When brake engineers start the work of designing a new brake system for a car, the first thing they do is create something called the “Ideal Brake Curve.” If this sounds like jargonese to you, fear not, your resident suspension engineer is here to help.
The Ideal Brake Curve is a graph that brake engineers create before they know anything about the brake system of a car. It is the first step in designing the new system. It shows us the stopping power of the front and rear axles under ideal conditions. In other words, if we had a perfect brake system that could use all the available traction of the front and rear axles at all times and under all possible road conditions, what would the stopping power of each axle be? It does not tell us what the actual brake system can do; that comes later.
At the point when we create the Ideal Brake Curve, we know nothing about the actual brakes. We don’t know how big the rotors will be or what type of calipers we will use or how big the brake booster is going to be. We know nothing at all about the brake hardware because that hasn’t been designed yet. The Ideal Brake Curve only tells us what the potential stopping power of the front and rear axles could be. It is then up to the brake system engineer to design a system that makes the best use of this stopping power.
The other thing the Ideal Brake Curve tells us is what the front and rear axle stopping forces could be on a variety of different surfaces, such as ice, wet, or dry pavement. Here, allow me to explain on my new YouTube channel, which you should absolutely subscribe to (please):
A Typical Ideal Brake Curve
Let’s look at a typical ideal brake curve:
The front axle brake force is on the horizontal axis of this graph and the rear axle brake force is on the vertical axis. The diagonal lines represent different surfaces based on their friction coefficients. Notice that the scale is a bit different on each axis; each marker on the X-axis is 2000 Newtons, while each on the vertical axis is just 1000 — the front axle will generate more brake force than the rear, so this should come as no surprise.
Before we go any further, we need a quick refresher on friction coefficients. Any time two objects sit against one another — imagine a block of wood sitting on a table, or a tire sitting on the road — it takes a certain amount of force to make the objects slide relative to one other. A block of wood on a glass table may be fairly easy to slide but a tire on the road will be much harder. The amount of force it takes to make the objects slide relative to one another depends on the force pushing the objects together and something called the friction coefficient.
Let’s take an example. Let’s assume have a block of wood sitting on a table, and the block of wood weighs 10 lbs. If it takes 5 lbs of force to slide the block across the table, then the friction coefficient between the table and the block would be 5 / 10 = 0.5. If on the other hand, we polish both the table and the block, and suppose it now takes only 2 lbs of force to slide the block then the friction coefficient would now be 2 / 10 = 0.2. The relationship between force, friction coefficient and weight (well, normal force) is Force = friction coefficient x normal force. For a car sitting with all 4 tires on dry pavement, the friction coefficient will be close to 1, meaning that if the car weighs 4000 lbs, it will take 400 x 1 = 4000 lbs of force to make the car slide across the road. For ice, on the other hand, the friction coefficient will be closer to 0.2.
Let’s get back to our graph and learn how to read it. The first thing we need to know is what surface we are driving on. If we assume. for instance, that we are driving on dry asphalt, then we could also assume our friction coefficient is about 1. We would then go the diagonal line marked 1 on our graph and follow it up until we reach the curve:
From there we can draw vertical and horizontal lines to our axes to find out what the maximum front and rear brake forces would be that our vehicle could achieve:
We see here that on dry pavement, our tires should be able to generate about 13,500 Newtons (N) force on the front axle and just under 6000 N force on the rear axle before they would lose grip. Of course, we would need a brake system that is powerful enough to generate this much braking force, but at least we know what our tires are capable of.
If on the other hand we assume we are on ice with a friction coefficient of 0.2, we would go to the line marked 0.2 and follow it to our curve:
Now, instead of being able to generate 13,500 N of braking force, the front tires are only able to generate a little over 2000 N of stopping force. Similarly, the rear tires can only generate a bit under 2000 N of force instead of the 6000 N we had on dry pavement. This makes perfect sense since ice is much more slippery than pavement so we would naturally expect to get much less stopping power on it versus pavement.
The Curvature of the Line
You probably noticed that the ideal brake curve is not a straight line, but has a lot of curvature to it. The reason for this is weight transfer. As we brake harder and harder, more and more weight transfers from the rear axle to the front. This is why when you hit the brakes in your car, the front of the car goes down and the rear comes up. The front has effectively gotten heavier, and the rear has effectively gotten lighter. If we had a super sticky road, super sticky tires, and massive brakes, we could imagine a case where we could brake so hard that there would be enough weight transfer from the rear to the front that the rear wheels would come off the ground. This is pretty common in bicycles and motorcycles since they are so much shorter and taller than cars, so if you ride a bike, you know all about doing “stoppies.”
But, if you look at the ideal brake curve, you can picture the curve continuing to the right until it curves all the way round and comes back down to the horizontal axis. This is the point where the rear wheels have lifted off the ground and are no longer able to provide any more stopping power.
How To Come Up With The Ideal Brake Curve
Let’s look into what it takes to generate one of these ideal brake curves. There are four basic parameters we need to know:
- Vehicle weight
- Front to rear weight distribution
- The height of the center of gravity
- The wheelbase length
The weight and weight distribution tell us how much weight is on the front and rear axles right from the start. The height of the center of gravity along with the wheelbase tell us how much weight transfer there will be when we hit the brakes. Once we know these numbers, we can easily calculate how much force is on the front and rear tires as we brake harder and harder. From there we can calculate the actual stopping power for all the different friction coefficients we want to look at, in this case everything between 0 and 1.
We can look at the effect of each of these four parameters by changing them one by one and seeing how the curve changes. The example above used a vehicle that had a mass of 2000 Kg, a front weight distribution of 50%, a CG height of 550 mm and a wheelbase of 2,800 mm. Here is that curve again as a reminder:
If we now change the mass of the car down from 2000 Kg to 1500 Kg, the curve would look like this:
Notice that the shape of the curve is basically the same, just a bit smaller since it would take less braking force to stop the lighter car.
How Weight Distribution Effects The Ideal Brake Curve
What if instead of reducing the weight, we changed the weight distribution? Let’s change it from 50% front weight to 60% — so a bit nose-heavier:
Now we see that the shape of the curve has really changed. It is much flatter than before, and this makes sense. We have a lot more weight on the front axle, so we need to get a lot more braking force from the front. The lower rear weight means we cannot get as much stopping power out of the rears as we did before.
CG Height Effect
We could also change the height of the center of gravity. If go back to our original example and change the CG height from 550 mm to 700 mm we would get this curve:
It’s not easy to see but the curve is more horizontal and more rounded than it was before. This makes sense because the higher CG height means we get more weight transfer the harder we brake. Of course, this effect gets worse the harder we brake so the curve has more “bend” to it.
The Wheelbase Effect
Lastly, we can see what would happen if we changed the wheelbase. Let’s shorten the wheelbase from 2,800 mm to 2,500 mm:
The effect is even more subtle here than with a CG height change, but you still see that the curve has more “bend” to it but it’s not as much as the CG height change we did before. This is because just like when we changed the CG height, a shorter wheelbase means more weight transfer the harder we brake. The effect of both would really be the same but they look different here because changing from 550 to 700 mm CG height is a bigger percentage change than going from 2,800 to 2,500 mm wheelbase.
I want to take a moment here to remind everyone that everything we have been talking about here has nothing to do with the actual brakes in the car. This is all theoretical and only shows what the stopping power of the front and rear axles would be under ideal conditions and with a perfect brake system. As I mentioned before, these curves are created very early in the design process when we know absolutely nothing about the real brakes yet. We don’t know how big the brake rotors will be or what types of calipers we will use, nor do we know anything about the brake booster. These curves only tell us what the tires are capable of — the maximum braking fore that we can possibly get from each axle under ideal conditions. It is now the task of the brake systems engineer to design a brake system that uses as much of the tires’ capabilities as possible to get the best stopping power.
Some Real World Examples
To bring this discussion some perspective, let’s look at two real world examples. We’ll use a 2022 Porsche 911 and a 2022 Honda Accord as comparators. We will unfortunately have to make some assumptions about the heights of the centers of gravity for these vehicles, but all the other parameters are published and easily available. Here is the ideal brake curve for the Porsche. Notice that I have assumed a CG height of 450 mm:
You can see immediately that this curve is much more upright than the ones we’ve seen so far. This is because the 911 has so much weight on the rear axle that we can use the rear brakes much more than on any other car. Also, the CG height is quite low so there is much less weight transfer happening. This reduces the amount of “bend” in the curve considerably.
Conversely, here is the curve for the Honda. I’ve assumed a CG height of 550 mm of this vehicle:
You can see how the huge difference in weight distribution means that the curve for the Honda is much more horizontal. There is much more weight on the front axle here, so we need to get much more stopping power out of the front brakes. Similarly, there is very little weight on the rear axle so we can’t use those brakes nearly as much.
Looking at these curves also makes it clear why when you look at the brakes of a Honda Accord, you will see that the rear brakes have smaller calipers and thinner rotors than the fronts. That is pretty typical of front heavy front-wheel-drive cars. The Porsche, on the other hand, has rear brakes that are as big, if not bigger, than the fronts. With all that weight in the back, the Porsche needs to use those rear brakes much more.
Now that we know what the Ideal Brake Curve we have the information we need to design a brake system that makes the best use of the stopping power each axle has. More on this in a follow-up article.