Nichrome wire

I'd like to build my own heat bed with nichrome wire. However, instead of using the 12v power from my power supply, I'd like to use a relay switch powering from mains 110VAC. I was thinking of using a signal from my arduino to control the relay once ideal temperature is reached.

Here are my questions:
how much nichrome wire should I use, and what gauge? Is it as easy as clamping down the wire and using kapton tape to heat the aluminum bed? (Please note that the temperatures I'll need it for shouldn't exceed 200 Celsius.) What's the cheapest way to achieve this (preferrably without having to buy power supplies, or adapters/transformers).

PS. how do soldering irons work? are they just steel rods with a buch of low resistance wires inside, or do they use transformers to drop down mains voltage? Maybe I can copy how soldering irons work..

Thanks!

You can look up the resistance per unit length for various gauges of nichrome wire. You divide the voltage (Volts) by the resistance (Ohms) to get current (Amps) and you multiply the current (Amps) times the voltage (Volts) to get wattage (Watts).
At 110 Volts if you have a 110 Ohm heater it will draw 1 Amp and produce 110 Watts of heat. If your heater is 220 Ohms it will draw 1/2 Amp and produce 55 Watts.

The hard part will be determining how many Watts of heat you need. That will depend on how quickly the heat transfers away from the stuff being heated. That will depend on surface area and air flow. You have not said how big your bed is or how well insulated it is.

You can make the resistance lower by making the heating wire shorter. You should over-estimate the length of heating wire you need and then cut it shorter if you need more heat to reach the desired temperature.

The wire has to be well insulated (electrically) from the aluminum. If the wire gets to hot it will burn through the Kapton, short against the aluminum and either cause a shock hazard for massive sparks and fire hazard.

I'd strongly advise against a home-made mains-voltage heater - where are you going to get all the exotic ceramics you need for insulation (mica?, alumina sheets or paste, etc etc)?

You need to be aware of the temperature dependence of resistance of nichrome - fortunately much less than many metals, but there is a dependence you need to be aware of.

Most soldering irons these days are low voltage for safety and convenience of temperature-control (solid state), but they are a heating element in ceramic insulation inside a metal tube usually I believe.

Thanks for your responses guys! Is this similar to how soldering irons work?

The heating element in my iron looks like a thin rod of ceramic with three wires sticking out. Not very practical to deal with.

Cheap glue stick guns sold at hobby stores contain an easily repurposeable ceramic resistor if you're looking for heat in the tens-of-watts range.

The manufacturers of the wire would be the best place to get answers. Here is a link that might get you started. As MarkT says, You also need to think about the substrate you will mount the wire on.

http://www.jacobs-online.biz/nichrome/NichromeCalc.html