12v to 230v inverters

For a standard hairdryer a 1000W quasi sine wave inverter will be fine. Just make sure you use adequate wiring- at least 25mm2 on the 12V side to avoid voltage drop and ensure there is a large Fuse inline on the positive cable as close to the batter as possible-
and fit a large inline isolator switch as well, between battery and fuse- and wire directly to battery. If you want to join to the internal wiring, then you would need either a changeover switch (so that the main inlet socket isn't live when the inverter is)
or fit a socket from the inverter to the standard mains inlet.

The inverter will be using roughly 85 amps so you need some heavy duty cables. You also need a decent sized battery thats capable of providing 85 amps. A 100 amp battery will give you about 30 minutes use before the battery starts to suffer damage. Then you have to put the energy back in again. Take 6 - 8 hours with a large solar panel on a nice sunny day.

I have a 1000w inverter, only used it twice, connected to the battery with short jump leads on a temp basis..It was hopeless even though the battery was charged unless the engine was running .

I use the inverter to power my electric toothbrush and in the winter I use it for my electric blanket.  It's well worth it, I can tell you. 

I fit inverters to boats which have substantial battery charging capability (as do motorhomes, I suppose!). I think for caravan use, you would need to carefully explore the pros and cons- expecially given that a safe, proper installation is important. Plus
I would never try and connect anything but the smallest inverter to a battery with crocdile clips- you need the correct size wiring (as I mentioned before at least 25mm2 cross sectional area), an isolating switch and a fuse (probably 100 or 125A) in the positive
line. Using crocodile clips is not good for sustained high current loads (ok for short ones, like jump starting a car!).

An inverter running a hairdryer will further deplete the battery due to its internal losses. You need to avoid an inverter and use 12v systems whenever possible, cutting out the middleman so to speak. 12v hair dryers are readily available on the Internet,
we have one. You might like to consider using it in your car with the engine running to save draining a lot of power from your van battery. The alternator will cope well. However, 12v hair dryers aren't very powerful, so you need a good toweling first. Did
you know that you can buy catalytic gas fuelled straighteners. Boots sell their small gas cartridges.

Reading the above posts, if it was me I’d stick to a towel! 

...an inverter is useful for powering other stuff as well....ours is mainly used for running the sky box (mains only) while off grid...it doesnt works very well with a towel 

Please advise what size inverter you use for your Sky box, I am not certain what size is required

Thanks

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Your electrical equipment should tell you it’s power requirements in Watts  just add all the items you want to run add a bit for safety and some spare capacity for power  I used a 300W inverter just a cheap one from Maplin to run a TV and digital top box
(before we went for a 12 volt modern TV)

I now use it for the odd charger here and there when off grid, anything that I can’t plug into my 12 volt supply

It works fine but cheep is not generally efficient OK for a few amps but anything over that and you are losing a lot in heat and electrical noise.

You have to remember Watts = amps X volts so 1 amp at 12 volts is just 12 W, 300 W will take all of 25 A without loses you can see from that how the amps rack up.

If in doubt use something like
http://www.rapidtables.com/calc/electric/watt-volt-amp-calculator.htm to work it out for you

 From your batteries capacity how long you can hope to keep things going, try not to go below 50% of you batteries capacity and always recharge ASAP or your battery will not live long.

Remember the power from an inverter is just as bale to give a shock as mains and it only takes 300mA to kill you if unlucky so always treat with the same respect as you would mains. It is amps that kill not volts and 230 Volts are enough to drive current
through you body.