There is a fundamental law of economics that says that as the price of a good or service increases, the demand for that product decreases. This is the Law of Demand: if prices are high, people cannot buy as much. But there are some products for which this is not the case.
Veblen Goods do not obey the Law of Demand: as their price increases, so does demand for them. This is a case of conspicuous consumption, people show off and demonstrate their status by buying increasingly expensive products. A £10000 gold Rolex watch does not really tell time any better than a £10 Casio, but owning a £10000 gold Rolex demonstrates that you are so wealthy that you can afford to spend £10000 on a watch. People do not want to buy a £10 Rolex, but they do want to buy a £10000 Rolex, to show off how much money they have.
There are some goods to which the Law of Demand does not apply, and which are not Veblen Goods. These are called Giffen Goods, and on the face of it, they seem to disobey all rational economic rules: demand for them increases even when their price increases, despite the fact that they cannot be used to demonstrate status via conspicuous consumption.
But imagine this situation: You need to feed your family. You normally buy a mixture of expensive (tasty) and inexpensive (staple) products to provide enough nutrition, but also some variety. But one day the price of rice quadruples: now you can’t afford the more expensive products and the rice, and you still need the staple rice to provide basic nutrition. Thus you buy more rice, even though its price has increased, and the rice is a Giffen Good.
Perpetual motion machines (which don’t exist) come in many forms.
Perpetual motion machines of the first kind violate the First Law of Thermodynamics. They produce mechanical work (i.e. movement) without any energy being input; this violates the principle of the conservation of energy.
Perpetual motion machines of the second kind violate the Second Law of Thermodynamics. They convert thermal energy directly into mechanical work, with no exhaust heat being emitted; this violates the rule of the production of entropy, that entropy in a system must always increase.
Perpetual motion machines of the third kind do not, as their name suggests, violate the Third Law of Thermodynamics. Rather they claim to maintain motion (once started) forever, and do so by assuming that frictional forces can be eliminated completely (often through operating in a perfect vacuum, which is also not possible).
The term elevation refers to the position of a point or an object on the ground above a fixed reference point, usually mean sea level. The term altitude refers to the position of a point or object in the air above a fixed reference point.
But defining altitude can be difficult, and so when altitude is referred to, the reference point must always be explicitly defined. Altitude is normally measured above mean sea level (AMSL) or above ground level (AGL). For example, if an aeroplane flew over the peak of Mount Everest, its altitude could be referred to as either 38 000 ft AMSL or 9000 ft AGL, because the peak of Everest has an elevation of 29 000 ft.
For aircraft it is difficult to measure altitude. You might think that GPS could provide this information, but GPS is designed for positioning on the surface of the Earth and isn’t very good at measuring altitude.
Pilots have always used atmospheric pressure to measure altitude. As an aircraft moves further upwards into the air, there is less air above it pushing down on it and the pressure decreases. This decrease is predictable and easy to calculate:
where is the pressure at height ; is the standard atmospheric pressure of 1013.25 hPa; is the rate at which temperature decreases with altitude (the temperature lapse rate); is the standard temperature; is the gravitational field strength; is the molar mass of dry air; and is the molar gas constant.
Aeroplanes do not fly at a set altitude. Rather they fly at a given flight level, which – although it sounds like a height – is actually a pressure. When a pilot flies at a flight level of 32 000 ft (FL320) they are actually flying at a constant pressure of 275 hPa, and may actually be far above or far below this altitude, depending on the local weather (and therefore pressure) conditions. If they enter an area of particularly high or low pressure they will have to ascend or descend correspondingly.
Using flight levels helps to prevent collisions between aircraft: in the UK aircraft flying on headings between 000° and 089° (north to east) they flight at odd numbered flight levels (FL310, FL330, etc); flying between 090° and 179° (east to south) at odd numbered flight levels plus 500 ft (FL315, FL335); flying between 180° and 269° (south to west) at even numbered flight levels (FL320, FL340); and flying between 270° and 359° (west to north) at even numbered flight levels plus 500 ft (FL325, FL 345). In other parts of the world different flight level rules are used.