Andrewg,
head wind does not alter the take off speed as such, but, in effect you have two seperate speeds to worry about, as I shall explain.
Air speed, the rate of which the aircraft is passing through the air
Ground speed, the speed of the aircraft across the ground...
Airspeed is measured in nautical mile per hour, aka Knots which are bigger than statute miles (common or garden imperial Mph to you and me) . 1 nautical mile = 1.15 statute (imperial) miles, this is due to the way the earth is divided up in degrees and minutes for latitude and longitude, as it all fits in nicely for navigation.... so in effect, 100 Knots = 115Mph.
IAS means indicated airspeed.
Just for example, say a cessna 150 needs to reach 65 Knots IAS to take off safely... (Aircraft always take off at 1.3x the stall speed, ie the speed at which the wing cannot produce enough lift to sustain the weight of the aircraft)
So, with a calm day, and zero wind, the Cessna will need to accelerate itself to 65 Knots IAS , and 65 Knots groundspeed to take off...
If there is a Direct HEADWIND of 35 Knots ( a very windy day), the Airspeed of the Cessna will still be 65 Knots IAS, but it will have a GROUNDSPEED of only 30 Knots to achive take off, and as you can imagine will use only half the runway distance that it would if there was no wind...
If the direct headwind speed is 65 Knots, the Cessna will still have an airspeed of 65 Knots IAS (remember it is the flow of air across the aircraft we are interested in), but a groundspeed of ZERO Knots!! In effect the aircraft can infact take off without actually moving along the runway!! here is a video of a Husky flying on a very windy day, just to show you the effect of a very strong headwind!
http://www.youtube.com/watch?v=c99ZHZw97rU
When I did my licence in Florida, you could actually fly a fixed wing aircraft backwards across the ground, as the wind in some areas was so strong that you could fly slowly enough for you to actually get blown backwards
So, all aircraft where possible take off and land into wind as far as possible, as it gives a much shorter ground roll and increases safty margins. It is possible to land with wind behind you, but you will have a large groundspeed and as such is much more dangerous, and uses up lots more runway!
Hughy,
Air obviously varys in density as it is affected by temperature and pressure.. If you are somwhere like Liverpool airport in December, you are fairly close to sea level air pressure, and the temperature is likely to be pretty cold. This will mean the air is nice and dense, and you will achive your take off speed in a shorter distance, as the engines will make more power, and the wing will have more air molecules to flow over it..
If you are somwhere like Kabul in Afghanistan, you are 6000 feet above sea level, so obviously atmospheric pressure is a lot lower, and chances are the temperature will be in the early 40° range
... This means the air is very thin, so engines will make far less power, and the wing will have far less air molecules to flow over it..
Say you are on an aircraft that weighs 10,000Kgs, in Liverpool you will need only 6500 feet of runway to take off with zero headwind.
In exactly the same aircraft, still weighing 10,000Kgs ,at Kabul, you might need 10,000 feet of runway to achive the safe takeoff speed....
Airspeed is measured by a pitot probe, which operates by measuring the pressure of the air being forced into it (by the aircrafts forward motion through the air) against the static (stationary) air pressure, so as air density falls or rises, less or more molecules are avaliable to operate it. So even though there is less or more air density, it remains accurate to the aircrafts speed through the air, not across the ground
Clever eh?
...
This means that in effect you could land at an airport in the dead of night, when it is cool, and not be able to take off the next day when the temperature has rocketed
As a wing passes through the air, the faster it goes the more lift it will produce for the same angle of attack, so the heavier an aircraft is, the more forward speed it will need to fly.... For example, a 737 that weighs 50,000Kgs will need less airspeed to take off than one that weighs 75,000Kgs..
This is why they put such a strict limit on baggage weights, and why fuel is measured in KGS rarther than litres or gallons. This is so the crew can calculate the Zero fuel weight of the aircraft with all the passengers, luggage and crew onboard, then work out how much fuel they need and can carry whilst staying inside the aircrafts max take off weight..