Making Sense of McLaren's New Suspension
2020 McLaren GT
After dropping some preview images earlier, McLaren has now introduced the 2020 McLaren GT and provided detailed photos and specifications. You can read summaries in all the usual media outlets. One of the more intriguing aspects of this concerns the design of the suspension, which I will quote in full:
The suspension is a lightweight aluminum, double wishbone design, paired in the new McLaren GT with hydraulic dampers to deliver Proactive Damping Control. Governed by the most sophisticated iteration yet of the pioneering Optimal Control Theory software algorithm developed for the 720S, the suspension uses inputs from sensors to ‘read’ the road, interpreting what will likely happen next and reacting predictively in just two milliseconds. Overall, body movement is tailored for occupant comfort and vertical load and contact patch variation are optimized to enhance grip levels, but each of the three active dynamics handling modes – Comfort, Sport and Track – has its own distinct set of parameters to reflect the selected preference, for example, a particularly compliant ride in Comfort mode.
If you’re not a controls engineer this probably sounds a bit confusing and the implications are not particularly obvious, so let’s try to sort it out without using too much math.
First, let’s review the simplified basics of suspension at one corner of a car. The wheel can move up and down from a neutral position, this is displacement. As it moves a spring, usually a steel coil but sometimes pressurized gas, resists motion proportional to displacement. Something pushes the wheel and the spring pushes back, pushing harder the further away from neutral that the wheel is displaced. The spring stores energy and, left unchecked, the wheel will continue to oscillate back and forth anytime it encounters a bump.
To control that oscillation we also have a damper, sometimes called a shock absorber, that pushes back on the wheel proportional to the rate at which the wheel is moving up and down. If you’ve ever held an automotive damper and tried to contract or expand it you’ll find that you can do so easily as long as you move slowly enough. Try to rush it and it becomes impossible. The damper removes the kinetic energy from the wheel-car system, causing the car to stop bouncing back and forth after you hit a bump, and turns it into heat. The classic way this is done is by having a little piston, perforated with holes, and moves back and forth in oil. The relationship between how fast you compress a damper and how hard it pushes back is the damping coefficient and you can control it by the number of holes in the piston. The more holes you have, the less the damper pushes back and the smaller the damping coefficient. It didn’t take long for suspension engineers to realize you’d like to have different damping coefficients for compression (when you first hit a bump) and rebound (when the damper starts extending again), which you can do with check valves. When your car gets older and starts to feel a bit bouncy and out of control, that’s the dampers wearing out and the damping coefficient dropping below the value it is supposed to be at. Time for new shocks!
Figuring out what damping coefficient to use on a car is complicated, something of a judgement call, and why good suspension and handling engineers are in demand. Essentially you’re trading off comfort, how the vehicle responds to bumps in the road, and handling, how the vehicle responds to driver inputs. Comfort generally asks for a small damping coefficient to give that classic 1970s American luxury car ride, while handling asks for a larger damping coefficient so the vehicle responds well when you ask it to turn. One solution to this is to have separate, discrete settings for the two conditions. An early example of this is the 1987 Ford Thunderbird Turbo Coupe. An electronics box looks at things like throttle position, steering angle, turbo boost, and so on, and when those exceed certain limits it decides, in effect, “The driver must be sending it! Stiffen up the suspension!” It then commands little actuators mounted on top of the dampers to turn an adjuster to the position that increases the damping coefficient. When things settle down it goes back to the comfort position. Systems like this are the origin of the “Sport Button” in your new car.
McLaren got more sophisticated. On the 720S the damping coefficient on each damper can be adjusted continuously, meaning it can be any value between two extremes as opposed to just “soft” and “stiff.” This is done using a computer controlled needle valve to control the flow of fluid. The input to the computer is the position and velocity of all the dampers, plus things like steering angle and speed. Broadly speaking you can intuit heuristics like “If the wheel is moving fast, increase the damping coefficient” or “If we’re turning, increase the damping coefficient on the outside dampers to give anti-roll behavior,” but we’d like a better, less arm-waving, more mathematical solution.
The question now is: How does the computer adjust the damping in order to give the best possible ride comfort and handling? This is where the “Optimal Control Theory” part comes in.
First McLaren defined some numerical parameters that mathematically describe what ideal ride and handling look like. In a very simplified way, you might say that in an ideal worth the chassis (including the driver) should not move vertically in response to a bump and should not roll in response to a turn input. It’s straightforward to define some mathematical parameters that describe these characteristics.
Remember, the damping coefficient is not a single value. It is a function of wheel position and vehicle, steering angle, speed, and probably other things. This is important.
They then created a physics model of how the car responds to simultaneous inputs from the road (bumps) and steering commands (driver). This allows you to see, for a given damping coefficient function and inputs (the road, the driver), how close the car gets to that mathematical ideal defined earlier. The driver steering inputs are simple, they’re just a function of the shape of the road. For the 720S suspension design the bumps in the road were modeled as random noise with a particular distribution. In other words, you get lots of little tiny bumps but a few big bumps.
Now we can define the problem in a nerdy, mathematical way. Given the physics model of the car, and the two inputs (random road bumps and defined driver steering inputs), find the damping coefficient function that makes the vehicle respond as close as possible to the ideal behavior (comfort and handling) we defined earlier. This is the Optimal Control Theory problem McLaren is talking about. The control is the damping coefficient function and the optimal control is a function that minimizes poor handling and ride discomfort. Optimal Control Theory is the process by which you solve this problem mathematically.
You can read about how McLaren solved this problem in a general way in this SAE article, or in a more detailed way in this academic journal paper.
What’s new in the McLaren GT is that the car can now sense the oncoming bumps in the road. The damping control algorithm now has a new input, the size of the bump we’re about to hit. The distribution of bumps in the road is still random, sure, but now we can adjust the damping, in advance, to give the optimal response for every bump we encounter rather than giving the optimal response for bumps in general. The result should be exceptional handling and ride comfort in most conditions.
The McLaren GT is, of course, a $200,000 supercar but in time this technology should flow down to more affordable vehicles. The era of putting up with painfully stiff suspension to get good handling is starting to wind down.
