From the Lotus Internet List
From: Mike Causer
Subject: Spring rates (long, but non-technical)
I've been asked off-list for an explanation of some of the issues, and I expect that there are a lot of folk who would also like to ask, but are afraid of appearing to be dummies. So I've taken out one or two clues to the identity of the original requester, tweaked it up in places, and here is a description of the effects of springs and dampers in 4-wheeled vehicle suspension. I'm not worrying about minor geometric effects, and the engineering caveats, or unusual stuff like titanium springs and Houdaille dampers, just the principles. I may have over-simplified, but let's do it one step at a time, OK?
First, a spring is a spring, it doesn't know whether the car is standing still, moving, cornering, or even whether it's holding up a Esprit or a 40 tonne truck. A load is applied to its ends and it compresses. If the load increases it compresses some more, and if the load decreases it extends. For any particular load the spring will move to the same length every time, which is a function of the wire size, the number of coils and the diameter of the windings.
Second, the damper ("shock absorber" -- but it doesn't absorb shocks) has no effect on the length that the spring will adopt for a given load -- all it does is slow down the speed with which it can move to its new position. Real world dampers (of the type called "coil-overs" in the USA) have one more effect, they limit how far the suspension can move overall, by the limits that they can open and close to.
When the car is standing still it has a weight that must be supported through the suspension and the springs. The suspension geometry has a lever effect on the spring such that the load on the spring itself is greater than the weight it's supporting. (I'm going to leave an explanation of how to calculate the ratio out of this, but it's about 2:1 for the front of a Europa or Elan, and maybe 1.25:1 for the back.) But, for any given load it has to support, a particular spring will always compress to the same length. It is going to compress to this length no matter what the ride height of the car -- it knows nothing about where the body of the car is relative to the road, and the spring is going to be the same length whether you've got 1" or 10" of ground clearance. So this is why AVO and some Spax have that thread down the outside of the damper body: you can move the car up & down relative to the road by winding the spring perches along the damper. Remember, no matter what the ride height that spring is always going to settle at the same length because it's still supporting the exact same weight.
OK, so what happens as the car moves? The wheels go up & down as the road surface ripples. In this case they are no longer supporting the exact weight of the car, if the road surface drops away the wheel will follow it, the spring will extend, and it is not holding up its corner of the car. So that corner of the car will also start to drop. By then of course the road surface has probably started to rise again, so the spring is compressing once more, and the spring is pushing harder than the weight it should be supporting and the body bounces up! Well, it would, but one of the main functions of the dampers is to slow down all these movements so that there is no bouncing. Too little damping and the spring reacts too fast and the car will bounce, which gives a "floaty" feel. Too much damping and the spring doesn't get a chance to follow the road variations and the ride feels harsh.
If the spring is a "soft" one, that is it has a small number of lbs force per inch of movement, when the wheel moves away from the car the change in force generated by the spring is small, so the body will not feel a big change in how its supported. If the spring is a "hard" one, that is a large number of lbs/in, when the wheel drops into the same hole the body will feel a much greater change in its support and react in a more rapid way. So soft springs give a soft ride and hard springs give a hard ride.
Now consider what happens when the car takes a corner. The actual force that moves the car sideways comes from the grip of the tyres on the road -- at road level. But the car is not all at road level it's _all_ above it, and for calculations we use a national point in the car called its "Centre of Gravity". The cornering load acts between the tyres in one direction and on that point but in the opposite direction, which means we have a rotating force on the car. This is trying to rotate it in "roll", which in the case of the Europa is along roughly the same axis that the crankshaft spins (probably a bit lower, it comes from suspension geometry, not through the CofG). From outside the car you can see this roll, quite dramatically in some cases like Citroen 2CVs and Luxo-barges.
Now think about what this roll does to the tyres, it pushes the wheels away from the vertical, so the tyres are no longer running flat on their treads. For motorbike tyres this is OK, they are designed to run that way, but for car tyres it's bad news, the grip is reduced. But also consider, what is this roll doing to the springs? On the outside of the turn they are going to be compressed, and on the inside they are going to be extended. We want to reduce the amount of roll don't we, and we can do that by increasing the spring rate so that it resists the compression of the outer side more (the inside has a much smaller effect). Why not make the springs very stiff and get rid of the roll entirely? Well it's because of the horrible crashing over bumps. The racers of the 1900-1935 era had cars with very stiff springs and they had to wear kidney belts to keep their internal organs in place because of it!
If you are using road tyres, especially those similar in grip to the '70s originals, they cannot grip enough to generate huge cornering loads, so the roll problem is not as great and the springs can stay soft which will give a better ride. If you fit modern sticky tyres the springs will have to be made harder to cut down the extra roll the car could otherwise generate, but you'll pay for it in a harder ride.
Let's look at the practicalities. If the car is going to be used mainly on the street you are going to want to keep the ride height the same, and you are going to need much the same suspension travel as it originally had. That means that the fully extended and fully compressed lengths of the damper need to be the same as original. If the car is going to be used on the track you can afford to reduce the ride height (and the main reason for doing that is to reduce the height of the CofG and therefore reduce the forces that cause the roll), and so the open & closed lengths of the damper need to be shorter by the distance that is the change in ride height divided by the lever ratio of the wheel/damper movement. Remember all of this is independent of spring rate!
Now you decide on your spring rate, if the tyres are similar to the original fitment keep the original spring rate. If the tyres are stickier increase the spring rate, but not by so much that the car will be airborne half the time. This is very tricky to judge, and I think you need specialist advice on what rates to use.
Fit whatever springs you pick to the dampers, put the spring-dampers on the car and move the spring perches until the ride height is correct. Easy! (Racers also get the "corner weights" the same, so the wheels are taking the same load side to side, but that's maybe going a bit too far for road use.)
Now comes the harder part. Those AVOs, Spaxes, or Konis will have some sort of damping adjustment. If it's just one screw per damper then turn it harder until it gets uncomfortable then pull it back a click or two. If it has two adjusters these act independently in compression and extension and getting the relative settings right is going to take a test-track session -- maybe several. Again, you will need specialist advice, and it may be worth getting some help from a professional racer if you can. In all cases try running the car with dampers full soft, then full hard, then one end soft and the other hard. Each of these will feel horrible, but it will help you with the tuning. You need to balance the front and back against each other, and you might find that the settings for best braking or cornering are opposite to best traction, it's all compromise.
This is a minor version of what the F1 teams go through for the two days prior to each race, trying to tune the car's characteristics to the track.
If you want to read a serious professional's description of all this you should get Carroll Smith's books, particularly "Prepare to Win" and "Tune to Win". You'll also learn a lot about fuel and water plumbing, bolts, riveting, and how to maintain a car generally. *Highly* recommended.
 Here's a caveat, although I said I was not going to include them. OK, so I lied, sue me ;-) The major factor in the roll angle is the suspension geometry, the springs have a lesser effect, and the "roll-bar/sway-bar" lesser still. But in practical terms we cannot change the suspension linkages and we have to concentrate on the things we can change, which are springs, dampers and roll-bar(s).
So now I've spent the morning on writing a 2,000 word essay, time to get on with some paid work perhaps......
Mike Thanks for your very erudite explanation.
The suppliers are too quick to recommend short travel dampers for cars that will not see race tracks. This has happened to me recently and I think I started some of this thread when I asked about spring lengths and rates to suit avo dampers with 2 inch total travel.
Have you got the leverage ratios correct for the Europa ?The back springs are nearly vertical so the ratio is 1 to 1 ? Could you tell us how to calculate the ratio for say the europa with the original wheels and tyres.
Is the "ratcheting down" effect serious in cars with dampers that only have rebound damping ? Certainly on bikes it was. The effect happens when you have hard rebound settings. The spring and damper are loaded in a corner and before the damper can allow the spring to recover, another bump or the corner tightens and more roll occurs. This can lead to the suspension being flattened to the bump stops and the next road bump throws the car off line. On a bike or on a banked track or people with wings (a la Red Bull ) increased g takes its toll.
Finally why do Formula 1 cars have any suspension when at any thing over a brisk walk the aerodynamics flatten it to the bump stops and how do you fit dampers to tyres which according to Martin Brundle and Murray Walker are the only form of real springing the GP car has. It was interesting to see how Coulthards car became faster / slower than Schumacher's dependent on his tyre pressures at each pit stop.
Geoff (I think I am getting less confused due to the incredible knowledge on the Lotus list) Ford
Cape Town South Africa
From: Mike Causer
Subject: Re: Spring rates (long, but non-technical)
G Ford wrote:
> Mike Thanks for your very erudite explanation.
Ooooo! Did you hear what he called me? Erudite indeed. Saucy devil!
> The suppliers are too quick to recommend short travel dampers for cars that will not see race tracks. This has happened to me recently and I think I started some of this thread when I asked about spring lengths and rates to suit avo dampers with 2 inch total travel.
Yes, I thought you had mentioned some strangely short travel, that's what prompted me to add it the discussion.
Have you got the leverage ratios correct for the Europa? The back springs are nearly vertical so the ratio is 1 to 1 ? Could you tell us how to calculate the ratio for say the europa with the original wheels and tyres.
I was working from memory, but a few years ago I did spend some time looking at the Europa rear suspension during a debate about whether the drive shaft ever pulled on the circlip that holds the bearings into the diff casing. (My analysis showed that it didn't.) Yes, it is vertical, but it still has an offset from the centerline of the wheel. In fact the ratio may be as low at 1.1:1. I _was_ generalising remember. If someone would care to supply me with a dimensioned drawing of the Europa front & rear suspension
I can run it through a program of mine and give you the exact curve of the ratio as the wheel moves through its travel. I've already done Elan front & rear, and Plus Two front. BTW, the program requires the Medusa CADCAM system to run, so there's no point in posting the code.
> Is the "ratcheting down" effect serious in cars with dampers that only have rebound damping ?
I know of no car that has rebound only, although if you get the bounce/rebound ratio wrong the effect can happen. Don't forget that cars & 'bikes load their suspensions very differently.
> Finally why do Formula 1 cars have any suspension when at any thing over a brisk walk the aerodynamics flatten it to the bump stops
1) regulations (why Ferrari do it)
2) to run over the curbs (why McLaren do it)
> and how do you fit dampers to tyres which according to Martin Brundle and Murray Walker are the only form of real springing the GP car has.
The tyres are going to be pretty self damping. Their energy absorbtion is quite good, which is why old tyres line the tracks rather than steel springs.
> It was interesting to see how Coulthards car became faster / slower than Schumacher's dependent on his tyre pressures at each pit stop.
Tuning the car's behaviour by playing with the tyre pressures is something that anyone on this list can try. In fact for many cars that don't have alternative springs & dampers available it's about the only way. Apparently Coulthard radioed in for different pressures and got it wrong. The F1 drivers all complain that the current cars are very hard to set up, and pigs to drive.
From: Mike Causer <email@example.com>
Andrew Denton wrote:
> I went to a spring maker a couple of weeks ago to get him to check the spring rate of a couple of coil springs I had been given. I expected him to put them in a machine, load them up and take a reading on a gauge. No he never left the office. He measured the diameter. the number of coils and the diameter of the wire and used a basic calculator.
> Does anyone know the calculation and the spring rate for wire diameter please?
p = ( G * d**4 ) / ( 8 * N * D**3 )
p = lbs per inch of deflection
G = Modulus of Elasticity = 11,200,000 for spring steel
d = diameter of wire in inches
N = number of active coils 
D = mean diameter = outside diameter minus wire diameter
* = multiplied by
** = raised to the power
/ = divided by
Most calculators and programming languages should get this right without the parentheses, but why take risks?
 counting the "active" coils is that hardest part, they are the coils that are free to move and do not touch either the spring platforms or other coils. There are several different ways to finish the ends of the spring, so you have to look carefully.
You can easily get 10% variation in two measured identical springs, there are an awful lot of things that make a big difference to the actual rate of spring. That's why the catalogues of stuff for racers all have a spring testing machine on offer, Demon Tweaks has two models for valve springs and two models for suspension springs. At 6-700 Pounds Stg each.
From: g ford
Subject: Re: Spring .formula
>I went to a spring maker a couple of weeks ago to get him to check the spring rate of a couple of coil springs I had been given. I expected him to put them in a machine, load them up and take a reading on a gauge. No he never left the office. He measured the diameter. the number of coils and the diameter of the wire and used a basic calculator.
>Does anyone know the calculation and the spring rate for wire diameter please?
S = G x d to the 4th power divided by 8 x D cubed x N
excuse the way I have shown it but I do not know how to show cubes etc.
S = spring rate in lbs per inch
G = modulus of rigidity of material in psi. for most steels use 11,500,000
d = wire Dia. in inches
D = spring dia in inches. This is the dia at the centre line of the wire.
i.e. inside dia + 1/2 wire dia =1/2 wire dia
N = Number of active coils. Makers add on about 1.5 coils to calculated
number to allow for the 3/4 dead coil at each end.
Above seems to give results which correlate against known designs. May be your spring maker has broken his bathroom scales !!