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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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The original intention was to make the frame
solely of 50 x 50 x 3mm aluminium tubing. And that’s just how it started out: a
longitudinal backbone of square tube. At the rear, a cross-member in the same
material provided pivot points for the rear longitudinal swing-arm. At the
front, a more complex double L-shaped lateral member provided the upper spring
and upper wishbone mounts. (The lower wishbone mounts are on brackets welded to
the main longitudinal tube.)
That was all well and good but then I had the seat
frame bent up. I’d intended that this was going to be made of large diameter,
thin wall aluminium round tube – and in fact sourced some 40 x 1.6mm wall
thickness tube very cheaply. But could I find anyone who could mandrel bend it?
Nope! I tried a crush bender – even though the bender didn’t have exactly the
right mandrels – but the result was terrible.
So the main criteria in selecting the seat frame
tube became: what aluminium tube could be mandrel bent? The answer was 32 by 3mm
wall, a much heavier and stronger tube than I’d envisaged. I got the seat frame
tubes (two of them) mandrel bent at a cost of AUD$15 for each of the six bends –
ouch! Just as well the bends were superb...
About this stage I started to become worried about
the increasing weight. It’s hard to accurately weigh everything when it’s still
in bits and pieces (parts aren’t accurately sized, lightening holes often yet to
be drilled, etc) but it was starting to look like the seat frame and its
supports were going to weigh more than the main square tube frame! And if that
was the case, the seat frame had better do a lot more than its original
non-structural role had suggested.
Structural Seat
The seat has two main forces acting on: it
supports the weight of the rider and very importantly, it provides the back
support when the rider is pushing forward on the pedals. This latter force is
trying to push the seat rearwards; the weight of the rider is of course trying
to push the seat downwards.
The weight was supported by two short members that
angled down to the main longitudinal square tube. It would seem logical that the
push of the pedals could be catered for by two tubes angled well forwards and
upwards to the seat frame from the rear cross-member. But there was another
factor: I wanted to be able to install a heavy duty – but removable – rear
carrier. This would – of course – be part of the sprung weight and so had to be
supported by the back of the seat and the rear cross-member. If more vertical
struts were used to support the rear of the seat, these members could also be
used as part of the carrier support frame. However, when the carrier wasn’t
there, pushing on the pedals would tend to move the top of these tubes backward,
putting bending loads on the lower welds. The solution to this problem was to
slightly angle the seat supports forward and to place small braces at each of
the corners.
The seat frame therefore triangulated the rear
half of the frame. The full length of the frame could be triangulated if the
forward edge of the seat rails were braced to the front suspension pick-up
points – but was the extra 400 grams of tube (at this stage, a total mass
increase of about 8 per cent) worth it? I decided to have the seat welded into
place without these forward tubes and then do some deflection tests – ie jump on
it and see if it moved. (Little did I realise that this decision would come back
to haunt me!)
Watching Weight
By this stage I was drilling holes in everything
but the round tube (very, very hard to put symmetrical holes along a length of
round tube.) The rear swing-arm was mostly air, the front wishbones had dozens
of holes in them and the main square tube frame and cross-members were, in part,
like Swiss cheese. While holes in the right places reduce mass without affecting
strength by anywhere near the same proportion as the loss in mass (see
Making Things, Part 2
), I now had a LOT of holes.
But I was determined that the weight was to be kept down.
In fact, I was actually appalled at how heavy some
things were that I’d never bothered even considering. The long chain – a full
kilogram! The front cogs, bearing, cranks and pedals – 1.6kg! The hydraulic disc
brakes – 1kg! The gears – derailleur, cables and selectors – 0.8kg. This was all
top quality, brand-name gear and so it all sounds light (and it probably is),
but these incidentals added up to 4.4kg.
Then add the rear wheel (including its internal
gearbox) at 3kg and the front wheels at 1.5kg each, and suddenly there’s a mass
of 10.4kg – without any frame, suspension arms, ball-joints, bushes, dampers,
springs, steering or seat! The dampers I was using weighed 500g each and the
steel springs totalled no less than 3.5kg – so there’s 15.4kg.... still with no
frame, suspension arms, ball-joints, bushes, steering or seat!
Clearly, I wasn’t going to get anywhere near my
goal of under 20kg, so instead I resigned myself to a heavy HPV – but one that
was engineered very well in terms of durability and strength.
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Talking
about durability and strength, have I told you about the clothes pegs man? No?
OK, well listen to this.
When
I started construction of the machine, I joined a few web discussion groups and
mailing lists, hoping to bounce ideas off other people who had built
pedal-powered recumbent trikes. Unfortunately, very few had had anything to do
with suspension and so most of my questions were met with blanks. However, one
guy had built some suspension machines and – according to his web site –
pedalled them far and wide in the US. He was the only person who seemed to
understand concepts like scrub radius and roll centre, and so I looked with
interest at his replies to my posts.
Until
he mentioned the clothes pegs.
I’d
brought up the topic of suspension dampers, telling people that I intended to
use modified motorcycle steering dampers as my shock absorbers. These are
hydraulic, very well made and compact. The downside is – as mentioned above –
their mass, which is about 500g each. Lots of people on the discussion group
suggested that using hydraulic dampers was a poor decision, not only because of
the mass but also because of odd ideas like “lack of reliability” (huh? How
‘bout a billion cars, trucks, trains, planes equipped with hydraulic dampers...?)
and being overly complex for the application.
Then
the guy who’d built more than a few HPVs chimed in. He suggested what I needed
to do was to get rid of the hydraulic dampers and use wooden clothes pegs. Yep,
wooden clothes pegs. He’d used clothes pegs (clamping them around an aluminium
rod that moved with the suspension) and he could tell me that wooden clothes
pegs were just the right thing for damping the suspension of Human Powered
Vehicles...
When
I recovered from my mirth I pointed out that this approach seemed to have a few
minor problems, ones like getting rid of heat, having separate adjustment of
bump and rebound, and durability.... But nope, this guy had none of that – for
example, heat problems could be solved by tipping some water on ‘em....
So
you can see that when I decided I was prepared to wear some extra mass, it was
with the realisation that some of the machines I’d previously been making weight
comparisons with weren’t very well designed....
(I
should add that I found three very helpful people on-line. One was a guy in New
Zealand who has made himself a superb fully suspended trike with front double
wishbones, and who sent me some good pics. Another was an Australian AutoSpeed
reader who noticed my name on the discussion groups and contacted me directly.
He’s built several recumbent trikes and consistently made excellent points
during the construction of my machine. And the third was a Swede who has done
lots of long distance touring on bikes and trikes and sent me a brilliant list
of what he’d taken with him and the volume it’d consumed.)
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Chain Drive
Recumbent pedal trikes use a very long chain,
about 2.5 times that of a conventional bicycle. The pedals and front cogs are
mounted on a boom extending forwards and upwards. The tension side of the chain
is guided and supported by toothed rollers that run on sealed ball bearings. The
non-tension side of the chain is largely left to follow its own path from the
derailleur back to the front cogs, although – like some lengths of the tension
side – it’s partly guided by plastic piping. The pipe guides also prevent the
rider’s legs getting tangled-up with the chain.
My HPV uses two rollers – the chain passes under
one positioned under the leading edge of the seat and over one positioned near
the rear of the frame.
Unlike a conventional pedal bike equipped with
suspension, the pedalling force of a recumbent trike is largely fore-aft, rather
than up and down. On conventional bikes the suspension has to be designed
(especially in damping behaviour) so it doesn’t compress with each downwards
thrust of the pedals, otherwise an unpleasant bobbing motion occurs. For this
reason many bike dampers have a ‘lock’ position that is manually set.
However, the other design aspect of conventional
bikes than can cause pedal-induced suspension movement still applies. In fact,
because of the immense torque a recumbent ride can develop (it’s not limited by
the rider’s weight: he/she can push back against the seat), the design aspect
applies even more strongly. So what’s the problem then? Basically, if the chain
alignment is not correct, the pull of the chain will cause the rear suspension
to extend or compress with each power stroke.
The conventional wisdom appears to be that to
avoid this, the chain’s tension path should be through the rear suspension’s
pivot point. In other words, the chain pulls along the same path as a line
joining the axle to the suspension pivot point. This is then claimed to place no
resulting vertical force (up or down) on the wheel.
But this is wrong.
In fact, the chain should be parallel to a line
that connects the axle to the trailing arm’s pivot. The pull of the chain is
then parallel to the resistance (ie normally compression) of the suspension arm,
so no upwards or downwards forces are applied to the wheel. However, when rear
derailleur gears are used, maintaining this relationship is easier said than
done because a chain idler location that gives a parallel chain in one gear will
result in a non-parallel chain in another gear! So in this area, a compromise
will be needed.
However, when the wheel moves up and down another,
entirely different, vertical force is generated that tries to extend or compress
the suspension. To see why this is the case, think of how the backwards push of
the tyre on the road results in forward push on the body of the machine. If the
suspension arm (either actual or virtual) is parallel with the road, this push
results in just a forward push on the vehicle, with no vertical forces involved.
But if the suspension arm is not parallel to the
road (perhaps because the wheel is experiencing bump or droop), there will be a
vertical component to the force being transmitted by the suspension arm to the
vehicle. If the arm is parallel at normal ride height, during suspension bump it
will head downwards to the suspension pivot, resulting in a downwards force on
the pivot. This will cause the suspension to compress – effectively the
suspension bump will be increased. When the suspension arm is angled the other
way in droop, there will be an upwards force transmitted to the suspension
pivot, effectively causing the droop to be increased. Significantly, the actual
effect of these changes will not only depend on the ‘at rest’ inclination of the
suspension but also on the amount of bump and rebound travel that is available
(since this will help determine the angle that the suspension arms adopt in each
direction).
And there are (at least!) three other aspects to
keep in mind.
Doing It
The above points are the result of external
engineering input and much experimentation – I couldn’t find any HPV resources
that dealt with any of these points in detail.
I started off with the ‘chain through the pivot
point’ philosophy but even simple testing with just a bare frame and the rear
wheel showed that this created a very large suspension extension force.
Unfortunately, I’d been so confident that there wouldn’t be problems in this
area I’d had the idler pulley mounts welded into position – so the rear mount
needed to be ground off and radically revised.
To find the best position for the idler, I rested
the back wheel on the ground, replaced the spring with a very soft, short spring
and placed the chain over the lowest rear gear. I placed packing under the
spring to give normal ride height and then applied pedal torque by hand, being
very careful not to input any vertical forces into the pedals as I did so. The
rear chain idler pulley was supported on blocks at different heights; the best
height was found when the suspension neither compressed nor extended before the
tyre slipped on the concrete.
(Note, as described above, it is vital that the
tyre is transmitting torque to the pavement during this testing. It is
not the same just jamming something into the wheel to prevent it
turning!)
Having then found the best idler height for this
ride height and bottom gear, I changed the spring packing to simulate movement
of the suspension arm from full bump to full rebound, testing each few
centimetres of travel. As a result of this testing, the idler pulley height
again needed changing to retain the best compromise.
Then, when this was done, I moved the chain to the
smallest cog and did it all again.
Having to move the idler from its previously
welded position was a pain but every cloud has a silver lining: I was able to
reduce the lateral angularity the chain was forced to adopt when moved from the
highest to the lowest gear. Previously, because of clearance issues with an
inner bolt holding one of the suspension pivots in place, I’d needed to have the
idler mounted pretty well in line with the largest rear cog (ie lowest gear).
That was fine for that gear but when the tallest gear was selected, the chain
had to bend pretty hard.
But with the idler pulley mounted further
rearwards and much higher, the clearance to the inner bolt was fine. This meant
the pulley could be positioned so that it lined up with a middle rear gear.
However, I went one better - there was the space to insert a mechanism that
allowed the pulley to float laterally, so that it was always in a straight line
between the front idler pulley and the selected rear cog.
This mechanism comprises a 12.5mm chrome-plated
steel rod (another one salvaged from a car shock absorber) on which the guide
pulley is mounted. The rod slides in wide-spaced high density polypropylene
bushes, allowing the lateral movement to take place.
Chain
Forces
The
forces acting on the chain are huge. But huh, isn’t this just a pedal-powered
machine? Let’s first take a look at the torque being generated.
The
pedal cranks on my machine are 170mm long. That is, the force applied by a pedal
is 170 mm from the shaft centreline. On a normal bicycle the maximum force that
can be applied to the pedal is dictated by the rider’s weight, so an 80kg rider
can apply a max of 80kg. However, a recumbent pedaller can push harder than
their body weight because they’re pushing back against a seat. So the force that
can be developed is high, perhaps by an 80kg person as much for a short period
as 120kg.
A
force of 120kg applied 0.17 metres from the axle is a torque of 20.4 kg/m or
almost 200Nm!
(kW
is Nm x rpm divided by 9550, so if the pedals are being turned once per second,
the power being developed is 200 x 60 divided by 9550, or 1.25kW, which is
possible for a human to develop for a very short period of time. A continuous
pedalling force of 15kg is easily able to be achieved by humans, which at a
cadence
[ie pedalling]
rate of 1.5 per second calculates out to 235W.... so the
figures make sense.)
So
don’t think that the forces involved are trivial...
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Frame Breakage!
At this stage I was able to ride the machine.
Clearly, it was unfinished but it was always my intention to do lots of on-road
development so changes could be made as necessary. At this stage I was having
problems with a slipping chain, something that was eventually traced to the use
of a secondhand rear gear cluster. (I hadn’t realised how critical it is that
the chain and cogs ‘wear in’ together.) However, when chasing the slipping
chain, I’d been really throwing the HPV around, thinking that the suspension
movement might have been causing gear cables to pull and so cause inadvertent
‘half‘ gear changes.
During this process I’d been heavily stressing the
frame in a way I’d never considered: torsion. Torsional (twisting) stiffness is
regarded as very important in cars, where any frame twist will cause the
suspension geometry of a wheel to be altered. But in a three-wheeled vehicle,
any twist in the frame is of little consequence because the three wheels will
still find an equal footing. But what I’d forgotten is that with the frame
design I’d built, all the torsional forces were being concentrated in one short
section of frame.
This plan view shows what the problem was. Shown
are the main longitudinal, front wishbones and wheels, and rear trailing arm and
wheel. (The scale is arbitrary!) The seat frame is shown in blue. Remember that
the rear wheel has no lateral roll stiffness, so any roll forces (cornering or
even simply leaning over in the seat) are all resisted by the front wheels and
suspension. The rear two thirds of the frame were much stiffened by the seat
assembly, so concentrating all torsional forces on....
...the bit shown in the pic by the arrow!
Making matters worse was this section of frame had
had several 32mm holes drilled through it. These holes were positioned for the
steering system – later abandoned – that used two laterally sliding rods mounted
in poly bushes. The holes were originally strengthened by having 32mm aluminium
tubes welded through them but when the steering system was changed, I ground-out
the welds and removed the tubes, leaving the holes behind.
And here was the result. A spectacularly failed
part, I think you’ll agree. The breakage didn’t dump me on the road (it just
made for some weird lean angles) but clearly things had to be changed. The seat
frame extensions (mentioned above) were no longer optional; they were critical!
So I replaced the failed part with some new tube
that was undrilled....
...and extended the rails to the front
crossmember.
This shows how the seat extensions provide much
better torsional stiffness – and bending stiffness too.
Conclusion
Even something as simple as the path of the chain
turned out to be pretty damned complex in real life. The frame – and its
failure? This was an engineering lesson in itself! The end result is a frame
very stiff in bending and moderately stiff in torsion, although with the latter
I wouldn’t want to quote it in degrees per Newton... I (still) don’t think it
would be very high.
In the next part of this series we’ll look at
the on-road tuning of the suspension
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