I’m thick! What is the meaning of linear?

When people describe a forks travel as being linear do they mean that it has a similar resistance through most of its travel (like some air forks) or do they mean the resistance steadily increases through the travel (like a coil fork).
Sorry for being thick, it’s in the genes y’know!

Linear it the first example.

2nd

The first.

The amount of (additional) force required to compress the suspension x mm does not change on where the fork is in the stoke.

Linear.
Like a line. ie The same all the way.
Your first example.

Thought linear would be if you charted the resistance to the stroke it would be a straight line on a graph, showing the same resistance throughout the stroke? And that a ramped resistance would be shown in a curved line on a graph. whether that applies to air or coil forks I’m not sure. Or haven’t I got a clue? (wouldn’t be unusual!)

I think your first example is linear, the second is progressive.

Personally, I always think these journos must be partaking in a whole different activity to me, because at normal riding speed, I couldn’t tell you what my suspension/forks are doing beyond making it all a bit more comfy for me.

They read the blurb on the website and then regurgitate it with a hint of personal opinion usually.

I’m pretty sure I can tell if my forks ‘dive’ through the travel and when they stiffen up through the stroke.

linear is your first example.
rising rate and falling rate are other options available to suspension systems (amongst many tricks available along the way) 😆

Aren’t coil springs usually more linear and air springs more likely to ramp up though?

IMO the first definition makes no sense. If the force did not vary with compression, it would go right through the travel to the end stop 🙁

Interestingly, an air spring is less linear than a coil spring, as the pressure is inversely proportional to the volume, though this can be mitigated by a separate reservoir

Matthew H, that’s what I’d heard.

Linear is x force makes the fork move y mm, 2x makes the fork move 2y mm.
Progressive x force makes the fork move y mm, 2x makes the fork move 1.5y mm.

numbers are for illustration, exact travel related to force depends on lots of things.

How this relates to what happens when you hit a log or a rock, depends on the angle your tyres hits, the pressure in the tyre the distribution of rider weight, the stiction in the fork, whether your going uphill or downhill, how fast your going, the weather, etc. etc.

coil springs in big DH forks are linear, in smaller forks they tend to be a little more progressive due to the lower air volume arround them, but not by a hugely noticable ammount.

air springs tend to have a S shaped curve, beign initialy hard to compress as the seals get moving, easier to compress in the mid stroke and ramping up at the end as the volume runs out.

In the context of forks linear can mean anything from "not progressive enough" to regressive. Thats what you get when the editor at MBR has a crucade agaisnt flat bars/linear shock rates/long stems etc etc etc.

IMO as long as the damping is adequate and stiction is low the rest is compensatable for by a good rider. My favourite 2 forks ever were some 2002 z1’s and some 2007/8 magura menja’s. Both very quickly damped, progressive at the end, and almost zero sticiton. but the magura is a typical air fork, with a very active mid stoke (i.e. its regressive once it starts moving in the first 70mm or so) whereas the z1’s were the same all through the travel.

linear would mean that the fork (or shock) travels as much for the same application of force.

Hence, apply force x, travels y distance; Double the force 2x, travels 2y, and so on.

A spring will do this up to the elastic limit. Without any fancy circuits, an airshock will require gradually increasing forces to go through the same travel, since the pressure inside the shock will increase exponentially.

ie: move an air shock through half its travel, pressure inside doubles. Now move through half again, pressure doubles again (fork has moved through 3/4 but all the gas is now squashed into 1/4 of the volume since PxV is a constant – Boyles law!) Half again (7/8 travel used now, pressure is 8x and so on)

Combine this with non-linear axle paths and hence different leverage ratios for rear suspension designs and you can do all sorts of smart things with suspension. Linear is not necessarily always good

"Linear" in these terms is defined as having a constant gradient on the force/compression graph. I.e. to compress 10mm takes 1kg, to compress 20mm takes 2kg.

Coil springs (generally) are linear. Their force is given by their springrate multiplied by their compression, until the coils bind and it becomes solid. This is used in some progressive springs whcih have sections of spring with varying spring rate, they all compress (to differing degrees) and when the softest binds the apparent spring rate is increased to that of the springs with remaining travel.
Air springs are (generally) linear, their resistance is given by faffing with the ideal gas equation pv=nrt – n and r are constant leaving pv=t, increase pressure times volume = temp. If you halve volume by squishing the spring you double pressure. You actually increase temp too, which is why the spring rate tends to rise a little at the extremes and under hard use.

n and r are constant leaving pv=t

is not linear :o)

is not linear :o)

– it is if you keep a constant T (which you will if you’re not talking about vast swings in pressure and you have good heat dissipation)?

it is if you keep a constant T

I agree PV=T is a linear (inversely linear if you will) relationship at constant T

But in the context of the current discussion of what ‘linear’ means it isn’t: pressure can be broadly thought of as equivalent to force (a school def of pressure being: the force of the molecules of gas pushing on the outside of the vessel)

If every time you halve the volume you double the pressure it is an exponential rate since the force required to halve the volume each time is doubled. Theoretically you’ll never reach full travel on an airspring since the final force to get the last few microns of travel will be impossible to apply.

>Theoretically you’ll never reach full travel on an airspring since the final force to get the last few microns of travel
>will be impossible to apply.

Full travel on a shock isn’t when the piston bottoms out on the end of the air can though – it’s when it hits a bump stop.

fwiw coffeeking, air springs develop T very quickly on stutter bumped DH sections. more than you’d imagine ! differntial temp of up to +60 deg C in a matter of seconds !

If every time you halve the volume you double the pressure it is an exponential rate since the force required to halve the volume each time is doubled.

Fair point, my in-head maths was feeling faulty today, on re-thinking (I always need a diagram) you’re right – arse! I wouldnt mind but I’ve already explained this to someone else this month and back then I told him it was non-linear! As brant says though, air springs are not designed with total volume=swept volume, I suppose this is what is "tuned" to give more or less linearity. LArge total vol/swept vol ratio would give more linearity, but still not linear.

tlr – where are you getting your delta-Ts from?! Have you been out measuring? <just curious>

I agree PV=T is a linear (inversely linear if you will) relationship at constant T

uh, ‘inversely linear’ is NOT linear – if you draw a graph, one is straight, the other is a hyperbolic curve. Sure enough a small part of the curve might be straightish, but it’s a different relationship.

there is some diabolical maths going down on this thread. y = 1/x is *not* a hyperbolic curve. having said that, it certainly isn’t linear either…

there is some diabolical maths going down on this thread. y = 1/x is *not* a hyperbolic curve. having said that, it certainly isn’t linear either…

From Wikipedia: "Hyperbolas arise in practice in many ways: as the curve representing the function y = 1/x in the Cartesian plane". I distinctly recall this from a maths lesson in 1966… except I should have said ‘a hyperbola’

I know nothign about this, but im enjoying this thread. They do say you learn something new every day 😀 I wonder how many folk will now be head over heels next time they are out riding solely from looking at their forks giving a prime (or not so) example of linear compression.

what a load of bollox

What a load of tosh air springs are progessive, Boyles law? half the volume double the pressure. coils springs can be either depending on how they are wound.

so rather than telling us what they aren’t, what are they then?

PS thanks for the help with that photo, the wife was chuffed to bits!

half the volume double the pressure Only when T is K, we established this earlier.

Keep up man!

half the volume double the pressure Only when T is K, we established this earlier. Keep up man!

but if it’s adiabatic it’s even less linear :o)

Besides which….I though all springs were linear?

Hooke’s Law = F = KX therfore F/X = K under all circumstances

That’s very true, but making a shock adiabatic could be rather difficult 🙂

Daffy – true – but has the singletrackworld science masters repealed boyles law?

take a syringe full of air with the nozzle blocked and try it out. the first bit of movement is easy but you will never compress it to the bottom as at zero volume you get infinite pressure.

a progressive coil spring is one that is wound so that the spacings are progressivly larger. Each section / turn of it is linear – but as you compress it more and more coils bind so you have less coils active so the total effective rate goes up.

Air springs will always be progressive but depending on the ratio between the volume at the start of the stroke and the end it can be very slight progression or great.

another experiment. Take a set of old school ‘zocchi open bath forks. take all the oil out – you get an almost linear spring. The more oil you add the more progressive it becomes as you alter the ratio of the volume at the start of the stroke to the end of the stroke until you reach a ponint where you cannot get full travel as you have zero air gap left thus infiniate pressure before you get full travel.

Cool, thanks TJ. Never really thought about the method of winding in the coil…Nice.

Wow, thanks for all the input everyone. I’ve got to go lie down after trying to digest all of that.

a progressive coil spring is one that is wound so that the spacings are progressivly larger.

Some progressive springs have equal spacing and different heat treatments through the spring. Easy to spot the difference though 🙂

I would like to see a few graphs showing the relationship between rear wheel travel and shock compression for some of the more popular frames, especially the virtual point/pivot systems. Even the single pivot designs won’t be linear.