Re: how is the speed of boats and airplanes measured?

The speed of an aircraft is usually measured with a device called a Pitot Tube. The central principle is due to Bernoulli's equation.

One way to interpret Bernoulli's equation (sometimes referred to as Bernoulli's principle) is to say, simply, that the pressure you feel from the wind is due to both its speed and it's static pressure. The static pressure is the pressure you'd feel if you were moving with the wind (same speed and direction).

This probably doesn't seem like a great insight at first, but Bernoulli gave us an equation to relate these properties:

Ps + (1/2)*p*(v^2) = constant for a "piece" of the wind
(a.ka. a streamline)

"static pressure" + (1/2)*"density"*("speed"^2) = constant

this constant is the pressure you feel when the wind hits you: the total pressure.

To compute the wind speed, all you need to do is measure everything static pressure, density, and know the constant.

* Measuring the static pressure

If the wind is only moving horizontally, you simply need a sensor that is oriented vertically. The wind has no vertical speed, so the sensor only senses the static pressure:

* knowing the density

Air density at sea-level is roughly 1.225 kilograms per cubic meter (kg/(m^ 3)). By observation, density seems to be reliably dependent upon altitude. In fact, there is a commonly agreed-to "standard atmosphere". this is simply a table of values from which we can look up our current altitude and read off the density. Of course, you must know your altitude! to get that, we often use the static pressure.

* knowing the constant (total pressure)

The total pressure is what you feel when the wind hits you so, we might reason that we simply need a pressure sensor that is hit directly by the wind. This is essentially what is done.

* computing the answer

Take the measured values and use them in the equation, below.

v = square root of ( 2*(Po - Ps)/p )

A representative Pitot Tube setup (taken from http://www.kele.com/Tech/Monitor/Flow/Images/Refflod.gif; Link defunct, 7/20/2006 ) is below

You can read a lot more about this topic in undergraduate aerospace engineering textbooks (or any textbook that discusses fluid mechanics). A very good start is John Anderson's book:

Anderson, John David, Introduction to Flight, Addison-Wesley, 1989. ISBN 0-07-001641-0, Library of Congress Catalog No. TL570.A68 1989

You will also find more information at the following URLs:

MadSci Answer 875573795.Eg

http://www.kele.com/Tech/Monitor/Flow/TRAirFlw.html

http://www.ceet.niu.edu/faculty/kostic/bernoulli.html

I haven't forgotten that you asked about boats, too. I'm not an expert on boats, but Bernoulli's principle applies to water just as it does air. That doesn't mean there aren't other ways to measure your speed in the water. I did a little search of my own and found knotmeters and found these

"Trailing Wire Impeller"
"The Trailing Wire Impeller consist of a docking bay with a 20 foot long piece of wire attached. A magnetic impeller is at the other end. A small induction coil, next to the impeller, picks up magnetic pulses generated by the revolving impeller and transmits them to the Speedmate Boat knotmeter/ log."

From http://www.dc.infi.net/~spdtech/trail.htm

"heaving the log"
Basically you throw a piece of wood overboard; it has a rope attached. You measure how much rope is pulled away over time -- thus, you know your speed! http://www.iws.net/wier/logline.html