The Physics of the World's Fastest Car

The Bugatti Chiron is perhaps best known in the automotive world to be the world's fastest car. It has a measured top speed of 302 mph, set just last year on a stretch of track in the forests of Germany. To put it into perspective, that top speed is approximately 25mph higher than the top speed of a Japanese bullet train. Both are pictured below. 

But just how is the Chiron able to reach these ludicrous speeds?

When reading an article on the ridiculous speed of the Chiron, I came across a graph depicting the velocity vs time data for the record-breaking run:

The graph was split into 4 distinct slopes, each of which I recognized to be parts in the car's acceleration. What I found the most interesting is how the car was still accelerating prior to the brakes being applied presumably in the last 10ish seconds. Wouldn't the car reach a "terminal velocity" so to speak much like a falling object does, due to the nonconservative forces at work against it at its top speed? I decided to analyze it further.

In considering a car's acceleration, there are several factors to consider. The most crucial one is obviously the force provided by the engine on the rear wheels (contributing to torque), called the traction force, or simply the applied force. The Chiron has an estimated torque value of 1600 Nm, mindboggling numbers even for a supercar. We all know well that the torque is equivalent to rFsin(θ), and in this case, the Chiron's incredible torque provides it an immense angular acceleration, as well as a powerful traction force provided by the turbocharged 1500 horsepower, 16-cylinder engine powerhouse that rests in the rear of the car. Provided the torque value and assuming the force is acting at a 90 degree angle and that the diameter of the tires is approximately 20 inches (0.508 m), the force would be approximately 6299 N for one wheel. However, nonconservative forces will work to counteract the car's acceleration, especially at higher speeds, explaining the decrease in rate of velocity change as time passes. These forces are the drag force and the force of friction. If these forces balance out the traction force, the total force is zero, and the car cruises at constant velocity. However, if the traction force exceeds that of the drag and frictional forces combined, the car accelerates. From this data and from the calculated traction force, it appears that this traction force would have to be greater than the combined nonconservative forces for the car to continue accelerating. To test this, I calculated the drag force and force of friction:

 F_drag =  0.5 * C_d * A * rho * v²

    where C_d = coefficient of friction
    A is frontal area of car
    rho (Greek symbol )= density of air
    v = speed of the car

C_d for a Chiron is 0.28. A is 2.1 m². rho is 1.2133 kg/m³. 

At 300 mph (just shy of top speed) (134 m/s), the F_drag is approx. -47.8 N. 

Ffr = μK * mg.  The mass of the Chiron is 1978 kg. the μK for asphalt track is approx. 0.6. 

The Ffr is approx. -11630 N. 

This means that the total force for the car while moving at basically top speed is 6299(2) - 11630 - 47.8 = 920.2 N. 

This is a positive value, and it indicates the car still accelerates somewhat before braking, supporting the chart trend. This also shows how powerful the engine is, generating all that force on the two rear tires to allow this machine to continously accelerate to such high speeds, all while combating the effects of air resistance and friction. Truly an engineering marvel.

Reference video of the run: https://youtu.be/PkkV1vLHUvQ  

Article: https://www.wired.com/story/bugatti-chiron-speed-analysis/ 

Second article for Bugatti Chiron specifications: https://drivetribe.com/p/technical-analysis-of-a-high-speed-P7t71_CaSSOMFdALcj_CWg?iid=G0-Lctx9R8GGnjd_hMCgGw