A New Era in Automotive Engineering
For decades, the dream of flying cars has remained just that—an aspiration. However, the unveiling of Tesla’s Roadster 2 by Elon Musk has introduced a vehicle that, while not entirely meeting the flying car criteria, boasts some remarkable features. This prototype is capable of limited flight, scaling vertical walls, and even leaping over the complete range of Tesla vehicles. These extraordinary capabilities lead to two pressing questions: Should we permit vehicles to traverse walls and soar through the air? Given the challenges humans face when navigating traditional roads, the answer seems to be a resounding no—a dilemma that will ultimately require legal and regulatory scrutiny. The second question is how the Roadster 2 achieves such feats, a query that can be addressed through the principles of physics.
The Mechanics of Scaling Walls
To understand how the Roadster 2 ascends a circular ramp and adheres to it upside down, we must delve into the concept of friction. When two surfaces interact—like rubber tyres on asphalt—static friction arises, which prevents them from sliding past one another. This static friction force (Ff) is influenced by the normal force (FN) pressing the surfaces together and the materials involved (μ).
The normal force acts perpendicular to the surfaces, while the static friction coefficient (μ) varies between different materials. The maximum practical static friction coefficient is around 1, with rubber on asphalt typically around 0.6. The ≤ symbol indicates that static friction is a “limiting force,” applying just enough to prevent sliding, up to a maximum value.
Consider a standard vehicle attempting to ascend an incline; as the angle (θ) of the slope increases, the gravitational force (mg) has a diminishing component perpendicular to the surface. Consequently, the normal force (FN) decreases, alongside the maximum static friction force. If this frictional force is insufficient to counteract the gravitational pull down the slope, the vehicle will slip. For a coefficient of 0.6, the steepest slope achievable without sliding is approximately 31 degrees—far from vertical.
Thus, how does the Roadster 2 manage to ascend a vertical wall? The solution lies in amplifying the normal force, and therefore the friction force. For a vertical surface, the frictional force must equal the gravitational force to prevent slipping.
This is where the Roadster 2’s innovative design comes into play; it employs fans to blow air beneath the car. By using side flaps, it reduces the air pressure beneath the vehicle, functioning similarly to a vacuum cleaner.
Let us calculate the necessary pressure beneath the Roadster 2 to enable it to adhere to a wall. The vehicle’s target weight is claimed to be 1,700 kilograms, with an estimated contact area of about 2 square metres. Using the formula F = P × A (where P is pressure and A is area), we must consider the difference in pressure relative to the atmospheric pressure of around 105 newtons per square metre. After performing the calculations, we find that the pressure required at the base would be about 86% of atmospheric pressure—certainly feasible. However, due to imperfect sealing beneath the vehicle, the fans must continuously expel air to maintain this effect.
While the spectacle of the Roadster 2 performing upside down serves as an impressive marketing tool, the suction generated also has practical applications when the vehicle is in an upright position. Enhanced downward force increases friction, improving acceleration, braking, and cornering capabilities. Automotive manufacturers have long harnessed this principle, albeit not to the extreme exhibited by Tesla’s latest prototype.
Unprecedented Acceleration Capabilities
The Roadster 2 boasts an astonishing acceleration of 0 to 60 mph in under one second—a feat unattainable by conventional vehicles. Traditional cars rely on friction between tyres and the road to accelerate, which is inherently limited by the coefficient of friction. With a realistic friction coefficient of 0.6, the maximum achievable speed from a standstill to 60 mph is around 4.56 seconds. While one could invest in superior tyres or harness aerodynamic forces as the vehicle speeds up, these enhancements do not permit reaching 60 mph in a mere second.
The Roadster 2, however, harnesses a different type of force—compressed air expelled from the rear. This principle is akin to rocketry. To illustrate, consider a simple experiment involving a toy car propelled by an inflated balloon. When the balloon is released, the tension in the rubber generates a force that propels air out of the balloon through an attached tube. Since this air has mass, it requires a force to accelerate it from rest to its exit velocity. This interaction between the balloon and the air exemplifies Newton’s third law: as the balloon pushes the air, the air exerts an equal and opposite force, propelling the toy car forward. Similarly, the Roadster 2 employs a compressed air reservoir to achieve thrust.
Rethinking the Concept of Flying Cars
While the Roadster 2 employs compressed air to lift and momentarily elevate the vehicle, it stretches the definition of “flying,” as the thrust can only sustain flight for mere seconds before pressure diminishes. Lower pressure results in reduced air velocity and thrust. If one were to envision a flying car, a flight duration of at least ten minutes would seem reasonable.
Additionally, there is the matter of acceleration. Given that rockets operate for only brief intervals, they must exert significant force to achieve rapid velocity changes, enabling the vehicle to leap over obstacles such as trucks. However, such substantial forces lead to high acceleration rates, which can be detrimental to human occupants. Estimating this acceleration can be accomplished through video analysis. By tracking the Roadster 2’s position as it jumps over a Tesla Semi truck, which is approximately 4 metres in height, we can derive its vertical positioning over time.
At the jump’s initiation, the vehicle’s vertical velocity is zero, and it subsequently accelerates upwards. Assuming constant acceleration during the jump, the positional data should form a parabolic curve. By fitting a quadratic function to this data, we can estimate the acceleration.
The resulting calculation suggests an approximate vertical acceleration of 98 metres per second squared—equating to around 10 g for a human. While this figure is merely an estimate, humans can endure such forces momentarily, though it is certainly uncomfortable and carries associated risks. Perhaps this explains why a robot was at the wheel during this particular demonstration.