Supercar Math: Estimating Gear Ratios for the New Bugatti




For those of you who are car enthusiasts, you may have heard about the unveiling of the 2018 Bugatti Chiron. The Chiron has managed to surpass its predecessor's (Veyron) impressive specs. The Chiron comes with an 8.0 L, quad-turbo W16 engine. This engine passes an astounding 1180 ft-lbf’s of torque (between 2,000 & 6,700 rpm’s) through a seven-speed dual-clutch transmission to accelerate the driver from 0 – 60 in just 2.5 seconds. Only 500 of these supercars will be produced and you’ll need to write a check for $2.6M to have it sitting in your driveway. Reading many articles online about this supercar made me interested in creating a mathematical model of what the engine performance curves may look like for a given gear.

 Using information gained online I created a crude graph of what the engine performance data may look like from 0 – 6700 rpms:

 

From there, I used torque, power, force, velocity, acceleration formulas to back out what single gear ratio would be required to get this car up to 60 mph in only 2.5 seconds.

 

 It turns out that a gear ratio of 4.55 would accelerate the 4400 lbf Bugatti Chiron to 60 mph in just 2.5 seconds. Now, the automotive engineers designing the Chiron did not use any transmission like that. They used the afore mentioned seven-speed dual-clutch transmission to get quick gear shifts between both odd and even gears of a standard seven-speed. I would not be surprised to hear that the Chiron shifted once or twice on its way to 60 mph given this type of transmission can shift between gears in mere milliseconds.

This type of calculation is something you could create for your own car, so that next time you’re at a red light you can determine exactly what rpm’s to shift at to ensure you’re transferring max power to the asphalt.

Try it out for yourself for free with PTC Mathcad Express.