When it comes to linearity, our driving experience offers little to none of it

Linearity is a mathematical principle, where if you were to plot all the data collected and put it in a simple X/Y axis graph, it would create a straight line.

If this were the case for each aspect of a vehicle it would make it a fair bit easier for beginners (and a lot easier for those getting into more advanced car control), but whatever data you look at from a car, there's almost no linearity to be found.

The engine's torque and power will usually have curves. Even in rare cases where one does happen to be a relatively straight line on the graph, your experience of it won't be linear for a variety of reasons, from driveline resistance to hills to throttle response.

If everything about driving a car was linear, it'd be much simpler. Photo: Shutterstock.

If everything about driving a car was linear, it'd be much simpler. Photo: Shutterstock.

To get vehicles to feel more spritely, manufacturers tend to ensure there's a lot of throttle response in the first half of the pedal movement (something that happens anyway due to complicated reasons related to air flow), and going past that point doesn't do a lot in terms of forward thrust (although, due to engine tuning, it can still increase fuel use).

There's just no linearity at all in a clutch pedal's motion. When releasing it from the floor, there's nothing, nothing, nothing, the feel changes and there's a bit of friction (the engine revs drop a tad, and we call this the friction point), then there's some more force pushing the pedal up and it wants to grab (possibly stalling the engine if it wasn't ready), then if you got going you can release the pedal the rest of the way (with it feeling quite light at this point).

With the brake pedal motion, and response, again, these are not linear. It's very light at the top of the pedal, and then, once the hydraulic fluid in the system is compressed, there's more resistance as it acts on the pistons inside the brake calipers to provide retardation. At this point the difference between not enough, just enough, and too much in terms of pedal movement is a mere twinge in your ankle.

The pads themselves, being pushed onto the discs, will also have an ideal operating temperature, just like tyres do, and plotting either set of performance data against temperature will also show curves.

Due in part to the tyres, and possibly the steering geometry (at least on anything really old or really simplistic), the response to turning the wheel isn't linear either. Typically you get almost nothing slightly off-centre, then a noticeable change in direction, and then eventually (mostly because the tyres start giving up at a certain point) turning it more makes no difference at all. That's assuming you get understeer. With oversteer you have to turn the wheel less, or the opposite way. That's completely non-linear.

Aha, but the suspension springs I hear you say. Yes, some springs are in fact meant to be linear, on a test bench. Doubling the compression distance (how far you squeeze them) requires double the downward force. However, there are also many examples of progressive-rate springs that get exponentially stiffer, so doubling their compression distance takes more than double the force.

Either way, the dampers you find on road cars these days are often deliberately non-linear. With the use of valving, they are softish at slow suspension speeds for comfort, and stiffer at higher suspension speeds for control. Even old dampers that kind-of tried to be linear weren't really, being that they're gas, hydraulic or both, and affected by use and heat just as the brakes or tyres are.

Even with a linear spring and a linear damper, you'll struggle to find them installed in a vehicle that has truly linear suspension movement (it usually follows a bit of a curve, so what's referred to as the 'effective spring rate', could change through that motion).

Another thing is air resistance, which is approximately proportional to velocity squared (exponential), under many conditions (and very weird curves when you look deeper into it). That affects any aero package too. Additionally, aero kits tend to be pitch sensitive (dive, roll, squat), and if wings and things are at a sharp enough angle they eventually reach an air speed where, like the tyres, they basically give up holding on (to the air beneath them, a condition referred to as stall).

Sam Hollier is an ACM journalist and a motoring fanatic who builds cars in his shed in his spare time.