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I wouldn't believe those articles claiming 1kg saved on a wheel is equivalent to 6kg of sprung mass, I recon it's closer to 2-3kg
The exact ratio is non-linear and based on many exponential terms related to the square of the speed of the vehicle, less the linear increases in drag and rolling resistance.
IE, we cant say the wheel/tyre weight saving is precisely a ratio like x2 or x6 of saving weight from the cars sprung mass etc. The 'ratio' at 80mph is likely to be 3 to 4 times the effect of doing the same tests at 40mph, hence wildly varying rules of thumb with some sources quote x4, others up to x10.
Put it another way, if you first measured a 1600kg cars acceleration precisely (eg a Brera !) then took out 20kg of weight from the inside (eg, fuel in the tank) and then measured acceleration again for it weighting 1580kg, there would be almost no perceptible change in its acceleration for being slightly lighter, possibly 0.08 of second for the proverbial 0-60mph sprint, in ideal and repeatable conditions. In other words, not worth worrying about no matter how anal one is.
However, if you took 20kg out of the rotational part of wheels (tyre and wheel weight) you would definitely feel the difference, possibly as much as 0.5seconds off the 0-60 time. Which is far more worthwhile…
That ratio of acceleration is, loosely speaking, about 6:1. That ratio will change up or down depending on many other factors, such as speed range over which it was measured, rolling resistance, Cd, CdA, even air density due to ambient temperature etc etc etc.
Another thing to bear in mind is the inertial effects on changing direction. Many people at school or Uni would have tried the experiment where you sit on a swivel chair holding a spinning bicycle wheel, and if so you might recall the resistance from the spinning wheel when trying to changes its angle or someone spinning the chair whilst you held the wheel.
A typical car tyre and wheel might weigh 24-28kg. Spinning 25kg at 800rpm (about 70mph for most cars) represents a considerable amount of rotational inertia and directional inertia. These inertial forces are exponentially related to diameter of the wheel and the distribution of mass on that wheel rim. Loosely speaking, the directional response / turn in of a road car with lighter tyres/wheels/smaller diameter etc, will be directly related to the square of the road speed. So, shaving a few kilos off will have a noticeable and non-linear effect on the turn-in feel.
The equations to prove all the above are a bit more involved than a few lines on a forum post, but I hope the way I've described it makes common sense. If someone can explain it better with succinct mathematical formula then I'm all ears !
And for people who reeealllly want to increase midrange performance, or just get better economy there's dozens of things you can do (money and time no object) eg, reduce the Cd by lowering the car, replacing wing mirrors with video cameras, putting an undertray in place especially at the front, blocking some of the air flow into the front of the car, tyre spats, etc. Then you can go hunting for tyres with lower rolling resistance, narrower cross-section, consider changing the final drive ratio, even replacing the prop shaft with a carbon fibre one etc etc. ...... or just buy a lighter car to start with !!!