Potential Energy and Spring Rate

[motomadness]

Anyone care to give me their opinions?

Many of us talk about preload and damping, but our suspensions aren't static devices, therefore, the combination of preload and damping relate to your suspensions potential and kinetic energy that is conserved not destroyed.

Hmmm!

I am starting this because SuperDave asked me during his VRU day at the last BHF round about how to explain some of the mechanical concepts.

Time for Dynamics 101 ...

[Zac]

Preload only determines sag, which is both a measure of ride height (for this discussion "traditional" ride height adjustment such as fork height and shock length will be considered fixed) and the ratio of positive to negative suspension travel at the sag point.  On vehicles that don't have ture ride height adjustment such as certain classes of cars, ride height is adjusted using preload.

In other words preload does not have any effect on the potential energy stored in the spring.

As far as energy in the suspension system, the spring will store potential energy as the spring is compressed and release this energy as it extends.  The dampening converts kenetic energy (movement) into heat, thus removing the energy from the system.

We can start going into the differential equations which govern all of this, but suspension setup is still a black art.  I know the physics well, but that doesn't mean I can apply it.  It is very difficult to simulate motorcycle dynamics.  MotoGP has proven that the simulations can (sometimes) get in the ballpark, but Rossi is a much better developement tool.

-z.

[motomadness]

Okay Zac,

I am glad you replied.  Preload does effect potential energy.  Thinking only in terms of ride height limits your understanding to only static equations.  When you think about the energy equation, you start looking at things dynamically, which is how we'll all increase our understand of the "art" of suspension movement - spring rate + damping effects.

For example, if you have a 6" spring preloaded to 12 mm, you have a PE = rate*(6"-(6"-12mm)).  If due to suspension movement, the spring further compresses 2", then your new PE = rate*(6"-(6"-12mm-2")), and the change in PE = rate*(2").    If you change the preload, you don't change the rate of the spring, but there's no guarantee that the change in potential energy will be maintained because it now takes more force to get the same change in PE.  If you knew how to account for the damping effect mathemetically, then you could estimate the kinetic energy part of the equation.  Therefore, it is theoretically possible in a viscous damping system to tune the damping with preload, of course due to the geometry effects, steering effects are coupled to the mathematics = the "art".  Furthermore, since nothing is absolute for all conditions choices are made to establish the best from what you've got.  

This approach begins to simplify the "art", not explaining it sufficiently, but allowing us to understand how changing a spring, for a different rate, can also allow us adjust the damping components to tune the spring effects.

This almost begs the question of whether just changing the spring on a stock shock would improve the damping performance of the shock because of where/how it changes the damping operating range.

[motomadness]

Also, heat isn't the only form of the energy in the suspension equation.  At some point, the fluid doesn't get hotter, the bike just moves differently in response to the damping changes.

[motomadness]

I rewrote the equations in my above message.

[Zac]

Okay Zac,

I am glad you replied.  Preload does effect potential energy.  Thinking only in terms of ride height limits your understanding to only static equations.  When you think about the energy equation, you start looking at things dynamically, which is how we'll all increase our understand of the "art" of suspension movement - spring rate + damping effects.

For example, if you have a 6" spring preloaded to 12 mm, you have a PE = rate*(6"-12mm).  If due to suspension movement, the spring further compresses 2", then your new PE = rate*(6"-12mm-2"), and the change in PE = rate*(2").    If you change the preload, you don't change the rate of the spring, but there's no guarantee that the change in potential energy will be maintained because it now takes more force to get the same change in PE.  If you then knew how to account for the damping effect mathemetically, then you could estimate the kinetic energy part of the equation.  Therefore in a viscous damping system it is possible to tune the damping with preload, of course due to the geometry effects, steering effects are coupled to the mathematics = the "art".

 I will still have to disagree a little Sean.  We have to disregard the potential energy stored in the spring when the suspension is topped out.  There will be some amount of potential energy stored in the spring - rate*(free length-preloaded length), but this energy is not available to any work on the system.  

The spring will always compress to the same length when loaded with a static bike and rider.  Changing preload will change the shock length, but not the spring length.  In your case the PE in the spring would change with sag if the PE was defined as zero at the point where the suspension was topped out.  The PE in the spring would not change with sag if the PE was defined as zero when the spring was at full length.  

I think the best way to define the system is that the PE is zero when at the sag point, and PE is positive when the spring is compressed, and negative when the spring is extended.  This works because the system is comprised of both the PE in the spring AND the PE of the bike and riders mass, the equilbrium point (static sag) is defined as zero.  In this case, as long as the suspension is not  bottoming or topping out (statically or dynamically), the PE of the spring is independent of the preload.

Also, heat isn't the only form of the energy in the suspension equation.  At some point, the fluid doesn't get hotter, the bike just moves differently in response to the damping changes.

The damper can only dissipate energy, it cannot add energy back into the system (negleting the gas compressing in the shock).  Therefore, all the energy dissipated within the shock is converted to heat.  At some point the oil doesn't get any hotter, this is the steady state point where the energy is coming into the oil as heat at the same rate it is being transfered into the air outside the shock.  The shock will act different depending on the viscosity index of the fluid, but will still be dissipating the kinetic energy of the suspension movement.

This could become a fun discussion for us nerds  ;)

-z.

[motomadness]

Counter once more.  Any time the spring is compressed or extended beyond its free length, it will store energy.  The direction that energy acts along determines its effect.

I agree that the spring will always compress to the same length with the static bike and rider.  However, the spring length does change, it's just that the larger the preload, the more precompressed the spring becomes.  In my earlier example, the rider's PE changes with sag, although the overall PE will remain constant.  The rider will probably feel the RPE more than the overall PE.

Wait a minute.  I think I see where you are coming from.  I'll need to take a look at my shock to verify this. If sag were measured at the shock, I'm sure the difference in lengths will always be small.

Based on your comments, if more preload reduces your sag, and the spring length doesn't change with preload, then preload is merely a geometry adjustment.  Again, I will have to verify this on my bike.

KE -
The damper dissipates energy not through heat, but through a change in kinetic energy, or a change in velocity of the fluid, not heat.  I am confident that the heat produced is adiabatic.  If heat were the main damping mechanism your fluid would probably break down faster.  I think brake fluid would apply the heat mechanism damping effect - brake fade. Remember the dampers are flow control devices.

It may be a couple of days before I can reply, but don't let that hold up the discussion.

[Thingy]

This could become a fun discussion for us nerds  ;)

-z.

It kind of makes my brain hurt, but I agree.

Aren't you guys both right about the PE stored with the preload?  Monsta is correct in real terms and Zac is correct in 'relative' terms?  I'm not an engineer.  I am just trying to follow along.  Maybe I should just sit back and watch...  :)

[Thingy]

OK, I am still thinking about this.  I went back and read it again.  

I guess what I meant by this is that there IS PE stored in the spring with pre-load.  So, Monsta is right.

HOWEVER, Zac, are you saying that this PE is not used other than to change ride height?

If so, I think I agree with Sean.   ???  I say this under the assumption that the more you compress the spring, the more force that is needed to compress it.

Maybe this is not true.  I am not sure.  Even using a straight rate spring, it still requires more force to compress one with lots of preload, opposed to one with little preload, right?  (ie: it is storing more PE)

Since I am not an engineer, just tell me to shut up if I don't make any sense.  I will just watch from the sidelines.  It is fun to watch the discussion.

[tzracer]

Some spring background (for the sake of people trying to follow this discussion).

Spring force = spring rate (k) * distance compressed or stretched (x). You will see a negative sign in this equation, it is because the spring force is opositely directed to the movement (displacement) of the spring (vectors).

Spring potential energy = 1/2 * k * x^2, with the displacement (x) measured from the equilibrium position - spring not loaded.

Example : k = 500lb/in, compress 2 inches,
PE = 1/2 * 500 * 2^2 = 1000 in-lb of energy. If I preload the spring 2 inches and compress it 3 more inches, the potential enegy released when the spring returns to the preloaded length will be
PE = 1/2 * 500 *(5^2 - 2^2) = 5250 in-lb ( 5 = 2 preload inches + 3 additional inches).

Measuring spring PE from a sag position does not make sense because of how the PE equation is derived, the zero position is the equilibrium length, and spring PE is always a positive number. You are not free to choose the zero position as you are with gravitational PE.

Damping is usually speed sensitive (usually linear for shocks). Damping is used to contol the speed at which the damper moves. Since the damper is slowing the spring (and all moving parts), it is dissipating energy. This energy is dissipated in the form of heat.

Changing preload will change the ride height of the bike and it will change how the bike reacts to smaller bumps. It does not change the spring rate, but it will make the suspension stiffer in the sense that it will take more force to compress the suspension the same amount with more preload.

example : k = 500 lbs/inch. preload 1 inch, move suspension 1 inch, spring moves a total of 2 inches = 500lb/in * 2 in = 1000 lbs of force. Increase preload to 2 inches, compress suspension 1 in, spring moves a total of 3 inches for a force of 1500 lbs. This is why adding preload can be used to reduce bottoming, but then becomes less sensitive to smaller bumps.

Changing the spring rate is different. Higher will make he suspension stiffer, lower will make the suspension softer. If you find yourself adding a large amount of preload to keep the suspension from bottoming (or when setting sag), you may want to try a stiffer spring. Similar, is you are using very little preload, or removing preload to use more travel (or setting sag), you may want to try a softer spring. The reason for measuring free (no rider) sag and rider sag is to get the proper (or at least in the ball park) spring rate.

Going to a higher rate spring usually requires less compression damping and more rebound. A lower rate spring, more compression and less rebound.

As far as energy, remember that the damper has to control the kinetic energy of all the unsprung parts (tires, wheels, some suspension parts). That is why changing to lighter wheels will cause your suspension settings to no longer work.

Suspension settings are very rider dependant, some like to use all/most of their suspension travel, others, such as Eddie Lawson do not (it slowed his ability to turn in rapidly waiting for the suspension to react). Different riders like different settings, this is why I think it is important to learn to set up your own bike (once your riding has gotten to the level where you are ready for this - you need to be able to ride consistant lap times to determine the affect of changes).

[motomadness]

Why is everyone referring to the energy dissipation in terms of heat.  It's not all about heat, it's about flow as well, probably more so.  At some point the suspension fluid will not heat up anymore and the suspension will respond with less variance in the presence of similar perturbations.  If heat was the only response, the system would continue to get hot and the suspension would fail. At least that's how I would envision a heat dissipating system.

Now preload vs ride height:
I haven't seen my bike yet, but I had about 600 miles of driving to St. Louis to think about this problem.  The reason why adjusting preload changes the ride height but not the spring length is because the collar on the shock is not the only thing that preloads the spring.  Think free sag.  If you were to take all of the support away from the swingarm - support the rear of the bike from under the foot pegs, the spring should extend.  If the spring does not extend, then any additional preload you add into the shock will compress the spring and take out ride height.  However, if the shock does extend, meaning you have some available free sag, then when the bike is being supported by its own weight, the bike's weight will preload the spring.  Then when you begin adding preload into the spring, for some amount of preload, the bike's ride height will change commensurate with the amount of preload the bike imparts on the suspension related to free sag.  In shorter terms - if you have free sag, you can change the ride height (+ height) without changing the length of the spring until you have no more free sag (-height).  

Furthermore the reason why your handling sucks when you don't have any free sag is because the suspension can only move in one direction, and is prone to topping out.  Not to mention the fact that the spring is storing lots of PE with the lack of free sag.  Increase the free sag, reduce the effective PE and your suspension will work better because you have more "ability" to control the movement.

[motomadness]

More on the energy thang:

KE and PE are measured in terms of Joules, which is a unit os heat.  However in this example, KE and PE have length units, so energy dissipation must to focused more on displacement terms, not heat terms - thinking ideally.  In my mind the heating effects are more like correction terms.

If you still think it's heat dissipation, explain the mechanism and why.

[Super Dave]

This is fun.

More preload on a shock...

Straight rate springs still have a tiny bit of progressiveness to them...they are cut and worked at the ends so that they bottoms of the springs are flat.

Adding more preload will "push through" that little bit of progressiveness.

Some suspension guys will talk about how the actual coils can touch each other also.  That changes everything.  Basically, it will spring bind.

[tzracer]

Energy dissipation.

There is actually very little flow in a shock. The piston moves through the fluid which moves from one side of the piston to the other. If energy were dissipated into flow, the flow would have to continually increase.

Energy is dissipated as heat. As you start to ride, your shock heats up (my Husky 250CR had piggyback Ohlins, the reservoirs would get too hot to touch). It will eventualy reach an equilibrium temperature. Remember the rate of heat loss is related to temperature difference. As the temp of the shock increases, the rate of heat loss to the air increases. If the energy is not being dissipated as heat, where is it going?

The reason heat has the same units as energy is because heat is energy. What do you mean by KE and PE having length units? Remember, 1 Joule (J) = 1 N*m (Newton*meter), so 10 J  = 10 N*m. Heat dissipation works - think work and energy.

Ride height changing with preload is easy, as you add preload, the shock will compress less supporting the bike and rider, hence the bike will sit higher.

Free sag depends upon the bike, 125s and 250s run very little if any free sag. This is because the bike itself has very little weight, and when set up for the rider sag, the bike alone sags very little or nothing. My 250 generally had no free sag.

Two good books.

Motorcycle Handling and Chassis Design the art and science by Tony Foale (tonyfoale.com). Erik Buell even had a copy.

The Racing Motorcycle  A Technical Guide for Constructors volume 1
by John Bradley (I think I got my copy through Whitehorse Press)

[motomadness]

Brian,

I think heat has a role in the energy equation, just not the main part.  You say there's not much flow, when there is not much movement either.  The smaller the reservoir, the more heat that's generated, but like you said the fluid will reach an equilibrium temperature, the damping variance reduces, and then the damping mechanism is mostly flow control.

[motomadness]

KE and PE have length units because PE = s.rate*displacement and KE = 0.5*mass*(time_derivative_of_displacement)^2.  I know these are Joules, but after an equilibrium temperature has been reached, changes in displacement define the damping effect.  

At this level, I think it's better to simplify the problem rather than wrap a complex operation such as heat dissipation into the equation.  Now the discussion should focus on hold a racer can control the movement of his/her suspension, not how they can control the heat generated from the movement.  Besides, none of us can do anything about the heat generated by making external adjustments.

You control movement by:
- adjust preloads (externally and internally)
- adjust fluid levels
- adjust fluid weights
- adjust spring rates and types
- adjust valve shim stacks
- adjust damping valve positions
- using of needle valves for rebound circuits
- changing fluids regularly
- changing damping catridges: 20mm to 25mm (more flow, less heat, more progressive damping)
- chassis geometry and linkages.

I'm sure there are more, but generally these probably represent the range of changes a racer will consider doing themselves, or have an expert perform for them.

[tzracer]

Spring potential energy = 1/2 * spring rate (k) * displacement (x)^2.

Heat, PE, KE are all different forms of energy, they all have the same units. PE and KE having length units does not make them fundamentally different than heat.

Heat is not really that important to the discussion of how to adjust suspension. Heat is the end result of energy dissipation, the energy absorbed by the suspension gets turned into heat by the friction of fluid flow. KE and PE in a damped oscillator system is not conserved.

What I suggest to racers is to learn what all the adjusters on their suspension do. Unfortunately it takes time, effort, and some money. I don't think there is a short cut.

Go to a practice day, a helper will come in very handy. Expect to spend the entire day learning about suspension, not trying to set a new track record. Take notes, don't try to rely on your memory.

Go out for a session and get down to a comfortable lap time, one you can easily do all day without having to push too hard. Now turn one of you suspension adjusters, such as shock compression damping, all the way up. Ride the bike a couple of laps. Stop on pitlane, write down what differences you felt. Turn the same adjuster all the way down. Ride the bike for a couple laps. Stop on pitlane, write down what differences you felt. Return the adjuster to the starting position. Repeat with all the suspension adjustments you care to learn about. this will give you first hand feel for what the suspension changes will do.

Sean, I am not quite sure in what direction you would like this discussion to go. What exactly are you after?

[motomadness]

Brian,

I apologize for the arguement.  It's been a while since I have used these brain cells.  I see where you are coming from.  I think I was loosely using the idea of PE and KE to describe how energy is "conserved", or better transfer from potential energy of the spring to kinetic energy of the whole system in motion.  However, to describe the relationship of a mass/spring/damper system, I intended to really be talk about the equation of motion based on some forcing function, which really doesn't consider any heating effects.

Again this would be too complicated to discuss on this forum, but it helps to explain what the suspension is doing.

I also agree in your technique of trial and error at the track, however, before you go to the track it would be good if a rider knew a little more about what his/her suspension did.  That was my intention for this note.  To more or less convey the concept of suspension displacement and the rate of displacement, and that external and internal adjustments can be made to tune the response, but understand that once you've explored the range of potential responses of your suspension, other things can be done to change it further.  Kind of get people (newer riders) out of the mindset the suspension that Traxxion, Thermosman or Trackside installed for you is only the beginning.

I was using the idea of energy to create an image of rate of movement.  Do you think this was an appropriate comparison?

[motomadness]

Did some reading.

In The Racing Motorcycle: A technical guide for constructors,  Chapter 5, Section 6, pp329-330, it was clearly stated that the energy of the damper is dissipated by heat.  Furthermore they went on to discuss the type of dampers we have in our bikes.  Since we don't have friction dampers in our suspension components, the heat being generated is lower and excess energy is used to force oil through valves and orifices - flow control.

Thanks Brian and Zac for enlightening me.

Let's continue.  Care to start another thread of another interesting suspension subject?  If you don't I will pick something in a couple of days.

[Super Dave]

Heat...

Controling it can be an issue on how the shock works.

Specifically, I did testing of pre production shock warmers.

Post information that I got was that some shocks, to remain nameless, generated so much heat trying to operate in colder conditiions that they got out of the optimum range of temperature.  

When "pre heated" the shock had a more consistent feel and operated in the proper temperature range.

Butt feel, yeah, it was night and day...and, as a result, I use Hyperpro shocks as they don't exhibit the heat issue that the shock we were using had....especially in cooler conditions.

[motomadness]

Check out these articles from Sportrider.com
http://www.sportrider.com/tech/146_9602_tech/
http://www.sportrider.com/tech/146_9510_tech/
http://www.sportrider.com/tech/146_9502_tech/
http://www.sportrider.com/tech/146_9804_tech/
http://www.sportrider.com/tech/146_9608_tech/
http://www.sportrider.com/tech/146_9604_tech/

[tzracer]

Thanks Brian and Zac for enlightening me.

Let's continue. ÊCare to start another thread of another interesting suspension subject? ÊIf you don't I will pick something in a couple of days.

No problem, it is a lot of fun.