i am gerard thomas bycycle dynamics

The abbreviated guide to bicycle dynamics

15 May 2023

Reading Time: 18 minutes

Why?

For better or worse, marketing departments managed to get their hands involved in telling people how bikes worked, meaning there has been an ever growing tide of misinformation about how and why bikes do what they do.

While very occasionally there is a major breakthrough that does actually change the way things work and the way you ride, for the most part the endless renewal is just an aid to sell people something ‘new’, not improved. Naturally things have been refined over time, with performance being increased at small, incremental rates, but ‘groundbreaking‘, ‘huge impact‘ and ‘change the way you ride‘ is 95% of the time just plain old marketing hype. Suspension Mountain Bikes are the prime victim of this hype. While the number of suspension systems continues to increase, with much of the afore mentioned claims attached, the reality is that true and innovative changes are few and far between. While advances in shocks have continued to make steady progress, to the point that they now are on par with the actual suspensions systems themselves (so now they can work together as a true single unit), there are still only a handful of suspensions systems that truly stand the test of time; the rest of them being an excuse to try and sell you something; usually replaced the following year with something else that of course is ‘newer and better’.

Note: My objective here is to provide information that allows you to familiarise yourself with the dynamics of your bike. While I could go into the minute details and complex equations of all the parameters, forces and dynamics that are applied to your bike as you ride it around, and probably loose many people in the process, I have tried to simplify everything as much as possible, keeping to the most relevant information. Naturally by doing this I will not talk about all the factors that make up the dynamics, so if you are familiar with this subject, please do not email me telling I’ve missed this or that – I know what I have omitted for the purposes of simplicity. I have also referenced key texts on the subject, listed on the last page, as well as at the beginning of key topics. If you are so inclined, track them down and have a read for the full and detailed explanation. I can assure you, after you do, you will not take your bike for granted again!

 

The fundamentals…
(or why I stopped complaining and accepted a really crappy design scenario)

The truth is that a suspended mountain bike is just a terribly underpowered motorcycle meant to take a hammering, yet still remaining light enough to be pushed around all day. The engine (you) is an unbalanced, underpowered, two cylinder engine directly connected to the drive sprocket (the cranks), with no counter balance (to offset the balance issue) and a gear box that mostly hangs out the back, at the wrong end of the chain!

To amplify issues, suspension is added into the mix but due to the need to be light and allow for the somewhat unusual need for the suspension to cancel out the wildly mashing pistons, it can neither be sized accordingly nor valved for maximum efficiency to do what it’s supposed to do well. Yet despite this, all the same dynamics that govern motorcycles (that do not suffer these unique issues) govern our mountain bike. The identical principles that keep a motorcycle upright, reactions under braking or applied power, and the effects of geometry, are all the same. All that changes are how the scales of weight, velocity and power are applied.

It is truly remarkable that mountain bikes perform as well as they do and for the most part, it’s a testament to the design and engineering efforts of all those working in the industry today.

 

What keeps you upright?

Reference the following for more details:

Motorcycle Chassis Design: Reference pages 33-43

How and why: Motorcycle Design and Terminology: Chapter 3

Motorcycle Tuning: Chassis: Chapter 1 Bicycles & Tricycles: Chapter XVII

Fundamentally larger two wheeled vehicles (ie. motorcycles) stay upright due to the simple principles of gyroscopic effect. As they move faster, the wheels create greater and greater gyroscopic forces which in turn keeps the bike under the rider staying upright. This effect is determined by speed (velocity) but under the ‘velocity threshold’ (approx 4ft/second for the pointy heads out there), it is diminished until it becomes more of a combination of rider balance, skill and bike setup (geometry, centere of gravity etc. discussed below) that ultimately keeps the bike upright.

In the case of bicycles, the gyroscopic forces created by the wheels are not enough alone to keep the bike upright, as the mass of the rider + the frame etc. (not including the wheels) far outweigh the wheels themselves. But here’s the cool bit….

Once past the velocity threshold where the wheels are creating a sufficient gyroscopic force (even though that force may not be enough to balance the bicycle), the bike and the rider are subjected to an effect called ‘gyroscopic precession‘ which occurs when the wheels, read the gyroscopes, are affected by a tilting or turning force.

Put in simplest terms, when vertical and in motion, tilting the axle to the left (like when you are banking into a turn) will cause the wheel to pull strongly to the left but if you apply a turning force from the left (like being shoved by an invisible hand… or steering through the bars), the wheel will bank to the right. Yup, at speed, steering to the left makes the bike pull to the right. But what keeps the bike upright when shunted to the left? While the gyroscopic progression tilts the bike to the right, it creates an arc (through the front wheel) that both you and the bike will travel on. A centrifugal force (which is created by spinning a mass, you in this case, makes a force that pushes said mass away from the centre of the arc) is then created which wants to throw you to the left, thus the two forces balance one another out and upright you stay. This is called the ‘righting effect’. You can feel these forces by holding the front wheel of your bike by the axle and having a friend spin it away from you. By tilting and turning the wheel while its spinning you will feel the different forces that act upon it.

 

Steering and not falling over:

So how then do you get a bike to turn, if we know that when we turn the bars to the left, the bike wants to pull to the right and ultimately stay upright?

This is where a secondary factor comes into to play – the centrifugal force of the wheels plus the bike+rider.

So the gyroscopic progression, created by the spinning wheels aids in keeping the bike upright, and by turning the bars to the left, we cause the wheel to pull to the right (an effect called ‘counter steer’, which is used to initiate a turn); this we know.

We also know that by initiating the turn to the right, the centrifugal forces want to throw both you and the bike to the left and in doing so a balance is achieved and the bike ultimately wants to stay upright. To break this then, we push harder to the left which causes you and the bike to tilt more to the right. But as you do this and the centrifugal forces continue creating a force that pulls you left, a thing called gravity now wants to pull to to the ground.

What happens next is called the equilibrium of lean (where centrifugal and gravitational forces balance), and around the corner you go… all without falling over.

At a certain point though, the ground forces on the tyre begin to pull the tyre to the right, which is felt as a pull to the right through the bars. If you go with it, the turn tightens, if you leave it, your arc stays the same and if you push against it, you start to straighten up.

So to sum it all up, past a certain speed, you initiate a turn by counter steering. Once into the turn and at a certain point that is felt as a pull on the bars in the direction of the turn, you can steer the bike normally, turning to the right tightens the turn to the right while turning to the left straightens you up.

 

Trail

Have a look at your forks, you’ll notice two things:

1: The dropouts place the axle in front of the forks.

2: The crown actually offsets the fork legs from the centreline of the headtube.

All up, the forks are forward of the headtube by ‘x’ amount and this is all done to create what’s known as ‘trail’.

In simplest terms, trail is the horizontal distance of the front axle from the angle of the headtube, where it intersects the ground; and is the complete distance created by the combination of rake/head angle and wheel offset (distance of the axle from the fork leg). While a simple measurement, trail affects the straight line stability of the bike by creating an angle between the contact patch of the tyre and the direction of travel, a factor known as the ‘slip angle’.

Slip angle works like so: When turning (let’s say to the left), a force is created through the contact patch of the tyre. This force occurs because the axle path lies behind the steering axis (the trail) thus it swings in an arc, creating a friction force against the direction of travel. As we know, for every action there is an equal and opposite reaction, thus a righting force is created on the wheel when the opposite force reacts on the turning wheel – remember our example about what keeps a wheel upright? In the most simplest terms (and believe us, we have boiled this right down!), the amount of trail determines the automatic righting effect of the front wheel when subjected to external forces such as bumps. If the trail is negative, meaning the contact patch is in front of the steering axis, a bump that causes the wheel to deflect to the right will make the bike turn sharply to the right as the righting effect is minimised; in other words the axle is being tilted rather than turned. This is all bad and will make the bike highly unstable in bumpy scenarios. In the case of positive trail, where the trail puts the contact patch behind the axis of steering, the righting effect is increased as the wheel is being turned through the axle rather than ’tilted’. As such the ‘self righting’ effect comes into play causing the wheel to want to remain upright when affected by our external bump force.

So, if a bike is to be stable when the going gets rough, or highly stable on flat trails, there needs to be enough trail t0 provide an element of automatic self righting. Too much trail though will make the bike’s steering sluggish and slow in tight twisty stuff, but to little and it becomes twitchy, fast reacting in tight turns but requiring higher levels of input from the rider to stay upright. Ironically, with telescopic forks, as they compress under braking the trail is automatically reduced and the bike becomes twitchy when you least want it to!

But wait, there’s more!

 

Head tube angle/aka Rake

But the forks are only part of the equation when it comes to creating trail and ultimately stability. Head angle is used to create more or less trail on a bike. The steeper the head angle, the smaller the trail and ultimately, more twitchy the bike. The slacker the head angle, the greater the trail and more stable. Modern long travel forks tend to have more offset than their shorter travel cross country brethren, thus when combined with slacker head angles, create quite slow steering but stable bikes, ideal for heading in the direction of down, fast. Given the same set of forks, you can change the steering and handling characteristics of a bike by altering the rake. This is why we are staring to see adjustable head angles on mountain bikes now, as riders want to be able to tune the way the bike handles based on personal preference or trail conditions. While factors such as changing your position on the bike, playing with geometry, tyre sizes etc. etc. can all affect the way the bike steers and stabilizes, the basic physics still apply and are common to all types and sizes of bikes.

 

Wheelbase

Wheelbase contributes directly to both directional stability and cornering agility. The longer the wheelbase, the more stable a bike is, while the shorter it is, the quicker it will turn into corners but in turn will also be less stable. Cornering reaction slows for a longer wheelbase as the front wheel needs to be turned further to initiate the turn, hence require more rider input. This is due to the fact that a longer wheelbase creates a longer tangent to the arc of the corner. For this same reason, a deflection, such as a bump, has less effect on the straight line stability as, in simple terms, reaction time is slowed. Another attribute of wheelbase is stability under weight transfer forces such as braking and climbing. A longer wheelbase distributes the center of gravity between the front and rear wheels more effectively (ie. evenly), as for the given height of the centre of gravity, the less the weight transfer from front to rear. Of course on a bicycle, the wheelbase equation is a little more complex and is split between two sub measurements, the chainstay to bottom bracket and bottom bracket to front wheel…

 

Chainstay length

Chainstay length is perhaps the most important component of the wheelbase length. Unlike a motorcycle which has a large lump of metal… and ‘stuff’ called the engine, which weighs a good deal, as well as a rider, a bicycle has a single mass – the rider who is also the engine. Correct biomechanics tell us where the rider should generally be positioned for good transfer of the power to the crank and that happens to be behind the bottom bracket (when measured vertically). As such, the centre of gravity (COG) on a bicycle automatically has a rearward bias pushing it towards the chainstays. The direct result of this is that chainstay length is a critical measurement in achieving a good blend of stability, agility and climbing ability. It is also the one geometry measurement that remains constant between different sizes. If the chainstays are too short*, with the natural rearward bias of the COG the bike will ‘pitch’ to the rear, or lift, on steep climbs as the weight transfer is ‘pushed’ to the rear on the incline, it will also pitch heavily forward under braking but be very nimble through corners (this is the common trait of the original San Andreas, which has relatively short stays for the travel the frame can allow). If on the other hand the stays are too long, then the bike will climb and brake ‘flat’ yet be sluggish through corners. Too long or too short will also contribute to straight line stability accordingly as previously mentioned.

*We are not accounting for additional affects such as chain climbing which is an effect of shorter chainstays and pulls the front of the bike up under power ie. is prone to wheelies.

 

Bottom bracket to front wheel

Bicycles come in different sizes to accommodate different sized riders and the two measurements that change accordingly are the seat tube, which raises or lowers the rider and the top tube, which allows for a comfortable reach for the rider to the bars. The bottom bracket (BB) to front wheel (FW) distance is the result of the combined lengths of both the seat and top tubes. As the BB-FW distance varies with the different sizes, it is an inherently compromised measurement when it comes to creating a bike’s geometry, as for each different size the COG shifts slightly and each size will behave a little differently.

In general, if the measurement is too short, it will will place more of the rider’s weight to the rear of the bike, pushing the COG towards the stays, enhancing front wheel lift in climbs; while if it’s too long, the rider might be uncomfortable and feel incapable of of riding the bike effectively, even though it will create a better climbing and more stable bike. Generally the BB-FW distance is a by product of determining the optimum top tube for the given use for the bike. A jump bike will obviously have a very short top tube (TT), due to the style of riding and need to lift the front wheel easily, while an XC bike will have a longer TT to create an effective riding position and overall stability under a number of applications. Ideally, for good all round performance the top tube will be sized to provide comfort in the ‘cockpit’ for the rider, while placing just enough weight over the front wheel to allow for stability while climbing. One can see the complexity of achieving the ideal balance, especially when you consider that a mountain bike might be ridden through a range of very different terrain that all demand something different in terms of handling characteristics. What’s more, the variation in the BB-FW measurement illustrates the need for the chainstays to be ‘dialled’ in order to create a predictable ride characteristic amongst a range of sizes.

 

Effects of braking

Reference the following for more details:

Motorcycle Chassis Design: Reference pages 101-104

How and why: Motorcycle Design and Terminology: Chapter 7 Pg 88-92

When it comes to the world of mountain bikes, the effect of braking is one of the most deliberately confused dynamics, often used to justify suspension designs. There are some simple basics though that can not changed, denied or overcome. The braking equation (way simplified)…

 

Front wheel forces

The division of braking power is generally attributed as a 70/30 split between front and rear. This means under braking, the majority of braking forces will go through the front wheel meaning that the weight shift of a braking bike is heavily forward bias.

This weight transference causes several reactions:

1. The fork dives as the momentum of the weight transfer is absorbed through the compression of the forks, causing the bike to pitch forward. Interestingly, this compression of the forks also steepens the head angle and reduces trail, making the bike more unstable under hard braking – just what you want coming into a hard, rough corner.

2. As the weight shifts forward, the rear suspension ‘unloads’ and automatically extends through the loss of weight derived compression. This also has a side effect of aiding the pitching forward of the bike, further enhancing the weight transference, which ultimately unloads the rear wheel and causing a loss of traction.

3. Through the lifting of the rear and the compression of the forks, the bike actually rotates and squats, lowering the COG.

These three actions are the basic physics of braking and can not be changed without rewriting the laws of physics. Despite claims to the contrary, or the importance placed on rear suspension systems, the single most important factor to the overall performance of a bike under braking come down to the tuning of the fork ,as the fork’s performance is paramount to the countering and balancing the various transfers that occur while braking.

A well tuned fork will aid the bike in remaining more level while still smoothing the trail conditions to allow for an effective cornering action.

 

Rear wheel forces

Reference the following for more details:

Motorcycle Chassis Design: Reference pages 99-100

How and why: Motorcycle Design and Terminology: Chapter 5 Pg 79-82

Rear wheel braking applies a different force to the bike, not to the front but to the rear suspension.

As disc brakes on a mountain bike are connected to the ‘rear triangle’, when they are applied the effect will be the same across the board regardless of the type of rear suspension employed – ie. when applied, the rear brake force causes a degree of suspension compression. This compression occurs because the braking force is opposite to the force of the applied traction. The amount of the force applied is proportional to the angle created between the pivot point (actual or virtual) and the point of traction.

As with the front brake forces, this effect is a direct cause of physics and can not be sufficiently overcome without sacrificing performance in some other area, namely the performance of the rear suspension.

Contrary to some claims, the application of the rear brake does not lock out the suspension, as this is physically impossible. Possibly this myth is derived from the physics of rear wheel braking itself. As discussed, the application of the rear brake can cause some compression of the rear suspension. It is plausible that if the rear shock has not been tuned to the rider and the bike, it could be undersprung, meaning that braking compression uses more of the shock’s stroke than would be normally deemed acceptable, hence making the rear suspension far less pliant over rough ground while under braking and ultimately giving the feeling that the rear suspension has been ‘locked out’. Rear brake suspension compression, when used by an experienced rider can actually aid in taking a bike through a corner in a more level manner. With the bike pitching forward under the front wheel braking forces, the rider can use an amount of rear brake to compress the rear suspension and help level the bike through the turn.

As you can see, a bike is by no means a simple beast and there are many different equations that come into play to create the ideal handling bike. What though can not be overcome, or denied, no matter how smart people/marketeers think they may be, are the core physics of a suspended bike in motion. No matter the size, weight, simplicity or complexity of a frame or a suspension system, physics dictate how a bike will react for a given circumstance. Attempting to overcome these physics will create a compromise, so ultimately any mountain bike that claims to over come this, or that, in this situation or that scenario, will be compromised in another.

So the next time you hear some mountain bike ‘folklore’, or claim, about how something is supposed to work, or not, think about the physics, because physics is a fact Jack and probably the only fact there is.

 

Bicycle construction

Reference the following for more details:

Bicycles & Tricycles: Numerous Chapters

Motorcycle Chassis Design Racer’s Encyclopedia of Metals, Fibers & materials

We are going to put it out there right now. The simplest, lightest and usually strongest bicycle frame design is a double triangle.

Simple engineering tells us that using this design creates the strongest frame possible for the least weight, as a fully triangulated structure is superbly efficient. But, as with many things, when you start adding elements into a simple structure that it was not designed for, it means the structure becomes compromised; hence is the case with a full suspension mountain bike frame.

Where once the bicycle’s frame sole purpose was to connect the head tube, bottom bracket and rear wheel in the stiffest possible manner (and keep the rider’s arse off the ground!), the frame now has to also allow for rear suspension, requiring pivot points as well as mountings for a shock absorber, linkages etc. etc; the simple clean double triangle no longer was going to cut it, at least not without some serious rethinking. Materials and process’ too have changed and while a simple round tube is still the the strongest structural element, we are now able to engineer shapes that can have specific characteristics that achieve more specific functions, ideal for full suspension designs that place unusual demands on what has to be a very light, strong and cost effective structure.

Also playing a part in all of this, like the automotive, the collective cycling industry is now engaged in design ‘aesthetics’. Simple round tubes are no longer enough to woo the customer, who is looking for swoops, curves and graphics, as they do when they buy a new car or motorcycle. But as with everything else these new, and previously un-addressed, design needs have placed more demands on the once simple bicycle frame.

To help you understand the various methods talked up these days, here is a brief run down…

 

Traditional round tube

As mentioned, a traditional round tube is the strongest and lightest of all structures. This is because it resists bending loads in all directions equally. This attribute also allows round tubing to be made lighter as by increasing the diameter of the tube, it becomes stiffer – ideal when using lighter weight materials. While for many designs, a round tube is the best option, their use is limited when it comes to achieving more complex solutions that require minimum joining, where any join is a weak point. Also, ultra light tubes with thin walls do not lend themselves well to even minor forming (bending etc.), meaning that from a design standpoint, the use of traditional tubes strictly limits design flexibility.

 

Shaped tubes

While round tubes deliver equal strength in all axis, basic shaped tubes ie. tubes with a constant cross section, can offer less or more strength for a given axis. The simplest way to think about this would be to think of a rectangular, or ‘box’ section. A box section can be employed to provide a high level stiffness in a single axis of bend via the deep section, while on the narrow section the stiffness can be significantly less. It is not unusual to see shaped and regular tubes used together to achieve a highly efficient design. Another form of shaped tube is where a basic round tube is subjected to a secondary process, such as swaging. In this example, swaging may be employed to modify a round tube where it is desired to create a area of increased stiffness. quite often you will see a round down tube swaged at the bottom bracket to create not only a more complete join but also to increase the stiffness in this specific area. Secondary forming can also be used to give a round tube an element of ‘cost effective’ form to create tubes with a similar, though simpler, to hydroforming…

 

Hydroforming

Hydroforming is a process of creating a formed (metal) tube by way of a mould.

By using a ‘blank tube’, placing it in a mould and injecting a hydraulic fluid to expand the blank, it conforms to the shape of the mould creating a tube with form, allowing for various design details to be created. Primarily a hydorformed tube is the only way to create detailed formed and fluid shapes in aluminium tubes and also offer the designer that ability to engineer shapes that can bear specific loads, or overcome specific spatial problems in an elegant manner. But while there has been a massive adoption of hydroformed tubes, primarily in the goal to create more formed designs, it should be noted that a hydroformed tube may not necessarily be the strongest or the lightest solution. Quite often a hydroformed tube is required to have a thicker wall thickness in order for a desired form to be achieved.

While the ‘blank tube’ can utilise butting in order to lighten the finished tube, it does not mean that the final product is as efficient as a simpler round tube, though it may look much more interesting. Additionally, the cost of tooling for hydroforming is very high, hence the end product will cost more than a similar and potentially stronger traditional design; also as the cost and complexity of tooling is high minor changes are often difficult to achieve. Hydroforming requires careful and extensive engineering and design in order to create lightweight, efficient results. When done right though, the end result will often be near impossible to achieve in any other manner other than through the use of far more expensive carbon fibre forming.

 

Monocoque

A monocoque construction, also known as ‘stressed skin’, is made from a skin of material that is formed to create a shape and can be either formed as a single piece, when using materials like carbon fibre, or by the joining of two clamshells.

The original Mountain Cycle San Andreas is a classic example of a monocoque structure made from two halves and the biggest monocoques employed today are found in the aerospace sector, where most aircraft fuselage are monocoque structures. The key advantage to monocoque design is that a ‘single’ skin can be formed to carry all the loads required, hence can often create a very light and very stiff end product. If we look at the original San Andreas, the head tube, swingarm pivot, bottom bracket and seat pod, are all directly linked to the one single piece, the skin itself bearing all the loads. The big advantages of monocoque design are that the skin can be designed to handle specific loads in specific locations, with the potential to create an undulating cross section from a thin skin. Manufacture can be highly simplified and the accuracy of aligning critical points can be increased. The key downside of a monocoque design is that it is highly unadaptable and minor changes can result in extensive re-tooling. As a result the use of monocoque designs for bicycles has been limited, where there is the need for not only easy manufacturing adjustments but also the requirement for a range of sizes.

 

Carbon fibre

The darling of the hi-tech sector, carbon fibre is in many ways the ultimate engineering material.

Unlike metal forming, where the end product is ultimately dictated by the inherent properties of the material, carbon fibre can be specifically engineered to behave in a predicted and desired way. By using various fabrics, weaves and layup techniques, carbon fibre is perhaps the most flexible of all materials. Additionally, as it starts life as a fabric, it can be formed to adapt to any number of shapes, including simple tubes, monocoque as well as easily replicate hydroformed shapes and forms unachievable with any other material. The drawbacks of the material though are the the base tooling is expensive and complex. The manufacture is slow and requires exacting standards as any introduced impurity, air pocket or misaligned fabric can lead to catastrophic failure. Furthermore, one can not take carbon fibre and copy an existing metal design as it has its own demands and weaknesses, especially when it comes to mating aluminium harpoints such as pivots, head tubes and drop outs.

 

Bibliography

But you don’t have to take our word for it. Below are the key references used in compiling much of this information. Look them up, buy them or hop to your local library and see if they are on the shelf…

Bicycles & Tricycles: An Elementary Treatise on Their Design and Construction, Archibald Sharp The MIT Press ISBN: 0-262-19156-3 / 0-262-69066-7/ 0-262-19156-3

How and Why: Motorcycle Design and Ternimology. Gaetano Cocco in collaboration with Aprilia Motorcycles. Published by Giorgio NADA Editore ISBN: 88-7911-189-2

Motorcycle Chassis Design: the theory and practice. Tony Foale and Vic Willoughby Osprey Publishing ISBN: 0-85045-560-X

Motorcycle Tuning: Chassis John Robinson Heinemann Newnes ISBN: 0-434-91724-9

Racer’s Encyclopedia of Metals, Fibers & materials Forbes Arid Motorbooks International ISBN: 0-87938-916-8

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Copyright 2023 Gerard Thomas. All rights reserved.

I've run mtb events, distributed some legendary brands, ran my own cycling clothing brand, designed bikes and was a GM and head designer for a famous but sadly now extinct mtb marquee; and after 20 odd years I decided riding bikes was more fun than working with them.
Over that time though, I wrote (and some wrote for me) a lot of stuff about bikes, on blogs and the like. Some was good, some, well... not so much. Rather than loose it all when I shut everything down once and for all, I have kept some of my favourite, and more popular pieces here for... prosperity?
I also am working on new pieces as well...

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