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As
the name suggests, this series is about the design and building of a
human-powered vehicle (HPV). In fact, one that’s powered by pedals.
Now
you might ask what such a series is doing in a high performance on-line magazine
devoted to cars. It’s in here because with the exception of the motive power,
many of the decisions were the same as taken when building a one-off car -
perhaps a kit car or one designed for the track.
For
example, the design of the suspension; the decision to use either a monocoque or
stressed tubular space-frame; the weight distribution; brakes; stiffness (in
bending, torsion and roll); measuring and eliminating bump-steer; spring and
damper rates; and so on. I’ve drawn primarily on automotive technology in design
of the machine – in fact it’s been much more about ‘cars’ than ‘bicycles’.
So
if you want stuff on the fundamentals of vehicle design and construction, read
on. Yep, even if this machine is powered by pedals...
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So
what happened? Why the huge delay since the previous part of this series?
There
are two reasons. The first is that the welder who has done all the aluminium TIG
welding on the HPV suddenly got a job at a gold mine in the Tanami desert.
Rather than being available pretty well any evening, he suddenly became
available only every two or three weeks. If that availability coincided with the
deadline for my monthly bag of articles for AutoSpeed, no welding on the trike
could occur.
Secondly,
there was a catastrophic failure in the main frame of the trike. What went wrong
will be covered in detail in the next part of this series but in short, the
development of the HPV ceased until the frame could be repaired and
strengthened.
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HPV Steering
Unlike a cars or motorcycles, the steering of most
HPVs uses vertical rods positioned each side of the seat (indicated as ‘1’ on this photo of the Greenspeed GT3). These rods are connected through a single pivot
(‘2’) below the seat – they’re rather like handlebars of a bike but with their
axis rotated through 90 degrees. Pushing forward on the right-hand side bar
causes the left-side bar to move backwards, and the wheels are steered to the
left. Therefore, steering is very quickly picked-up because it’s much like a
bicycle - even though initially it appears nothing like it!
Tie-rods are used to join the handlebars to the
front wheel steering arms, with a number of different systems used. Some
approaches have long tie-rods that are crossed-over while others use shorter,
direct tie-rods (one is arrowed on this pic of a GT3).
However, and this is a critical point, in HPVs
without long-travel front suspension (ie, nearly all of ‘em!), the design of the
steering is much simpler because no account needs to be taken of bump-steer. So
what’s bump-steer, then?
Bump-Steer
Bump-steer is the term given to unwanted steering
inputs that occur when the suspension moves through its travel. In other words,
when the steering wheel (or in this case, handlebars) are held in a fixed
position, the wheels may still be inadvertently steered as the suspension moves
from full droop to full bump. This undesirable trait occurs if the tie-rods are
moving through different arcs to the wheels’ uprights, so causing the tie-rods
to pull or push on the steering arms. In other words, you go over a bump
(especially when cornering when the loads on the front wheels are unequal) and
the vehicle darts right or left.
For a given suspension, the amount of bump-steer
that occurs is dependent primarily on three things: the position of the inner
steering ball-joint, the position of the outer steering ball-joint, and the
length of the tie-rod. This diagram
[taken from Fundamentals of Vehicle
Dynamics (Gillespie)]
shows the ideal length of the tie rod (here called a
‘relay linkage’) and the correct position of the inner and outer balljoints to
avoid bump-steer in a double wishbone suspension.
In my case, the suspension was by this stage built
and the outer ball-joint position largely fixed. (Well, I thought it was fixed –
as you’ll see later, it had to be moved!) That meant that tuning-out of
bump-steer was to be done by altering the length of the tie-rod and the position
of the inner ball-joint.
But the first task was to precisely measure
bump-steer. To do this, a 1-metre lever (arrowed) was attached to the wheel
upright. The lever protruded forwards, parallel to the ground. A piece of
particle board was then positioned vertically and parallel to the lever. Any
steering of the wheel showed as unequal gaps between the board and the
lever.
A trial tie-rod was then installed and the inner
ball-joint clamped in position. The suspension spring was removed and the frame
jacked off the ground, leaving the wheel hanging on its damper in the full droop
position. The suspension was then lifted to its maximum bump position and the
wheel released. As it slowly sank on its suspension, the ‘steering’ movement of
the wheel lever was assessed.
This simple test gave some stunning results. It
was quite easy to have the location of the inner ball-joint (and/or the length
of the tie-rod) sufficiently wrong that bump-steer over the full suspension
travel of ~100mm was more than 14 degrees! Furthermore, with a fixed tie-rod
length, changing the position of the inner ball-joint by as little as 5mm made a
clearly measurable difference to the amount of bump-steer!
And it’s even more complex than this. With some
combinations of inner ball-joint location and tie-rod length, the amount of
bump-steer changed asymmetrically as the wheel moved from full bump to full
droop. For example, the wheel would initially steer in one direction before
reaching a mid-point and then steering back the other way! Remember, in all
cases the steering ‘wheel’ is being held fixed in the one position...
However, it didn’t take more than a few hours of
experimentation to locate an inner ball-joint position and tie-rod length that
gave bump-steer of only about half of one degree through the full suspension
travel.
Steering
With the position of the inner ball-joints fixed,
the next task was to steer them. This apparently simple task proved to be a
bloody nightmare. It is without a doubt the single hardest mechanical
design-and-build exercise I have ever undertaken.
The rebuild of the BMW six? Easy!
The fitting of a turbocharger to a hybrid Toyota
Prius? A walk in the park!
Stuffing a water/air intercooler and big turbo
under the minuscule bonnet of a Daihatsu Mira? Straightforward!
To give you some idea, developing the steering
system took as long as designing and building the whole of the rest of the
vehicle... suspension and all. So what made the steering system so difficult?
After all, it is only steering...
First, as indicated above, the measurement of
bump-steer had shown that the fore-aft positions of the ball-joints were very
important – so if the ball-joints were moved backwards or forwards as part of
the steering process, bump-steer was likely to re-intrude. And most (all?)
HPVs with indirect steering move the inner ball-joints backwards and forwards as
the machine is steered. (So do cars with steering boxes as opposed to racks –
interesting....)
Second, with the use of vertical handlebars
positioned either side of the seat, the distance that the handlebars can be
moved before they run into things depends a lot on where their pivot point is
located. If the pivot point (green in this diagram which is a plan view) is
offset a long way forwards or backwards, the handlebars will have a lot of
sideways movement, which greatly limits how far they can be moved before fouling
the seat. Of course, even with no pivot offset, the handlebars will still foul
the side of the seat when moved a long way.
Since movement of the handlebars controls the
steer angle from straight-ahead to full lock, the shorter the total distance the
handlebars can move, the greater the sensitivity of the steering. I wanted
slower steering than my Greenspeed GTR, so a short handlebar travel was no good
(ie for the same amount of steering lock I want to move the handlebars further
than the GTR, not less).
Third, the system had to weigh little, and
fourthly, I had to be able to build it! And there’s even more: fifth, the system
had to provide a reasonably tight turning circle; six, had to conform at least
loosely to Ackermann steering principles (see below); seven, had to clear the
chain – the list went on and on.
I designed on paper perhaps 30 different systems;
I built working models of six different systems; I physically built parts of
five steering systems and completed and tested on the road four different
systems.
So what were the problems? One system gave light
and precise steering but the turning circle was too large. To tighten the
turning circle, the wheels had to point through a tighter angle (duh!) but to
achieve that without the tied-rods/steering arms going ‘over centre’ (see below
under Ackermann), the inner ball-joints needed to be moved forward. This
necessitated a complete redesign to prevent bump-steer re-intruding.
The next system had a good turning circle but
because the wheels now turned further for the same amount of steering lever
movement, the steering was much too heavy. In fact it was so heavy that, when
attempting to gain full lock, the steering system components deflected under the
load. This was partly because I was using lighter materials in the steering than
I was generally using in the rest of the HPV (trying to reduce the daily
increase in weight!) but the bending was primarily because the steering loads
were very great. (This is something I never considered. If you’re running lots
of castor and/or steering axis inclination, the forces required to steer the
wheels can be very high.)
The next system connected the two inner
ball-joints to one another via a rod sliding laterally in high density
polypropylene bushes. This allowed the wheels to be steered with the inner ball
joints not moving even a millimetre forwards or backwards – no bump-steer
here!
However, because of the offset design of the
ball-joints, this rod wanted to rotate when the steering loadings were placed on
it, so changing the amount of toe. To prevent the swivelling, I added a second
chrome-plated steel rod in parallel to the first, with both rods passing through
their own set of plastic bushes. But getting the two rods perfectly parallel in
both planes so that they slid sweetly through the bushes was a nightmare. Even
the slightest misalignment (eg 1/10th of a millimetre) dramatically
increased stiction. With this system I could just imagine having zero feedback
through the steering and the inputting of tiny corrections being very difficult.
So that was another system scrapped.
The final system looks like this.
Two side-mounted steering levers are mounted from
the seat frame. The pivot point is low on the lever; close on the other side is
a ball-joint that translates the arc of the lever into a fore-aft movement. This
set-up is mirrored on the other side of the seat. So when the steering lever is
moved back and forth a long way (red arrow), the longitudinal link moves a much
shorter distance (green arrow).
The longitudinal movement of these rods causes a
lever to move sideways (green arrows) as it pivots around a large bearing (blue
circle). In turn this causes the lateral movement of the other end of the lever
(red arrows). The Y-shaped lever is attached to the tie-rods at either end of
the red arrows.
So in summary, the two inner ball-joints are moved
sideways by a 370mm long Y-shaped member that is mounted along the longitudinal
axis of the frame. Each end of the uppers arms of the Y connect to a ball-joint.
The pivot is placed at the other end of the member – down the bottom of the
upright of the Y. This results in a long lever being used to steer the front
ball-joints - minimising (although not eliminating) the fore-aft movement of the
two inner ball-joints as they move laterally. (Click on pic to enlarge it.)
The vertical steering rods – one each side – are
pivoted from the seat frame. They can therefore move fore-aft from a relatively
high pivot point parallel to the seat, which gives a greater steering lever
travel (400mm) than is achievable with a central vertical pivot under the seat.
Incidentally, the Y-piece is shaped in that way
(rather than like a ‘T’) to give clearance to the chain drive.
This steering system gives the following
positives:
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Steering handles have a lot of travel – ie a
slower ratio steering
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The ability to change the leverage ratio manually
by gripping the rods high or low
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The ability to easily change the leverage ratio
during development by having differing mounting points on the lower part of the
steering levers for the push/pull rods
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Conventional ‘one lever moves back as the other
moves forward’ steering, where pushing forward on the left-hand lever and/or
pulling back on the right-hand lever causes the trike to turn
right
And the negatives?
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A slight arc of forward/rear movement of the inner
ball-joints
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Changing Ackermann compensation which complicates
this aspect of design
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The use of 8 ball-joints in the steering
system
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Increased weight over other approaches
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A greater possibility of deflection in the
steering components because of their lengths and the fact some are subject to
bending forces not just compression/tension.
It’s a measure of how difficult I found the
steering system development that I was not at all confident that even this
system would work well until I could test it on the road. So it was with immense
relief that I found it to work very well!
Variable
Ratio Steering
One
of my criticisms of the Greenspeed HPVs is their steering. It’s ultra-quick and
direct; fine for slowly traversing cycle paths but very nervous at high speed.
(Think Evo 6.5 Lancer but even more direct at speed!) So it had always been my
intention to create a variable ratio steering system – one that is slower around
centre than it is at the extremes.
Implicitly,
a variable ratio system of this type means that as more steering lock is
applied, the steering arms are moved by an increasingly greater amount. (See
The New Breed of Controls - Part 1
for more on variable ratio car steering.) However, just as implicit is the point
that without power assistance, the steering will therefore get heavier as more
and more lock is applied.
That
might be OK but when there’s not lots of castor being run and Ackermann steering
geometry isn’t present, but when you have both, you in fact need more and more
assistance as you apply steering lock. In other words, even with a fixed
ratio, the steering will get heavier and heavier as steering lock is applied.
So, to keep the steering weight even, you actually need a variable ratio that
works in the other direction – one that gives you more leverage (and so a
greater movement of the steering input) as more lock is applied.
So
which do you want – steering that is slower around centre and quicker as lock is
applied (but gets ultra-heavy at the extremes), or steering that retains a
similar weight at all turning angles but gets slower as lock is applied? Keep in
mind that in some iterations of my HPV steering system, the steering became so
heavy that it was impossible to get full lock, and you can see that the
leverage ratios might need to be organised quite differently in the real world
to what might first appear attractive in a paper analysis!
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Ackermann
Ackermann refers to the fact that when a vehicle
turns a corner, the inner wheel needs to turn at a tighter angle than the outer
wheel. Well, it doesn’t have to, but if it doesn’t then bad tyre scrub will
occur. The difference in the two wheel angles achieved during cornering is
called the Ackermann angle. Most HPV constructors consider Ackermann to be
absolutely vital, primarily because tyre scrub in cornering creates drag and so
slows the vehicle (or makes the rider work harder!).
Ackermann compensation is usually achieved by
angling the steering arms. The extension of these angles meet somewhere along
the centreline of the vehicle. The point at which they meet was traditionally
the rear axle line, however in practice, this point can be quite a lot further
forwards or backwards. Note that Ackerman steering geometry can also be achieved
without angling the arms in this way – the Greenspeed trikes use a variety of
methods of achieving Ackermann.
Despite other HPV constructors considering
Ackermann to be vital (there is even spreadsheet available to calculate optimal
Ackermann – (see
www.eland.org.uk/steering.html)
, I found that while
it was important that Ackerman compensation be present, quite a wide variety of
steering arm angles gave sufficient variation in the inner/outer wheel angles
that scrubbing was quite small or not discernible at all. And the scrubbing that
did occur did so only at large steering angles, so it wasn’t a huge problem in
normal use anyway.
But as part of the design process, why not
optimise the steering arm angles for best Ackermann? The answer is that the
steering arm angles also influence the amount of lock that can be achieved
before the tie-rod becomes in-line with the steering arm. One constructor told
me that his steering arm could even go over-centre versus the tie-rod – this is
an easy mistake to make. The more Ackermann that is achieved by angling the
steering arms inwards, the smaller the angle through which the wheels can be
turned before this becomes a problem.
These diagrams show the issue. Here the steering
pivot can be seen in blue, the steering arm in green and the tie-rod in brown.
The inner and outer balljoints are both shown in red. In this plan view, to
steer the wheel to the left, the tie-rod must move to the right.
But as the wheel turns to the left, the steering
arm and tie-rod become increasingly in-line. This has two effects. (1) It limits
the steering angle that can be achieved, and (2) the steering of that wheel
becomes heavier as the mechanical advantage diminishes. (See below for more on
levers!) And the critical point is that the more the steering arms are angled
inwards towards the centreline of the vehicle to gain increased Ackermann
compensation, the greater this problem becomes.
I chose to prioritise a tight steering lock and
zero bump-steer over Ackermann compensation, with the result that – as seen here
– the extension of the steering arms’ angles meet a bit behind the rear wheel.
(And of course this is also affected by how much static toe is run – here, the
HPV is running a few millimetres of toe-in.
Steering
Steering
ratio, weight, feedback, consistency and the presence/absence of kickback make
an enormous difference to how a steered vehicle feels - whether that’s a car or
HPV.
For
example, Australian Ford Falcons tend to have steering that's very quick either
side of centre, giving an initially slow response then almost a sudden darting.
The driver gets used to it and compensates, and it's one of the reasons these
large cars feel more nimble than you'd expect. But you can equally well point to
cars that have steering that's too slow around centre for driving quickly - the
Mitsubishi Magna is an example. The Evo 6.5 Lancer has steering that’s nervous
at high speed on bumpy roads, partly because the hard ride makes holding the
wheel dead-steady difficult. (Subsequent Evo models far easier to drive on real
roads.) The Toyota Prius – all models – have dreadful steering, partly because
of the tune of the electric power steering and partly because of the steering
geometry. The Mitsubishi 380 has excellent steering until you’re going really
hard around bumpy corners where it can kick-back strongly.
I
find the steering of my GTR Greenspeed trike nervously twitchy at high speed,
primarily because of the overly quick steering ratio – the top of the levers are
moved only 300mm to go from full left lock to full right lock. However, at low
speed, the quick ratio gives the trike a nimble, kart-like feel. The steering is
light at low speed and lighter still at high speed.
Sorting
steering requires thinking about all the different aspects, not just applying a
generic ‘good’ or ‘bad’ tag. It’s really important that the nuances of steering
are recognised – steering is simply not just steering.
(This
might all seem pretty obvious to car nuts but in on-line discussion with other
HPV riders and constructors there appeared to be little recognition of how the
subtleties of steering design can have a major affect on how the machine feels
on the road.)
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Levers....
Read
any basic engineering textbook and the coverage of levers will be apparently
straightforward. As this diagram shows, a lever provides a mechanical advantage.
When the end of the longer side of the lever is moved, the other end of the
lever will move a shorter distance but is able to provide a greater force. In
this case, an effort of 5 Newtons results in a developed force of 30 Newtons.
The relationship between the forces at each end of the lever is dictated by the
relative lengths of the lever to the pivot point. Easy, huh?
The
trouble is, in nearly all situations where the lever works in conjunction with a
link or another lever, this is only half the story! In fact,
levers working with other levers or links almost always change their
mechanical advantage as they move. Or, more precisely, the mechanical
advantage of the system changes. (If I’d known this before I started the
steering, it would have halved the time it took me to develop an effective
steering system design!)
Saying
that the mechanical advantage of the system changes is akin to saying that the
pivot points of the levers move when they are being used – a pretty radical idea
if you’ve been brought up with the idea that levers have a fixed mechanical
advantage!
In
the final HPV steering system you can see this changing mechanical advantage –
if you know what to look for.
Here
mechanical advantage is being lost as the left-hand wheel is being steered left
and the steering arm and tie-rod are becoming increasingly in-line.
And
here at the same time on the right-hand wheel the mechanical advantage has
reached a maximum and is declining.
Here
the mechanical advantage increases as lock is applied, from this....
...to
this. This has two benefits – as seen by the straightened elbow, it makes
gaining the last degrees of steering lock easier (a near straight arm can’t
provide the force of an arm bent at the elbow) and it also offsets the increased
effort needed as the steering arms (see above) reach full lock.
Discussion
of the idea that linkage systems vary in mechanical advantage is covered in a
few textbooks – although it isn’t even mentioned in many more that purportedly
deal with mechanisms and levers. While in general it is much too complex for to
me understand, the Mechanical Advantage chapter in Mechanical Design –
Analysis and Synthesis, Vol 1 (Erdman, A and Sandor, G, Prentice Hall, 1991)
at least showed I wasn’t going mad and there were good reasons why my initial
steering systems didn’t work, even though the leverage ratios around centre
looked and felt fine.
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Conclusion
Trying to optimise the magnitude and linearity of
the steering effort, produce a small turning circle, reduce scrub on sharp
corners to a minimum, provide near zero bump-steer, and have good steering feel
and straight-line stability was a huge task. It’s one element of the HPV with
which I am now really happy, but it’s also one that took an enormous amount of
work.
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