Friday, January 01, 2010

Ronnie Peterson and roll resistance

A couple of years ago, ESPN broadcast the full fifty-minute highlights of the 1973 British Grand Prix, complete with commentary by Raymond Baxter. For the motorsport cognoscenti, this was pure manna. Whilst the Grand Prix is infamous for the multi-car accident triggered by Jody Scheckter at the end of the first lap, the re-started race is itself both exciting and interesting.

The dramatis personae consist of the iconic, John Player Special Lotus 72s of Ronnie Peterson and Emerson Fittipaldi, resplendent in their sable and or livery, Jackie Stewart's Tyrrell, and the Yardley McLarens of Denny Hulme and Peter Revson. There is also an impressive cameo from Niki Lauda's BRM, and a strong showing from James Hunt's ridiculously short-wheelbase, Hesketh-run March.

When the race re-starts, the cars on the front row of the grid (Peterson's Lotus, and the McLarens of Hulme and Revson) light up their rear tyres, and the noses of their cars visibly lift! Peterson's Lotus takes an immediate lead, but is hunted down first by Jackie Stewart's Tyrrell, then by Emerson Fittipaldi's similar Lotus, and finally by the McLaren M23 of Peter Revson. Revson eventually slipstreams Peterson down the Hangar straight, calmly takes the lead into Stowe, and ultimately takes the victory.

But what really grabs the attention is the extraordinary body language of the cars. Peterson's high-speed oversteer drift through Woodcote is perhaps one of the most famous images in the history of the sport, but Jackie Stewart looks similarly impressive through the same corner, the right-front wheel of his Tyrrell pawing the inside white line on one particular occasion. (There appear to be no kerbs whatsoever at either the inner or outer margins of the track). In addition, the Lotus 72s both exhibit a quite astonishing amount of chassis roll into corners such as Copse and Stowe, visibly more than all the other cars in the field, which themselves display far greater suspension travel than modern Formula One cars.

Why would this be? Well, according to Paul Fearnley's article on the Lotus 72 in Motorsport magazine (October 2002), Lotus switched from Firestone to Goodyear tyres between the 1972 and 1973 seasons, and with the waning of the erstwhile tyre war, found they were unable to generate sufficient heat in the harder Goodyear tyres. The consequence was that the Lotus 72s suffered from understeer in 1973.

One might therefore hypothesize that Lotus softened the front suspension of the Lotus 72 in an attempt to combat this understeer. To understand why doing so might reduce or eliminate understeer, we need to briefly digress into some vehicle dynamics and suspension theory.

When a car corners, the grip provided by the tyres generates a lateral (centripetal) force towards the inside of the corner. From the perspective of a reference frame in which the car is at rest (a reference frame which effectively travels around the circuit with the car; i.e., the coordinates of the car's centre of gravity remain constant in this reference frame), this induces a reaction force towards the outer wheels of the car. This reaction force is not a real force, but a fictional force, created by the use of a reference frame which is travelling around with an object undergoing acceleratory motion. Such a reference frame is called a non-inertial reference frame. The fictional reaction force is simply the result of the sprung mass of the car attempting to follow an inertial trajectory, in a straight line at a constant speed, when viewed from a reference frame undergoing centripetal acceleration.

The reaction force acts on the centre of gravity, and generates a moment around the roll centres of the front and rear suspension. (In dynamics, a moment is a force which generates a rotation about some axis). This roll moment has the effect of reducing the vertical load on the inner tyres, and increasing the vertical load on the outer tyres. The total load transfer is proportional to the height of the car's centre of gravity, and inversely proportional to the track width (the lateral distance between the wheels).

Generally speaking, this load transfer reduces cornering grip. To maximize cornering grip, one would wish to distribute vertical load equally amongst the inner and outer tyres.

The stiffness of the suspension front and rear, determines the amount of roll which the sprung mass of the car experiences for a given roll moment. The stiffness of the suspension can therefore be referred to as the amount of roll resistance. However, the stiffness of the suspension cannot really alter the total load transfer between the inner and outer pair of wheels. Rather, the relative stiffness of the front and rear suspension can alter the distribution of the total load transfer between the front and rear of the car.

The stiffer the suspension at one end of the car, the greater the load transfer at that end of the car, hence the lower the cornering grip available at that end. Conversely, the softer the suspension at one end, the less the load transfer at that end, and the greater the cornering grip available.

Hence, if a car suffers from understeer, one potential course of action is to soften the front suspension, either by softening the front spring/damper rates, or by means of softening the front anti-roll bar. Such logic might explain why the Lotus 72s wielded by Peterson and Fittipaldi at Silverstone in 1973, exhibited such a remarkable degree of roll.

Racecar suspension expert Mark Ortiz agrees, but also points out that Lotus "could have freed the cars up by stiffening the rear too, which would have reduced the roll, or stiffening the rear a bit and softening the front a bit, keeping the roll about the same.

"In other words, there is no necessary relationship between roll angle and oversteer/understeer balance. Cars that roll more don't always understeer less or oversteer more."

It's the type of speculation rarely open to modern Formula One fans.

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