Brake System Design and Optimization: HPA Brake Calculator
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HPA Brake Calculator
16.14
| 00:00 | - So far in this section of the course we covered the calculations and decisions we need to make when designing a braking system and choosing appropriately sized components. |
| 00:10 | This knowledge can be used to design a system from scratch or to understand the potential drawbacks of an existing system and how to correct it while retaining some of the components. |
| 00:21 | Now that we have a sound understanding of how we can calculate these results manually, we can use a more automated approach to save some time in the form of the HPA online braking system calculator. |
| 00:35 | Using this calculator, you'll be able to enter the measurements from your vehicle, the target pedal effort and the size of the components involved in the braking system. |
| 00:44 | The required master cylinder sizes will then be calculated while highlighting any potential issues with the system. |
| 00:52 | From here, you'll be able to experiment with changing certain components and seeing how they affect the system as a whole as well as getting a clear view of how the proportioning valve can be incorporated and how it varies the brake bias to approximate an optimum result over the range of conditons. |
| 01:11 | Before we get started with the calculator, we need to cover the assumptions and simplifications that have been made in the interest of keeping this calculator simple and fast to use without the need for excessive inputs or engineering knowledge. |
| 01:25 | All of these assumptions are related to tyres which as we mentioned before, are extremely complex and difficult to include in calculations. |
| 01:35 | The first being that the same tyre compound is used front and rear which is most likely going to be the case anyway but also that the size of the contact patch is the same and ignoring the effects of tyre load sensitivity. |
| 01:49 | This was discussed in more detail in the previous modules so check back if you need a refresher. |
| 01:56 | Tyre deflection under load is also a function of the tyre's vertical stiffness and that varies with inflation pressure, size and construction. |
| 02:04 | Since the resulting reduction in tyre radius from unloaded to loaded has a relatively insignificant impact on the bias, we can ignore it for these calculations. |
| 02:15 | With all these points in mind, it's easy to see how the actual situation may be different from what we calculated but again the difference is relatively small and different track conditions will have more of an impact than anything else so you can still quickly find a really solid starting point and then use the tuning tools to hone in on the best solution. |
| 02:37 | So let's jump into the calculator and see how it works. |
| 02:41 | We have 3 main sections here and a plot to help paint a picture of the resulting bias. |
| 02:46 | Up top is the section where we input our vehicle's data, next is the intermediate calculation section which will populate automatically and is just shown for reference. |
| 02:57 | And next is the results section which naturally gives us our important outputs as well as some potential warnings. |
| 03:05 | Naturally we'll start back up the top in the inputs section. |
| 03:08 | Every cell in blue requires an input and the units required are noted next to each cell. |
| 03:14 | There's also a small question mark next to each parameter which can be clicked for some more information. |
| 03:22 | The vehicle's dimensions and mass are those related to the longitudinal load transfer. |
| 03:27 | The wheel base, total mass of the vehicle and front weight distribution as a percentage are all relatively simple to measure. |
| 03:35 | However you'll need some corner weight scales for the mass measurements or alternatively if your vehicle is relatively close to factory configuration, you'll likely be able to find some approximate values online. |
| 03:47 | It's also possible, if not a bit more difficult to measure the vehicle's centre of gravity height. |
| 03:53 | Learning this process is beyond the scope of this course but if you'd like to see how it's done, make sure you check out our HPA Suspension Tuning and Optimisation course. |
| 04:03 | For now, just like finding the vehicle's weight, it's possible to find reasonably accurate values online for a factory vehicle and we can make some educated guesses on where our vehicle's COG might be if it's been lowered from there. |
| 04:17 | A quick note here, if you'd lowered your car by 50mm, that doesn't mean the COG has been lowered by 50mm, since the COG height is a function of the sprung and unsprung weight which hasn't been moved. |
| 04:32 | We'll continue with our example from the previous modules and enter the data into our calculator. |
| 04:37 | A wheel base of 2570mm, a mass of 1200kg, with a 53% front distribution and a COG height of 450mm. |
| 04:49 | The aerodynamic loads are significantly more involved though and I wouldn't recommend adding these into the equations unless you have a good understanding of how much aero load your vehicle is generating from testing. |
| 05:02 | We'll leave these as zero for our example since the rest of our brake package from the previous modules wasn't designed around significant aero loads. |
| 05:11 | This brings us to our next input, the maximum sustained G force we'd expect we're going to pull under brakes. |
| 05:19 | This requires another assumption as we discussed in the previous modules. |
| 05:23 | To recap, a modern production car on decent tyres might be in the vicinity of 0.8G, whereas a performance focused car on suitable tyres could see up to 1G. |
| 05:34 | Well sorted race cars with minimal downforce are able to achieve between 1 and 2G and adding more downforce into the mix could bring this up to 3G. |
| 05:44 | If we're redesigning a braking package on a vehicle due to performance issues, we may already have this G force data. |
| 05:52 | Using this as a reference, it would be safe to say that with improvements, we'll be able to achieve higher Gs. |
| 05:58 | But we also need to be realistic as assuming your vehicle can achieve much higher deceleration than it actually does will mean that you target an excessively forward brake bias and too aggressive brake torque. |
| 06:11 | Basically, resulting in a car that locks the front brakes too easily. |
| 06:16 | As with our previous example, let's go with 1.2G. |
| 06:21 | We'll leave the proportioning valve setting as no for now so our calculations assume there is no proportioning valve but we'll come back to this soon. |
| 06:30 | Next we can set our target pedal ratio and effort. |
| 06:34 | If we have a fixed pedal ratio, check the pedals and pedal boxes module in the brake systems components section if you want a refresher on how to calculate that. |
| 06:43 | We can put this in here. |
| 06:45 | Or for more motorsport style pedal boxes with an adjustable pedal ratio, 5:1 is usually in the middle of this range so this is a good target to start with. |
| 06:55 | For pedal effort, 50kg is also a good starting point for a race car but anywhere between 20kg to 80kg could be acceptable depending on your preference and requirements. |
| 07:07 | Moving on, we need to know the tyre size we plan on running and enter this for the front and rear tyres in the standard tyre format of tyre width, aspect ratio and rim diameter. |
| 07:19 | Our example car actually uses a racing slick where the size is expressed in width, tyre diameter and rim diameter being 27/65/R18. |
| 07:29 | Which is about the equivalent of a 275/35/R18. |
| 07:34 | Next we move onto the size of braking components and how we determine what these should be has been covered in depth over the last few modules. |
| 07:42 | However this is an area of the sheet that lends itself nicely to experimentation so feel free to try different combinations of disc size, calliper pistons as well as pad compounds. |
| 07:55 | Of course keeping in mind that we'll need to fit these inside your wheels and ideally have the same pad compound for the front and rear. |
| 08:03 | Sticking with our previous example, on the front we use the disc with a 370mm outer diameter, a pad with a 53mm radius and a coefficient of friction of 0.4. |
| 08:16 | The Endless MONO6 callipers have 27, 32 and 38mm diameter pistons. |
| 08:23 | On the rear, a 280mm disc, a pad with a 47mm radius and the same compound, and the Endless MONO4r callipers which have 2 pistons on each side of 27 and 32mm diameter. |
| 08:38 | We can just enter a zero into the 3rd calliper piston cell. |
| 08:42 | That completes our primary inputs and by now we can see all the intermediate calculations and results populate. |
| 08:50 | Looking at our results section, we're recommended a front master cylinder with a 17.11mm diameter and on the rear, we're recommended an 18.33mm diameter master cylinder. |
| 09:03 | A few more inputs are required at this stage as the recommendation is just a theoretical number of the exact master cylinder size needed to generate the required hydraulic pressure. |
| 09:14 | And this is more than likely not going to be a commonly available size. |
| 09:18 | We've compiled a list of the commonly available sizes here. |
| 09:23 | The blue cell will automatically select the closest size but can still be changed if you want to experiment with different master cylinder sizes. |
| 09:31 | For example, if we use an 11/16th inch or 17.46mm front master cylinder, the rear cylinder now needs to be about 18.71mm to maintain the same bias. |
| 09:45 | A 19mm rear master cylinder is the closest available option to this. |
| 09:51 | In this case all the warnings seem to be OK because the master cylinder travel is close enough that the bias bar tilt shouldn't cause excessive bias migration, the expected pedal travel is between 30 and 40mm, the disc size should fit under our wheels and the pad compounds are the same front and rear and the hydraulic pressure generated should be within the safe working range of most components. |
| 10:16 | From here, we could experiment with how changing our pedal ratio would change the pedal travel and the effort required to generate our target brake torque. |
| 10:25 | For example, our 5:1 pedal ratio requires 38mm of pedal travel and 53kg of effort. |
| 10:33 | But leaving our master cylinder inputs as they are and changing the pedal ratio to 6:1 increases the pedal travel to 46mm but lowers the effort required to 44kg. |
| 10:46 | We'll leave our pedal ratio as 5:1 for now and experiment with master cylinder changes. |
| 10:51 | If for example our master cylinder supplier didn't offer the 3/4 inch or 19.05mm size that we'd selected for our front brakes, but rather offered the 7/10th inch master cylinder, looking at our list, we can select the 17.78mm equivalent. |
| 11:10 | To maintain our target bias, we're now recommended a rear master cylinder size of 19.05, again this isn't available and is actually relatively close to the 7/10th offering from our supplier. |
| 11:25 | So what happens if we select this? First, moving down sizes in master cylinder has had a similar effect to increasing the pedal ratio. |
| 11:35 | Increasing the pedal travel but decreasing the required effort for the same brake torque. |
| 11:41 | The issue is we've changed the relative size of the front to rear master cylinders and therefore changed our bias away from the target at the 1.2G deceleration. |
| 11:52 | This can be clearly seen in our brake bias plot. |
| 11:55 | On this plot, the black line shows the optimal forward bias for our vehicle and how this increases with the rate of deceleration. |
| 12:03 | Anywhere to the right of this line in the shaded red area is too much rear bias and we want to avoid being in this zone as we know it can cause the car to be unstable. |
| 12:13 | The green shaded area is therefore more front bias than optimal but within 7%. |
| 12:19 | So a stable condition that's close to our maximum braking performance. |
| 12:24 | Anything in the grey area is also a safe stable overly front bias but we're leaving a lot of braking performance on the table. |
| 12:34 | The blue line is our actual brake bias and since we're not using a proportioning valve yet, this is a straight horizontal line showing a constant value. |
| 12:44 | The main issue we have is that the brake bias isn't optimal at 1.2G. |
| 12:49 | The sweet spot is actually closer to 1.05G meaning at 1.2G, we'll end up with too much rear bias and therefore some instability. |
| 12:59 | The reason for this is we decrease the size of our rear master cylinder relative to the front, meaning more hydraulic pressure in the rear circuit and therefore more rear bias. |
| 13:09 | If we look back at the results section and change the rear master cylinder size to the commonly available 20mm size, we can see that our bias has now moved further forward and is optimal at 1.3G. |
| 13:25 | Still not ideal for our setup but much more desirable since it's stable and allows for some improvement. |
| 13:32 | It's clear we'll never be able to get the balance exactly right here, simply due to the availability of master cylinders. |
| 13:38 | But it's critical to understand the effect it has so we can make the best choice. |
| 13:43 | We'll also be able to adjust for this when tuning our system using the bias bar. |
| 13:48 | Now it's time to add the proportioning valve into the mix and see what effect it has. |
| 13:53 | Heading back up to our first input section we'll change the preference to yes to include the valve. |
| 13:59 | The knee point and slope setting will depend on the proportioning valve we intend to use. |
| 14:04 | Considering the Tilton lever type product from the previous examples, this has a slope of 3:1 after the knee point which was about 320 psi for position 2 which we discussed in the previous module. |
| 14:19 | As we know, the use of the proportioning valve changes our rear master cylinder requirements so we need to head back to our results section and update the size of the master cylinders. |
| 14:30 | We'll first change our front cylinder size back to the 11/16th of an inch or 17.46mm size and a 5/8th or 15.88 master cylinder is closest to our recommended size of 13.06. |
| 14:47 | We can see how our proportioning valve approximates the optimum bias over a range of pedal inputs, helping to avoid the front wheels locking prematurely in lower grip conditions or at light brake application. |
| 15:01 | From here, we can experiment with different proportioning valves in different settings to see how the slope and knee point can be adjusted for the best results. |
| 15:11 | Just be sure to update the rear master cylinder being used for each change. |
| 15:16 | To summarise, this calculator requires the input of various vehicle measurements along with the size of components involved in braking. |
| 15:27 | Using this information, it will provide a recommendation for master cylinder sizing which we need to match to an available product. |
| 15:35 | The calculator will also give some warnings if the setup will likely result in potential issues but as we know, there are a large number of additional problems that can present themselves in a braking system unrelated to the brake bias calculations so these need to be kept in mind and considered alongside the results. |
| 15:55 | The intention here is to allow us to quickly determine an effective starting point for a new system or highlight areas of improvement in an existing system as well as experiment with changing components to get an understanding of the effect on the braking system as a whole. |
