|
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,
much 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...
|
With the suspension links finished front and rear,
it was time to organise the springs and dampers.
As covered in previous parts of this series, the
front suspension comprises unequal length double wishbones. The coil spring is
held captive between the lower spring mount – located about a quarter of the way
along the lower wishbone – and a frame extension. The separate damper is largely
in parallel to the spring; however it is mounted further outboard and is
slightly angled.
The rear suspension comprises a longitudinal
swing-arm. It also uses a separately mounted spring and damper, with the spring
leverage ratio in this case being about 2.5 to one.
Corner Weighting
Before having the springs made, the first
important step was to measure the weight acting on each wheel.
Measurement of the corner weights was achieved
using digital bathroom scales, positioned under one wheel at a time. (At this
time the yet-to-be-made springs were replaced with appropriate length blocks of
wood.) The two wheels at which the measurement was not being taken were
supported on blocks the same height as the scales and the human occupant (me!)
positioned on the HPV. The scales were then read, the support blocks and scales
moved, and the measurement process repeated at the next wheel. This showed that
each of the two front wheels supports about 43kg and the rear wheel, 27kg.
Weight
Distribution?
In
Part 1 of this series (see
Building a Human-Powered Vehicle, Part 1 )
I
said of the Greenspeed GTR:
However,
the Greenspeed has some brilliant design characteristics, optimised in the long
period over which the machines have been constructed. The relationship between
the seats, forward-mounted pedals and the side-mounted steering arms is perfect.
The weight distribution (a third on each corner) is the optimal compromise
between rear wheel traction up steep hills (more weight wanted on back wheel),
lateral cornering performance (more weight located between front wheels), and
braking performance (weight wanted on the back to stop the trike lifting its
rear wheel).
So
what’s this about the front wheels of my design having 43kg each on them and the
rear wheel only 27kg?
Partly
it’s just how it turned out (especially with the front suspension ended up much
heavier than I had expected), and partly it’s where I decided to place the seat
within the wheelbase. Paul Sims of Greenspeed made the point to me that better
cornering is achieved by placing more of the mass between the front wheels of a
three-wheeler. However, the downside of this is reduced traction up hills and
potential rear wheel lifting under brakes. However, by this stage I realised my
design was going to end up heavier than the Greenspeed so I knew that even with
a more forward weight bias, there’d still be enough on the rear wheel to keep it
planted for grip and braking.
|
Sprung vs Unsprung Weight
So the two front wheels each support about 43kg
and the rear wheel, 27kg.
These are the total weights acting on the contact
patch under each of these tyres. These comprise a little unsprung mass (the mass
of the wheels and axles; about half the mass of the control arms; and about
one-quarter the mass of the springs) with the rest being sprung mass. The
springs support only the sprung mass so if we’re to work out how much mass the
springs are going to support, the unsprung mass needs to be subtracted from the
sprung mass. When this is done, the figures become approximately front: 40kg
each and rear: 23kg. However, if a heavy load is placed on the carrier, the rear
spring’s load will increase a lot, perhaps as by as much as an additional
30kg.
The Rear Spring
So from the foregoing, the rear spring needs to
cope in normal conditions in supporting 23kg and at times as much as 53kg. But
that’s not quite right: in fact, because of the leverage ratio designed into the
rear swing-arm, the spring loading is going to be much higher than these figures
suggest. The easiest way of working out what leverage ratio is acting on the
spring is to carefully measure the wheel travel from full bump to full rebound
and compare it with the distance the spring is compressed.
However, there are a few major practical traps in
this. Firstly, as you’ll subsequently see, the ratio of spring to wheel movement
is mathematically squared, so even a small error in the ratio measurement will
result in a large error in the calculations. For this reason, it is best to
measure the wheel and spring movements over small increments all the way through
full travel. Secondly, the spring compression measurements must be made from
centre to centre of the spring, rather than – for example – at the edge of the
spring seat. Finally, in some systems the leverage ratio will vary as the
suspension moves through its travel, so you’ll need to take an average.
On the HPV, the rear measurements were:
|
Wheel movement increment in
bump (mm) |
Spring compression (mm) |
|
17 |
7.5 |
|
17 |
7 |
|
17 |
7 |
|
17 |
7 |
|
17 |
7 |
|
17 |
7 |
|
Total |
102 |
42.5 |
In other words, over the usual suspension
movement, the wheel moves 2.4 times as far as the spring. This is called the
motion ratio, as shown in the table below.
|
Wheel movement in bump
(mm) |
Spring compression (mm) |
Motion Ratio |
|
17 |
7.5 |
2.3 |
|
17 |
7 |
2.4 |
|
17 |
7 |
2.4 |
|
17 |
7 |
2.4 |
|
17 |
7 |
2.4 |
|
17 |
7 |
2.4 |
However, the motion ratio must be squared
to work out the relationship between the wheel rate and the spring rate. In this
case, that means the spring rate (eg expressed in kg per millimetre) is 5.8
times the wheel rate (again in kilograms per millimetre). That’s a very
important calculation...
|
Wheel movement in bump
(mm) |
Spring compression (mm) |
Motion Ratio |
Wheel rate vs Spring Rate
ratio
(ie Motion Ratio squared) |
|
17 |
7.5 |
2.3 |
5.3 |
|
17 |
7 |
2.4 |
5.8 |
|
17 |
7 |
2.4 |
5.8 |
|
17 |
7 |
2.4 |
5.8 |
|
17 |
7 |
2.4 |
5.8 |
|
17 |
7 |
2.4 |
5.8 |
The next step is to calculate the required wheel
rate. In the case of the rear suspension, the total travel is about 100mm. Let’s
say that we want to proportion that travel as about 1/3rd in rebound
and 2/3rds in bump. (That would place the wheel one-third of the way into its
travel when stationary with the rider on board.) Taking the mass being supported
by the wheel as 23kg, we want 23kg to move the wheel up by about 33mm. In other
words, we want a wheel rate of 23/33, or 0.7kg/mm. That means that for every 0.7
kilograms of weight the rear wheel supports, it compresses the suspension by one
millimetre.
From above we know the spring rate is 5.8 times
the wheel rate, so the required spring rate is the wheel rate (0.7 kg/mm)
multiplied by 5.8, giving 4 kg/mm. So if the rear suspension is to compress by
33mm when the rider is aboard, a spring rate of 4 kg/mm (in imperial units
that’s 223 pounds/inch) is required.
But what about when that load on the carrier is in
position? That was the weight that would take the rear wheel load from 23kg to
53kg. The wheel rate is 0.7 kg/mm which indicates that with a total load on the
back wheel of 53kg, 76mm of the 100mm suspension travel will be used up. Even
with an adjustable height spring seat, that suspension compression is a bit high
– so why not increase the wheel rate a little? Lifting it to 1 kg/mm means that
the 53kg load compresses the rear suspension by 53mm and the normal body weight
load compresses it by 23mm. That latter figure leaves only 23mm of droop
capability – hmmm, a bit small.
OK, then what about a wheel rate of 0.8 kg/mm?
Full load will compress the rear suspension by 66mm while normal rider body
weight will compress it by 29mm. Perhaps that’s a good compromise, and a 0.8
kg/mm wheel rate when multiplied by 5.8 results in a final spring rate of very
close to 4.6 kg/mm (or 259 pounds/inch).
Specifying the Spring
From the above we know we want a spring with a
rate of 4.6 kg/mm. But more information than that needs to be known before a
spring manufacturer can be contacted!
-
What is the spring’s required free length? The
above calculations assume that there is minimal preload on the spring – in other
words, in needs to be compressed only a tiny bit to keep it captive between the
spring seats at full droop. Since this distance is 122mm (as measured on the
HPV), a spring length of 123mm will keep it captive without upsetting the
calculations too much.
-
What is the spring’s required travel? This is
vital because under full bounce you don’t want the spring to be compressed to
the extent that it’s coil-bound – ie that all the wire coils are closed right up
and are touching each other. From the motion ratio of 2.4 we know that when the
wheel has moved 102mm (that’s full travel), the spring will have compressed by
42.5mm. Therefore, we want a spring travel of at least 42.5mm or to put it
another way, our spring must be able to compress from 123mm to 80.5mm long
without getting coil-bound.
-
What is the required outside diameter of the
spring? In this case, where clearance to the drive chain was an issue, this was
set at 45mm. Considering the length and required rate, this is a small diameter
– something which has implications for the spring stress level (see
below).
-
What ‘end treatment’ should the spring be made
with? The main options are unfinished (where the coil just stops) or ground and
close-wound, where the ends of the spring are flat. The latter is much easier to
deal with in that a simply made flat-bottomed spring cup spreads the load
evenly.
Together with some discussion about the
application, this information is sufficient for a good spring maker to:
These are both very important. Despite equations
existing to allow you to easily calculate what the required wire thickness and
number of free coils to give the desired rate, for two reasons this is best left
to the spring maker. Firstly, they know what wire gauges they have available to
them, and secondly, the ‘number of free coils’ depends a lot on their winding
style – eg where or not the final coils are closed-up, etc.
In any application where the spring is being used
in a vehicle you must have the spring stress level calculated. Spring
manufacturers use software programs to do this; once the spring specs are input,
the data is available in seconds. As a guide, the first spring I considered for
the rear had a calculated stress level almost five times greater
than the maximum normally allowed spring steel stress.
Simply put, the spring would have broken in
use.
Final Rear Spring Specs
Rate: 4.6 kg/mm
Free length: 123mm
Spring travel: at least 42.5mm
Outside diameter: 45mm
End treatment: flat ground
Max spring stress level: suitable for a road
vehicle suspension
Mass: as light as possible
Measuring
Spring Rates
Spring
rates up to about 13 kg/mm (or over 700 pounds/inch) can easily be tested by
using a drill press and bathroom scales. Place the scales on a supporting block
of wood on the drill press table (or base, if the table is too high). Compress
the spring onto the scales using the drill press feed handle and at the same
time read the spring deflection with a digital caliper. Compress the spring by
10mm and then divide the reading by 10 to get the rate in kg/mm. Multiply by
55.88 to get the results in pounds/inch.
When
testing, make sure the spring can’t fly out sideways under the pressure!
|
The Front Springs
Much of the same calculation process was followed
with the front springs. The weight acting through each wheel is about 40kg. With
the same suspension travel of 100mm, and the desire to have the suspension
sitting at about one-third of full bump, the same requirement of having a 33mm
deflection arises, this time with a 40kg per wheel load. That gives a desired
wheel rate of 40/33, or 1.2 kg/mm.
Whether from measuring inaccuracies or because
this is what actually occurs, the motion ratio in the front suspension varied to
a greater degree that in the rear suspension, and so of course did the
calculated relationship between the wheel and spring rates. However, the average
of the latter is 11.9 and that’s the number that was used.
|
Wheel movement in bump
(mm) |
Spring compression (mm) |
Motion Ratio |
Wheel rate vs Spring Rate
ratio
(ie Motion Ratio squared |
|
17 |
6 |
2.8 |
7.8 |
|
17 |
5 |
3.4 |
11.6 |
|
17 |
4.5 |
3.8 |
14.4 |
|
17 |
4.5 |
3.8 |
14.4 |
|
17 |
5 |
3.4 |
11.6 |
|
17 |
5 |
3.4 |
11.6 |
With a desired wheel rate of 1.2 kg/mm and a
spring:wheel rate relationship of 11.9, the calculated required spring rate is
14.3 kg/mm or 800 pounds per inch. As can be seen, the required stiffness of
spring increases very fast when there’s a high leverage ratio working on it!
Final Front Spring Specs
Rate: 14.3 kg/mm
Free length: 140 mm
Spring travel: at least 26mm
Outside diameter: approx 55mm
End treatment: flat-ground
Max spring stress level: suitable for a road
vehicle suspension
Mass: as light as possible
Checking
Calculations
Wherever
possible, it makes a lot of sense to source a trial spring to see if your
calculations are in the ballpark. For the rear suspension I had available to me
a spring that I shortened to fit by cutting off the end (and so ruining the
previously flat end!). When inserted in the rear suspension, it looked about
right. And its actual rate? I measured it at 43 kg/cm, or 4.3 kg/mm. That
compares with the calculated requirement for a 4.6 kg/mm spring.
The
very high spring rate required in the front suspension was harder to simulate.
In the end I used a block of solid rubber which deflected by an appropriate
amount when inserted in the suspension. (It didn’t have anywhere near the travel
to cope with bumps but it showed the appropriate spring rate needed for the
required deflection with just the rider on the HPV.) Its measured rate was 13.5
kg/mm – and calculations showed a 14.3 kg/mm spring was needed.
|
Getting the Springs Made
The springs were made by Thomas Marsh and Co Pty
Ltd of Brisbane. (Contact details at end of article.) For no additional cost,
they used their software to design the springs so that the correct rates were
achieved with the lowest mass and without exceeding an appropriate stress level.
Unfortunately, the very stiff front springs
(10.5mm wire thickness!) and large number of turns (8.5) resulted in a mass per
spring of just under 1kg. (It may have been better to design the front
suspension with a lower motion ratio and so use a lighter spring.) With its
lighter rate, the rear spring has a much lower mass of 435g.
Here are the design specs of the front springs. (Click on the images to enlarge them.) As
can be seen, all the specs were met with an outside diameter of 57mm (approx
55mm was the request).
Here are the design specs of the rear springs. The
really tight spec is in the travel achieved before coil bind. A spring travel of
42.5mm was requested and in fact the travel to solid length is 43.1. However,
the spring designer pointed out that the allowable travel is only 36.7mm. The
difference is because the spring rate starts to change when the spring is
compressed nearly fully. (This occurs as because of manufacturing tolerances,
some coils close right up before others.) So a travel of 36.7mm is the
recommended maximum although the possible physical travel is 43.1mm. In a
vehicle application, where a bump rubber is being compressed as full travel is
reached, this compromise is acceptable.
The springs cost AUD$77 each.
Delivery
After waiting for a week to have the springs made,
I was pretty excited when I picked them up. But I was initially a bit taken
aback - the front ones looked so stiff! In fact, they looked more suitable for a
car than a light-weight HPV... Clearly, at a rate of 14.3 kg/mm they were going to
be stiff, but when I first saw them, I was very worried that I’d made a mistake
somewhere in the measurements and calculations. To give you an idea of how stiff
they are, when I stood on top of them the deflection barely registered –
scary!
However, with the front and rear springs
trial-installed in the HPV suspension and with my weight aboard the partly
completed frame, the suspension deflected by within a few millimetres of the
amount I’d designed: the calculations were correct.
The Dampers
The dampers used on the Human Powered Vehicle are
based on steering dampers from Suzuki GSXR 1100 motorcycles. While they’re (in
HPV terms!) heavy at 500g each, they’re also exceptionally strong, can be easily
pulled apart and at AUD$75 each at a motorcycle wrecker, are relatively cheap.
However, because of their original function, they have equal damping force in
each direction. So what are the implications of that?
Bump vs Rebound Damping
Dampers tend to get surrounded by mysticism or
broad statements like “the dampers need to be matched to the springs” that don’t
stand up to close scrutiny. (It sounds good but what does it mean, precisely?)
In short, the function of a damper is to stop the suspension bouncing after the
bump has been met and passed. ‘Bump damping’ refers to the damper’s resistance
to movement encountered when the suspension is compressed over a bump; ‘rebound
damping’ refers to the resistance to extension. Clearly, the bump damping is
massively aided by the spring, while the rebound damping is really all about
resisting the spring’s extension force.
It’s all made clearer if the damper has equal bump
and rebound damping – as the motorcycle steering dampers originally had. Even
without the HPV being able to be peddled, testing of the rolling chassis showed
that having equal bump/rebound damping resulted in a much firmer ride than was
achieved without the dampers in place. After all, every bump wasn’t being
resisted just by the spring but also by the damper! And the sharper the bump,
the more the damper resisted the compression – dampers being the sort of device
that rapidly increase in firmness with higher shaft speeds.
Two examples show what was happening.
When the rear suspension was finished (but the
front springs still replicated with blocks of wood) I was able to roll the
machine slowly forward on the workshop floor. I placed the rear wheel on a 75mm
high block, sat on the machine and then rolled off the block. The rear wheel
dropped 75mm and I could judge the firmness of the ride. And, it was firm!
However, I could increase the height of the drop to a stunning 200mm without
damaging myself, the frame or the rim. The suspension had the travel, but the
bump damping made it very firm when doing so. A softer bump damping would use up
more of the travel (perhaps to as far as the rubber bump-stop) but in more
normal circumstances, would give a far better ride.
So why have any bump damping at all? That’s a
question I posed to the experts at Whiteline Suspension and they made an
interesting point (obviously it was about cars!).
“If there is insufficient bump damping,” they
said, “it takes too long for a car to take a ‘set’ when cornering.”
In other words, when you think about cornering and
not just straight-line bumps, the bump damping is important in resisting roll,
especially transient roll of the sort encountered when swerving through an
S-bend. Or, to put it another way, high bump damping results in minimal weight
transfer when the vehicle is thrown around.
And that brings me to the second example. When the
front springs were in place (and again the HPV working just as a rolling
chassis) I was able to corner at a constant speed. And even with the bump
damping as firm as the rebound damping, body roll was obvious. With softer bump
damping, body roll could be expected to increase...
It’s for this reason that separate anti-roll bars
are normally used specifically to counter body roll – the mix of spring
stiffness and bump damping is insufficient to do so, especially on a long corner
(where, irrespective of their bump damping rate, the dampers will continue to
compress).
To achieve a decent ride without the springs
oscillating, it’s normal to run much firmer rebound damping than bump damping.
Modify the Steering Dampers?
Disassembly of the Suzuki steering damper showed
the internals. Mounted on the 12.5mm chrome-plated steel through-shaft was a
small piston that was slightly undersize the bore. When the damper was stroked,
the oil squeezed through the gap between the piston and the inner bore. This
gave equal damping force in each direction, with damping force able to be easily
altered by changing the viscosity of the oil within the damper. (That’s possible
without damper disassembly because a small fill plug is provided.)
So how to modify this design to give unequal
damping force? And, furthermore, was it possible to give altered high- and
low-speed bump behaviour?
Initially I looked at the possibility of
installing flow regulating valves within the existing piston. I cut open some
twin tube car dampers and extracted the piston and valve assemblies. (Note:
cutting open gas pressurised dampers is dangerous and so should not be
undertaken – there are warnings to this effect written on gas dampers.) The
valves from the twin tube dampers could then be further disassembled until just
the valve orifices and their associated spring shims were available. However,
their design and size did not match the piston used in the steering dampers and
so adapting them for this use would have been extremely difficult.
I then considered have two threaded fittings
welded to the side of the steering damper’s aluminium body so that external
valving could be used to regulate the flow of oil. (The internal piston could be
left as standard – if thicker oil was used, little would bypass the standard
piston resulting in most oil passing through the external regulating valving.)
However, what form should the external valving take? That depended very much on
the required sophistication of the damper design. The valving was required to
provide a softer bump than rebound, but what else was needed? High speed bump
and high speed rebound could also be made adjustable, although at an increasing
level of complexity.
Rather than try to fabricate valves from scratch,
I sought out existing valves that could be adapted for this use, starting off
with the criteria that just a softer bump than rebound should be provided.
Industrial valves tend to be quite expensive and so I turned to cars, deciding
that rear brake pressure proportioning valves may be able to be adapted to this
application. I searched a wrecking yard and decided the valves installed on the
brake booster of the Daewoo Cielo looked the best bet. These valves are
standalone (ie one for each rear brake circuit), are made from light aluminium,
are designed to be easily disassembled, and contain a sophisticated inner spool
valve assembly. However, it turned out that the metric threads used on this
valve made getting cheap hydraulic fittings for it impossible. In fact, by the
time the valves were modified to take off-the-shelf fittings and then high
pressure braided hoses were made up to suit, the cost would have been in the
order of AUD$100 or more per damper!
Just Change the Oil...
The costs and complexity were rapidly spiralling
out of control so I decided that before taking the drastic step of drilling
holes in the damper bodies and having fittings welded on, I should simply try
running a thinner oil in the damper and leaving the bump/rebound resistances
symmetrical. Part of the reason for this decision was by now I’d been able to
ride the machine and the unmodified front dampers - even with their standard
bump/rebound behaviour - were working pretty well, giving an excellent ride but
still resisting roll and quickly damping out oscillations.
I sourced some very thin 2.5W 5 oil (designed for
use in the front forks of motorcycles) and filled the rear damper with it. And
the results were again pretty good – sufficiently so that I abandoned (for a
while at least) the thought of complex external valving. The ride isn’t quite as
good as would (presumably) be obtained by having unequal bump/rebound damping
rates (or even adjustable high speed damping), but it’s still excellent.
The front and rear suspension designs had
consumed lots of time and energy - but their design and construction were
nothing when compared with the steering... next, the nightmare really
begins! Note: due to problems (that included frame failure!) there will be a delay before the next article in this series appears.
Spring manufacturer: Thomas Marsh and Co
Pty Ltd, 10 Cobalt St Carole Park 4300, (07) 3271 3500, www.marshsprings.com.au
Did you enjoy this article?
Please consider supporting AutoSpeed with a small contribution. More Info...
|
More of our most popular articles.
|
|
|
Email a friend
Print article
|