Railroad tracks.
The standard railroad gauge (distance between the rails) is 4 feet, 8.5 inches. Why?
Because that's the way they built them in England.
Why did the English build them like that?
Because they used the same tools that they used for building wagons, which used that wheel spacing.
Why did the wagons have that particular wheel spacing?
Because that was the spacing of the wheel ruts on the roads in England & if they tried to use any other spacing, the wagon wheels would break.
So who built those old rutted roads?
Imperial Rome built the first long distance roads for their legions.
The roads have been used ever since.
Roman chariots formed the initial ruts, which everyone else had to match for fear of destroying their wagon wheels.
Since the chariots were made for Imperial Rome, they were all alike in the matter of wheel spacing. Therefore the standard railroad gauge of 4 feet, 8.5 inches is derived from the original specifications for an Imperial Roman war chariot.
The chariots were made just wide enough to accommodate the rear ends of two horses.
So the next time you are handed a specification/procedure/process and wonder 'What horse's ass came up with it?', you may be exactly right.
Now, a twist to the story :
When you see a Space Shuttle sitting on its launch pad, there are two big booster rockets attached to the sides of the main fuel tank. These SRB's are made at a factory in Utah. The Engineers who designed the SRB's would have preferred to make them bigger, but they had to be shipped by train. The railroad line from the factory runs through a tunnel in the mountains, and the SRB's had to fit through that tunnel. The tunnel is slightly wider than the railroad track, and the railroad track, as you now know, is about as wide as two horses' behinds.
So, a major Space Shuttle design feature, of what is arguably the world's most advanced transportation system, was determined over two thousand years ago by the width of a horse's ass.
Gives one a new perspective of a horse's ass.
Thursday, February 4, 2010
Steering geometry
Tricycle steering geometry - introduction
Correct steering geometry is particularly important for human-powered vehicles, because if tyres scrub as you turn, the energy wasted can significantly slow you down. It can also end up being expensive in tyres! The design method often used to minimise this effect is also useful for lightweight electric or solar vehicles - in fact, pretty much any multitrack vehicle.
There are several aspects to steering design:
* First, you need to make sure the steering linkage turns the wheels at the correct angle when you go round corners: this is Ackermann steering geometry.
* Then, you may wish to minimise bump and brake steer by using what is known as centrepoint steering or zero scrub radius geometry, usually achieved by kingpin inclination (side-to-side).
* Also, for stability and a 'self-centring' effect, the front wheels must employ some 'caster effect' or 'trail'. This is usually achieved by inclining the kingpins fore-aft.
* Finally, there are a few other considerations, such as the type of handlebars to be employed, and some quick notes about detail design
In more detail:
Ackermann steering geometry
When a trike or quad goes round a corner, it turns around a point along the line of its rear axle. As the diagram shows, this means that the two front wheels will have to turn through slightly different angles so that they are also guiding the vehicle round this point, and not 'fighting' the turn by scrubbing. As the diagram below shows, the inside wheel turns through a greater angle than the outer.
Ackermann steering diagram
Ackermann geometry is simply steering which achieves this, keeping each front wheel at the correct angle, through the whole range of the steering motion.
Even with perfect Ackermann steering, there will still be some scrub, because of dynamic effects (the trike tries to go straight on, the tyres push it round the corner, so it tends to understeer). Some builders 'tweak' the Ackermann model to take account of this, usually by arranging that the wheels remain more close to parallel than exact Ackermann would suggest. Having said that, pure Ackermann works pretty well - and it doesn't have to be perfect.
Centrepoint steering
Look at most recumbent trikes from the front and you'll notice that the kingpins slope outwards, like this:
Centrepoint steering pic Centrepoint steering pic Images courtesy of ICE via the Trikes CD-ROM.
The idea is that the kingpin axis meets the ground at or near the contact point of the tyre - the so-called 'centre point'. The rather crudely-drawn red line on the diagram shows this.
Then if the wheel hits a bump, the forces from this impact will be in line with the turning axis, so no torque can be exerted which might jerk the steering. Also, if just one of the front wheels is braked, or the two front wheels are braked unevenly, the forces should again all pass through the kingpin axes and not affect the steering.
The kingpin inclination which is used to achieve this should be kept to a minimum to keep the steering from becoming heavy: the greater the angle, the more steering motion needs to lift the weight of the trike as you turn. Most builders keep the kingpin inclination to around say 15 degrees, preferably less.
Many designs have the kingpin axis hit the ground a little in from the exact centre of the tyre contact point: this gives a certain amount of 'road feel'. Others put the intersection of kingpin axis and ground outside the tyre contact point in an effort to reduce or eliminate brake steer.
Commercial manufacturers have done a lot of work refining their steering: some have virtually eliminated brake steer, and use separate braking systems for each front wheel, each one controlled by one of the rider's hands. Lack of brake steer makes this a practical arrangement, as the handling is relatively unaffected when braking with just one hand, such as when indicating.
Others link the front brakes using hydraulics, careful adjustment or mechanical linkages to balance the braking between the two front wheels, and controlling both front brakes from a single lever. Centrepoint steering is less critically important in this arrangement.
Caster, trail
Just like a two-wheeler, a trike's steering needs to self-centre if it's to handle well, and especially to be stable at speed. And just as on a two-wheeler, this is usually achieved by inclining the steering axis (the steerer tube on a bike).
Caster pic Caster pic Images courtesy of Greenspeed via the Trikes CD-ROM.
Clearly, this inclination is in a plane at right angles to the centrepoint steering inclination we've just mentioned: that is an angle seen as viewed from the front of the trike: the caster angle is as viewed from the side.
Around 10-14 degrees of kingpin caster inclination seems to work OK on most designs.
Caster effect can also be achieved with no kingpin inclination, offsetting the axle mounting points from the kingpin axis instead. Read up about 'trail' at, for example, Sheldon Brown's splendid website if you're interested. But most commercial trikes seem to just mount the axle right on the kingpin axis.
Other considerations
* There are various possible linkages which can be used to connect the two front wheels in a way which will give correct Ackermann - and also any number of ways by which you can connect the handlebars. Some possibilities are shown at Rick Horwitz' website. Use whichever seems appropriate for your design - but bear in mind that only certain of them are fully modelled in these spreadsheets - see later.
*
How 'twitchy' or 'slow' the steering feels largely depends on the 'steering ratio': how far the wheels turn relative to the handlebar movement. This is determined by the width of the bars, linkage (or direct connection) between the bars and the linkage between the two front wheels.
Ideally, in the middle of the steering motion (when you're going in a straight line) the steering should be relatively insensitive, for ease of control at speed. So a degree of handlebar movement has only a small effect on the steering.
But towards the extremes of the steering motion, which would only be used for low-speed manoeuvring, handlebar movement may as well make a big difference to steering direction.
In this way you can make the best use of available handlebar movement, which will be limited by space available.
In any case, wider bars will always make for more stable steering.
* The minimum diameter for an axle supported at one end only seems to be 12mm of hardened steel. Some MTB hubs have 12mm axles and bearings already: another possibility which avoids excessive machining is to use hubs with 20mm thru-axles, as used on some MTB suspension forks, or wheelchair hubs. Sturmey-Archer now make a rather neat quick-release drum brake one-sided hub for wheelchair use, which would also do fine on a trike.
*
Toe-in or toe-out is usually not necessary for human-powered vehicles: usually all either achieves is to slow you down and scrub your tyres away. Having said that, some users of various commercial designs have found beneficial effects on handling at speed.
To measure toe-in or toe-out (also known as tracking) you can simply use a tape measure from rim to rim at front and back - for zero toe-in the distances should be equal. Various other methods are also possible of course.
Sometimes a little toe-in or toe-out is recommended so that as any slack/flex in the steering is taken up by the rolling resistance and rider's weight, the wheels come perfectly parallel. Definitely worth doing if your linkage is a bit sloppy.
*
It's occasionally suggested that the wheels be tilted out at the bottom (known as camber): the idea is that the outside wheel is then better able to withstand cornering forces, and the wider track will also enhance stability.
However, almost all commercial machines and the vast majority of home-builts just have the wheels vertical: this seems strongest and simplest all round. Tilted wheels are weaker; kingpin design becomes harder if you want zero scrub radius steering, and tyres wear on the sides rather than on the usually thicker top.
Steering home -- Next: the spreadsheets
Correct steering geometry is particularly important for human-powered vehicles, because if tyres scrub as you turn, the energy wasted can significantly slow you down. It can also end up being expensive in tyres! The design method often used to minimise this effect is also useful for lightweight electric or solar vehicles - in fact, pretty much any multitrack vehicle.
There are several aspects to steering design:
* First, you need to make sure the steering linkage turns the wheels at the correct angle when you go round corners: this is Ackermann steering geometry.
* Then, you may wish to minimise bump and brake steer by using what is known as centrepoint steering or zero scrub radius geometry, usually achieved by kingpin inclination (side-to-side).
* Also, for stability and a 'self-centring' effect, the front wheels must employ some 'caster effect' or 'trail'. This is usually achieved by inclining the kingpins fore-aft.
* Finally, there are a few other considerations, such as the type of handlebars to be employed, and some quick notes about detail design
In more detail:
Ackermann steering geometry
When a trike or quad goes round a corner, it turns around a point along the line of its rear axle. As the diagram shows, this means that the two front wheels will have to turn through slightly different angles so that they are also guiding the vehicle round this point, and not 'fighting' the turn by scrubbing. As the diagram below shows, the inside wheel turns through a greater angle than the outer.
Ackermann steering diagram
Ackermann geometry is simply steering which achieves this, keeping each front wheel at the correct angle, through the whole range of the steering motion.
Even with perfect Ackermann steering, there will still be some scrub, because of dynamic effects (the trike tries to go straight on, the tyres push it round the corner, so it tends to understeer). Some builders 'tweak' the Ackermann model to take account of this, usually by arranging that the wheels remain more close to parallel than exact Ackermann would suggest. Having said that, pure Ackermann works pretty well - and it doesn't have to be perfect.
Centrepoint steering
Look at most recumbent trikes from the front and you'll notice that the kingpins slope outwards, like this:
Centrepoint steering pic Centrepoint steering pic Images courtesy of ICE via the Trikes CD-ROM.
The idea is that the kingpin axis meets the ground at or near the contact point of the tyre - the so-called 'centre point'. The rather crudely-drawn red line on the diagram shows this.
Then if the wheel hits a bump, the forces from this impact will be in line with the turning axis, so no torque can be exerted which might jerk the steering. Also, if just one of the front wheels is braked, or the two front wheels are braked unevenly, the forces should again all pass through the kingpin axes and not affect the steering.
The kingpin inclination which is used to achieve this should be kept to a minimum to keep the steering from becoming heavy: the greater the angle, the more steering motion needs to lift the weight of the trike as you turn. Most builders keep the kingpin inclination to around say 15 degrees, preferably less.
Many designs have the kingpin axis hit the ground a little in from the exact centre of the tyre contact point: this gives a certain amount of 'road feel'. Others put the intersection of kingpin axis and ground outside the tyre contact point in an effort to reduce or eliminate brake steer.
Commercial manufacturers have done a lot of work refining their steering: some have virtually eliminated brake steer, and use separate braking systems for each front wheel, each one controlled by one of the rider's hands. Lack of brake steer makes this a practical arrangement, as the handling is relatively unaffected when braking with just one hand, such as when indicating.
Others link the front brakes using hydraulics, careful adjustment or mechanical linkages to balance the braking between the two front wheels, and controlling both front brakes from a single lever. Centrepoint steering is less critically important in this arrangement.
Caster, trail
Just like a two-wheeler, a trike's steering needs to self-centre if it's to handle well, and especially to be stable at speed. And just as on a two-wheeler, this is usually achieved by inclining the steering axis (the steerer tube on a bike).
Caster pic Caster pic Images courtesy of Greenspeed via the Trikes CD-ROM.
Clearly, this inclination is in a plane at right angles to the centrepoint steering inclination we've just mentioned: that is an angle seen as viewed from the front of the trike: the caster angle is as viewed from the side.
Around 10-14 degrees of kingpin caster inclination seems to work OK on most designs.
Caster effect can also be achieved with no kingpin inclination, offsetting the axle mounting points from the kingpin axis instead. Read up about 'trail' at, for example, Sheldon Brown's splendid website if you're interested. But most commercial trikes seem to just mount the axle right on the kingpin axis.
Other considerations
* There are various possible linkages which can be used to connect the two front wheels in a way which will give correct Ackermann - and also any number of ways by which you can connect the handlebars. Some possibilities are shown at Rick Horwitz' website. Use whichever seems appropriate for your design - but bear in mind that only certain of them are fully modelled in these spreadsheets - see later.
*
How 'twitchy' or 'slow' the steering feels largely depends on the 'steering ratio': how far the wheels turn relative to the handlebar movement. This is determined by the width of the bars, linkage (or direct connection) between the bars and the linkage between the two front wheels.
Ideally, in the middle of the steering motion (when you're going in a straight line) the steering should be relatively insensitive, for ease of control at speed. So a degree of handlebar movement has only a small effect on the steering.
But towards the extremes of the steering motion, which would only be used for low-speed manoeuvring, handlebar movement may as well make a big difference to steering direction.
In this way you can make the best use of available handlebar movement, which will be limited by space available.
In any case, wider bars will always make for more stable steering.
* The minimum diameter for an axle supported at one end only seems to be 12mm of hardened steel. Some MTB hubs have 12mm axles and bearings already: another possibility which avoids excessive machining is to use hubs with 20mm thru-axles, as used on some MTB suspension forks, or wheelchair hubs. Sturmey-Archer now make a rather neat quick-release drum brake one-sided hub for wheelchair use, which would also do fine on a trike.
*
Toe-in or toe-out is usually not necessary for human-powered vehicles: usually all either achieves is to slow you down and scrub your tyres away. Having said that, some users of various commercial designs have found beneficial effects on handling at speed.
To measure toe-in or toe-out (also known as tracking) you can simply use a tape measure from rim to rim at front and back - for zero toe-in the distances should be equal. Various other methods are also possible of course.
Sometimes a little toe-in or toe-out is recommended so that as any slack/flex in the steering is taken up by the rolling resistance and rider's weight, the wheels come perfectly parallel. Definitely worth doing if your linkage is a bit sloppy.
*
It's occasionally suggested that the wheels be tilted out at the bottom (known as camber): the idea is that the outside wheel is then better able to withstand cornering forces, and the wider track will also enhance stability.
However, almost all commercial machines and the vast majority of home-builts just have the wheels vertical: this seems strongest and simplest all round. Tilted wheels are weaker; kingpin design becomes harder if you want zero scrub radius steering, and tyres wear on the sides rather than on the usually thicker top.
Steering home -- Next: the spreadsheets
Subscribe to:
Posts (Atom)