From: veritasium
Physics and aerodynamic principles underpin the operation of vehicles designed to travel faster than the wind while moving downwind. A notable example is the Blackbird vehicle, which sparked a $10,000 bet regarding its counterintuitive ability to maintain speeds faster than the wind pushing it [00:00:19]. This phenomenon has been a subject of debate among physicists and engineers.
Core Principles
The fundamental challenge to understanding such vehicles lies in the idea that a vehicle can derive propulsion from the very medium (wind) it is outpacing. A key counterintuitive claim is that a car without a motor or batteries can go downwind faster than the wind itself [00:00:11].
Objections and Explanations
Professor Alex Kusenko of UCLA challenged the explanation of the Blackbird’s operation [00:00:28]. His main objections and the subsequent explanations are detailed below.
Gusty Wind and Inertia
Objection: Kusenko argued that the vehicle might operate in a gusty wind, where an initial strong gust pushes the car to a high speed [00:01:46]. When the wind speed drops, the car, moving by inertia, would momentarily travel faster than the wind, but it would be decelerating [00:01:57]. He concluded that whenever the velocity is faster than the wind, the acceleration must be negative [00:02:13].
Rebuttal:
- Video analysis of the back wheel’s rotation showed that the car continued to accelerate even after the tell-tale (wind indicator) flipped backwards, indicating it was going faster than the wind [00:08:42].
- The tell-tale consistently pointed straight back for over 30 seconds, not jumping around as would be expected with gusts [00:09:00].
- When Blackbird set its record speed of 27.7 mph in a 10 mph tailwind, it was still accelerating, confirmed by multiple GPS units and wind speed measurements at the propeller’s height [00:09:13].
Wind Gradient
Objection: Kusenko also pointed out that wind speed is measured at about a meter or a meter and a half off the ground, while the propeller extends to about three meters above the ground [00:02:26]. Due to interactions with the ground, there is a wind gradient: wind travels slower closer to the ground and faster higher up [00:02:33]. He estimated the wind speed at the propeller’s height might be 10-15% higher than at the tell-tale, suggesting the car might appear faster than the measured wind but slower than the wind at the propeller [00:02:41].
Rebuttal:
- Measurements using tell-tales mounted on fishing poles at various heights, including above the propeller, showed that all tell-tales eventually flipped backwards, indicating every part of the vehicle was traveling faster than the wind at its respective height [00:08:16].
Treadmill Tests and Bias
Objection: Alex was skeptical of treadmill tests, which simulate a perfectly steady tailwind by moving the ground backwards in still air [00:03:50]. If the car can move forward on the treadmill while the treadmill itself moves, it indicates acceleration faster than the wind [00:04:05]. However, he suggested that fluctuating treadmill speed or unconscious human steering could introduce bias towards the desired result [00:04:19].
Rebuttal: Subsequent attempts to replicate the treadmill experiments with models, initially failing, eventually succeeded [00:06:41]. A fourth version of a 3D-printed model cart worked spectacularly on a treadmill [00:15:01].
Theoretical Analysis: The “Divide by Zero” Problem
Objection: Kusenko identified a problem in theoretical analyses, such as one by MIT Aero Professor Mark Drela. The equation for net force included the difference between the speeds of the car and the wind in the denominator [00:05:14]. This implies infinite force when the car’s speed is exactly equal to the wind speed, which seemed problematic [00:05:21]. Alex’s own analysis, free from this issue, concluded there is no way for the car to accelerate at or above wind speed; its acceleration should always be negative [00:05:51].
Explanation:
- Propeller Function: The propeller does not work like a windmill, pushed by the tailwind [00:10:25]. Instead, it turns in the opposite direction, acting like a fan to push air backward [00:10:30]. This fan is powered by the wheels, which are connected to the propeller by a bike chain [00:10:35]. This mechanism allows the car to accelerate even at wind speed, as the wheels turn the fan, generating forward thrust [00:10:40].
- Force and Power Analysis (Car’s Frame of Reference):
- Power Input (Wheels): Power is input into the system by the ground moving underneath the car. The power generated is the force of the ground on the wheels multiplied by the velocity of the car [00:11:18].
- Power Output (Propeller): Work is done on the air as the propeller pushes it backward. The power out equals the force of the prop on the air multiplied by the speed of the car minus the speed of the wind [00:11:30]. The propeller moves slower through the air due to the tailwind [00:11:42].
- Conservation of Power: Assuming no losses, the power in at the wheels equals the power out at the propeller [00:11:46].
- Force Relationship: From this, the force at the propeller will be greater than the force at the wheels [00:11:51]. Since the propeller pushes air back, the air applies an equal and opposite thrust force forward on the prop, which is greater than the backward force on the wheels [00:11:58].
- Lever/Pulley Analogy: The car operates like a lever or pulley system. It applies a small force to the wheels over a larger distance, allowing the propeller to apply a larger force over a smaller distance [00:12:12]. This is analogous to riding a bike uphill, where fast pedal movement with smaller force results in slower wheel movement but with a bigger force [00:12:24].
- Resolving the Divide by Zero: The “divide by zero” problem is a theoretical artifact.
- Lever Analogy: Theoretically, with a lever, if one arm is zero, infinite weight can be lifted with any force on the other side, but its displacement would be zero [00:12:53].
- Propeller Efficiency: In practice, propeller efficiency is ill-defined when the propeller is not moving through the air [00:13:08]. There is a “better formula for the prop proficiency” that is well-defined in the zero-speed limit, eliminating the divide-by-zero problem, though it makes the algebra more complex [00:13:15].
- Conceptual Model (without aerodynamics): A simple cart model with a big wheel rolling on two smaller spools demonstrates the principle [00:13:32]. When the board underneath is pushed to the right, the cart moves down the board faster than the board is moving [00:13:55]. Crucially, the big wheel rotates in the opposite direction of the board’s push, just like the Blackbird’s propeller pushing back against the air to achieve speeds faster than the wind [00:14:06].
Historical Context
The concept of a successful downwind cart dates back to 1969, when Andrew Bauer built the first one to settle a wager [00:07:29]. This bet was inspired by a student paper from 20 years earlier [00:07:39]. Rick Cavallaro, the builder of Blackbird, was unaware of this history until after his cart was built [00:07:44]. Other analyses have been published under names like the “push-me pull-you boat” [00:07:49]. In 2013, the U.S. Physics Olympiad Semifinal Exam included questions about Blackbird, confirming that both downwind and upwind modes faster than the wind are possible with sufficiently low energy loss [00:09:36].
The evidence and explanations ultimately convinced Professor Kusenko, who conceded the bet [00:15:16].