The Monty Hall Problem

Given that a contestant on the Monty Hall Show has a choice between 3 doors. 1 door has a new car that the contestant wants. 2 doors each have a goat, which the contestant doesn’t want.

After the contestant chooses a door which has a 1 in 3 chance of being the new car, Monty Hall opens one of the other doors to reveal a goat. Monty Hall then offers to allow the contestant to change which door the contestant chooses.

Should the contestant change which door they chose to the other of the two remaining doors?

The Monty Hall Problem 3

There is a 1 in 3 chance that the contestant chose the door with the car. There are 2 out of 3 chances that the contestant chose the door with a goat.

If the contestant choses the door with the new car, which happens 1 time out of 3 games, then Monty Hall will eliminate one of two goats. If the contestant always changes the door, then the contestant will lose 1 out of 3 times.

If the contestant choses a door with a goat, which happens 2 times out of 3 games, then Monty Hall will eliminate the other goat. If the contestant always changes the door, then the contestant will win 2 out of 3 times.


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How the Blackbird goes Dead Down-Wind Faster Than The Wind (DDWFTTW )


   The Blackbird is a land car that is able to go directly downwind faster than the wind. In a 13.5 mph wind, the Blackbird reached a 38.5 mph sustained speed as verified by NALSA (North American Land Sailing Association). While sailors have been able to sail faster than the wind for hundreds of years, they have done this by going at an angle. This is called “jibbing”. But sailors haven’t been able to go directly downwind faster than the speed of the wind. The Blackbird does this, but the explanations have been poor or complicated with variables which aren’t properly defined for non-aeronautical engineers, so there are many doubters. Rick Cavallaro and John Borton built the Blackbird, but didn’t invent the concept. The concept seems to date back to 1949 from D. L. Elder at the University of Michigan to whom it was communicated. The originator of the concept appears to be currently lost.

How the Blackbird Works

   The Blackbird’s wheels are connected by a transmission to a propeller. As the wind coming from behind the Blackbird pushes the Blackbird, the wheels turn which turns the propeller. The propeller then pushes the Blackbird faster.

   The conceptual problem people have with this is that as the Blackbird gets close to windspeed, they expect that the friction would result in the vehicle never going as fast as the wind, let alone faster than the wind. The misconception is that the you only see the force on the propeller which is less than the force needed to turn the wheels which would slow the Blackbird down.

   But what is actually happening is that the force from the propeller is pushing against the force of the wind. This means that the force of the wind and the force of the propeller add together. Since the Blackbird is efficient and the wind is strong, this more than equals the force on the wheels slowing the vehicle.


   As the Blackbird goes faster than the wind, the efficiency goes down mainly due to wind resistance. Eventually, the total forces pushing the Blackbird equal the forces holding the vehicle back. When this happens, the Blackbird can’t go any faster, but the vehicle doesn’t start slowing down unless the wind slows down.

The Blackbird Going Upwind

   When the Blackbird is going directly against the wind, the propeller is turned by the wind which turns the wheels which pull the vehicle upwind.

Propeller Driven Ships

There is no reason that the propeller can’t be made to swivel. This would allow for the jibbing used by sailing ships. But sailing ships only catch the wind’s force with their sails. A ship with propellers driven by water screws would catch the wind and add the water screws force (minus efficiency losses) to the wind’s force. Since the screws driving the propellers aren’t as efficient as wheels at transferring energy, this wouldn’t be as high as 85% efficiency. Let’s assume 50% efficiency and see what we get.

e = efficiency (calling it 50%)

Fd = Drag Force (from the water screws)

Fp = Propeller Force

Fw = Wind Force

Fp = e * Fd = 0.50 * Fd

Ft = Fp + Fw – Fd = 0.50 * Fd + Fw – Fd

Ft = Fw – 0.50 * Fd

   If the force of the drag from the water screws is twice the wind force, you will see no force increase by making a sailing ship into a propeller ship. Whether adding propellers driven by water screws is viable depends on both the drag force from the water screws and the efficiency which the force turns the propellers.

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