Inerter in Engineering and F1

This is one I made very soon after I got the idea. It was back in 1997. So this is the first prototype. This is the first one that I made out of a child's toy, a car doll. Today I'm at the University of Cambridge to speak to a professor who has invented what has been called a genius device. We're going to hear the story behind this device directly from its inventor. And this is a fascinating story that has it all. The biggest spy scandal in the history of Formula One. A humble professor who has proved that an established engineering principle used for more than 70 years was wrong, and a secret device that some of the best engineers in the world were not able to understand despite looking right at it. Before moving on, let me briefly recall some elements of the spy scandal, to give you a clear sense of the impact that this professor has had on Formula 1. In 2007, the Formula One world was rocked by what became the biggest spy scandal in the history of the sport. One of the elements at the center of that scandal was a mysterious device called a J-Dumper. Renault had obtained a drawing of the never-heard-before J-Dumper from an ex-employee of McLaren. And Renault tried to have McLaren disqualified because they thought that the J-Dumper violated Formula One regulations. In turn, McLaren tried to have Renault penalized because they committed industrial espionage by getting hold of the drawing of that device. When the proceedings of the World Motorsport Council investigation were made public, they kept secret the nature of the device. The only information made public was that McLaren was not disqualified because the J-Dumper did not violate any rule and in fact the engineers at Renault misunderstood what this device did. Medias around the world tried to figure out what this device was and eventually a connection was made with Malcolm Smith, Professor of Control Engineering at the University of Cambridge. Today we have the opportunity to speak to Professor Smith and have those events narrated by his very protagonists. So let's go. Professor Smith, your background is in mathematical control theory and then later on you became known for your work on the Inerter. You invented this device called the Inerter. But in this interview, I would like to... go through the story of the Inerter and how you came with the idea. And maybe we can start with your background. So you can tell us a bit what you did before the Inerter. Yes, well, Giordano, thank you. And it's always a pleasure to explain this. And it connects with my background. As you say, I started out in control theory. My first degree was in mathematics. And for my PhD, I did I worked on multivariable, robust multivariable control, frequency response methods, so how to design controllers when you've got many inputs and many outputs, how to generalize the classical theory to that situation. And later I got involved in something called H-infinity control, partly through visiting George Zames at McGill University in Montreal. And one of the key ideas is stabilizing. or looking at the class of all controllers that stabilize a given plant. So then you try to optimize over that class to minimize whatever you, a robustness measure or sensitivity. But that being able to solve over a general set and to optimize something in the frequency domain was a very important idea. Okay, thank you very much. And so then how did you get involved in Formula One? Yes, that was a chance event. I had just joined this university as a new lecturer in 1990. And the first summer, 1991, August of that year, everyone was on holiday except myself, really, among the academic staff. And a phone call came through from Williams Grand Prix engineering from Paddy Lowe, who I didn't know at the time. And those... who know about Formula One will know that he eventually became a very famous Formula One designer and engineering director at McLaren and then later Mercedes. At the time, he was in charge of active suspension development at Williams Grand Prix, and they had a stability problem. So he phoned the group. He was Wanting to speak to Professor Keith Glover, he'd been taught by him at Cambridge as an undergraduate, but Keith was on holiday for another two weeks, and Paddy explained they had a test at Silverstone the following week. And so I was rather bold in taking the job and was hoping that Keith would not be annoyed. Fortunately, Keith was pleased that I took the job. But that got me started in consulting on this active suspension system. So you started to be involved as a consultant. Yes. Then this idea started to have an influence on your search. Yes. Well, Not initially. Perhaps one should say a little bit about active suspension first. A normal car suspension has springs and dampers and anti-roll bars. Those are also springs. That's the basic normal passive suspension. With an active suspension, you're replacing the springs and dampers with powered hydraulics. You'd have a piston and a cylinder and you'd have pressured hydraulic fluid that can be directed with silver valves above and below the piston to extend and contract. So that's, if you like, the actuator in the control system. Then you have measurements all around the car, accelerometers, deflection sensors, pressure gauges. You can have as many as 20 measurements on the car being fed back into a computer that implements the controller and then that drives these four actions. that extends and contracts the strut at each wheel station. I was brought in as a control specialist, knowing about multivalve control design. And of course, you bring those methods in and you apply them. As we made progress, and I worked more on these, I became interested in the systems themselves. and it's... I started to develop some research problems. There are many different layouts, mechanical layouts that are possible and different sensing arrangements. And then the question is, which is the best? And then how do you design the controller to produce maximum improvement in mechanical grip? That's how the tire deflects and contacts with the road. And how do you best control the ride height and so on? So the engineering setup, the design of these systems becomes fused with the control system design in possibly a complicated way. So that became a research question for me. How do you simplify things down and find a way to approach this, which could answer some basic questions? So you started then. to do research on active suspension systems. Yes. Was this then implemented by Williams? Well, there wasn't really time. The consulting work and the implementation of the control system happened so fast. From August 1991, the system was actually raced for the first time with Nigel Mansell at the South African Grand Prix in 1992. And Williams had extraordinary success. In the 1992 season and the 1993 season, they won the championship easily by a big margin. And then active suspension was banned at the end of the 1993 season. Why was it banned? This is often a complicated story, but technologies often come and go and get banned in Formula 1. And most commonly, a technology, when it's successful... and is producing a big advantage for one team, it can get banned at that stage because the races become boring. Because a team is always winning. One team is always winning, so people don't want to watch the races or are not so interested. And then there is pressure on the authorities to equalize things so that the sponsors are happy and so on. Okay, so unfortunately, what you were developing couldn't be used anymore. But then Did you manage to do some other progress? Yes. Well, all was not lost in the sense that I'd started to think about the design of these systems and to bring in some of the methods I mentioned, H infinity. And one of the ideas there is to parameterize all controllers that can stabilize a given plant and to be able to optimize a performance measure over that set. But then that's the start of the Inerta story because you can take that same idea and instead of optimizing all overall stabilizing controllers, you can try to optimize overall passive suspensions. Now, I knew some theory from my PhD time about passivity of electrical circuits, and I knew it was possible to completely characterize all the electrical circuits you can build out of passive components. So then it seemed natural to say, well, we should do the same with mechanical mechanisms. passive mechanical mechanisms. And I think people who knew that theory would have expected that it was a direct correspondence, and that would be a relatively simple thing to do. It turned out not to be straightforward. And some of the difficulties illustrate why the Inerta hadn't been done before, if I can put it that way. So if I understand correctly, so um, given the fact that you know how to realize a circuit, you want to apply the same ideas on mechanical systems. And I actually studied something like this in the university, and the idea is that there is an analogy between electrical circuits and mechanical systems, hydraulic systems, heat systems, basically any linear system. And the idea is that you need to identify what behaves like a current, so this is called a true variable, and... what it behaves like a voltage, which is on a cross variable. And so for mechanical systems, you have the force that behaves like a current and you have the... What do you have for the voltage? The voltage becomes the velocity. The velocity. And the force becomes the current in the analogy you're speaking of. Right. Yeah. The force-current analogy. I remember the book said that... I mean, it was very convincing in the fact that the analogy then of the components where that the damper is a resistor, so it dissipates energy. The inductor behaves like a spring, and then the capacitor behaves like a mass, right? So the problem is solved. You just have to use this mapping, or not? Yes, the mapping that you've described is the one that we use to understand this. And the first important thing to say is it's power-preserving, because you're mapping... voltage and current onto velocity and force. So the product of voltage and current is a power, and the product of force and velocity is a power. So anything that's passive in the electrical domain, if you map it over exactly, will be passive in the mechanical domain and vice versa. And the analogy you've just described is what you find in the textbooks. with the element correspondences. By the way, just a brief aside, there are two analogies, but the advantage of the one we've described that's based on through and across variables is that series connections in one domain become series connections and the other parallel become parallel. So the circuits are topologically identical. And the other thing that's very good about that analogy is that ground, electrical ground, which is a datum voltage, becomes a point with constant velocity, which is a reference point in the inertial frame. So that allows one to go one step further to discuss the analogy you've described. Spring and inductor, resistor and damper, those are straightforward because those are both two terminal devices. So let's think, what are terminals in the mechanical domain? People often don't think about this. If you take a spring, the terminals are the attachment points, the two endpoints of the spring. And we're looking at the force, the equal and opposite force, at the terminals produced by the spring from its relative displacement. Right, you push the spring and you will receive a force. Yes. Yes, that's right. But it's an equal and opposite force applied at the terminals. Similarly with the damper, the terminals are the connection points. One connection point will be the housing of the damper and the other will be the piston rod. And those are the two connecting points. And both the terminals of the spring and the damper are freely movable in space. Now, let's go to the third element, the mass. So what are the terminals on the mass element? Well, if you think about the way we do mechanical modeling, the mass is usually treated as a point mass. And its motion is governed by Newton's second law. And that's the acceleration in an inertial frame. So if you're careful and you write the circuit diagram of the element, you'll see that the mass element is actually analogous to a grounded capacitor. So there's only one. You can't slide the mass in and out with two ends that are freely movable in space in the way you can do with a damper. The mass is a point mass. So the mass is analogous to a grounding capacitor. And that's... That's what you can do. Yes. That's not my observation. Okay. That's in a sense well known. But most of the textbooks don't really explain it. And also some of the books that really appreciate it the most try to cover it up by drawing a symbol for the mass that looks like a slider. So here it is. The theory, if you like, from electrical circuits forces a certain question, because to build our electrical circuits, you need three elements, resistor, capacitor and inductor. And they all need to have two terminals. So, the natural equivalent, you have a problem with the mass because it's a one-terminal device and so the circuits that you can realize with it are more limited. So, it's impossible then to go from the circuit to the mechanical device. Well, yes. So, I became puzzled at this point and the theoretical work forced a question. So it's easy to see that if one were to have a device which is genuinely two-terminal, like the spring and damper, it has two attachment points, which are freely movable in space, with the property that the equal and opposite force at the attachment points is proportional to the relative acceleration between those terminals. So if one had such a device, then the mapping would... be perfect for the synthesis theory. And then you could say, we can build any of these positive real complex impedances. We can build them mechanically. We can have a mechanism here that we can design and build and hopefully put it on the car if we can make it small enough and light enough. So that was the point. I was stuck at that point for a while and thinking that spring mass dampers. So it's in all the books. That's the standard and that's how it must be. And maybe there is a limitation that mechanical circuits are not completely equivalent to electrical ones. When did you realize that actually something more could be done? Well, it was a thought experiment. I was trying to prove that you couldn't do it, You couldn't make something like that. But if you think positively, supposing you could build such a device and you held it in your hands, what would it feel like? And one of the properties would be that once you've set it in motion, it keeps going with constant velocity. Having realized that, it's fairly quick, it's almost immediate really to think of a way. of making such a thing. And I sketched something like this that we have on the table. And this is the first thing I did after having thought of that idea that, would you try to build one and play with it and understand it. So this is the device. This was the first one I made and it's made out of a Meccano. which is a child's modeling building kit that I was familiar with from childhood. So you can see it's a two-terminal device. The housing here is one terminal. And the end of the rod here that moves in and out is the other terminal. And the rod itself is a rack connecting with a pinion. So we have a rack and pinion mechanism. And the pinion is on this first axle here. And then there's a... a gear, an opinion connecting to a second shaft. And a similar gear, they're both five to one ratio, gear wheel, pinion here. And on the third shaft, we have this flywheel. So as the rod moves in and out, the flywheel shaft and the flywheel rotates in proportion. So we need to think about inertance. Inertance is the constant of proportionality between the force. and the relative acceleration, and it's in kilograms. That's different to the mass of the device. This weighs less than a kilogram. That's the mass of the device. The inertance is the constant of proportionality between the relative acceleration and the force. And that's typically, for inertors, is much larger than the mass. So we can get an idea approximately of the value of the inertance here. The two five-to-one ratios, that gives a multiplier of 25. The other thing that's significant is the pinion radius and the radius of gyration of the flywheel. It's approximately two to one. So that gives another factor of two, making 50. But the 50 is a ratio of forces, but also it's an inverse relationship of velocities. So it actually squares up. You get a multiplier of 2,500 times the mass of the flywheel. The flywheel is 100 grams, 0.1 of a kilogram. So overall, this device has an inertance of 250 kilograms approximately. So that's a quarter of a ton between the terminals. You can, with a small force, you can move the rod, but not very quickly. So what you have to think here is resistance to acceleration or resistance to relative acceleration. is the... characteristic. So can you actually explain a bit better this point? So here you have an inertance of 250 kilograms, right? But you can move it with very little force. Can you explain better why that's the case? I mean, because if you imagine a mass that is 250 kilograms, it's difficult to push it. So what is actually what that 150 kilograms mean? Yes. So if you imagine if we had a 250 kilogram mass on this table, and it was a frictionless table, So like on ice? Yes. You would be able to push it with a small force and it would start to accelerate and it would keep going for some period of time, just like the Inerta does. And so what makes you think that you can't move 250 kilograms is, first of all, if you had to support that weight, most people would not be able to lift 250 kilograms. But if you're just pushing it. along a plane, you still wouldn't be able to do that if there's a lot of friction. So a small car, for example, one person can't push a car because of the friction in the bearings and the tires. It's not because of the mass itself. A small force will accelerate it a bit, so it'll move a little bit. And that's the same with the Inerta, because these have rather low friction. Okay. In a certain way, this reminds a bit a damper in the sense where there is one terminal which you push and there is some kind of resistance. Maybe you can explain what is the difference? Yes, all right, let's look at this device here. This is a Formula One damper that was made by Penske Racing Shocks. So this is just a rubber handle so one can move it by hand, but you would have have a ball joint here which would connect to some suspension element and another connector at this end. But it's a two-terminal device, and we have a rod moving in and out of, we have a piston and cylinder here and a floating piston and fluid inside. But this is a totally different device than the Inerta because the force, the equal and opposite force, is proportional to relative velocity. So to keep it moving, you have to apply a constant force. To move it faster, then the force increases. So this is force proportional to relative velocity, whereas the inertial is force proportional to relative acceleration. So essentially, with the inertial, you will feel a resistance when you start to push. Exactly. It changes in velocity. It changes in velocities. Yes. Okay, so this is one particular realization of the inertial. But is this what has been done implemented in Formula 1? No. Fairly soon... We started to think of different ways to do it. What turns out to be a nice construction is to have the flywheel spin axially about the rod. And you can do that with a ball screw mechanism. Do you have an example? Yes, I can show you one of these. Take a look at this. This is a demonstrator that we... made in the engineering department. And it has a Perspex cover so you can see the mechanism inside it. So you see the threaded rod, and inside of this assembly here is the nut, which spins when there's relative velocity between the two ends of the device. And attached to the nut here is the flywheel. This is the flywheel. which rotates as you get a relative displacement between the terminals. So this is a compact, simple way to implement inertas without having multiple shafts and racks and pinions and so on. So maybe you can now try to understand how these are used in Formula 1. So, okay, you came up with this new... device. Then what happened? Having got the idea and having explored it with Cambridge Enterprise in terms of whether to protect it, we put it to the test and we approached a team in Formula One. And by this time, Paddy Lowe, that I'd worked with at Williams, he'd moved to McLaren. And I also knew other people at McLaren, Dick Glover, for example. And we decided to contact them. and to take the Inerta idea, together with some initial calculations I'd done on possible benefits, and McLaren were interested. And they signed an agreement with the university to develop it. And we went through all the stages of engineering design and simulation and what it can improve in the car in terms of reduced oscillations or improving mechanical grip and all the way through to testing and to producing an actual lap time gain on the car and once that was achieved it went on the car really for the next race and that was an exciting event in it was 2005 so time has elapsed so yeah what is exactly a timeline. So when is that you come up? with the idea, the first prototype, and then eventually got it on the car? My first Meccano model goes back to 1997. My approach to McLaren was around about 2002. And the development happened... Well, there's not a lot I can say about the internal development, but let me just point out the known facts that it was raised for the first time in 2005. And... It produced a lap time gain. And the first race was with Kimi Raikkonen driving. And it was the Spanish Grand Prix in 2005. And he won the race for McLaren's first victory of that year. And in fact, it led to several victories, a number of victories throughout the year. McLaren were close to getting the championship, but didn't quite manage it that year. That was very exciting. Yes, it was very exciting for me, thrilling really, that a theoretical concept is on the car that you're watching the Grand Prix at the weekend. So at that stage, it wasn't a story I could relate to anyone because McLaren went to fairly elaborate lengths to conceal the nature of the device. In fact, this one is an illustration of an early ball screw inertor of roughly the size and packaging that we used in Formula One. And so, again, it's a two-terminal device, and it's similar to the one I showed you before with the ball screw and the flywheel rotating actually about the line joining the two terminals. But otherwise, you might think this is some sort of exotic damper. Indeed. And if you look at the car from some distance, you wouldn't really think that there's anything unusual here. So McLaren... was able to conceal it for quite a while. Can you tell us a bit about how they did that? Yes. So they had, first of all, they named it something different. They called it the J-damper. And that was a deliberate attempt to decouple what they were doing with the technical literature. We were publishing papers on the Inerta and describing the idea and its advantages. So the idea was public? It was public domain. And that was part of the agreement with McLaren that we would continue with the academic research and that that wouldn't be held back. And so their strategy was to try to cover it up quite legally in terms of the sport. You don't have to tell your competitors exactly how you're doing things. So that was fine. Also, they did another clever thing. they stopped calling the inertance or describing the units of the inertance as kilograms, I went to a meeting and suddenly found that the x-axis was Zoggs rather than kilograms. And so that was again a decoy. In case a team member left McLaren and went to another team and described this device, knowing that one of the axes is kilograms is a giveaway. It's a clue to what's actually going on. So those two things together, they succeeded really in keeping their approach quiet for a couple of years. But then what happened is exactly what you described, that an employee from McLaren moved to another team and it leaked some information, right? That's correct. So McLaren found out about this because they hired someone from that team. It was Renault, in fact. And the person coming back from Renault was able to say, well, we have one of your drawings of the J damper, and it's been circulated in the company and examined and so on. So McLaren at that stage knew that the device had leaked out to another team. I should say this happens all the time in Formula One because the market for... engineers is quite fluid. People get hired from one team to another all the time. And you can take what's in your head. That's allowed. You're not supposed to take drawings. But that does happen as well. But the story is that even if they had a drawing, actually, this was not enough, right? Yes. Well, there's a very amusing story about how this eventually became... came into the public domain. And it was through what is now called the 2007 Formula One espionage controversy. And it started with a case being brought against McLaren. It concerned two of their, or one of their employees who'd had drawings of the Ferrari. And that became known and Ferrari brought a case against McLaren and they were found guilty of breaching the sporting code at a World Council hearing. Even though the actual impact on the design of the McLaren, it wasn't shown to be a significant impact. Nevertheless, they were found guilty and they received the largest fine in sporting history. It's still the largest fine. It was $100 million that McLaren was fined. And at this point, and in fact, as part of the defense, in anticipation of this, they were expecting a large fine. McLaren tried to say, well, actually, there's a lot of this going on. And we know. There's a case that we can prove. And so McLaren took their case to the FIA. Or as soon as McLaren blew the whistle, Renault owned up and said that they had various things. There were other things apart from the J damper, but the J damper was one of them. And there was another hearing. And Renault was found guilty of breaching the sporting code, but they... were given no fine, which is quite a lot less than $100 million. And in regard to the J damper, there was, again, an interesting sub-story. Renault had used to advantage a device on their car for a number of years called the mass damper, the tuned mass damper. That's essentially a mass on a spring, and it's a classical idea in mechanical vibrations. but they managed to find a way to get an improvement. Now, it turned out that Renault's reaction to the drawing of the J damper was to contact the FIA to try to get the J damper banned under the interpretation that it was a mass damper. Which was banned at that time. Which was banned. Renault had success with the mass damper and it was banned sometime. I forget the exact year. But by that stage, it was banned. Okay. So Renault wanted to say, well, this thing should be banned because this is a mass damper. And McLaren were able to counter that it's not a mass damper. It's something completely different. And the mass damper is a mass on a spring. So it has a one-point connection to the car. So it's not a two-terminal device. as the inerter is, so that you connect between two movable points in the suspension. So McLaren were able to argue that the inerter shouldn't be banned because it didn't come under the description of the device that was relevant to the mass damper. That was used at the World Council hearing. And in fact, in the transcript of the hearing, the justification for the no fine. being applied to Renault is that they had fundamental misunderstandings of the nature of the device and therefore it couldn't affect the championship. Nevertheless, as far as the Inerta is concerned, it's an amusing story to tell. So then at this point still no one knows what the jet damper is, right? So when the connection was found between the jet damper and the Inerta? Yes, there was a lot of pit lane gossip because information leaks out. and people leave one team and join another. And eventually people start to figure out what it is in the pit lane and so on. And still, though, it wasn't widely known. And it was an autosport journalist, Craig Scarborough, who published the scoop in Autosport. in, I think it was 2008, describing the connection between the J-damper, the mysterious J-damper, and the Inerta. And at that point, the cat was out of the bag. So everyone then in the Formula One world knew that McLaren's device was the Inerta, and it connected with the technical literature. Okay. And so since then, the Inerta has been used. The Inerta very quickly was used on most, if not all, cars within Formula 1 and became a standard component. And it continued that way until 2022, until the Inerta was banned. Oh, that must be very disappointing for you. Yes, in Formula 1 circles it's almost inevitable because this happens so often. So we had a long run with the Inerta. up to that point. But the reasoning in this case didn't seem really as strong. It was argued on the grounds of cost cutting. How much is any nectar? Well, Penske Racing Shocks was licensed by the university to supply them. And they're of the order of some thousands of dollars, $5,000, perhaps $4,000. That's a lot of money. That kind of range. That's like a rounding error in the budget. One would think so, yes. But nevertheless, the Inerto, it became a target when they were looking to reduce the costs of the sport. The cost of the device is only one aspect of it. The design and simulation of the suspensions and the testing, of course, has to be added to that as well. So if you go back to a spring and damper, suspension. It's more You can argue it's less expensive, though in fact the cars started to have stability problems when the Inerta was removed. In fact, the ban was delayed by one year so they could dial out these difficulties. So some of the stability problems that we had with the Active, they commonly occur with... these types of racing cars which are very, very stiffly sprung and have ground effect aerodynamics. Do you think that it's possible that in future the Inerta will be brought back or you think that's not a possibility? It's hard to tell. Someone within the sport would have to advocate that. It would be nice if it did come back. It gives more, from an engineering point of view, it gives more to explore for the engineering designer. Formula 1 cars are supposed to be advanced vehicles from an engineering design point of view. So you described what the damper does, and it's quite clear, right? So it dissipates energy. So maybe can you tell us what actually an inverter does? Yes. So that's always an interesting question, because you're faced with the electrical engineer's way of thinking about things, that you have a box of components and you shape your impedance and you don't ask. This capacity here, what is it doing? Whereas the mechanical engineers, they like to, this spring is supporting a load. This damper is reducing energy. What does the inert do? Well, it's producing a force proportional to relative acceleration. That doesn't always satisfy them. So you can think analogously and get insight in various ways, which is not necessarily the complete story, but the insights are always useful. so if we take the Inertor again. And one interesting little experiment you can do with an inertor is to try to impose an oscillation. And one thing that is very striking is that the maximum force occurs at the maximum displacement. That's the same as if we had a spring, but the device is pulling rather than pushing. So the electrical engineers would say that the inertor is 180 degrees out of phase with the spring, just as the capacitor is 180 degrees out of phase with the inductor. So some people like to think that way, that if you're in a state of oscillation and you have an inertor in parallel with a spring, then the sum of those two forces, in a way, they partially cancel out. And at resonance, they would cancel out exactly. But the other thing to note is how the force varies with frequency. As frequency increases, the force in the inertum increases much more rapidly than the damper or the spring. And that's something, again, that has to be brought into the picture. It's not just the phase characteristic. So... I would stress the inert as an energy storage device, and it's the jewel of the spring in a mechanical sense, just as the capacitor is the jewel of the inductor. And that it is the third component that allows you to produce this complex impedance of an arbitrary shape. You might need, for a very complex frequency varying impedance, you might need a large number of components. In the electrical domain, that's not a difficulty. In the mechanical domain, you want to restrict the number of components. So you perhaps can't shape the most complicated impedance functions that you would like to shape. Nevertheless, the analogy, I think, is important to explain the device. the idea of the Inerter seems quite simple, right? It's about analogies with the circuit theory. And so probably also looking at the beginning when you started to work on this, you probably wondered if this was already in the literature, for instance. And maybe later on when you come up with the device and this was implemented, people misunderstood how this was working. So in one way, the idea is very simple, but in the other way it escaped so many people. So why do you think this is the case? Yes, I think that it's partly to do with... Electrical engineering thinking versus mechanical engineering thinking. Systems thinking versus a more reductionist way of thinking about a mechanical system. The latter, where you want to ask, what does this element do on its own? Whereas the systems way is you're asking what is happening to the whole system. the closed looping control systems terms or the vehicle together with the suspension system and all the components working together. And it's the richness of the component set that one thinks about in terms of the availability, widening the available behavior. We saw that the Inerter was banned in 2022, but maybe there are other uses for the Inerters, maybe in other fields. Can you tell us a bit about Yes, well it's still used in some areas in motorsport, but perhaps the first applied area for inertas was apart from vehicle suspensions was buildings, building suspensions. One sees applications there in Japan with ball screw inertas being applied in building suspensions to improve. response when you have earthquake excitations. You can think of the vibration suppression in a helicopter, for example, between the rotor and the fuselage, trying to damp out or even prevent vibrations being transmitted. Or motorcycles, we looked at weave and wobble instabilities in motorcycles and found that there could be an advantage of the inerter in that context. I mean, I guess that, you know, we had springs and dampers for thousands of years, while in esters just for 20 years. So probably we still are exploring all the possibilities. I think it's still early days. And for example, we're looking at railway suspensions. And there's a possible advantage there in terms of reducing track wear. So we have some projects looking at that. Okay. Thank you very much for your time. This was a wonderful story. Giorgio, a pleasure talking to you. Thank you.

And this is a fascinating story that has it all. The biggest spy scandal in the history of Formula One. A humble professor who has proved that an established engineering principle used for more than 70 years was wrong, and a secret device that some of the best engineers in the world were not able to understand despite looking right at it.

Before moving on, let me briefly recall some elements of the spy scandal, to give you a clear sense of the impact that this professor has had on Formula 1. In 2007, the Formula One world was rocked by what became the biggest spy scandal in the history of the sport. One of the elements at the center of that scandal was a mysterious device called a J-Dumper. Renault had obtained a drawing of the never-heard-before J-Dumper from an ex-employee of McLaren. And Renault tried to have McLaren disqualified because they thought that the J-Dumper violated Formula One regulations.

In turn, McLaren tried to have Renault penalized because they committed industrial espionage by getting hold of the drawing of that device. When the proceedings of the World Motorsport Council investigation were made public, they kept secret the nature of the device. The only information made public was that McLaren was not disqualified because the J-Dumper did not violate any rule and in fact the engineers at Renault misunderstood what this device did. Medias around the world tried to figure out what this device was and eventually a connection was made with Malcolm Smith, Professor of Control Engineering at the University of Cambridge. Today we have the opportunity to speak to Professor Smith and have those events narrated by his very protagonists.

So let's go. Professor Smith, your background is in mathematical control theory and then later on you became known for your work on the Inerter. You invented this device called the Inerter. But in this interview, I would like to...

go through the story of the Inerter and how you came with the idea. And maybe we can start with your background. So you can tell us a bit what you did before the Inerter. Yes, well, Giordano, thank you.

And it's always a pleasure to explain this. And it connects with my background. As you say, I started out in control theory.

My first degree was in mathematics. And for my PhD, I did I worked on multivariable, robust multivariable control, frequency response methods, so how to design controllers when you've got many inputs and many outputs, how to generalize the classical theory to that situation. And later I got involved in something called H-infinity control, partly through visiting George Zames at McGill University in Montreal. And one of the key ideas is stabilizing. or looking at the class of all controllers that stabilize a given plant.

So then you try to optimize over that class to minimize whatever you, a robustness measure or sensitivity. But that being able to solve over a general set and to optimize something in the frequency domain was a very important idea. Okay, thank you very much. And so then how did you get involved in Formula One?

Yes, that was a chance event. I had just joined this university as a new lecturer in 1990. And the first summer, 1991, August of that year, everyone was on holiday except myself, really, among the academic staff. And a phone call came through from Williams Grand Prix engineering from Paddy Lowe, who I didn't know at the time. And those... who know about Formula One will know that he eventually became a very famous Formula One designer and engineering director at McLaren and then later Mercedes.

At the time, he was in charge of active suspension development at Williams Grand Prix, and they had a stability problem. So he phoned the group. He was Wanting to speak to Professor Keith Glover, he'd been taught by him at Cambridge as an undergraduate, but Keith was on holiday for another two weeks, and Paddy explained they had a test at Silverstone the following week.

And so I was rather bold in taking the job and was hoping that Keith would not be annoyed. Fortunately, Keith was pleased that I took the job. But that got me started in consulting on this active suspension system. So you started to be involved as a consultant.

Yes. Then this idea started to have an influence on your search. Yes.

Well, Not initially. Perhaps one should say a little bit about active suspension first. A normal car suspension has springs and dampers and anti-roll bars. Those are also springs.

That's the basic normal passive suspension. With an active suspension, you're replacing the springs and dampers with powered hydraulics. You'd have a piston and a cylinder and you'd have pressured hydraulic fluid that can be directed with silver valves above and below the piston to extend and contract.

So that's, if you like, the actuator in the control system. Then you have measurements all around the car, accelerometers, deflection sensors, pressure gauges. You can have as many as 20 measurements on the car being fed back into a computer that implements the controller and then that drives these four actions.

that extends and contracts the strut at each wheel station. I was brought in as a control specialist, knowing about multivalve control design. And of course, you bring those methods in and you apply them.

As we made progress, and I worked more on these, I became interested in the systems themselves. and it's... I started to develop some research problems. There are many different layouts, mechanical layouts that are possible and different sensing arrangements. And then the question is, which is the best?

And then how do you design the controller to produce maximum improvement in mechanical grip? That's how the tire deflects and contacts with the road. And how do you best control the ride height and so on?

So the engineering setup, the design of these systems becomes fused with the control system design in possibly a complicated way. So that became a research question for me. How do you simplify things down and find a way to approach this, which could answer some basic questions? So you started then. to do research on active suspension systems.

Yes. Was this then implemented by Williams? Well, there wasn't really time.

The consulting work and the implementation of the control system happened so fast. From August 1991, the system was actually raced for the first time with Nigel Mansell at the South African Grand Prix in 1992. And Williams had extraordinary success. In the 1992 season and the 1993 season, they won the championship easily by a big margin.

And then active suspension was banned at the end of the 1993 season. Why was it banned? This is often a complicated story, but technologies often come and go and get banned in Formula 1. And most commonly, a technology, when it's successful...

and is producing a big advantage for one team, it can get banned at that stage because the races become boring. Because a team is always winning. One team is always winning, so people don't want to watch the races or are not so interested.

And then there is pressure on the authorities to equalize things so that the sponsors are happy and so on. Okay, so unfortunately, what you were developing couldn't be used anymore. But then Did you manage to do some other progress? Yes. Well, all was not lost in the sense that I'd started to think about the design of these systems and to bring in some of the methods I mentioned, H infinity.

And one of the ideas there is to parameterize all controllers that can stabilize a given plant and to be able to optimize a performance measure over that set. But then that's the start of the Inerta story because you can take that same idea and instead of optimizing all overall stabilizing controllers, you can try to optimize overall passive suspensions. Now, I knew some theory from my PhD time about passivity of electrical circuits, and I knew it was possible to completely characterize all the electrical circuits you can build out of passive components.

So then it seemed natural to say, well, we should do the same with mechanical mechanisms. passive mechanical mechanisms. And I think people who knew that theory would have expected that it was a direct correspondence, and that would be a relatively simple thing to do.

It turned out not to be straightforward. And some of the difficulties illustrate why the Inerta hadn't been done before, if I can put it that way. So if I understand correctly, so um, given the fact that you know how to realize a circuit, you want to apply the same ideas on mechanical systems.

And I actually studied something like this in the university, and the idea is that there is an analogy between electrical circuits and mechanical systems, hydraulic systems, heat systems, basically any linear system. And the idea is that you need to identify what behaves like a current, so this is called a true variable, and... what it behaves like a voltage, which is on a cross variable.

And so for mechanical systems, you have the force that behaves like a current and you have the... What do you have for the voltage? The voltage becomes the velocity. The velocity.

And the force becomes the current in the analogy you're speaking of. Right. Yeah.

The force-current analogy. I remember the book said that... I mean, it was very convincing in the fact that the analogy then of the components where that the damper is a resistor, so it dissipates energy. The inductor behaves like a spring, and then the capacitor behaves like a mass, right? So the problem is solved.

You just have to use this mapping, or not? Yes, the mapping that you've described is the one that we use to understand this. And the first important thing to say is it's power-preserving, because you're mapping...

voltage and current onto velocity and force. So the product of voltage and current is a power, and the product of force and velocity is a power. So anything that's passive in the electrical domain, if you map it over exactly, will be passive in the mechanical domain and vice versa. And the analogy you've just described is what you find in the textbooks.

with the element correspondences. By the way, just a brief aside, there are two analogies, but the advantage of the one we've described that's based on through and across variables is that series connections in one domain become series connections and the other parallel become parallel. So the circuits are topologically identical. And the other thing that's very good about that analogy is that ground, electrical ground, which is a datum voltage, becomes a point with constant velocity, which is a reference point in the inertial frame. So that allows one to go one step further to discuss the analogy you've described.

Spring and inductor, resistor and damper, those are straightforward because those are both two terminal devices. So let's think, what are terminals in the mechanical domain? People often don't think about this.

If you take a spring, the terminals are the attachment points, the two endpoints of the spring. And we're looking at the force, the equal and opposite force, at the terminals produced by the spring from its relative displacement. Right, you push the spring and you will receive a force. Yes. Yes, that's right.

But it's an equal and opposite force applied at the terminals. Similarly with the damper, the terminals are the connection points. One connection point will be the housing of the damper and the other will be the piston rod.

And those are the two connecting points. And both the terminals of the spring and the damper are freely movable in space. Now, let's go to the third element, the mass. So what are the terminals on the mass element?

Well, if you think about the way we do mechanical modeling, the mass is usually treated as a point mass. And its motion is governed by Newton's second law. And that's the acceleration in an inertial frame.

So if you're careful and you write the circuit diagram of the element, you'll see that the mass element is actually analogous to a grounded capacitor. So there's only one. You can't slide the mass in and out with two ends that are freely movable in space in the way you can do with a damper.

The mass is a point mass. So the mass is analogous to a grounding capacitor. And that's...

That's what you can do. Yes. That's not my observation.

Okay. That's in a sense well known. But most of the textbooks don't really explain it.

And also some of the books that really appreciate it the most try to cover it up by drawing a symbol for the mass that looks like a slider. So here it is. The theory, if you like, from electrical circuits forces a certain question, because to build our electrical circuits, you need three elements, resistor, capacitor and inductor. And they all need to have two terminals. So, the natural equivalent, you have a problem with the mass because it's a one-terminal device and so the circuits that you can realize with it are more limited.

So, it's impossible then to go from the circuit to the mechanical device. Well, yes. So, I became puzzled at this point and the theoretical work forced a question.

So it's easy to see that if one were to have a device which is genuinely two-terminal, like the spring and damper, it has two attachment points, which are freely movable in space, with the property that the equal and opposite force at the attachment points is proportional to the relative acceleration between those terminals. So if one had such a device, then the mapping would... be perfect for the synthesis theory.

And then you could say, we can build any of these positive real complex impedances. We can build them mechanically. We can have a mechanism here that we can design and build and hopefully put it on the car if we can make it small enough and light enough. So that was the point. I was stuck at that point for a while and thinking that spring mass dampers.

So it's in all the books. That's the standard and that's how it must be. And maybe there is a limitation that mechanical circuits are not completely equivalent to electrical ones.

When did you realize that actually something more could be done? Well, it was a thought experiment. I was trying to prove that you couldn't do it, You couldn't make something like that. But if you think positively, supposing you could build such a device and you held it in your hands, what would it feel like?

And one of the properties would be that once you've set it in motion, it keeps going with constant velocity. Having realized that, it's fairly quick, it's almost immediate really to think of a way. of making such a thing.

And I sketched something like this that we have on the table. And this is the first thing I did after having thought of that idea that, would you try to build one and play with it and understand it. So this is the device. This was the first one I made and it's made out of a Meccano.

which is a child's modeling building kit that I was familiar with from childhood. So you can see it's a two-terminal device. The housing here is one terminal. And the end of the rod here that moves in and out is the other terminal. And the rod itself is a rack connecting with a pinion.

So we have a rack and pinion mechanism. And the pinion is on this first axle here. And then there's a... a gear, an opinion connecting to a second shaft.

And a similar gear, they're both five to one ratio, gear wheel, pinion here. And on the third shaft, we have this flywheel. So as the rod moves in and out, the flywheel shaft and the flywheel rotates in proportion.

So we need to think about inertance. Inertance is the constant of proportionality between the force. and the relative acceleration, and it's in kilograms. That's different to the mass of the device.

This weighs less than a kilogram. That's the mass of the device. The inertance is the constant of proportionality between the relative acceleration and the force. And that's typically, for inertors, is much larger than the mass. So we can get an idea approximately of the value of the inertance here.

The two five-to-one ratios, that gives a multiplier of 25. The other thing that's significant is the pinion radius and the radius of gyration of the flywheel. It's approximately two to one. So that gives another factor of two, making 50. But the 50 is a ratio of forces, but also it's an inverse relationship of velocities. So it actually squares up.

You get a multiplier of 2,500 times the mass of the flywheel. The flywheel is 100 grams, 0.1 of a kilogram. So overall, this device has an inertance of 250 kilograms approximately.

So that's a quarter of a ton between the terminals. You can, with a small force, you can move the rod, but not very quickly. So what you have to think here is resistance to acceleration or resistance to relative acceleration.

is the... characteristic. So can you actually explain a bit better this point? So here you have an inertance of 250 kilograms, right? But you can move it with very little force.

Can you explain better why that's the case? I mean, because if you imagine a mass that is 250 kilograms, it's difficult to push it. So what is actually what that 150 kilograms mean?

Yes. So if you imagine if we had a 250 kilogram mass on this table, and it was a frictionless table, So like on ice? Yes. You would be able to push it with a small force and it would start to accelerate and it would keep going for some period of time, just like the Inerta does. And so what makes you think that you can't move 250 kilograms is, first of all, if you had to support that weight, most people would not be able to lift 250 kilograms.

But if you're just pushing it. along a plane, you still wouldn't be able to do that if there's a lot of friction. So a small car, for example, one person can't push a car because of the friction in the bearings and the tires.

It's not because of the mass itself. A small force will accelerate it a bit, so it'll move a little bit. And that's the same with the Inerta, because these have rather low friction. Okay. In a certain way, this reminds a bit a damper in the sense where there is one terminal which you push and there is some kind of resistance.

Maybe you can explain what is the difference? Yes, all right, let's look at this device here. This is a Formula One damper that was made by Penske Racing Shocks. So this is just a rubber handle so one can move it by hand, but you would have have a ball joint here which would connect to some suspension element and another connector at this end. But it's a two-terminal device, and we have a rod moving in and out of, we have a piston and cylinder here and a floating piston and fluid inside.

But this is a totally different device than the Inerta because the force, the equal and opposite force, is proportional to relative velocity. So to keep it moving, you have to apply a constant force. To move it faster, then the force increases.

So this is force proportional to relative velocity, whereas the inertial is force proportional to relative acceleration. So essentially, with the inertial, you will feel a resistance when you start to push. Exactly.

It changes in velocity. It changes in velocities. Yes. Okay, so this is one particular realization of the inertial. But is this what has been done implemented in Formula 1?

No. Fairly soon... We started to think of different ways to do it. What turns out to be a nice construction is to have the flywheel spin axially about the rod.

And you can do that with a ball screw mechanism. Do you have an example? Yes, I can show you one of these.

Take a look at this. This is a demonstrator that we... made in the engineering department.

And it has a Perspex cover so you can see the mechanism inside it. So you see the threaded rod, and inside of this assembly here is the nut, which spins when there's relative velocity between the two ends of the device. And attached to the nut here is the flywheel. This is the flywheel.

which rotates as you get a relative displacement between the terminals. So this is a compact, simple way to implement inertas without having multiple shafts and racks and pinions and so on. So maybe you can now try to understand how these are used in Formula 1. So, okay, you came up with this new...

device. Then what happened? Having got the idea and having explored it with Cambridge Enterprise in terms of whether to protect it, we put it to the test and we approached a team in Formula One.

And by this time, Paddy Lowe, that I'd worked with at Williams, he'd moved to McLaren. And I also knew other people at McLaren, Dick Glover, for example. And we decided to contact them. and to take the Inerta idea, together with some initial calculations I'd done on possible benefits, and McLaren were interested.

And they signed an agreement with the university to develop it. And we went through all the stages of engineering design and simulation and what it can improve in the car in terms of reduced oscillations or improving mechanical grip and all the way through to testing and to producing an actual lap time gain on the car and once that was achieved it went on the car really for the next race and that was an exciting event in it was 2005 so time has elapsed so yeah what is exactly a timeline. So when is that you come up?

with the idea, the first prototype, and then eventually got it on the car? My first Meccano model goes back to 1997. My approach to McLaren was around about 2002. And the development happened... Well, there's not a lot I can say about the internal development, but let me just point out the known facts that it was raised for the first time in 2005. And...

It produced a lap time gain. And the first race was with Kimi Raikkonen driving. And it was the Spanish Grand Prix in 2005. And he won the race for McLaren's first victory of that year.

And in fact, it led to several victories, a number of victories throughout the year. McLaren were close to getting the championship, but didn't quite manage it that year. That was very exciting.

Yes, it was very exciting for me, thrilling really, that a theoretical concept is on the car that you're watching the Grand Prix at the weekend. So at that stage, it wasn't a story I could relate to anyone because McLaren went to fairly elaborate lengths to conceal the nature of the device. In fact, this one is an illustration of an early ball screw inertor of roughly the size and packaging that we used in Formula One. And so, again, it's a two-terminal device, and it's similar to the one I showed you before with the ball screw and the flywheel rotating actually about the line joining the two terminals. But otherwise, you might think this is some sort of exotic damper.

Indeed. And if you look at the car from some distance, you wouldn't really think that there's anything unusual here. So McLaren...

was able to conceal it for quite a while. Can you tell us a bit about how they did that? Yes.

So they had, first of all, they named it something different. They called it the J-damper. And that was a deliberate attempt to decouple what they were doing with the technical literature.

We were publishing papers on the Inerta and describing the idea and its advantages. So the idea was public? It was public domain.

And that was part of the agreement with McLaren that we would continue with the academic research and that that wouldn't be held back. And so their strategy was to try to cover it up quite legally in terms of the sport. You don't have to tell your competitors exactly how you're doing things.

So that was fine. Also, they did another clever thing. they stopped calling the inertance or describing the units of the inertance as kilograms, I went to a meeting and suddenly found that the x-axis was Zoggs rather than kilograms. And so that was again a decoy.

In case a team member left McLaren and went to another team and described this device, knowing that one of the axes is kilograms is a giveaway. It's a clue to what's actually going on. So those two things together, they succeeded really in keeping their approach quiet for a couple of years.

But then what happened is exactly what you described, that an employee from McLaren moved to another team and it leaked some information, right? That's correct. So McLaren found out about this because they hired someone from that team. It was Renault, in fact. And the person coming back from Renault was able to say, well, we have one of your drawings of the J damper, and it's been circulated in the company and examined and so on.

So McLaren at that stage knew that the device had leaked out to another team. I should say this happens all the time in Formula One because the market for... engineers is quite fluid. People get hired from one team to another all the time. And you can take what's in your head.

That's allowed. You're not supposed to take drawings. But that does happen as well. But the story is that even if they had a drawing, actually, this was not enough, right?

Yes. Well, there's a very amusing story about how this eventually became... came into the public domain.

And it was through what is now called the 2007 Formula One espionage controversy. And it started with a case being brought against McLaren. It concerned two of their, or one of their employees who'd had drawings of the Ferrari. And that became known and Ferrari brought a case against McLaren and they were found guilty of breaching the sporting code at a World Council hearing.

Even though the actual impact on the design of the McLaren, it wasn't shown to be a significant impact. Nevertheless, they were found guilty and they received the largest fine in sporting history. It's still the largest fine.

It was $100 million that McLaren was fined. And at this point, and in fact, as part of the defense, in anticipation of this, they were expecting a large fine. McLaren tried to say, well, actually, there's a lot of this going on.

And we know. There's a case that we can prove. And so McLaren took their case to the FIA.

Or as soon as McLaren blew the whistle, Renault owned up and said that they had various things. There were other things apart from the J damper, but the J damper was one of them. And there was another hearing.

And Renault was found guilty of breaching the sporting code, but they... were given no fine, which is quite a lot less than $100 million. And in regard to the J damper, there was, again, an interesting sub-story.

Renault had used to advantage a device on their car for a number of years called the mass damper, the tuned mass damper. That's essentially a mass on a spring, and it's a classical idea in mechanical vibrations. but they managed to find a way to get an improvement. Now, it turned out that Renault's reaction to the drawing of the J damper was to contact the FIA to try to get the J damper banned under the interpretation that it was a mass damper. Which was banned at that time.

Which was banned. Renault had success with the mass damper and it was banned sometime. I forget the exact year. But by that stage, it was banned.

Okay. So Renault wanted to say, well, this thing should be banned because this is a mass damper. And McLaren were able to counter that it's not a mass damper. It's something completely different. And the mass damper is a mass on a spring.

So it has a one-point connection to the car. So it's not a two-terminal device. as the inerter is, so that you connect between two movable points in the suspension. So McLaren were able to argue that the inerter shouldn't be banned because it didn't come under the description of the device that was relevant to the mass damper.

That was used at the World Council hearing. And in fact, in the transcript of the hearing, the justification for the no fine. being applied to Renault is that they had fundamental misunderstandings of the nature of the device and therefore it couldn't affect the championship. Nevertheless, as far as the Inerta is concerned, it's an amusing story to tell. So then at this point still no one knows what the jet damper is, right?

So when the connection was found between the jet damper and the Inerta? Yes, there was a lot of pit lane gossip because information leaks out. and people leave one team and join another.

And eventually people start to figure out what it is in the pit lane and so on. And still, though, it wasn't widely known. And it was an autosport journalist, Craig Scarborough, who published the scoop in Autosport.

in, I think it was 2008, describing the connection between the J-damper, the mysterious J-damper, and the Inerta. And at that point, the cat was out of the bag. So everyone then in the Formula One world knew that McLaren's device was the Inerta, and it connected with the technical literature.

Okay. And so since then, the Inerta has been used. The Inerta very quickly was used on most, if not all, cars within Formula 1 and became a standard component. And it continued that way until 2022, until the Inerta was banned.

Oh, that must be very disappointing for you. Yes, in Formula 1 circles it's almost inevitable because this happens so often. So we had a long run with the Inerta.

up to that point. But the reasoning in this case didn't seem really as strong. It was argued on the grounds of cost cutting. How much is any nectar?

Well, Penske Racing Shocks was licensed by the university to supply them. And they're of the order of some thousands of dollars, $5,000, perhaps $4,000. That's a lot of money. That kind of range.

That's like a rounding error in the budget. One would think so, yes. But nevertheless, the Inerto, it became a target when they were looking to reduce the costs of the sport.

The cost of the device is only one aspect of it. The design and simulation of the suspensions and the testing, of course, has to be added to that as well. So if you go back to a spring and damper, suspension.

It's more You can argue it's less expensive, though in fact the cars started to have stability problems when the Inerta was removed. In fact, the ban was delayed by one year so they could dial out these difficulties. So some of the stability problems that we had with the Active, they commonly occur with...

these types of racing cars which are very, very stiffly sprung and have ground effect aerodynamics. Do you think that it's possible that in future the Inerta will be brought back or you think that's not a possibility? It's hard to tell.

Someone within the sport would have to advocate that. It would be nice if it did come back. It gives more, from an engineering point of view, it gives more to explore for the engineering designer.

Formula 1 cars are supposed to be advanced vehicles from an engineering design point of view. So you described what the damper does, and it's quite clear, right? So it dissipates energy.

So maybe can you tell us what actually an inverter does? Yes. So that's always an interesting question, because you're faced with the electrical engineer's way of thinking about things, that you have a box of components and you shape your impedance and you don't ask. This capacity here, what is it doing?

Whereas the mechanical engineers, they like to, this spring is supporting a load. This damper is reducing energy. What does the inert do? Well, it's producing a force proportional to relative acceleration. That doesn't always satisfy them.

So you can think analogously and get insight in various ways, which is not necessarily the complete story, but the insights are always useful. so if we take the Inertor again. And one interesting little experiment you can do with an inertor is to try to impose an oscillation. And one thing that is very striking is that the maximum force occurs at the maximum displacement. That's the same as if we had a spring, but the device is pulling rather than pushing.

So the electrical engineers would say that the inertor is 180 degrees out of phase with the spring, just as the capacitor is 180 degrees out of phase with the inductor. So some people like to think that way, that if you're in a state of oscillation and you have an inertor in parallel with a spring, then the sum of those two forces, in a way, they partially cancel out. And at resonance, they would cancel out exactly. But the other thing to note is how the force varies with frequency.

As frequency increases, the force in the inertum increases much more rapidly than the damper or the spring. And that's something, again, that has to be brought into the picture. It's not just the phase characteristic. So... I would stress the inert as an energy storage device, and it's the jewel of the spring in a mechanical sense, just as the capacitor is the jewel of the inductor.

And that it is the third component that allows you to produce this complex impedance of an arbitrary shape. You might need, for a very complex frequency varying impedance, you might need a large number of components. In the electrical domain, that's not a difficulty. In the mechanical domain, you want to restrict the number of components.

So you perhaps can't shape the most complicated impedance functions that you would like to shape. Nevertheless, the analogy, I think, is important to explain the device. the idea of the Inerter seems quite simple, right? It's about analogies with the circuit theory. And so probably also looking at the beginning when you started to work on this, you probably wondered if this was already in the literature, for instance.

And maybe later on when you come up with the device and this was implemented, people misunderstood how this was working. So in one way, the idea is very simple, but in the other way it escaped so many people. So why do you think this is the case? Yes, I think that it's partly to do with...

Electrical engineering thinking versus mechanical engineering thinking. Systems thinking versus a more reductionist way of thinking about a mechanical system. The latter, where you want to ask, what does this element do on its own? Whereas the systems way is you're asking what is happening to the whole system.

the closed looping control systems terms or the vehicle together with the suspension system and all the components working together. And it's the richness of the component set that one thinks about in terms of the availability, widening the available behavior. We saw that the Inerter was banned in 2022, but maybe there are other uses for the Inerters, maybe in other fields. Can you tell us a bit about Yes, well it's still used in some areas in motorsport, but perhaps the first applied area for inertas was apart from vehicle suspensions was buildings, building suspensions.

One sees applications there in Japan with ball screw inertas being applied in building suspensions to improve. response when you have earthquake excitations. You can think of the vibration suppression in a helicopter, for example, between the rotor and the fuselage, trying to damp out or even prevent vibrations being transmitted. Or motorcycles, we looked at weave and wobble instabilities in motorcycles and found that there could be an advantage of the inerter in that context.

I mean, I guess that, you know, we had springs and dampers for thousands of years, while in esters just for 20 years. So probably we still are exploring all the possibilities. I think it's still early days.

And for example, we're looking at railway suspensions. And there's a possible advantage there in terms of reducing track wear. So we have some projects looking at that. Okay.

Thank you very much for your time. This was a wonderful story. Giorgio, a pleasure talking to you. Thank you.

Transcript for:Inerter in Engineering and F1

Transcript for:
Inerter in Engineering and F1