius of the cylinder , r 3 is the inner radius of the helical tube , r 4 is the radius of the helix , h is the pitch of the helix , n is the number of turns in the helix , l is the inner length of the cylinder , and ρ is the liquid density . further , a 1 = π ( r 2 2 − r 1 2 ) is the cross - sectional area of the cylinder , and a 2 = πr 3 2 ; is the cross - sectional area of the tube . the total mass of liquid in the helical tube is approximately equal to : ρ nπr 3 2 √{ square root over ( h 2 +( 2π r 4 ) 2 )} =: m hel . ( 1 ) the total mass of liquid in the cylinder is approximately equal to : if the piston is subject to a linear displacement equal to x , then a fluid element in the helical tube may expect an angular displacement θ ( rads ) approximately equal to : the moment of inertia of the total liquid mass in the helical tube about the axis of the piston is approximately equal to m hel r 4 2 =: j . now suppose that device 1 has an ideal behavior with b representing the proportionality constant wherein the generated inertial force between the terminals is proportional to the relative acceleration between the terminals . then we would expect : let m tot = m hel + m cyl for the total liquid mass . exemplary values are tabulated below for two different liquids used in the embodiment shown in fig1 . in the following examples it was assumed that r 4 = r 2 + r 3 , h = 2r 3 and l = nh . the outside diameter ( od ) of the device was taken to be equal to 2 ( r 4 + r 3 ). as shown in tables 1 and 2 , the modeling and testing work demonstrated that the produced inertance effect ( force proportional to acceleration ) could be sufficiently large ( the proportionality constant b is greater than 50 kg ). such effect would be needed where the device is placed in parallel with a spring and damper . furthermore , the modeling and testing demonstrated that the viscosity of the liquid provides a departure from ideal behavior . a further parasitic element might be provided by the compressibility of the fluid which might be modeled as a spring in series with the two parallel elements . in u . s . pat . no . 7 , 316 , 303 , an ideal device is defined ( i . e ., the force proportional to relative acceleration ) and deviations caused by friction , backlash etc . are regarded as parasitics which can be made as small as needed so that the essential function of the device is achieved . in the case of the present invention however , the non - linear damping caused by liquid viscosity is intrinsic , and will cause a deviation from ideal behavior at large piston velocities . the non - linear damping intrinsic to the present invention is “ progressive ”, namely the force increases with a relative velocity at a faster rate than linear . practical dampers in automotive applications are often regressive , namely the force increases with a relative velocity at a slower rate than linear . even when using ordinary liquids such as hydraulic fluids , the device according to the present invention can be configured to display an ideal behavior , using adjusting means 80 . for example , shim packs at the orifices 6 , 7 could be employed to achieve a more linear damping characteristic , although this would leave a non - negligible parallel damper . this has the potential to create a convenient integrated device with the behavior of an ideal device according to the present with a linear damper in parallel . in other circumstances it may be advantageous not to correct for the viscosity effect . the following details the effects of damping . let u be the mean velocity of fluid in the helical tube , δp the pressure drop across the piston μ the liquid viscosity , and l the length of the helical tube , where l = n √{ square root over (( h 2 +( 2 πr 4 ) 2 )} ( 6 ) the pressure drop δp across the main piston required to maintain a flow in the tube of mean velocity u will now be calculated . this will allow the steady force required to maintain a piston relative velocity { dot over ( x )} to be calculated , and hence a damping coefficient . given that a 1 { dot over ( x )}= a 2 u , the reynolds number ( re ) for the tube is equal to ( re ) = 2 ⁢ ρ ⁢ ⁢ r 3 μ ⁢ u = 2 ⁢ ρ ⁢ ⁢ r 3 ⁢ a 1 μ ⁢ ⁢ a 2 ⁢ x . ( 7 ) with transition from laminar to turbulent flow occurring around ( re )= 2 × 10 3 . assuming that u is small enough so that laminar flow holds , and using the hagen - poiseuille formula for a straight tube gives : the force on the piston required to maintain a steady relative velocity { dot over ( x )} is equal to δpa 1 . this suggests a linear damping rate coefficient equal to : the pressure drop needed to maintain a turbulent flow , according to darcy &# 39 ; s formula is : where f is a dimensionless friction factor . for a smooth pipe the empirical formula of blasius is : this gives the following expression for the constant force on the piston required to maintain a steady velocity : let the fluid be water with ρ = 100 kg m − 3 , μ = 10 − 3 pa s . take l = 7 m , r 1 = 8 mm , r 2 = 20 mm , r 3 = 4 mm , l = 300 mm . this results in a device with : the transition to turbulent flow occurs at a piston velocity of { dot over ( x )}= 0 . 0119 m s − 1 at velocities consistent with laminar flow , the damper rate is the pressure drop and linear force in conditions of turbulent flow are shown in fig3 and fig4 , respectively . if r 1 , r 2 and r 3 are all increased by a factor of 2 and 1 is reduced by a factor of 4 and then m hel and b are left unchanged , m cyl is increased by a factor of 4 and the damping force in turbulent flow is reduced by a factor of 2 1 . 25 = 2 . 38 . the helical tube shown in fig1 may be replaced in other embodiments of the invention with different shaped tubes . furthermore , the liquid path may be provided inside the cylinder , with the piston being shaped to provide for example a helical liquid flow path or several concentric helices . clearances around the piston may also be employed to provide the flow path inside the cylinder . in practice , the best results appear to be achieved by a helical flow path . for automotive suspension applications , an embodiment of the present invention in parallel with the regular spring and a damper is advantageous if the suspension is relatively stiff . for ordinary passenger cars , the parallel configuration may need to be combined with other series elements .