Tag Archives: physics

Motorcycle Suspension Part 2 – Things about springs.

Motor vehicle suspension is comprised of two systems.  One deals with absorbing bumps in a controlled manner and the other deals with returning the wheel to its correct location relative to the vehicle.  It is the job of the spring to perform this latter task. 

A spring has a state at which it is described as being “at rest”.  In the case of springs used in motorcycle suspension, the spring can be compressed or expanded from this position.  This only occurs through the application of force.  For the most part, simple metal springs conform to Hooke’s law.  The more force (which can be measured in Newtons) applied to the spring, the more it compresses.  Hooke’s law is a linear equation.  So, if you apply twice as much force to a spring, you will compress it twice as far.
When a spring is released, it will return to its state of rest.  But, because the end of the spring is moving and has a mass, it has inertia.  This inertia is a force, which causes the spring to extend beyond its length at rest.  The spring continues to extend until the inertia can no longer overcome the force required to continue extending the spring.  At that point, the spring then starts to compress again to reach its state of rest.  If the spring were not losing energy in other ways, this expansion and compression would continue forever.  Here is a neat-o demo of springs doing what springs do.

Because the gradual dissipation of energy through air resistance and heat loss takes too long to keep motorcyclists happy, the shock absorber is used to overcome the spring’s inertia.  It dampens the rate at which a spring is compressed and expanded.

The more mass you attach to the end of a spring, the more momentum / inertia the spring end gains as it moves.  Because of this, the pogo effect of the spring is increased and stopping it requires more damping.  This in turn, reduces the efficiency of the shock absorber to do other things, such as absorb shocks from bumps!  On any vehicle, the mass attached to the end of the spring (such as the wheel, brake components, etcetera) is referred to as “un-sprung mass”.  As already indicated, unsprung mass compromises the effectiveness of shock absorbers and as a result, motorcycle designers and after-market specialists place an emphasis on reducing this mass as much as possible.

When replacing springs for a motorcycle, there is a measurement referred to as the “spring weight”.  The larger this number, the more force is required to compress the spring, meaning the spring feels “stiffer”.

The other factor in motorcycle springs is the preload adjuster.  Preload, is as it sounds.  It is the amount of extra load placed on the spring before the motorcycle hits a bump.  When you increase the preload, you are compressing the spring and taking it away from its state of rest.  Because of this, increasing the preload, increases the upward force the spring provides when the motorcycle suspension is at rest.  As you may have guessed, the mass of the motorcycle and rider (excluding the unsprung mass) also loads the motorcycle suspension, compressing the springs.  If the springs are compressed too much when the bike is at rest, it will not be able to adequately deal with any bumps you come across when riding.  Motorcycle designers can pick a spring weight suitable for the mass of the bike, but as they do not know the mass of the rider, they cannot be 100% accurate in their choice of springs.  Therefore, preload adjustment is used to fine-tune the suspension.

As per usual, this article is based upon my observations and my understanding of the laws of physics.  If I have made an error, please feel free to leave a comment.

Motorcycle Suspension (Part 1)

Motorcycle suspension has a variety of roles to play.  While rider comfort is one of the roles, the most important role is actually keeping the tyres in contact with the ground surface.  As the ground surface is rarely perfectly smooth, this means wheels need to travel “up and down” relative to the rest of the motorcycle to stay in contact with the surface.  This comes back to the laws of inertia.  The bike with its mass and velocity will not “track” to the bumps and so the suspension alters the distance between the road and the bike’s sprung mass.

After my own spectacularly underwhelming career as a motorcycle racer, my interest in motor-sport (and in particular motorcycle road-racing) has remained.  Club level racing is a great way of witnessing the enormous difference in talent from the A-graders down to the “also rans”.    I have attended club-days as a spectator and they provide an insight that watching top-level competition does not provide. 

One such revelation was the difference between suspension that has been set up well, and suspension that has not.  The event that stands out in my mind was at Victoria’s Broadford circuit.  At the end of the front straight was a particularly bumpy entry into turn one.  The riders would be braking heavily for Turn one, across a series of “ripples” that had formed in the track.  Watching the bikes at either end of the field (i.e. the fastest riders and the slowest riders) revealed vastly different “behaviour” from the bikes:  The fastest bikes were smooth and composed across the bumps.  The slowest, jumped and skipped across the bumps.  If you watched the two and were asked which ones looked faster, you would have probably guessed the wrong way around.  Put simply, the slowest riders were trying far harder to control their bikes, whilst the fastest riders didn’t look to be expending hardly any effort at all! 

There is obviously more to being good at motorcycle racing than having decent suspension, but the difference was striking.  Bad suspension fails to keep in contact with the road surface.  A wheel in the air, has no grip.   Good suspension also relays the “feel” of the road surface through to the rider.  The feedback given allows a rider the ability to judge the grip levels available.

Motorcycle suspension has an extra limitation applied to it, that cars do not have:  Motorcycles lean.  If you hit a 25mm high bump (approximately one inch) when travelling in a straight line, the suspension needs to compress 25mm to avoid the bump being transferred through to the rest of the motorcycle.  Once the motorcycle leans over, compressing the suspension changes both the vertical distance between bike and ground, as well as the horizontal distance. 

Amy O'Mara from 2008 ASC Round at Qld Raceway

By recalling year nine trigonometry, we see that if you hit a 25mm bump at a 45 degree lean angle, the suspension now has to travel 29.4 mm.  Increase the lean angle to 50 degrees (from vertical), and the distance the suspension needs to travel increases to 33.6 mm.  (And you used to complain that you’d never use the stuff you learnt in maths in real life!)

On a lot of roads, the notion of a bump only being 25mm high is laughable.  In the real world, motorcycle suspension does not prevent some of the bump being transferred to the rest of the motorcycle.   Some transference is necessary or else the rider cannot feel what the bike is doing.  Bump (or “shock”) absorption occurs not only through the motorcycle suspension, but through the flexing of the tyres and indeed the motorcycle chassis.  If I recall correctly, in the early 90s, a lot of race bike manufacturers would make their frames with as little “flex” as possible in an attempt to improve the handling of their machines.  They reasoned that such an approach worked for car racing.  However, they found that some chassis flex (in certain directions) actually improved the handling of their bikes. 

In terms of components used for motorcycle suspension there are some fairly common approaches and a few that are less common.  Most modern sports-bikes consist of two front telescopic forks with internal springs controlling the front wheel and a single rear shock absorber with an external spring, controlling the rear wheel.  This is a fairly-standard evolutionary design, but by no means the only one.  Like most aspects of motorcycle design, this system is a compromise and alternative systems offer alternative advantages and disadvantages.  But that is a story for another time.

Uphill vs. Downhill.

 

For most motorcyclists, enjoyment is somewhat limited by straight roads.  As such, motorcyclists head for where the roads aren’t straight.  Predominantly this means riding in the hills and mountains where road engineers are forced somewhat by the constraints of nature and have to design roads with corners.  If I had some background in psychology I could probably derive a hypothesis as to why riding on windy roads is more fun than a straight line, but it is suffice to say “it just is”.

The nature of mountain roads is that they change elevation and as such you are either going uphill or downhill.  I am sure there will be exceptions, but most motorcyclists prefer going uphill.  Here are my ideas as to why:

Uphill helps prevent too much speed. Corners can only be taken at a set speed.  This speed will vary on many factors including (but not limited to) grip levels, rider ability, corner radius, motorcycle design etc.  What happens if you enter a corner too fast?  Well… apart from an involuntary clenching of certain muscles one of two things are likely to happen.  Either you slow down, or you crash.  If you’re lucky you can substitute “crash” for “run wide” and then hope that “run wide” does not entail “meet on-coming vehicle” or “visit the scenery”.  Slowing down mid-corner is problematic.  It’s not impossible, but it is made more difficult by the fact that tyres are already closer to their maximum grip level due to forces at work in cornering. (Think of centrifugal acceleration)  When going uphill, gravity is your cautious friend.  It’s always working with you to slow the bike down.  When going downhill, gravity is more like the bad influence that used to get you in trouble when you were in school.  It’s there saying “yeah, go faster!”

Going uphill gives the bike a rearward weight bias.  As seen in Biking 101 Turning Corners, the rear wheel helps you go around corners.  Whilst the front wheel changes your direction, it is the gyroscopic forces acting upon the rear wheel that keep you turning through the corner.  Gentle mid-corner acceleration can be used to aid weight transference to the rear wheel.  It works whilst going downhill too, but it takes more acceleration to get the same effect, so you’re left in an awkward situation…  Remember the point above:  “Corners can only be taken at a set speed”. You really don’t want to be increasing this at a rapid rate when going downhill…  While I know and understand the theory behind the weight transference, I simply don’t think it is what I try and achieve when down-hilling.  Rather, the weight transference stays on the front, loading the smaller and more easily varied gyroscopic effect.  It is a lot of stress to be putting on the front tyre, but it is the same for all riders so you just have to put up with it.

Uphill corners have a natural positive camber.  Camber is the term used to describe the “banking” of the corner.  Where the outside of the corner is higher than the inside, the corner is described as having “positive camber”.  Look at a cycling velodrome, or a NASAR oval for an extreme version of a positively cambered corner.

A badly drawn image of a banked corner

Positive cambering makes people feel like heroes, because they allow for higher corner speeds.  The centrifugal acceleration that is attempting to fling you wide on the corner is partially negated by the ground.  Put another way, it’s pushing you onto the road, meaning you will be gripping it better.  Also, the lean angle (relative to the banked surface) will be less than if you are on a flat corner.  This generally means you have a bigger contact patch on the ground – again meaning more grip.  Unfortunately, there are such things as negatively cambered corners too.  Because they are banked away from the apex, they have the exact opposite affect: You have lower grip, greater lean angles, lower speed and less self admiration of your hero status.

A simple corner can be described in terms of “corner entrance, apex and exit points”.  For the purpose of this discussion, the most critical factor for a positively cambered corner is that the exit point is higher than the apex.  Conversely, a negative camber has its exit point lower than the apex.

If the road is level looking left to right, going uphill will make the road “act” like it has a positive camber.  Due to the uphill slope, the exit point will be higher than the apex.   Coming downhill has the aspects of negative camber.  The corner exit is lower than the apex. 

So, that is my explanation of why motorcyclists never tell you they are better going downhill, than up.  

Biking 101: Decelerating

So far we’ve covered going faster and we’ve covered going around corners.  The last essential ingredient is of course, stopping (or just slowing down).  Motorcycles use two separate hydraulic braking systems which operate independently of each other and (for most cases) affect one wheel each.  The front brake is controlled by a hand-lever on the right hand side whilst the rear wheel is controlled by a pedal activated by the rider’s right foot. 

Ironically, my current motorcycle (a Honda VFR 800) uses a system that sends a differing proportion of the braking force to both wheels when using either the brake lever or pedal.  It does this in an attempt to make braking a safer venture than it may normally be in the hands of an unskilled operator.  The weight transference (towards the front of the motorcycle) that occurs when braking, adversely affects the amount of braking force that can carried out effectively by each wheel.  Some figures suggest in dry conditions as much as 90% of the braking force can be delivered via the front wheel.  The “linked brakes” of the VFR are Honda’s solution to removing this judgement from the rider.

When you look at the contact patch that the front wheel has on the ground, you begin to realise that there is a lot of momentum being shed through a very small area.  Motorcycle training will teach riders that they need to “set up” their braking: transferring weight progressively to the front and thereby compressing the suspension and tyre gently.  As this weight transfer occurs, the tyre is flattened out on the ground, increasing the size of the contact patch.  This in turn allows more force to be applied in a controlled manner. 

There is a theory in physics known as the “Conservation of Energy”.  It states that “energy can neither be created nor destroyed. – It can only be converted from one form to another”.  A motorcycle, or indeed any mass when moving is said to have “kinetic energy”.  The faster it goes, the more kinetic energy it has.  Therefore, stopping a motorcycle reduces the amount of kinetic energy the bike has.  But, because of the “conservation of energy”, we know that this energy hasn’t been lost.  What has happened to it?  Chiefly, it has been converted into heat energy.  – That’s what brakes do, they turn kinetic energy into heat energy.  This heat energy is then dissipated through both the air and the braking components, thus doing its own little bit to help keep the planet warm…

Now the astute amongst you may be thinking along the lines of “it takes a lot of power to accelerate a motorcycle quickly, how can I generate the strength required to stop it as quickly, simply by squeezing the brake lever?”  If this thought has crossed your mind: Well done!  It shows you’ve been paying attention…  The answer lies in the fact that you are utilising a hydraulic brake system.  In cars and some top-end motorcycles featuring ABS systems, the brakes include a mechanical/electrical system to increase the force you can apply to the brakes yourself.  I’m not going to go into how these systems work, rather, I’ll stick to a plain-vanilla style brake set up found on most “conventional” motorcycles.

Hydraulics work on the principal that you can’t compress liquid.  In our case this liquid is brake fluid.  At the lever (or pedal) end, moving the level pushes a piston, which in turn pushes the liquid through the brake line(s).  At the other end of the brake line is the “brake caliper” which contains one or more pistons of its own.  With nowhere else for the liquid to go, these pistons are now displaced too, which pushes the brake pad onto the brake disk.  The disk is attached to the wheel, and so is rotating, whereas the pads and caliper are fixed.  When the disk and pads come into contact, there is friction which converts the kinetic energy into heat energy and “voilà!” you are slowing down!  (Hopefully slowing fast enough to avoid a sudden impact with the scenery…)

This still doesn’t explain how you manage to provide enough force for the brake pads to grip the disk with the necessary bite to stop.  Well, the really cool thing about hydraulics is known as “Hydraulic Multiplication”.  If you change the size of the piston at one end, you can increase the force this piston pushes with.  If this sounds too good to be true, it isn’t…  Although you are gaining more force, the distance you are moving the piston at the other end is reduced.  Fortunately for us, we don’t have to move the brake pads very far to make them grip the disk.  For a more in depth look at how hydraulics work, you may want to look at the brilliant “How stuff works” page.

Biking 101: Accelerating

One of the amazing performance aspects of a sports motorbike is its ability to accelerate.  Standard 1/4 mile times and 0-100kph / 62mph times are staggering and leave all but the most exotic supercars lying in their wake.  Getting these sorts of figures is a test of courage as much as clutch / throttle control, but the potential is there if you possess the right qualities. 

Unlike turning corners, accelerating doesn’t require any seemingly counter-intuitive input from the rider.  Having said that, there are some interesting points to make about acceleration*.   Under hard acceleration, the rear suspension of a motorbike becomes less compliantNewtonian physics states that an object at rest is inclined to stay at rest until a force acts upon it.  This is quite observable in everyday life – you can feel a weight transference when a vehicle begins to move.  This is because initially, this weight is at rest and until the energy is transferred to it, it will continue to remain at rest.  On any vehicle with sufficiently compliant suspension, this will cause the vehicle to “squat” at the rear when accelerating.   However, after an initial compression of the rear suspension, the motorbike appears to “stiffen up”.  Even though there is more suspension travel to be had, it becomes harder for it to use.  Here’s my explanation of this:

A chain driven motorcycle has a small amount of slack in the chain.  This slack is necessary, as the distance between the two sprockets changes as the swingarm moves up and down.  – This is because the front (drive) sprocket is not located at the pivot point for the swing-arm.  At rest, gravity ensures that this slack is present on both sides of the chain.

Image showing the slack in a chain

When accelerating, the chain is pulled through by the drive sprocket.  Due to the tendency of the rear wheel to remain at rest, this pulls the top part of the chain taut. 

Tensioning of chain 

The harder you accelerate, the greater the difference in inertia of the two sprockets.  As a result, the distance between the top of the sprockets is minimised.  This is achieved with the aid of the weight transference and the suspension squats.  Once this shortest distance has been achieved, further suspension travel requires the distance between the tops of the sprockets to be extended again.  It’s not that this can’t occur, it is just an additional force that needs to be overcome.  Any let-up in this force will see the suspension return to the state where the tops of sprockets are minimally spaced.  As such, under hard acceleration, the rear suspension becomes distinctly non-compliant.

The second point to make about hard acceleration is the tendency for the bike to “wheelie”(or “wheel-stand” if you prefer to sound like a boffin).  In its simplest explanation, this is just a characteristic of a large weight transference to the rear of the bike.  Normally, the speed of the sprockets at their outer radius is the same.  If you can increase the speed of the front sprocket such that it exceeds the rear, then the front sprocket will “climb the chain”.  This can be demonstrated with two pens and a rubber band:

  1. Place the rubber band around the two pens to represent the chain and sprockets of the bike.  Keep the rubber band under enough tension, to ensure it grips the pens.
  2. Hold one pen in your right hand on the surface of a desk.
  3. Twist the pen in your left hand anti-clockwise (or counter-clockwise if you live in the US!)
  4. If you’re holding the right hand pen still, the left hand pen will “climb” in a clockwise direction around the right-hand pen.

This characteristic also holds true in shaft drive motorcycles, but the right-angle gearing makes it more difficult to demonstrate with mere office stationery.

Modern sports-bikes and drag bikes run longer swingarms than older bikes.  This helps prevent the bike from wheel-standing, for the same reason that a fat kid needs to sit closer to the middle of a see-saw to balance a light kid on the other end.  That is, the amount of torque required to lift the front of the motorbike becomes greater, the longer the swing-arm.  If you don’t have offspring of wildly differing weights (or a see-saw) you can try my second desktop experiment.  For this one, you will need a ruler and a smallish weight.
1. Place the ruler on the desk, such that one end extends 5cm (2 inches) past the edge of the desk.
2. Place your weight on the opposite end of the ruler.
3. Now push down gently, on the end of the ruler that sits over the edge of the desk.
4. Move the weight closer to the edge of the desk, and repeat step 3.

You will note that as the weight gets closer to the pivot point, it becomes easier to lift. (By now, I expect most of you are going “well duh!”).  It’s this same idea that makes the longer swingarm a less wheelie-prone bike.  Like every element of design, there is a compromise that must be reached – as swingarm length increases, suspension performance is reduced as is the turning ability of the bike.  But that’s a story for another day.
* Like my previous entry on cornering, what I state here is based on my observations and my understanding of physics.  Please feel free to leave a comment if you think my statements are not correct.

Biking 101: Turning corners

Believe it or not, riding a motorbike and knowing how one turns are two different things.  Professional rider training organisations will introduce you to the concept of “counter-steering” and some may even attempt to explain how this phenomenon works, but, you don’t have to understand it to ride a bike.  Here’s the briefest summary I can give you on what counter-steering is:

If you want to turn left, you turn the front wheel to the right. 
If you want to turn right, you turn the front wheel to the left.

After you’ve read that, I think you’ll understand why the technique is called “counter-steering”.  What’s more is, it actually works!  Here’s my attempt at something between a layman’s explanation and the physics nerd’s explanation.  The explanation given is based off my understanding and what I’ve observed first hand.  I promise I won’t go close to using mathematics in my explanation!

The gyroscopic effect of the turning wheels is what holds a motorcycle up once it is moving at any sort of speed.  (Say around 20kph / 12mph).  The two wheels on the bike have different roles to play.  If we discount the effect of suspension travel, the rear wheel remains with its axis fixed relative to the rest of the motorcycle, whilst the front wheel allows its axis to pivot left and right (when viewed from the rider’s perspective). 

The rear wheel is responsible for keeping the motorcycle moving in the same direction of travel.  The front wheel is responsible for changing this direction of travel.

Lets look at the rear wheel effect first:
If you spin a gyroscope where the top of the wheel is not centred above the bottom, it will maintain this angle, providing the gyroscope does not lose momentum.  Given the freedom of being able to move, it will circle in the direction matching the side the top leans to.  Therefore, once a motorcycle is leaning, it will move in an arc in the direction of the lean. 

Figure 1: Trajectory of leaning wheel 

Once the rear wheel is spinning with a fair degree of velocity, the weight of the rider and motorcycle become insignificant compared to the gyroscopic effect of the rear wheel.  Although you can use your body-weight to lean the motorcycle into a corner, it’s a slow and arduous process unless you can influence the direction the front wheel is pointing.

Here’s where the front wheel comes in:
Forcefully altering a gyroscope’s orientation will cause it to behave in strange ways.  This is best demonstrated with a loose pushbike wheel.  Spin the wheel up whilst holding the ends of the axle. 

A badly drawn arrow indicating a spinning wheel

Push the left end of the axle “forward” and pull the right end toward you.

Oh look, now there are dodgy green arrows as well! 

You will feel the wheel “react” to this movement and the wheel will lean to the left. 

Dodgy red arrow removed to make blue arrow easier to spot

The easiest way to return the wheel to the vertical plane, is to reverse the action you just did.  That is: pull the left hand toward you and push away with the right.

Putting it all together:
With our increased understanding of what is going on, we’re ready to “hit the road”.  (That should be taken as a “figure of speech”, rather than a “literal interpretation”)

  1. Travelling forward on the bike we push the left handlebar away from us.  As explained above, this will cause the front wheel to lean to the left.  The rest of the motorcycle will follow, resulting in both wheels now leaning to the left.
  2. We stop pushing the left handlebar, allowing it to resume a “neutral” position.  It requires some force on our part to remain at this current lean angle, as the gyroscopic effect of the front wheel will now make it “want to” turn in more.
  3. Because the wheels are leaning, the bike travels in an arc.
  4. Once the joy of turning left has worn thin, we need to stand the bike back up.  So, we reverse the process and push the right handlebar forward.

And that’s the simplified version of turning corners on a bike!  I will leave “turning right” as “an exercise for the reader”. 

Some points in closing:

  • I’ve heard it claimed that the Wright brothers (as in the bicycle makers who forgot that push-bikes weren’t meant to fly) noted that you counter-steer bikes.  Later observations (such as “look, my brother is flying”) seem to occupy most text that you see written on the duo.
  • Whilst counter-steering works for push-bikes, the relative weight of the rider compared with the bike means it is much harder to observe the effect.  Body weight / balance play a bigger role.
  • Rider training will teach you to push  the bars, not pull  on the opposite bar.*  I believe this is taught to stop you gripping the bars too tightly.  A loose relaxed grip with your hands is a safer way to ride.
  • Throttle control also plays a large part to how well you can ride around a corner, but that is a story for another day. 

* Personally, I find it easier to feel the gyroscopic effect of the front wheel by pulling on the bars, probably because my arms are tense when doing so.  From changing between the two techniques, I find pushing the bars easier to control.