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Building a Human-Powered Vehicle, Part 4

The springs and dampers

by Julian Edgar

Click on pics to view larger images

At a glance...

  • Sprung vs unsprung weight
  • Calculating motion ratios
  • Calculating wheel rates
  • Calculating required spring rates
  • Spring design
  • Dampers
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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, 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.

Click for larger image

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.

Click for larger image

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

Click for larger image

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!

  1. 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.

  1. 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.

  1. 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).

  1. 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:

  • Specify the wire thickness and the number of free coils to give the required spring rate

  • Work out the spring stress level and advise on the likely spring longevity

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.

Click for larger image

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).

Click for larger image

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

Click for larger image

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

Click for larger image

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.

Click for larger image

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

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