The question of whether a car can drive upside down—along the roof of a tunnel, for example—has fascinated engineers and driving enthusiasts for decades. The trick is certainly possible in certain circumstances, and there are numerous analyses exploring the various forces involved. Indeed, students are often asked to calculate these forces as an exercise.
So it’s easy to imagine that the question has been thoroughly explored; that there can be no new method of solving the challenge. Not quite.
Today, Fernando Dall’Agnol and colleagues at the Federal University of Santa Catarina in Brazil have discovered an entirely new way to think about this problem that has somehow been overlooked until now. “This solution is mathematically uncomplicated, yet it has not been depicted in the literature; not even in movies or games,” they say.
Their approach has some significant advantages over others. “There is a solution for the dynamics of a stunt car, which can keep it upside-down in a circular track, not for a split second, but indefinitely,” say Dall’Agnol and co. They even demonstrate it with a toy car.
First some background. One way of driving upside down is to use aerodynamic forces. Formula 1 cars, for example, have front and rear wings, which generate a force that presses them into the road. A few back-of-an-envelope calculations show that these high-performance vehicles would generate enough downforce to hold them onto the roof of a tunnel at relatively low speeds of around 140 miles per hour. (However, there is some debate about whether the engines would continue to work in these conditions.)
There is another force that can hold a car on the road—centripetal force. Numerous daredevils have driven cars through loop-the-loop tracks where the vehicle is momentarily upside down, held against the track by these forces.
A similar effect occurs in “wall of death” circus demonstrations. Here, a vehicle drives around a circular track with walls at 90 degrees. At high enough speeds, it generates enough centripetal force to press it against the vertical wall, where friction prevents it from falling. The forces involved are straightforward to analyze.
But Dall’Agnol and co take the effect even further. They ask what would happen on walls with an angle greater than 90 degrees. The question they investigate is how much greater the angle can be and still sustain the circular motion of a car. “We call tracks with banking angles larger than 90 degrees an inverted track,” they say, adding that this situation appears to have never been studied.
The analysis is straightforward. The team developed the equations that govern the forces involved and showed that it is possible for a car to drive more or less indefinitely on an inverted track, banked at up to 150 degrees, even without aerodynamic forces to help.
For example, at a banking angle of 135 degrees, a car would have to drive at almost 200 mph to stay on the track. Obviously, favorable aerodynamics change the calculations. “With sufficient aerodynamic downforce, it is possible to drive on tracks of any inclination,” say Dall’Agnol and co.
The team even put the idea to the test with a toy car on an inverted circular track. Instead of driving the car around a stationary track, they rotated the entire track, keeping the car stationary relative to the road. “We take advantage of this equivalence because it is much easier to make the whole track plus the toy to spin than making a functional electric toy car to drive under an inverted track,” they say.
Indeed, they do not need the entire track because the car is stationary relative to it. So they use a short section of track covered with sandpaper to maximize the friction with the car wheels. They attach this at an inverted angle to a horizontal bicycle wheel that can be rotated with the car held in place by a magnet. When the wheel rotates at a certain rate, the magnet flies off, leaving the car pressed against the track. You can see a video of their experiment here.
That raises the obvious question of whether such a trick could be performed for real. Dall’Agnol and co suggest a circular track shaped like the inside of a doughnut. This allows the driver to transition to the upside-down position relatively slowly and to stay there for as long as is necessary. Such a design is relatively safe, since if the speed drops below the minimum required, the car should simply slide down the track rather than falling. “So, if the velocity ever drops below [the minimum velocity], the pilot won’t just plummet head first,” they say.
There are various other practical problems to address, however. For example, any internal-combustion engine would need to be modified to ensure it doesn’t seize up. That’s certainly possible—aircraft engines operate upside down with ease. And things like the braking fluid system would need to be modified to ensure a smooth flow when upside down.
But these are straightforward modifications. Indeed, an electric vehicle might be even easier to modify for upside-down travel.
That’s fascinating work that is bound to trigger the interest of petrol-heads—err, electric-heads—the world over. For this reason, there would be no shortage of volunteers to drive such a vehicle. The missing ingredient is merely a sponsor with enough money to pay for the demonstration. Did anyone say Red Bull?
Ref: arxiv.org/abs/1905.03825 : Driving Upside-Down in a Circular Track