# Suspension Tuning & Optimization: Measuring and Calculating Centre of Gravity

## Measuring and Calculating Centre of Gravity

### 10.50

00:00 | - In this section of the course, we're going to be leaving the theory side of motorsport suspension behind and jumping into the practical world. |

00:06 | The following modules each focus on an essential skill that we've been learning about in previous modules and can now be put into practice on real world vehicles. |

00:16 | In this case, our Toyota 86 circuit cars. |

00:19 | Let's start with our centre of gravity. |

00:21 | Knowing the position of the centre of gravity of the vehicle is useful for a number of reasons. |

00:26 | For us and most relevantly for this course it allows us to calculate the amount of lateral load transfer for our vehicle more accurately which we'll make use of later on. |

00:36 | To fully define the position of a centre of gravity we need to define it in all 3 dimensions. |

00:40 | Laterally, longitudinally and vertically. |

00:44 | Calculating the lateral and longitudinal positions is straightforward. |

00:47 | We can do this really simply just with a set of corner weighting scales. |

00:51 | Finding the vertical component though is a little more difficult. |

00:54 | With that said, we can still do useful lateral load transfer calculations without knowing the exact position of the centre of gravity. |

01:02 | Most sports orientated road cars have a centre of gravity height between 450 and 550 mm above the road surface. |

01:10 | By using a figure in this range, while we won't be exactly calculating the right numbers for the load transfer, we can still make a lot of useful predictions. |

01:18 | If you do want to know the exact centre of gravity positon for your car, there are 4 main approaches. |

01:24 | First and by far the most simple is to find existing data for measurements that someone else has made. |

01:31 | This isn't usually easy to find but if you can get it, it'll save you a lot of work. |

01:35 | The second option is using a CAD system which is only going to work if you have a fully defined CAD model of your car. |

01:42 | A big caveat here is that while it is possible to get an accurate calculation of the centre of gravity from a CAD model, it does require an enormous amount of time and effort to fully define the materal and mass properties for each single component in your vehicle right down to every single last nut and bolt. |

02:00 | Because of this, the CAD method is realistically outside of the equation for most people except those working at the higher end of professional motorsport. |

02:09 | A slightly more practical method is to pivot the car and define the balance point. |

02:13 | The idea here is that if you can orientate the car such that the centre of gravity is above the pivot point the car will balance there. |

02:21 | The car can be pivoted either on its side or longitudinally. |

02:25 | Although in the real world it's usually more practical to pivot the car on its side. |

02:30 | Once you know the angle you need to rotate the car to find the balance point it's a simple calculation to find the centre of gravity height as the centre of gravity must be directly above the pivot point with the system being balanced. |

02:42 | The 4th option and the one we'll use to demonstrate in this module is to raise one end of the car a defined amount and then measure the change in corner weights. |

02:51 | We can then use some simple math to find the centre of gravity height. |

02:55 | Regardless of the measurement method you choose, in order to get good results, you need to be meticulous in your process, being careful to keep certain parameters constant and as close to as realistic to as how the car will run on track as possible. |

03:08 | In reality, each of these methods has a number of sources of error. |

03:12 | These errors all stack up to give us some variation in the calculations. |

03:16 | So really it's more correct to call these methods estimations rather than saying calculations. |

03:22 | In saying that, with some care, we can still get really useful results. |

03:27 | In order to carry out the method we're going to go through, at minimum you'll need a set up the corner weighting scales, a way to safely lift one end of the car, a tape measure and a way of locking the suspension solid. |

03:39 | While not strictly necessary, a digital level does make things a little easier. |

03:44 | The procedure for this method is as follows. |

03:46 | First, drain the fuel tank. |

03:48 | This is an important step as the movement of the fuel inside the tank will skew the results. |

03:53 | In order to account for this, we'll be performing the test twice. |

03:57 | Once with an empty tank and once with a full tank. |

04:00 | You should also pump up the tyres significantly higher than their hot pressure. |

04:04 | This is to account for tyre squish when one end of the car becomes more heavily loaded. |

04:08 | For this test we've chosen to use 45 psi. |

04:12 | The car needs to be set at its normal static ride height in order for the test to be useful. |

04:16 | Set this as normal and record these ride height values. |

04:20 | If you don't have a normal ride height set yet, another one of our practical skills modules in this section covers this exact process. |

04:27 | Next we need to lock the suspension solid at the normal ride height. |

04:31 | If we didn't do this, the suspension position at each end of the car would change as we lifted one end which would skew our results. |

04:39 | One method for locking the suspension is to fit solid spacers in place of the springs. |

04:45 | You first need to find the compressed part of the springs when the car is sitting at its static ride height. |

04:51 | Once that's been measured, you can measure all of the springs and replace them with the solid spacers of the correct length. |

04:57 | In our case, we've cut and machined some pipe of approximately the right diameter of the springs. |

05:02 | There are a number of options available for locking suspension at the correct ride height, you just have to use a method that's most practical for you. |

05:10 | Next we need to record the wheel base and tyre radius values which will come in handy in later calculations. |

05:16 | The design of your wheels will determine the easiest way to measure your wheel base. |

05:20 | As long as your wheels are the same diameter front and rear and the steering is set straight ahead, you can measure from the back of each rim as shown here. |

05:29 | Measure both sides and take an average value. |

05:32 | Next add either a volunteer to the driver's seat or some ballast to simulate the driver's mass. |

05:38 | It's important to account for the influence of the driver's mass, especially in particularly light cars where this can have a significant effect on the centre of gravity calculation depending on the driver positioning. |

05:49 | Now we're ready to measure the corner weights with the car sitting normally at its normal ride height. |

05:54 | Zero your scales without any weight on them then lower the car onto them and record the measurements. |

06:00 | These are the values we recorded during our test with an empty fuel tank. |

06:04 | If you have a digital level, now is the time to place it on the car. |

06:07 | Find a suitable place to fit it and zero the level. |

06:11 | This will be our reference angle for how high we're lifting the vehicle. |

06:15 | Now we're ready to raise one end of the car. |

06:17 | As we do, the weight readings on the scales at the end of the car remaining on the ground will increase. |

06:23 | The height of the centre of gravity has an affect on the rate this increases at and this is the fundamental principle we're using to calculate the centre of gravity height. |

06:33 | The method you use to raise the car will depend on the equipment you have available. |

06:37 | The higher you can raise the car, the more accurate your calculations will be. |

06:42 | There's a tradeoff here, both in terms of the amount of effort required to carry out the test and also safety. |

06:48 | Any time you're lifting a car off the ground, safety needs to be a primary focus. |

06:53 | Because this method may require you to use some unorthodox techniques, you need to take more care than normal. |

07:00 | Please keep in mind that no matter which method you choose to raise and support the car, it is your responsibility to ensure the safety of yourself and anyone helping you. |

07:09 | If you're not confident in any way, or sure in the way you're going to carry out this job, don't carry out this test for yourself. |

07:16 | The way we chose to raise our power was to remove the front wheels and using proper lifting strops rated to many times the required load limit, secured them to the front hubs in a way they remain secure throughout the process. |

07:28 | We then raise the front of the car, leaving the rear wheels sitting on their scales. |

07:33 | Before it was lifted, the car was first moved back to minimise the canter levering on the forward arms of the hoist. |

07:40 | These were then used to lift the car from the front axle. |

07:43 | As we touched on earlier, the higher you can lift the car, the more accurate your calculations will be. |

07:49 | Your chosen method will determine the highest you can safely lift but at minimum, you should aim for around 400 millimetres in order to get satisfactory results. |

07:58 | You can lift from the front or the rear of the car, we chose to lift from the front in this case as it allows us to lift to a higher angle without the bodywork touching the ground which would affect the results. |

08:09 | The front bumper touching the ground is more limiting than the rear in this case. |

08:14 | Just ensure that you lift from the axle itself and allow it to freely rotate. |

08:19 | With the front raised to your chosen height, record the tilt angle. |

08:23 | If you aren't using a digital level, then you can measure the height the front has been raised at the lifted axle. |

08:28 | This is where using a digital level becomes a little more convenient as you can simply read off the tilt angle. |

08:35 | We can see here that we reached a tilt angle of 19.7° for our first test. |

08:40 | While the car is tilted, record the new weights from the scales at the non lifted end. |

08:45 | With these recorded, we now have all the values we need to properly calculate the position of the centre of gravity in all 3 dimensions. |

08:53 | Before we move onto the calculations we first need to repeat the entire process but this time with a full tank of fuel. |

08:59 | This will allow us to understand the affect of a full tank of fuel on the centre of gravity height. |

09:06 | And will also allow us to estimate the centre of gravity at any fuel level between full and empty. |

09:11 | In order to simplify the calculation process, we've provided you a spreadsheet that you can download from the related resources section below this video. |

09:19 | This will do the calculations for you and also allow you to visualise the position of the centre of gravity in all 3 dimensions. |

09:26 | Taking the values we recorded during the empty fuel tank test and entering them into this spreadsheet, the height of the centre of gravity is 503 mm above the ground. |

09:35 | Which, based on the values we discussed earlier in this module, seems resaonable. |

09:39 | With the full tank test, the centre of gravity remained at the same position laterally but moved rearward 14 mm, lowering the forward weight bias to 55.4%. |

09:51 | The centre of gravity height has been raised slightly to 506 mm. |

09:56 | All these differences make sense with the fuel tank being mounted relatively centrally and just ahead of the rear wheels. |

10:03 | When entering the values into the spreadsheet, you'll need to keep all of the units consistent in order to get accurate results. |

10:10 | In this case, I've entered all the values in metres, kgs and degrees. |

10:15 | You can choose to use imperial units if you prefer, you just need to keep them consistent. |

10:20 | In summary, by using this tilting method, you can get a useful estimate of the centre of gravity position in all 3 dimensions. |

10:26 | It's not strictly necessary to measure the centre of gravity in order to do useful load transfer calculations. |

10:33 | An estimate of a comparable car will do in most cases. |

10:36 | Just remember, that if you do go to the trouble of measuring it yourself, it's worth taking your time and being meticulous in the details as errors can quickly stack up and skew your results. |