so now that we have established, that we need to compensate for the shaft volume, and that our shaft volume depends on our shaft diameter and it´s stroke --> meaning, that if we have two dampers with equal stroke (let´s say 100 mm) the one with the larger shaft diameter will displace more fluid, and that our preload depends of our shaft diameter and the pressure inside the gas reservoir, let´s see what this means for our damper.
The increase in pressure inside the dampers gas reservoir can be calculated, using the "law of the ideal gas".
substituded for P2 -->
which means, that if we start with an given volume, and assuming that the temperature does not change, our pressure will increase when our volume decreases.
As an optical representation, it looks like this.
This shows the gas volume in our example (JRZ) damper, and a staring pressure of 10 bar. I have taken the 10 bar (the preload) off the graph, so that it will show only the increase in pressure.
(But I increased the shaft diameter to 45 mm, to show the effect.
This is not a true representation of the characteristics of an JRZ damper. I will show some real values later)
According to our "ideal gas law" every time we half the volume, we double the pressure inside our reservoir, and thereby doubling the force on our shaft
Let´s see:
We reduce the volume from 160 cm^3 to 80 cm^3 and our pressure goes from 10 bar to 20 bar. (20 bar - 10 bar offset = 10 bar) and we see our pressure increases by 10 bar.
If we multiply this pressure by our shaft area, we have a force increase over the stroke ( force incease/stroke = spring rate)
Now if we reduce our new volume of 80 cm^3 by 50% again, we double our pressure again.
At 75 mm stroke we have 40 cm^3 volume and (2x 20 bar - 10 bar offset) = 30 bar.
As you can see, that spring rate of an gas spring is extremly progressive.
Everybody who has calculated the ancient "rice corn game" on a chess board, will know that if you keep doubling your values, things get interesting towards the end.
So what does it mean for our damper.
That the effect of the gas spring depends a lot on the ralationship of gas volume/shaft volume.
As larger the number, as smaller the effect.
If our gas volume only reduces by 10-20% with the stroke of the damper, the change in force is small, and depending on the shaft size (pressure x shaft area = force)
the change in overall springrate (main spring+damper spring rate) is perhaps insignificant for stiffly sprung cars, which only using small amounts of damper stoke.
It´s simple:
small stroke = small change in volume (for a given shaft size) --> small change in gas volume = small increase in pressure/force /damper spring rate
small spring rate change in comparsion to a stiff main spring = very small change in percent of overall vehicle spring rate.
This is perhaps one of the examples Speedsense is refering to - and rightly so
On the other hand, if our gas volume is a bit marginal in comparsion to our stroke, we could
(Disclaimer: I DONT ENCOURAGE/ADVOCATE THIS PRACTICE)
use the very progressive increase in springrate as a tuning aid for our car.
A change in gaspressure can tune our damper gasspring into a sort of bumpstop.
I know of at least one team, which used this practice with an Porsche 996 during a 24h race at the Nurburgring.
They increased the gaspressure in the front dampers (25mm shaft) to stop the car bottoming out at some parts on the track.
You can do things like this, but you walk on a very fine line, as things can get out of hand very quickly, when we add temperature to our equation.
some examples:
this would be a example close to what happened with the Porsche Damper.
A increase in pressure = a increase in force on the shaft
pressure/force / stroke would give the spring rate which gets added to whatever your main spring rate is.
comparsion of two dampers with the same stroke, gasvolume and gas pressue, but different shaft diameters.
now let´s see what would happen, if we take our example damper, and reduce the canister volume by 50%:
You can see, that the size of the initial gas volume in relation to the shaft volume has an influence on how our gas spring force will change over stroke.
This is an important point to keep in mind, and a possible differentiation factor inbetween diffeent damper designs, when it comes to determine gas spring effects due to stroke or temperature.
While the JRZ damper shown has a gas chamber length equal to it´s stroke length, this is not allways the case.
(but it´s not uncommon, and a good "rule of thumb" for a "safe" relationship, between shaft and gas chamber volume, for most applications.
If you increase the stroke, and you increase the reservoir/canister length by the same amount your relationship/progression value will stay the same)
with packaging and weight constrains, damper designers are sometimes forced to decrease the relationship.
In such dampers the progression in relation to stroke, and the effects due to temperature incease will be more pronouced.
As allways you have to find the best compromise for your needs.
An example for a damper with a smaller gas volume: