Looking at Moments for a moment

We've recently been investigating the benefits of different steel sections for our frame parts. Rectangular and square box section are easy to come by and have flat faces which can simplify assembly. The question is - would they be any more or less rigid?

To answer this we modelled some comparative parts on a CAD system, whilst not a definitive answer it did produce some results of interest.

Stiffness or Rigidity
For some sections the best orientation to maximise stiffness is obvious just from looking at a shape. In the example below the part can be expected to be stiffer in scenario A than in scenario B.

It is possible to visualise that the same force applied to the same material but in different orientations, will produce more or less deflection.

It is possible to visualise that the same force applied to the same material but in different orientations, will produce more or less deflection.

In this case the difference was clear, but we can use the maths behind this difference and apply it to more complex shapes. The property calculated to define this stiffness is the "Moment of Inertia" also known as the "Second Moment of Area". This mathematical value explains why the flat piece of material is more flexible in one direction than the other.

The samples.
In this simple deflection modelling exercise a round tube and a square box section were created. Both were made of standard 1023 steel, had a wall thickness of 3.5mm and the test pieces were to be 800mm long.
The box section had an outside dimension of 25mm and an inside dimension of 18mm.
To make a fair comparison the round tube also had a wall thickness of 3.5mm and the overall diameter was drawn to give the same section area as the box section.

To maximise the box section stiffness in the direction of the load, it was modelled rotated at 45° to the normal axis. The table below details the parts.

Results.
The moment of inertia of the round tube was calculated to be 26024mm^4
The moment of inertia of the box section under a vertical load was 23804mm^4
This would suggest the round tube as more stiff as it had a higher second moment of area.

The simulation provided the following output.

Round tube deflection 3.199mm
Square box deflection 3.499mm

Conclusion
Although the round tube was marginally stiffer that the box section there was very little to differentiate the two. However one possible upside of the round tube would be that the stiffness would be the same in every orientation, whereas you could expect the square tube to be less stiff with a load applied perpendicular to a face. In fact a quick recalculation of the deflection of the square tube with the force perpendicular to a face, showed and increase in deflection of 42% which was equal to 7mm.

When we design our bikes we always consider simulation data like this to look out for any unexpected weaknesses. Of course nothing can replace a road test on a prototype bike, but being analytical doesn't hurt (especially when the computer's doing the hard work for you).

Fatigue.............................yawn

Fatigue failure of a material is always a concern to design engineers because it is difficult to calculate for a given part and therefore presents an unknown risk in the final product. Factors that affect fatigue strength include the material, shape of the part, any defects, corrosion, heat treatment and loading.

Fatigue is defined as "the progressive and localised structural damage of a material subjected to cyclic loading", but within this definition there are two types of fatigue to consider.

High cycle fatigue.
This is the repeated cyclic loading of a part inside the material's elastic limit. Typical cycles to failure would be 100,000 or more. A good example is a bicycle spoke which undergoes tensile and compressive loads for each wheel revolution.
Low cycle fatigue.
This describes events which stress a part beyond its elastic limit, causing plastic deformation. The bending of a bicycle fork after an impact could be an example of this and after such an event the remaining strength of the part is reduced.

In the bicycle world components are almost entirely operating in the high cycle fatigue arena under normal riding / loading conditions.

SN Curves
Fatigue performance of a metal sample can be tested in the lab to produce an S-N curve.
S = stress. N=number of cycles. A graph for an aluminium sample is shown below

SN curve for a Brittle Aluminium sample Note : Stress is in Mpa (mega Pascals : where 1 Pascal is 1 Newton per square metre)

SN curve for a Brittle Aluminium sample
Note : Stress is in Mpa (mega Pascals : where 1 Pascal is 1 Newton per square metre)

Fatigue testing of this type is usually stopped after 1.0xE07 cycles, at which point the lowest point on the graph is used to define the "fatigue limit" or "fatigue strength" of the material. The graph shows how the material can be used under higher stress applications, but only if the cyclic loadings are kept low enough. Point A on the graph shows that the part can withstand a 260Mpa cyclic loading but only for 100 cycles. Point B shows the same part can take 10,000 cycles before failure, but only if the load is kept below 120Mpa.

Interestingly (to me at least) the Steel SN curve will typically reach a point where the curve ceases to decline. This implies an infinite fatigue strength if this loading is not exceeded.

Comparison of Steel and Aluminium SN curves Note how the steel curve ceases to decline below 300Mpa

Comparison of Steel and Aluminium SN curves
Note how the steel curve ceases to decline below 300Mpa

The reality is that any metal will likely fail given unlimited test cycles, but we can still state that by designing a part to operate below the fatigue limit, we will have the best performance from the chosen material. In the graph above using the steel part in an application not exceeding 300Mpa should result is an (almost) infinite life for the component. This is one of the reasons we favour Steel for the construction of our cargo lugging bikes.

Product design is another area where designers can make a difference to fatigue performance. Sharp corners on parts create stress concentrations. Famously the handsome de Havilland Comet suffered several crashes in 1954 and this was eventually traced to fatigue fractures propagating from the corners of the windows. Today, all passenger jets have oval windows as a consequence.

Finally a rule of thumb to bypass some of this theory. Fatigue strength in a steel part is typically half the ultimate tensile strength. So by specifying materials and designing parts so that they are operating at less than 50% of their tensile strength; we can be confident the part will have robust fatigue performance in service.

Taking of fatigue; this text is likely sending you to sleep, suffice to say we know what Fatigue is here at Rodford and how dangerous it can be, so we take all possible steps to design it out of our products.

Now have yourself a coffee.

An old school Chain Tensioner?

Many of our hub geared bikes favour the use of a chain tensioner but comments from observers indicate that some people think this an unnecessary complication. What can we say about this?

First of all, there is the fact that we have chosen vertical slots for our custom drop outs. This ensures that the back wheel is nicely centred in the mudguard wrap and allows the easiest removal of the wheel from the bike. However it also means tension cannot be set by moving the wheel.

A horizontal drop out would be a simple solution. It would allow the chain tension to be set manually without the need for a tensioner, but removing the wheel could be an issue depending on the tyre size and mudguard clearance. The more the wheel is moved back the worse the mudguard clearance can get until a link has to be removed from the chain and the wheel moved forward again. Moving the wheel can affect brake adjustment too.

An alternative is to set the tension at the bottom bracket end of the drive using an eccentric bottom bracket. This is a neat solution and allows the wheel location to remain consistent when the chain is tensioned. A classic single gear chain line is maintained, however setting tension needs bespoke tools and bottom brackets can seize.

Eccentric bottom bracket bush

Eccentric bottom bracket bush

Ultimately, the downside of all these ideas is the requirement for the owner to spend time adjusting the chain periodically to keep it running sweet. Chains will always stretch and the only solution that provides automatic adjustment is a sprung chain tensioner. A self adjusting chain of this nature gives the longest service intervals which is desirable on a family transport bike and essential on a working delivery bike. Many of our courier and delivery bikes are ridden all hours by multiple riders. Maintenance is seldom conducted unless a part has failed so it is not expected that chain tension would be monitored and adjusted in this usage model.

Looking at various transport around the world there are other examples where self tensioning is used for ultimate reliability. A typical car cam chain has a spring tensioner and this gives huge service intervals up to 80,000 miles by which time the car engine may have done over 14 billion revolutions. It also provides peace of mind and reduced maintenance for the owner.
Self tensioning is also seen on overhead Catenary wires for trams and trains. The tension is applied using weights but the same advantage of self adjustment, reliability and (in this case) temperature compensation can been seen.

Typical Catenary wire tensioning system.

Typical Catenary wire tensioning system.

When you buy a Rodford bike you buy reliability and that's why a simple chain tensioner can often be seen keeping our bikes running at their best.

Aerodynamics. Why it matters (and why it doesn't).

Aerodynamics is a heavily debated subject in all transport systems, but why is it so important?

One reason is that aerodynamic drag increases massively as speed increases. Roughly speaking it can be viewed as a "Cube Law". A cubed number is a number multiplied by itself twice. For example 2 cubed = 8. or in longhand 2x2x2=8.
This means that when you double your speed, you require 8 times the power because you are experiencing 8 times the wind resistance. This is evident when you ride a motorcycle. Sitting behind the bars of a motorcycle you can feel the wind pressure against you at 30mph. Double your speed to 60mph, and you'll not feel twice that force, but 8 times the wind pressure pushing you back. This annoying aspect of physics is what limits every transport medium known to man (with the exception of space travel).

The increase in wind resistance becomes more evident the faster you go. For example the fast Bugatti Veyron can drive at 250mph and for this it needs 1180hp to push through the air. However a fairly decent Aston Martin with 552hp will top 200mph. So the Bugatti has to have twice the power to gain the (comparatively modest) extra 50mph.
The same is evident when you look at fuel consumption. Despite the Bugatti's superb aerodynamics, it exhausts its 26 gallon fuel tank in 12 minutes at top speed. At 250mph the car will cover 50 miles in this time, but this is a shameful 2 miles per gallon. Impressive though the Bugatti is, it has to process a huge amount of fuel in a short time to attain its speed and the majority of this fuel is used to overcome air resistance.
So aerodynamics affect efficiency in a big way and getting it right provides the best output from the power available.

An aerodynamic car.

An aerodynamic car.

Applying this to bicycles we are considering lower speeds, but also a more modest power source; so just how important are aerodynamics?

Well this depends who you speak to.

A time trial rider will say it is important - and they'd be right. These riders are aware of the energy increase needed to overcome any aerodynamic drag so they will wear a streamlined hat, have aerofoil shaped tubing and will make their body frontal area as small as possible. All of this is important because at speed approximately 90% of the rider's effort is used to overcome drag.
Ironically the faster these riders go, the harder they have to work to maintain this speed, because even a slight increase in speed will produce a much more noticeable increase in drag.
It is also worth noting that the rider on a bicycle accounts for 65% to 80% of the frontal area, so tucking down to ride may give much more benefit than fitting narrower tyres, but it all helps. Competitive riders use everything possible to eek that extra performance from their ride. The aero shaped tubing used on racing bikes is not so much about reducing frontal area, but more about reducing the drag behind the tube caused by the swirling air. The diagram below shows a typical efficiency gain for a given tube diameter.

A tear-drop shape who's length is 4 times its width makes for an efficient shape in moving air. A shape like this has 1/10 the drag of a round tube with the same frontal area.

A tear-drop shape who's length is 4 times its width makes for an efficient shape in moving air.
A shape like this has 1/10 the drag of a round tube with the same frontal area.

And what about Cargo bikes?

Aerodynamics are less important here, although not totally irrelevant. Cargo bikes are typically moving slower and therefore experience less wind resistance due to movement; but it is true that their larger front area will make any speed increase or head wind more noticeable. However expecting a cargo bike to be streamlined is not altogether fair. It is like comparing a sports car with a truck. The truck has less performance but excels in other areas.
There are other options to overcoming wind resistance too. If the aerodynamics cannot be improved for practical reasons lower gears can help keep a box bike moving into a head wind and of course electric assist** can be a huge help to the rider of a loaded bike. A case of working round a problem rather than addressing it head on. As a side benefit - these modifications also help with hills of course.

Air resistance is the enemy of the performance seeking rider in the world of competition; but with transport bikes we must draw a compromise with other considerations. So we can't promise your cargo bike won't make you work a little harder in that head wind, but just swivel your cap round, tuck your head down and enjoy the ride.

**E-assist coming to Rodford bikes soon.

Lumens, lux and luminous flux. Eh?

Here is a short text on measurement and characterisation of light to help when selecting a bulb or lighting system for a bicycle. This is bit scientific but might be good background detail to have in mind when comparing various lighting systems.
The most important point when choosing a light is how bright it is and this will be determined by the power of the light source. However; the focus of the light and likewise the distance to the subject being illuminated affect lamp intensity on the target.

How bright is a light?
Light output is called "Luminous flux" and it is measured in Lumens. This characteristic is also sometimes called radiance since it describes the brightness of the light at source and therefore the light output. In a given system, this number is governed by the power supply and the lamp design and can be considered a constant. A lamp with a higher Lumens number will therefore be brighter.

But this is not the whole story because how the light is focused can make a huge difference to the lamp performance.

It stands to reason that the more you focus the light onto a given spot the brighter that spot will become; so the light appears to get brighter but of course the bulb is still giving out the same amount of light (Lumens), it is the distribution that is different.
To quantify the focused light performance, a different term called Luminous intensity is used, measured in Candelas. If we imagine a focused light beam in the shape of a narrow cone, the Candela number will tell you the intensity of light in that cone. The narrower the angle, the higher the Candela for a given light source. This fact means that Candela numbers are the same regardless of distance to the light source.

Candela. The amount of light at position A is the same as Position B and is governed by the angle of the focused cone.

Candela. The amount of light at position A is the same as Position B and is governed by the angle of the focused cone.

Decreasing the distance to the subject has a similar effect to reducing the angle, because as you move the subject towards the light source, the area illuminated by the light becomes smaller and so subject appears brighter. The quantification of this characteristic is called LUX. Lux is the measurement of actual light available at a given distance. One lux equals one lumen incident per square meter of illuminated surface area, in other words : Lux = Lumens/square meter.

If we agree that the lumens from a particular light source are fixed, then we can see from the formula that the Lux increases as the area is decreased. Halve the area where the light falls and you get double the Lux on the target. This is the reason a single bulb might be enough to illuminate a small bedroom, but inadequate in a factory warehouse; the increase in area on the factory floor makes the Lux value much lower, even though the Lumens are the same.

B is further from the source than A. The cone of light means more dispersal further away and so B appears dimmer even though it has the same area.

B is further from the source than A. The cone of light means more dispersal further away and so B appears dimmer even though it has the same area.

The difference between Lux and Candela is that lux measures the illumination of a surface, instead of that of an angle. The result is that the distance to the surface becomes an important factor: the more distant the surface is from the light source, the less well it is illuminated.

Yawn - How can we sumerise this?

Let's get back to something we understand - bicycles.

When selecting a lighting system more Lumens means more light which is a good thing. More Candela is also preferable but be aware that this might just be because the light is more focused rather than brighter. This may be what you want or you may prefer more of a floodlight which will have a lower Candela. Lux is a less useful number in a mobile application because the distance to the target will vary and may not be known like it is in a static scenario. However it could be considered a guide to how visible a rider is from their light since it indicates how bright the light appears at a distance.

Hopefully all this helps rather than hinders.
Of course how visible an object is when illuminated depends on it's reflectance, absorption, scatter, refraction and some other factors, but let's leave that for another time.
Cup of tea anyone?

Drum Brakes! Really?

Bicycle brake systems can be disc, drum, roller or rim. There are hydraulic and cable versions too.
Rodford bikes are often fitted with drum brakes and people have questioned their suitability.
Here we set out to describe the benefits and drawbacks of some of the available systems and the considerations you should make when choosing brakes.

Rim brakes
Rim brakes are the simplest and oldest brake system. The components are lightweight and because they work on the wheel rim there is little stress in the fork or in the spokes.
The downside is that they wear the rim particularly in off road applications and their effectiveness is affected by changing weather conditions.
However their simplicity makes them good for long distance touring in remote places and their light weight makes them a favourite on racing bikes. They are easy to inspect, easy to adjust and easy to get parts for.

Disc brakes are the most modern system available.
Discs are very powerful and because they are located near the wheel hub they are less affected by mud and road debris and negate rim wear concerns entirely. Styling wise disc brakes are the most sporty and they allow a painted rim to be used on the wheel. Discs give a reassuringly firm braking effect in most conditions although initial braking effort can still be affected by heavy rain.
One downside of their power is that a stronger fork and wheel assembly is needed to cope with the loads. This produces a weight penalty for the bike but it also makes discs particularly suited to fast, off-road, downhill riding where weight doesn't matter and is overshadowed by the need for effective braking.
Another known downside is the torque reaction against the front wheel axle. The location of the caliper behind the fork leg means it produces a torque reaction which tends to pull the axle out of its drop out; this risk is increased with quick release wheels. The solution is lawyer lips on the drop outs or a non-vertical drop out slot, plus a bolted on wheel to reduce the likelihood of the wheel coming out.

Disc Brake torque reaction. Note how caliper becomes the fulcrum for the axle movement.

Disc Brake torque reaction. Note how caliper becomes the fulcrum for the axle movement.

Disc brakes are a nice system for a fast cyclo-cross bike and essential on a modern downhill mountain bike.

Drum brakes.
Drum brakes have the lowest maintenance of all the systems.
They are not as simple as caliper brakes but they are unaffected by weather conditions and are very long lived between service intervals.
Drums also don't have the axle lifting issue of discs systems, but still give the benefit of zero rim wear.
The drums ability to dissipate heat is its limitation and a long mountain decent may produce brake fade, but for city riding and commuting they are ideal.
We've had a 70mm Sturmey-Archer dynamo hub brake on long term test nearly 10 years. In that time the bike has covered 10,000 miles with almost no maintenance. The only issue was a squeaking caused by brake dust in the drum. The drum was removed and wiped clean to return it to good working order. Drum brakes rarely need adjustment and wear of the friction surface is the lowest of all the systems available.
Drum brakes work well in the cities and towns, on the daily commute, and they provide a low maintenance solution for transport bikes.

Our 10,000 mile SA Dyno Hub.

Our 10,000 mile SA Dyno Hub.

Bottom Bracket Height

In cargo bike design a lower bottom bracket is favourable. It gives a lower step over and a lower centre of gravity; but the ground clearance is also reduced, most notably the pedal clearance when cornering.
So what is the ideal bottom bracket height and how does is relate to pedal strike angle?

It is obvious that pedal strike is most likely to occur with the widest pedals, lowest bottom bracket height and longest crank set. If we know what these parameters are, then it is easy to work out the maximum lean angle before the pedal will touch the ground. Referring to the sketch above, a formula like this should do it............

This seems over complicated but it is one way to work out pedal strike angle before buying components.
If the bike is on hand it is easier to measure the distance from the pedal tip to the frame centreline, let's call that "pedal Offset" (L) and the distance from the pedal underside (with the pedal at its lowest position) to the ground with the bike upright (H).
Then use the sum arcTan(H/L)

The graph below shows how the bottom bracket height affects maximum cornering angle before pedal strike, for a given crank length and pedal offset.

Very approximately this graph shows that lowering the bottom bracket 10mm reduces the pedal strike angle by 2.5°.

The next questions is - What sort of lean angle would we expect a rider to use in normal riding?
This is difficult one to answer and depends on many factors, mostly the rider's style of riding. However we should be able to estimate some boundaries.
Mathematically any more lean than 45° is unlikely and this would be from the most aggressive riders.
A sedate City rider might only lean 25°.
Here at Rodford we are using the formulae and these numbers as a guide to design bikes which are low and easy to ride, but which still have the ground clearance for every day riding.

 


 

Gears without the tears

A bike can have anything from 1 gear to 27 or more.
One gear is OK if you are a sporty rider, have a light bike and don't live in the mountains.
But with transport bikes, we expect riders will want mudguards, a light system, probably a rack and will want to cycle with maximum efficiency to avoid arriving in a sweat.

For carrying cargo too, gears are your best friend and enable more efficient use of the rider's energy whatever the terrain or load.

How to measure gears.
Bicycle gearing can be measured in gear inches. The easiest way to understand this unit is to think of an Ordinary cycle (sometimes called a penny-farthing). These bikes had one large wheel fixed to the pedals; the larger the driven wheel, then the higher the possible speed, but with the downside that it would be more difficult to climb a gradient. The diameter of these wheels was measured in inches. Modern bikes have chains and sprockets which avoids the need for such a large wheel, but the diameter of a "theoretical" wheel can still be used to indicate the overall gear ratio and compare systems.

So what ratio is normal?
Single speed riders typically run with 55 or 57 gear inches.
A modern mountain bike with triple front chain wheel might get you a gear spread of 21 to 110 gear inches.

The chart below shows a selection of gear systems and what spread of gears you get with a 26" wheel.

Although the number of gears on a bicycle is defined by the gearbox; changing the chain and sprocket ratios moves the gear range.
For example, the Sturmey Archer S3X can be configured to give a range of 30 to 48 gear inches; or 48 to 76 gear inches, depending on the chosen chain set.
However be aware that this also changes the gear spread. In the first case gear spread is 18" from lowest to highest ratio, but with the larger front sprocket the same gearbox gives a spread of 28". So choosing a faster gear set also increases the size of the steps between the gears. Wheel diameter also affects the gear spread as it affects the final drive ratio. A small wheeled bike with a large front sprocket may have the same gear spread as a 26" wheeled bike with smaller front chain ring.

Hubs and dérailleurs.
Dérailleur gear systems are very efficient and give the greatest number of ratios. However a bike with 27 dérailleur gears will have some overlap in the system and gears 9 and 19 are not recommended for use because of the extreme chain line. Looking at the chart this leaves 20 discrete gears for the rider to use. This is still a huge number of gears but the other quirk of this system is that they are not sequential so the rider may have to sweep through the gears to find a comfortable cadence. Of course a dérailleur system with only one front chain ring gives a good compromise of a decent spread of gears, but in a sequential pattern.

Hub gears can have anything from 2 to 14 speeds. They are always sequential and can be designed to give even steps between ratios in terms of a percentage increase/decrease from the neighbouring ratios. The Rohloff hub has 13.6% difference between each gear. This means as you go into the higher gears the steps as measured in gear inches get wider apart; but the percentage change remains constant and as a rider this is known to be more comfortable.

Come and talk to us if you need help choosing the best gear system for your needs. It will depend on the bike wheel diameter, overall gear spread required and number of gears needed. We work with both dérailleur and hub systems including the Nu-Vinci variable transmission.

Brakes, forks and braking forks......

Forks are one of the most critical parts on a bicycle. They are responsible for bike steering and therefore balance of the bike and they also define the handling in terms of rake and trail.
In use they are responsible for the majority of the braking effort as well as taking a share of the rider weight and cargo. Forks are constantly subjected to high cycle fatigue loads due to road undulations and vibrations; as well as low cycle impact events such as potholes and kerb bumps.
All of this means they have to withstand significant forces during use.

Recent years have seen the introduction of new braking systems for bicycles particularly disc based systems, but there are also hydraulic rim brakes, drum and roller brakes, as well as traditional rim caliper and vee brakes.
Different brake systems put different levels of stress on the forks and so here at Rodford we decided to employed some basic physics and some computer modelling to ensure our forks were up to the task.

Disc brakes.
Bicycle disc brakes originated from the mountain bike community where a suspension fork is typically used, this being much thicker and stiffer than a road or urban bike fork. For the mountain bike a disc brake is an obvious choice because the fork is already strong enough and the environment these bikes are used in can rapidly wear wheel rims.
However combining a disc brake with a conventional fork requires a degree of care.

First of all the braking forces for a given rate of deceleration are different between rim and hub based brake systems. By simple fact that the wheel diameter gives the bike momentum (mass x velocity) leverage over the smaller brake rotor diameter. Even a small 20" wheel as fitted to our Sherpa Box Bike can increase the load on the fork by 2.5x for a given braking effort.

Things are further stressed by the fact that the rim brake force is distributed through both legs, whereas the hub brake load is applied to one fork leg resulting in a twisting load at the fork crown. Finally the stress is multiplied a third time because the rim brakes operate near the fork crown whereas the hub brake is at the end of the fork leg giving additional leverage and further amplifying the force applied.

A simple computer simulation provided an insight in to the total forces expected with a hub braked system.

The model was configured to simulate three loads for a given braking effort.
1) An increased share of the rider weight pushing down during braking due to weight transfer
2) A rearward force on the axle as the momentum of the bike pushes against the braking effort.
3) The multiplied braking force itself acting on one fork leg.

The results were quite surprising.
The rim brake fork showed hardly any noticeable stress at the fork crown with a value of 0.7Mpa (mega Pascals).
The disc brake by contrast had all the loading on one fork and as such there was some twisting hurting the axle a little; but more surprising was the fact that the stress up at the fork top was 21Mpa. A whopping 30 times higher.

That was our conclusion.
Consequently our Rodford plate crown fork has been design to operate safely under these amplified loads; suitable for use with disc, drum, rim or roller brakes.

Stress in the workshop.

Building a safe bike is our top priority. Some things are straightforward such as fitting efficient brakes and choosing good tyres. However, being sure a frame and fork design is strong enough to survive a lifetime of hauling cargo, takes a little more thought.

With this in mind; we've used some computer wizardry to measure stresses and deflections of our box bike frame.
We took our CAD model and applied some forces to simulate some cargo and the rider weight. In this case a rider weight of 130Kgs as a point load on the seat post and an Uniformly distributed Load (UDL) of 70Kgs along the load area.
Finally we placed reaction (supporting) loads to represent both axles.

The computer did the maths to indicate expected deflection of the frame and also highlight any stress concentrations. This process (known as the Von-Missers stress) takes the ultimate tensile stress of the material and shows where that stress might be exceeded. Simple and clear.

The results were good. Our step over cross bar was shown to take some strain from the bottom bracket and bracing at the front end was keeping things in check. Of course none of this simulation is a substitute for empirical testing, but it is an indication that we are on the right track.

stress-bw-coloured-screen2.jpg


More on Geometry and Handling

Our box bike frame and has 50mm of trail to give the best handling under all conditions.
However 50mm trail can be achieved in a number of ways.
The sketches below show various front end geometries. They all have 50mm of trail but all look very different and would handle very differently.

The parameter that makes these forks handle differently is "wheel flop".
Mathematically Wheel flop = Trail x Sine Headstock angle x Cosine headstock angle

Practically what this means is that as the steering on a bike is moved left and right the front end of the bike will rise and fall slightly. This is true for any bike that has some trail. This change is height gets more exaggerated for shallower head stock angles. So a bike with 50mm of trail but a 60° headstock angle will still have large amounts of wheel flop.

With our cargo bikes, wheel flop is more noticeable with the bike loaded. Extra weight on the front wheel makes it more difficult to "lift" the steering to find the straight ahead position. This makes the steering feel heavy and causes the bike to "fall in" on corners.
For this reason our box bikes have a steep head tube angle and low trail to strike the best compromise between loaded and unloaded handling.
 

Forks, Angles, Rake 'n' Trail

Forks, trail and rake are hot topics in the world of cycle construction.
Each parameter is affected by the other, and by mixing them up you can produce either a fine handling machine or something with a mind of its own.

As far as road and touring bikes are concerned all of this 'art' is well defined and makers have their preferences and know what works; but here in the cargo arena things are a little less conventional.
With our box bike design, it was therefore necessary to go back to the theory, run some experiments and gather feedback on what worked best.
Also unique to the cargo bike is that fact that significant load is carried by the front wheel. Unlike solo machines there is no risk of clash between the front wheel and the rider's feet and shock to the handlebars is also less of a problem.

Other considerations were the brake type to be used. Discs provide strong progressive braking but require a stiffer/stronger fork because of the increased loads and the fact that only one fork is taking the braking force.
In fact we ran some calculations on comparative braking forces and found that the calliper could exert up to 30 times the load on a fork leg when compared to a standard rim brake.

So what should our fork trail be?
Experiments were used to determine a trail that would produce a decent handling bike and one which was not too affected by increased loads on the front wheel.

Something worth knowing is that a given trail can be achieved with a straight fork and with no rake, just by getting the correct headstock angle. The graph below shows the relationship between the headstock angle and the resulting trail using a 20" front wheel. Obviously with no angle, there is no trail and much beyond 50 degrees things start to look pretty ridiculous (but don't tell the custom bike boys we said so).
In our case a headstock angle of 78.69 degrees would give 50mm of trail for a straight leg fork.

In reality we decided to add some fork rake to increase clearance between the frame and wheel to allow for mudguard fitment.
We also designed a plate crown fork that should provide the strength we need under braking and under heavy loads.

Out on the road forks have to resist high cycle and low cycle fatigue.
High cycle fatigue is the constant small vibrations, braking forces and steering forces that the bike frequently takes. Low cycle fatigue is the less frequent impact loads such as pot holes, kerbs and incidents involving careless motorists.

Our box bike fork is designed to be strong enough and responsive enough for a light steering effort and predictable handling.