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# Suspension Tuning & Optimization: Suspension Frequency

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## Suspension Frequency

### 05.39

 00:00 - Frequency describes how a system oscillates between two states. 00:04 In this context, we're interested in the frequency of oscillation of our suspension. 00:09 This can relate to the vertical oscillation of the chassis, the wheels and tyres themselves, the dampers, the anti roll bars and other components. 00:18 Taking a simple suspension and removing any damping so that it consists only of a single idealised spring, if we initially compress the suspension and then let it go, it'll oscillate indefinitely. 00:31 If we plot the change in displacement over time, the duration of each complete cycle of the oscillation, tells us the frequency. 00:38 The frequency of this simple oscillation is determined by the magnitude of the supported mass and the stiffness of the spring. 00:45 This is known as the undamped natural frequency of the system. 00:49 Simply put, it's the frequency that the system will naturally oscillate at without any damping to control the compression or rebound. 00:57 This is generally defined in hertz which is cycles per second. 01:01 In the case on the left side where we have a 1 Hz frequency, and in the case on the right we have a 5 Hz frequency. 01:07 It's clear that the 5 Hz frequency is oscillating much faster. 01:11 While making use of frequency based analysis in suspension is useful, it can quickly become extremely complex. 01:19 So for the purposes of this course, we'll only be looking at it from a heavily simplified but still useful perspective. 01:25 So how do we actually figure out our natural frequency of the sprung mass? This is calculated by taking the square root of the spring stiffness divided by the suspended mass, supported by that corner of the car. 01:38 Shown in this equation. 01:40 That's a pretty simple equation as long as we know the numbers. 01:43 But how do we actually put the results to use? In short, it can help answer one of the most common questions I get as a motorsport engineer. 01:51 How do I choose the right spring rate for my car? I completely understand why there's so much confusion on this topic and I clearly remember having the same questions early on in my career. 02:02 Essentially there are some well understood guidelines for the target natural frequency of the sprung mass for a given type of car and competition. 02:10 The simple idea being that with the proportion of the sprung mass being supported by each corner of the car known, as well as the type of car and intended purpose, we can define the appropriate spring stiffness. 02:22 Here's a table of the suggested range of frequencies for different types and applications of cars. 02:28 Low performance road cars are generally in the frequency range of 0.5 to 1 Hz. 02:33 Whereas high performance road cars, may be between 1 and 1.5 Hz. 02:38 Rally cars will usually operate between 1 and 2 Hz while low downforce circuit racing saloons and single seaters will be in the 1.5 - 2.5 Hz range. 02:49 Medium downforce circuit racing cars operate around the 2 - 3.5 Hz vicinity and high downforce single seaters and prototypes will usually be in the 3.5 - 5 Hz + range. 03:02 It's important to understand that this only gives us a starting point for a suitable spring stiffness choice. 03:08 It's a ballpark but it'll usually get us pretty close. 03:10 In reality, the exact stiffness needed is something we'll need to experiment with around the calculated baseline stiffness. 03:18 Don't stress about these numbers right now though, we're going to be working through a real world example in our practical skills section so you'll be able to see how it all comes together. 03:27 In reality, fully defining and calculating the complete dynamic frequency response of the unsprung and sprung masses, particularly when we consider heave, roll and pitch modes independently as well as the effective spring rate of the tyre and then including the damping is a much more complex undertaking. 03:46 In this course, we'll only be considering the calculation of the undamped natural frequency of the sprung mass and ride. 03:53 This is a significant simplification of the suspension but it's still extremely useful for someone looking to calculate a sensible starting point for spring rates. 04:01 The result of this calculation gives us our target spring stiffness at the wheel but if we don't have a 1:1 motion ratio between the wheel and the spring then we need to use our own calculated motion ratio to convert the required wheel rate to the required spring rate. 04:16 To figure out the required spring rate for a given target wheel rate, all we need to do is to multiply the target wheel rate by the motion ratio squared. 04:25 Let's take the case of a target wheel spring rate of 280 pounds per inch for the rear of our car which has a motion ratio of 1.4. 04:34 The required spring rate is 280 multiplied by 1.4 squared which is approximately 550 pounds per inch. 04:42 In the end, there are many parameters that'll determine the optimal suspension frequency and therefore, spring stiffness required for your car. 04:50 In the real world, these requirements change based on a huge number of parameters. 04:54 Things like road surface and its condition, tyre type and pressure, weather conditions, even the session type and driving style. 05:02 However, this is still a very useful process to go through in order to get a sensible starting point. 05:08 In summary, we can use the sprung mass natural frequency concept to determine the spring rate for each end of the car. 05:15 Making sure that we take the motion ratio between the wheel and the spring into account. 05:20 This will give us a useful starting point for choosing a spring rate for our application. 05:23 But it won't be optimum for all conditions. 05:26 This has to be found through testing. 05:28 Don't forget that we'll be going through an example of calculating the required spring rates in the practical skills section later in this course.