james nolan (nolan_laboratories@email.msn.com)
Sat, 22 May 1999 14:00:32 -0600

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West Wight Potter Website at URL
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I believe the "correct" answer to the teaser is wrong because it violates
the law of conservation of energy. Here's why:
Consider the boat, water and air a closed system. The water pushes the boat
forward at 2 knots through the drag force of the hull on the water. The
water supplies the only energy into the system. The apparent wind is
generated by the boat and water moving relative to the still air. The energy
contained in the apparent wind is supplied by the water pushing on the boat,
which in turn pushes against the wind. Therefore the only energy input into
the system is from the water pushing on the boat.
Now the sails are raised in an effort to gain energy from the apparent wind.
The sails increase the drag force against the boat. If the sail did increase
the speed of the boat relative to the water, the water would be putting less
energy into the boat and the boat would experience more drag against the
water. The kinetic energy of the boat would increase with a net decrease of
energy into the boat. This is not possible, remember the apparent wind power
comes from the water pushing the boat.
Here's two easily performed experiments to show this:
On a dead calm day, get your sailboat towed at 2 knots. Raise your sails and
try to overtake the towing boat on the apparent wind.
On another dead calm day use your motor to get up some speed and apparent
wind. Raise you sails and kill the motor. Should you be able to sail the
rest of the day on the apparent wind?

In each case the energy for the apparent wind is supplied by the towing boat
and the motor. Once the towline becomes slack or the motor stops, the boat
will stop too. In the case of the boat in the river, the river acts as the
tow rope. The river is in equilibrium with the boat and supplies force for
both the apparent wind and the force to push the boat. If the boat speeds up
relative to the river, the river's pushing force is less and negative drag
force increases. If the river is the sole source of energy (generating both
water and wind force) the boat will never go faster than the river because
it takes more energy than the river can supply.

Air foil argument:
A typical rigid NACA airfoil has a ratio of 10 for lift to drag at an angle
of attack of 0 degrees. If we replace the sail on the boat with a more
efficient rigid wing, the lift force is ten times the drag force for wind
head on. To tilt the wing to generate a forward lift force vector equal to
rear pointing drag vector the angle of attack comes to about negative six
degrees. (The assumes the lift is normal to the wing, not normal to the
airflow, which violates physical principles) . However at the angle of
attack, the lift and drag of the wing section are about equal, blowing the
boat backwards. I believe the drag force of a sail is worse than a rigid
wing, so I dont think the boat will move forward faster propelled by the
apparent wind.

Jim Nolan