Brake System Design and Optimization: Brake Master Cylinder Sizing
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Brake Master Cylinder Sizing
13.14
| 00:00 | - The size of the brake master cylinder is a key factor in the leverage the driver has over the braking system. |
| 00:06 | To be clear, before we start this module, when we talk about master cylinder sizing, we're specifically talking about the bore size of the cylinder. |
| 00:15 | If all other components remain the same, an increase in the master cylinder bore size will result in a shorter and heavier pedal feel. |
| 00:23 | This means that more pedal effort will be required to generate the same hydraulic pressure. |
| 00:29 | However, less master cylinder stroke and therefore pedal travel will then be required to displace the same volume of brake fluid to move the brake calliper pistons and engage the brakes. |
| 00:40 | Of course, the opposite is also true, a smaller diameter master cylinder results in a longer and lighter pedal feel. |
| 00:48 | What's important is finding the right balance of pedal force. |
| 00:52 | It needs to be firm enough to provide feedback but also doesn't require too much effort from the driver. |
| 00:58 | We also need to ensure that the pedal travel is long enough to allow for modulation but short enough that the driver can comfortably use the full stroke of the system and still allow for techniques like heel/toe rev matching. |
| 01:11 | Some compromise may be required here but with a bit of effort, we'll be able to find a setup that works effectively. |
| 01:18 | Since changing the master cylinder size, changes the fluid pressure generated and the volume displacement for a given input, then changes to the front hydraulic leverage ratio relative to the rear will result in changing the brake bias. |
| 01:33 | Which as we know is critical for the braking performance and the dynamics of the car under braking. |
| 01:39 | The brake bias is the reason we have dual master cylinders in motorsport applications, making it easier to tune the bias using a bias bar. |
| 01:48 | In this module, we'll be discussing the sizing of the master cylinders, assuming a dual setup with separate front and rear circuits. |
| 01:56 | However, the same ideas apply to a tandem master cylinder setup but it's just more difficult to make the changes. |
| 02:03 | With all this said, there are really 2 ways to look at master cylinder sizing and this depends on our current brake setup, the issues it presents and what we're trying to achieve. |
| 02:14 | Put simply, are we trying to change the pedal feel or the brake bias? Either way, the effects on the other will need to be addressed. |
| 02:22 | Let's first consider the brake bias, in a situation where our braking system components are sized in a way that we have too much front bias. |
| 02:31 | Ideally we'll continue using the same pad compound front and rear that's suitable for our application and changing the size of the mechanical components being the callipers and the disc, is a lot less practical than changing the hydraulic bias. |
| 02:45 | This can of course be done by adjusting the brake bias bar but this method means our bias bar will always be offset to one side and we'll lose our range of adjustment. |
| 02:55 | Assuming we've sized the components in our braking system properly, we want the bias bar to be centred and then allow for some adjustment in either direction as the bias requirements change in different conditions. |
| 03:08 | Keeping the bias bar centred, the same force will be applied to the front and the rear circuits. |
| 03:15 | So to compensate for our overly front bias situation, to move the hydraulic bias further backwards, we need to increase the front master cylinder size which will reduce the front pressure and hydraulic leverage ratio relative to the rear. |
| 03:31 | Alternatively we can decrease the rear master cylinder size which will increase the rear pressure. |
| 03:37 | Either way with an increase to the front master cylinder size relative to the rear, the master cylinder we changed will now move through a different stroke to displace the same fluid volume. |
| 03:49 | This means we need to readjust the master cylinder rod lengths into the clevis of the bias bar to ensure that the front and the rear brakes engage at the same time. |
| 03:59 | Ideally we want to keep the differential here as low as possible but this is the compromise of not readdressing the mechanical system. |
| 04:07 | The key aspect we really want to consider is the hydraulic leverage ratio the driver now has over the brakes. |
| 04:14 | In each circuit, this is determined by the total piston area on one side of the calliper divided by the master cylinder area and then multiplied by the pedal ratio. |
| 04:26 | The pedal ratio is of course the same for the front and the rear circuits but the callipers and master cylinders are most likely different. |
| 04:34 | We only need to consider one caliper rather than both sides of the vehicle in order to determine the leverage ratio and then comparing the leverage on the front brakes to the rear, this gives us the front to rear hydraulic bias capability of the system. |
| 04:49 | So let's look at an example of calculating the leverage ratio for a standard setup. |
| 04:54 | We'll work in metric units for these examples although with some conversion to imperial since the master cylinder sizes are generally expressed in fractions of an inch. |
| 05:04 | Starting with the front, we'll stay that it has 6 piston callipers with 27, 32 and 38mm pistons. |
| 05:12 | A 7/8th inch or 22.2mm master cylinder and a pedal ratio of 5:1. |
| 05:19 | The area of a circle is equal to the radius, being half the diameter, squared and then multiplied by the constant pi, being 3.14 and so on. |
| 05:31 | The radius of the front calliper pistons is therefore 13.5, 16 and 19mm. |
| 05:38 | So the total area of one side of the calliper is 13.5, 16 and 19 squared, multiplied by pi which gives us an area of about 2510mm². |
| 05:52 | Likewise, the area of the master cylinder is 22.2 divided by 2 giving us a radius of 11.1 which is squared and multiplied by pi to give us an area of 387mm². |
| 06:06 | Now we can put these together to determine the leverage over our front brakes. |
| 06:10 | The total piston area of 2510 divided by the master cylinder area of 387 and then multiplied by the pedal ratio of 5:1 gives us a leverage of 32.4:1 over our front brakes. |
| 06:27 | Moving onto the rear brakes which we'll say consists of 4 piston callipers with 27 and 32mm pistons and an 11/16th inch or 16.8mm master cylinder and of course the same pedal ratio of 5:1. |
| 06:42 | If we follow the same method, we'll find a leverage of about 31:1 over our rear brakes. |
| 06:48 | With the front and rear leverage, we can now find the front to rear bias capability. |
| 06:53 | This is done by dividing the front leverage by the sum of the front and the rear leverage. |
| 06:59 | So 32.4 divided by 32.4 plus 31 which gives us a front to rear hydraulic leverage bias of 51.1%. |
| 07:10 | Now we've calculated the hydraulic bias capability of the system, we can understand our current setup and make educated changes to the system with a good idea of what the results will be. |
| 07:23 | It's important to understand that what we've just found is a theoretical value and although it gives us a good indication, it isn't always completely accurate as factors like compliance have a significant effect over the pressures. |
| 07:36 | This is where brake pressure measurement comes into play which we covered in the earlier brake measurements module. |
| 07:42 | As this is really the best way of understanding how changes to the hydraulic bias actually translate. |
| 07:49 | The pressures can be used to more directly determine the clamping force at each calliper. |
| 07:55 | If the driver applied 50kg of force to the pedal with a 5:1 ratio, that means 250kg is applied to the bias bar. |
| 08:05 | If the bar is centred, that force would be distributed evenly into both master cylinders so 125kg into each. |
| 08:14 | We know from the fundamentals section of this course that the pressure generated by the master cylinder is equal to the force applied, divided by the master cylinder bore area in metres square. |
| 08:27 | In our case, with a 7/8th inch front and 11/16th inch rear master cylinder, this means 3169 kilopascals or 460 psi of pressure is generated in the front circuit and 5531 kilopascals or 802 psi in the rear. |
| 08:49 | Obviously if we had the data, we'd just use the actual pressure measured in the system and we could also understand how this really changes with adjustments to the brake bias bar. |
| 09:00 | But for our example, let's continue with these theoretical values. |
| 09:03 | The next step is to understand how the pressure is used in each calliper or more specifically, how it's converted into clamping force. |
| 09:13 | This is found by rearranging the pressure equals force over area equation and using the calliper piston area. |
| 09:20 | So the clamping force in the front callipers is equal to the pressure being 3169 kilopascals multiplied by the calliper piston area which as we figured out earlier is 2510mm². |
| 09:37 | This gives us a clamping force of 7954 newtons or 810kg at the front callipers. |
| 09:45 | Likewise for the rear, 5531 kilopascals multiplied by the calliper piston area of 1376.8mm² gives us a clamping force of around 7615 newtons or 776kg. |
| 10:05 | Comparing these again, we can find the same 51.1% front to rear leverage bias as before as well as the same leverage ratios for the front and rear. |
| 10:17 | Before finishing up, let's consider pedal feel. |
| 10:20 | Assuming we have the bias correct and the front to rear brakes engage at the same time, we can change both master cylinder sizes, keeping the bias front to rear the same. |
| 10:30 | We know from what we've just covered that this means retaining the leverage ratio between the front and the rear so if the pedal feels too short and/or requires too much effort, we can increase the leverage over the front and rear brakes by the same percentage. |
| 10:47 | This is done by decreasing the master cylinder sizes. |
| 10:51 | If the pedal feels too long and/or vague, assuming this isn't caused by excessive compliance in the system, we want to decrease the leverage over the front and the rear again by the same percentage and this is done by increasing the master cylinder sizes. |
| 11:07 | It's unlikely that we'll be able to find the exact master cylinder sizes to keep the leverage ratio exactly the same so this will result in changes to the bias which if small enough can be compensated for with the bias bar without moving too far from the central position. |
| 11:24 | Changing the pedal ratio can of course help change the pedal feel as well as changing the leverage over both brake circuits by the same amount. |
| 11:32 | An increased pedal ratio will give a similar result to a smaller master cylinder size, essentially increasing the leverage making the pedal lighter but longer and vice versa with decreasing the pedal. |
| 11:46 | Making changes to the pedal ratio may be easier or more difficult than master cylinder changes, depending on your setup so it's just something to keep in mind. |
| 11:54 | We've covered a lot in this module so let's summarise the key points. |
| 11:58 | The master cylinder size is a key factor in the leverage the driver has over the brakes. |
| 12:04 | For a pedal input of a given force, an increase in master cylinder size will decrease the pressure generated in the brake lines. |
| 12:12 | Meaning the leverage over the brakes will be reduced. |
| 12:15 | This has the effect of making the pedal feel firmer but also shorter. |
| 12:20 | The opposite is also true, a decrease in master cylinder size will increase the pressure generated for a given pedal force, meaning the leverage over the brakes is also increased. |
| 12:31 | This will make the pedal feel lighter but also longer. |
| 12:35 | The hydraulic leverage is determined by the calliper piston area divided by the master cylinder bore area and then multiplied by the pedal ratio. |
| 12:44 | Changing master cylinder sizes allows us to change the leverage over the front and rear brakes, relative to each other which results in changing the hydraulic bias capability of the brakes. |
| 12:56 | We can calculate the theoretical value for this bias or use pressure measurements to get an accurate representation. |
| 13:02 | All of this makes it possible to correct bias issues while retaining brake feel or correct brake feel issues while retaining the bias. |
