This article was first published in AutoSpeed.
Last week in Part 13 of this series I described
how testing had shown a problem with the back wheel. When cornering on long,
bumpy and fast (ie downhill!) sections of road, the rear wheel would patter
sideways – something very disconcerting when you have only a very short
After considering tyre and spring natural
frequencies, I’d decided that it wasn’t a damping issue but instead it must be
the rear suspension arm torsionally winding-up and unwinding over cornering
bumps. I’d tried hard to make the rear suspension arm stiff in torsion, but it
looked as if I hadn’t succeeded. So how torsionally stiff was the design – and
could it be made stiffer?
Assessment of the stiffness of the current rear
suspension was required. But how to do this? I thought of mounting a video
camera pointing downwards at the rear suspension arm, or mounting potentiometers
or strain gauges. But by far the simplest approach was to use a pen and paper –
I mounted a long vertical arm on the rear
suspension. This arm projected upwards and through the rear carrier. On the end
of the arm I mounted a whiteboard marker. The marker pressed against a piece of
white laminated chipboard mounted on the carrier. The marker was held in contact
with the board by means of an extension spring.
As the rear suspension arm moved up and down, the
marker drew a vertical line on the board. Any torsional twist in the rear
suspension caused the marker to move sideways. At 50cm in length, the arm was
about twice the radius of the wheel, so the sideways movement of the marker was
about twice the sideways movement of the tread on the road.
This close-up of the board shows the results of
throwing the trike around (including two-wheeling). The width of the scatter of
points (arrowed) is about 15mm, implying a lateral tread movement of about
7.5mm. Do the geometry calculation and that’s a total torsional twist of just
1.7 degrees! However, the testing wasn’t done travelling down the long bumpy
hill at high speed. Also, if I physically held the trike and then grabbed the
top of the wheel and pulled it sideways, a greater amount of torsional movement
could be seen.
The first step was to try to stiffen the existing
I removed the rear suspension arm. The forward
cross-piece (arrowed) was no longer required – it was initially installed to
support a bump stop which testing had shown was (probably) not needed. However,
the semi X-shape of the rear suspension arm gets a lot of its torsional
stiffness from the way the two parts of the X are joined at their centre – and
removing one of the cross-braces reduces the strength of this join.
To make a stronger join, in fact one stronger than
the original, I inserted a 1.6mm chrome moly steel plate as shown here by the
green highlight. Tested on the ground this clearly increased stiffness but when
reinstalled on the trike, the old ‘yank the wheel’ test still showed plenty of
movement in the rear suspension arm.
Identifying where this movement was
happening was difficult, but some appeared to be occurring across the leading
part of the arm. I then brazed-in a brace as shown here. But it made no
difference to the on-trike stiffness.
Reluctantly, I then decided the whole rear
suspension arm needed to be redesigned and rebuilt from scratch. But hold on!
What about the wonderful X-factor described so lovingly in Part 10 of this
series? Was all that misinformed or misdirected? The answer to that is ‘yes’ and
Firstly, without any doubt the X-brace design
gives improved torsional stiffness over a simple ladder frame. However (and as
shown in that original article), if it is to be stiffened as much as possible,
the arms of the X must extend right to the ends of the frame. In the case of my
design, this did not (and cannot) occur. Secondly, the integrity of the central
join is vital – my design was lacking in this area. And finally, and this is a
big one, the tube I used was simply not stiff enough for the forces involved.
An indication of the latter can be gained from an
experiment I did. I bolted the rear wheel in its drop-outs and then clamped the
suspension assembly in a big vice, with the vice gripping the suspension arm at
the spring location (ie as close to the wheel as possible). And even with the
suspension arm reduced to just the rear ‘forks’, there was still some torsional twist visible. In other words, the tube simply needed to be
Comparing Tube Stiffness
If all that you are doing is comparing torsional
stiffness of different tubes, the maths is surprisingly easy. There are two
factors to take into account – the wall thickness of the tube and its diameter.
The tube that was used to construct the first rear suspension was 22.2mm in
diameter with a 1.2mm wall thickness. Torsional stiffness is proportional to the
wall thickness x diameter x diameter x diameter, that is, wall thickness
multiplied by diameter cubed. Therefore, the stiffness is 13,129 (units don’t
matter in a ratio comparison). So what if I went up in tube size to 35 x 1.2mm?
The stiffness factor calculates to 51,450 – a stiffness that’s nearly four times
Interestingly, the maths is also the same when
comparing bending stiffness. Therefore, a good feel can be gained for the
relative stiffness of different tube diameters and wall thicknesses by doing
just a simple calculation.
And it gets even better. Working out the relative
mass of the different tube sizes can be found simply by multiplying the diameter
by the wall thickness.
(Note: all these calculations are approximations
that apply to only thin walled tubes. RS Edgar provided the engineering
So what do the figures look like when a number of
different tube diameters and wall thicknesses are compared?
Tube Size (mm)
Stiffness Change over Original
Weight Change over Original
22.2 x 1.2
32 x 0.9
35 x 1.2
44.5 x 0.9
This is a pretty stunning table. By upsizing to
44.5 x 0.9mm tube, the weight is half as great again – but the stiffness
increases by an incredible six times! Or, looking at the 32 x 0.9mm tube, the
stiffness increases by 2.3 times but the weight is only 10 per cent greater. And
as can be seen from the Stiffness/Weight Ratio column, the bigger the tube, the
greater the strength you can get for a given weight.
Clearly, it makes sense to use the smallest wall
thickness / greatest diameter tube that is available and can be fitted into the
space. The only caveat is that, to avoid wall buckling, the loads must be
carefully fed into the whole tube, not just one part of the thin wall.
So, having absorbed all that – what next? The
original rear suspension design was made in the largest diameter tube my small
bench tool can bend. Anything bigger would either need to be commercially bent
(and it’s very hard to find good benders that have the tooling for such small
wall thicknesses) or use a different trailing arm design. Any new design would
have to still match the existing position of the suspension pivots, wheel axle
and spring location. In addition, clearance to the chain and frame would need to
If the original design layout was followed (say
with brazed joints where previously bends were used), any increase in tube
weight would increase overall weight. Yes, stiffness would be up – but so would
weight. On the other hand, if vastly stiffer tube was used, the design could be
changed so that less tube was needed. On that basis, overall weight would not
In a move designed to radically boost rear
suspension arm stiffness, I went for the largest tube available to me with a
0.9mm wall – 44.5mm. As shown in the table above, this has six times the
stiffness of the original tube size but it weighs 50 per cent more. However, the
rearmost section of the suspension arms (the rear “forks”) could not be made
from this 44.5mm tube – there simply wasn’t the clearance. But I figured 32 x
0.9mm tube could be used, carefully flattened and shaped to appropriately join
to the rear lugs (“dropouts”) and clear the chain. This tube has 2.3 times the
original stiffness and weighs only 10 per cent more than original.
So with 44.5 and 32mm tubes, stiffness would be
way up – but weight would also increase. So how to reduce the amount of tube
required? After juggling various designs, I decided to go for a completely
different approach to the previous trailing arm. In the new design a ‘Y’ section
connects to the two forward mounted suspension pivot points. The upright of the
‘Y’ is extended rearwards to a crosspiece that mounts the rear ‘forks’. The Y
and crosspiece calculated out as requiring 105cm of tube, which would all be in
the large diameter 44.5mm. The rear forks needed about 60cm of 32mm tube. The
total weight of the tube is 1050 + 400 = ~1450g. Add the two dropout lugs at
~200g and another ~150g for the bearings and bearing supports and you’re looking
at around 1800g. The original rear suspension arm weighed 1.5kg, so at 1.8kg the
proposed new design would be 17 per cent heavier.
Construction of the new arm was straightforward,
except that the leading end of the ‘Y’, where the arm connects to the suspension
pivots points, needed to use short lengths of 22.2 x 1.2mm tube to allow the arm
to be positioned downwards for chain clearance. This looks a bit ugly but
degrades stiffness very little (the tubes are only about 30mm long and are
placed in compression/extension when the suspension is subjected to torsion). In
fact, talking about aesthetics, the new rear suspension is clearly not as
elegant as the previous design.
But has it solved the rear wheel patter problem?
We’ll find out next week.
Kamikaze Test Rider
a subscriber to a recumbent trikes mail list (ie a discussion group run by
email), I occasionally get people wanting to ride my trikes. Someone from
overseas or interstate might be in my area, and email me a request. Usually,
such a request doesn’t gel with my plans or the stage of construction the trike
is in. However, one day I got a ‘ride request’ and it seemed that it would work
– the new rear suspension design had just been finished and the trike was ready
I was very curious as to what another recumbent trike rider would think of my
design – whether, for example, they’d immediately identify a shortcoming that I
was so familiar with I could never see.
youngish bloke – I’ll call him ‘Ben’ – duly arrived. I described to him the
front and rear suspension, and then demonstrated the trike by riding around the
cul de sac on which I live. I went up on two wheels, cycling a big circle. Then,
back on three wheels again, I rode over some bigger bumps formed where
neighbours’ concrete driveways cross the grassy verge.
then offered Ben a ride. He donned my helmet and then immediately started
pushing the machine fairly hard – within moments he was riding over the driveway
bumps and drop-offs, picking a route that gave even bigger bumps than I’d
traversed. It was interesting as a bystander seeing the behaviour of the trike:
I had not seen it ridden in this way by someone of similar mass to me.
it around a bit here,” I said – pointing to the flat and smooth bitumen of the
cul de sac.
rode forward at a fair speed – say 15 km/h – and then banged on some steering
lock. The trike immediately came up on two wheels. He then turned around, rode
in the other direction, travelling even faster. This time he yanked on steering
lock as hard as he could.
trike immediately rolled.
held out one hand to stop himself turning right over as the front right wheel
hub gouged a 1.5 metre line in the bitumen. Besides his hand and the wheel
retaining bolt, the other part sliding along the road was the rear derailleur.
from deep scratches, the trike was undamaged. After he picked gravel out of his
hand, Ben also appeared undamaged.
given that in skidpan testing – performed on just the same surface – I’ve
exceeded the lateral acceleration of any other recumbent trike I have access to,
the fact that my trike rolled is not indicative of a lack of cornering prowess.
But what it does show – and especially since at the time Ben rode the trike, the
road surface was damp – is that the front-end grip is very high indeed.
on lock and this trike doesn’t scrub straight on – instead the tyres grip and
you start cornering! And, as with all recumbent trikes, if you corner hard
enough, the trike will lift the inner wheel. Corner even harder and it will
here I was thinking that, since I changed the steering to give toe-out in bump,
turn-in performance had been reduced ...