Learn more about springs than you ever thought possible! Springs might seem simple but there’s a whole lot of science behind that little piece of coiled metal. Words: Gerry Speechley. Photos: Eibach, Air Lift Performance, KW, Owen Springs.
SUSPENSION: THE BASICS
When most of us think about a vehicle’s suspension, the things that come to mind first are usually springs and dampers, commonly thought of in a combination as shock absorbers, and maybe anti-roll bars (known as sway bars in the US). The interaction of these components can have a considerable effect on the handling, comfort and performance of a vehicle, and the effect and interaction each system has on the others cannot be emphasised enough in discussion.
The optimum performance handling of a vehicle is all about control. The control of the constantly moving and swaying mass of the vehicle under different surface conditions. Taken to the limit, this can mean different suspension setups on the left- and right-hand side of the car (NASCAR), huge travel with minimal damping (off-roading) or different setups for different race tracks (F1 and Touring Cars etc).
We are looking here for the optimum setup for the ever-changing conditions seen by the performance road car, complete with different road surfaces, potholes, speed bumps, country lanes and newly Tarmac’d dual carriageways, so we will inevitably have a compromise between comfort and handling. We want a suspension system to be soft and compliant enough to retain tyre contact with the road and offer an acceptable level of comfort whilst being hard enough to control body roll and pitch during cornering, acceleration and braking.
In a very basic view of the suspension system, the springs support the weight of the vehicle and control the ride height and vertical motion of the vehicle over bumps. They do this by storing the energy used to compress them by the bump and then releasing it back into the car, hopefully in a controlled manner. The dampers react to the motion of the vehicle by controlling that vertical movement through resisting the pressure exerted from the springs by the release of that stored energy.
We will firstly consider the spring and its function on the vehicle and its suspension system.
THE FOUR TYPES OF SPRINGS
There are four main spring systems used on vehicles. These consist of: the leaf spring; the torsion spring; the air spring (airbag suspension); and the coil spring.
Our main focus will be on the most common spring type used on passenger cars, and that is the metal wire coil spring, although we will mention the others in passing.
The leaf spring, still used on many light commercial vehicles, consists of a rectangular metal ‘leaf’ section that is curved into an arc shape, usually anchored at one end and connected to the vehicle at the other through a shackle allowing the end mounting point to move as the spring straightens up, effectively increasing its total length. The axle is fixed to the vehicle by attachment to the leaf spring but this system causes problems, such as interaction between one wheel having an effect on the other, spring wind-up, and squat and vibration make. Therefore this system is unsuitable for a modern performance vehicle.
The torsion spring operates as a metal bar, twisting in reaction to the weight and travel applied to it by the motion of the vehicle. It has the advantage of being very compact below the floor of the vehicle but the disadvantage of not being able to offer a progressive spring rate. It’s a good system for compact cars that are not particularly sporting and where performance tuning is not a priority.
The airbag spring, commonly used on commercial, 4×4 and luxury vehicles (and usually referred to just as ‘airbags’), is a pneumatic suspension system where sealed bellows, usually made of reinforced rubber, are inflated or deflated to support the vehicle and adjust the ride height. In manufacturer OEM fitments it is almost always installed to allow manual or automatic ride height adjustment or self-levelling to take into account vehicle load. The vehicle is equipped with an on-board compressor that can inflate or deflate the bellows, either at the will of the driver to account for rough terrain, or electronically by using sensors on the suspension that measure the current ride height and adjust it automatically through the electronics to maintain the vehicle at the correct ride height. It has also been used on some performance vehicles to deflate and lower the vehicle at speed to reduce drag (Porsche and Tesla) and is obviously popular as an aftermarket suspension option, from the likes of Air Lift Performance, as it also offers extreme lowering capabilities.
The wire coil spring, being the most common form of performance vehicle support, has been around for many years and is, without doubt, the top choice for the performance suspension install. Although the material is actually an alloy steel rod on a vehicle coil spring, we still refer to it as ‘wire’. Now, while at the outset, it may seem a pretty straightforward component, the theory and practice behind it is rather more involved, as we will demonstrate. After alloy wheels, the coil spring lowering kit is probably one of the most common modifications the performance-orientated owner/driver will do to their vehicle. Whilst lowering the vehicle, and therefore the centre of gravity, can improve handling, it can also detract from performance if the springs are not selected properly.
The material used for the manufacture of a suspension coil spring is an alloyed carbon steel that has high ‘elastic’ properties, i.e. it will return to its pre-deformed condition without entering its ‘plastic’ state by yielding structurally and therefore retaining a permanent bend or distortion. It can be tempered for durability and one of the best alloys is chrome vanadium steel, which has a very high yield strength. The wire coil spring, or simply coil spring as we shall refer to it, can be manufactured either as a constant diameter spring or with one or both ends tapered in overall diameter.
SPRING RATE
The spring rate, usually referred to in pounds per inch, dictates how much a spring will compress depending on the load applied. A spring with a linear rate of say, 250lb per inch, simply compresses an inch for every 250lb of load applied to it. So a load of 125lb will compress it half-an-inch and a 500lb load will compress it two inches. It really is as simple as that.
A spring with a progressive rate gradually gets stiffer as the load increases, so a 150/500lb per inch spring will compress one inch with a 150lb load on it but may need 250lb to compress the next inch and then 400lb for the third inch until it reaches a 500lb load to move another inch. Looking at it the opposite way, as the load increases, lets say 150lb at a time, the spring compresses less and less until 150lb may only compress it a further quarter-inch.
A coil spring works simply by the deformation of the material in the spring. The easiest way to imagine this is to envisage opening out the material into a single, straight rod, held horizontally and fixed at one end. If you press on the end of the rod, it will bend and the amount it moves is proportional to the force you exert on it. This depends on the spring rate (material and diameter), and on a spring with a constant rod diameter will follow the formula for spring deflection, known as Hooke’s Law after the physicist Robert Hooke who discovered it in 1676.
Hooke’s Law states:
Spring rate x spring deflection = force exerted by a spring
So the force exerted by a 250lb per inch spring, compressed 2.5” would be: 250 x 2.5 = 625lb The spring rate of any given spring is determined by the wire diameter, material and number of coils (wire overall length). The larger the diameter of the wire, the higher the spring rate. But the more coils the spring has, the lower the spring rate – which is difficult to imagine because the spring looks so much beefier. Going back to our comparison with the straight rod, though, the longer the rod, the more leverage you have to bend the bar and so it is softer. Similarly, you can increase spring rate by shortening the spring. For example, cutting a full coil-and-a-half from a parallel wire spring with 12 original coils will increase spring rate by 1.5/12, or 12.5%. Cutting springs is not recommended because although the spring rate increases, it may not allow the end of the spring to correctly sit in the spring cups either end of the spring. Many factory springs are not flat at the end and sit in correspondingly shaped cups or rubber moulded seats to hold them securely or have tapered spring overall diameters that will not sit in the original position, whereas springs installed on most coilover applications have flat seats, something difficult to reproduce when cutting. There is also the possibility of lowering the car with cut springs leading to the suspension bottoming-out due to insufficient spring rate causing the shock absorber to reach its minimum installed length and crashing onto the bump stops. This can cause serious handling issues with the sudden loss of suspension travel.
The spring rate can be made progressive on a single coil spring by tapering the wire so that the thinner wire has a lower spring rate than the larger diameter wire. However, on most high performance applications where a variable spring rate is required, the system of ‘stacking’ coils of differing rates on a coilover shock absorber, which allows both progressive and digressive suspension setups, is undertaken.
On a replacement performance spring setup the spring manufacturer will have undertaken development to ensure the springs are sufficiently strong to prevent bottoming-out or causing other bodywork interference but without being so strong as to affect the ability of the shock absorbers to control the springs. As we mentioned in the beginning, the suspension components all interact and so a spring rate that is too high through excessive lowering will cause the weaker, damped OEM dampers to lose control of the strong bouncing effect of the stronger spring and, again, loss of control will deteriorate the handling. In track focused applications where the car is significantly lowered with very highly rated springs, the dampers are both uprated and shorter so the range of travel seen by the damper is all within the dampers’ stroke.
A fixed rate coil spring will still offer the same spring rate whether it is pre-loaded or not at any position of travel. For example, if you have a 2000lb vehicle and had perfect 50/50 weight distribution front and rear and symmetrically, then if you installed a 500lb per inch spring on each corner, (ignoring the motion ratio which we will discuss later), lowering the car onto the springs would compress each spring one inch. If you installed these springs on coilovers and compressed them during installation half an inch, then you would be preloading them 250lb each, so they would be pushing up 250lb each before you lowered the car onto them, and so the car would only compress each spring half-an-inch with its weight. In either case, though, the spring rate the car experiences would still be 500lb per inch.
This explains why many car manufacturers preload the spring a great deal to support the weight of the car but still with a very soft, comfortable spring rate, albeit at the detriment of performance handling. The preload on any spring also reduces the risk of the suspension extending fully and allowing the ends of the spring to dislodge from the seat. This is where the aftermarket has introduced the suspension kit, comprising a developed combination of uprated springs with suitably uprated dampers to suit. These kits can be offered in different stages from replacement springs and dampers to replace the original OEM components as a direct swap or as a complete system comprising a set of coilover dampers with concentrically mounted coil springs.
PROGRESSIVE SPRINGS
We have mentioned progressive spring rates but what exactly does that mean? Most common is the progressive spring, achieved by the OEM manufacturer usually by altering the coil diameter as opposed to the wire diameter for ease of manufacture and cost. On the coilover setup, however, a progressive rate is achieved by stacking two or more springs on top of each other.
A progressive spring rate starts soft and then progressively gets harder so that as the suspension starts to travel the spring rate is soft and comfortable, soaking up small bumps and keeping the tyres in contact with the road. As load increases, the spring rate also increases, allowing for control in more spirited situations.
At first glance, it seems that adding a spring on top of another will increase the overall spring rate but this is not the case. The formula for obtaining the overall spring rate for a pair of stacked springs is as follows:
Overall spring rate = Spring rate 1 x spring rate 2
Spring rate 1 + Spring rate 2
So an example would be using two springs with a rate of 200lb per inch and 400lb per inch respectively would be:
200 x 400
200 + 400
= 80,000 ÷ 600lb per inch
= 134lb per inch
It’s difficult to imagine that a combined 200 and 400lb spring would give a combined rate of just 134lb! This brings us to the use of a stacked pair for optimum performance using a lighter spring for soaking up smaller bumps, known as a tender spring, which can be fixed rate or progressive and which is designed to fully compress into coil bind and then allow the main spring to deliver the final spring rate. To give an idea of the flexibility of this system, if we look at the range of spring rates and lengths available from just one popular manufacturer, we find springs in lengths of 4” to 16” in open lengths and spring rates from 80lb per inch up to 4100lb per inch. And this is just the main springs and excludes the tender springs available from 150lb per inch to 1300lb per inch.
There is also another type of spring used in a stacked spring setup called a ‘helper’ spring which has a very low spring rate (circa 12lb per inch) and is only designed to retain the main spring on the spring perches during full suspension travel or when the suspension is ‘hanging’. It has virtually no effect on the spring rate of the combination.
On off-road applications and on long travel suspension, two or three main springs can be stacked to offer compliance on normal bumpy surfaces and a higher rate on big jumps. On a stacked spring system, the spring ends where they contact are joined by a spring coupling which holds the two coils concentrically. There is also a twisting motion when any coil spring is compressed as the coil tries to unwind under load and this is compensated for in most standard applications by the compression of the rubber pads at the end of each spring. In coilovers, where the spring usually sits on a metal seat, a thin needle bearing called a torsion release bearing (pictured) can be installed on the seat to allow this twisting without stressing the seat or shock absorber body and allow easier adjustment of the spring seat by relieving friction against the spring.
MOTION RATIO
Earlier, we mentioned the motion ratio and this is a hugely important factor to consider if you are making calculations yourself to determine the desired spring rates. The motion ratio is the ratio of the leverage of the control arm acting on the spring because the spring is not mounted directly upright at the same distance from the pivot of the arm as the tyre. Therefore, to simplify the maths, if the spring was mounted two thirds along the control arm nearest the wheel, in an upright position, and you had determined you wanted a sprung rate at the wheel (wheel rate) of 600lb per inch, then the two thirds of leverage offered (D1 and D2 in the photo on p92) against the spring would require a spring rate of 900lb per inch. Okay so far. However, the spring is unlikely to be mounted directly upright, i.e parallel to the wheel but at a slanted angle. This then introduces an angle correction factor because the force on the spring is amplified by the angle of the spring from the vertical.
This factor is calculated as the cosine of the angle made between the spring and the vertical:
Angle correction factor = cosine (spring angle)
WHEEL RATE
So, you have hopefully decided on the spring rate you want acting on the corner of the car, and this will be called the wheel rate. In almost all competition cars, this can be determined by measuring the corner weights of the car with the driver in the car and so the spring rate required can be calculated for each corner so that suspension travel is the same over bumps and during cornering. To find the spring rate needed to get your wheel rate you need the following formula:
Spring rate = Wheel rate
(Motion ratio)² x (Angle correction factor)
SUSPENSION FREQUENCY
Another consideration to make when selecting the spring rate is the resultant suspension frequency. The frequency is the rate at which the vehicle would bounce indefinitely if left uncontrolled by any form of damping. There will always be some minor damping to this continuous bounce because of resistance in the bushes and ball joints, although without any specific damping control, the vehicle could continue to bounce at the suspension’s natural frequency for a few seconds.
The natural frequency of the suspension is a function of the spring rate and the unsprung weight of the vehicle acting upon it. The unsprung weight is the mass of the wheels, tyres, suspension and any other components that move with the wheels on the road side of the spring. The sprung weight of the vehicle is all of the rest. An estimate can be made of the unsprung mass as around 15% of the vehicle’s total mass if the components cannot be weighed individually.
Calculation of the suspension frequency will indicate the comfort expected from the springs. The frequency will be reduced in amplitude but not frequency by the addition of the dampers but there will be a very good indication of ride comfort from the frequency.
Suspension Freq. (Hz) = 188
60 x √ wheel rate ÷ sprung weight
To give some idea of comfort level, a frequency of between 1.0 and 1.5Hz is generally considered to be the most comfortable whereas a frequency of around 2.0Hz tends to feel harsh. A high performance car will have a frequency more like 2.0 to 2.5Hz but would be expected by the driver due to the vehicle type. Frequencies from 0.5 to 0.9Hz tend to induce motion sickness and give rise to boat-like handling comments. You will need to consider a higher frequency for the rear suspension so that over a bump, the rear ‘bounce’ catches up with the front bounce otherwise you will get a pitching effect front to rear until the dampers control the spring oscillations.
Critically Damped
Under Damped
Over Damped
Time
Amplitude
A damped spring will have the oscillations reduce over time
Vehicle will continue to bounce (oscillate) in the pattern of a sine wave if left undamped
