I recommend you read through the Transformer Info (Understanding Transformers) page so you understand transformers better if you are not familiar with them. The Power Supply Design page explains how to build a complete power supply for a hot wire foam cutter after you have selected the wire and transformer.

This page combines information on how to choose both the nichrome wire and the transformer for the power supply because the two go together--one depends on the other.

Wire Measurement

Wire is measured in gauge. There are several different gauge standards so it is common to use the decimal measurement instead of gauge now. Nichrome wire and other non-ferrous metals use the AWG gauge standard, American Wire Gauge, and this is the standard I use on my Web site but I also list the decimal inches. The AWG is the same as B&S standard, Brown and Sharp. This standard is also used for copper and aluminum wire so is the same gauge as is used for electrical wiring in your home.

Ferrous wire like iron and stainless steel wire most commonly use the W&M, Washburn & Moen, wire gauge.

A comparison chart that shows the decimal wire diameter and the associated gauge size in the SWG, BWG, W&M, and AWG standards can be found here
http:/dave-cushman.net/elect/wiregauge.html. For the reverse, showing the gauge number and the associated decimal equivalent for the SWG and AWG standards can be found here https://bsfixings.uk/resources/wire-gauge-chart/

As the gauge number gets larger, the wire size gets smaller. AWG 40 gauge is hair fine while AWG 14 gauge is nearly as large as a household wire clothes hanger.

What wire size should I use?

You can use any wire size you want to. Foam can be and is cut with wire sizes from 40 gauge (.003" dia.) all the way up to 11 gauge (.091" dia.). The most common size is 26 gauge. A short piece of 40 gauge wire has been used with a 9 volt battery to cut very thin (.020") and narrow strips of foam for air surfing walk-along gliders. Two D cell batteries can power a 4" piece of 32 gauge nichrome wire in a small hobby hand held foam cutter.

A 12 volt power supply will power up to 24" of 26 gauge wire at 800F or 17" to 1000F. This would include nearly all table top foam cutters which is the most common type of foam cutter, and would include small bow cutters. This is why 26 gauge is the most common. 24 gauge to 30 gauge has also been used for table top models.

16 gauge to 11 gauge is used for foam cutters to cut shapes such as molding because they are stiff enough to hold a shape rather than being straight. A 12" piece of 14 gauge nichrome wire requires only 3 volts but almost 19 amps. Larger diameter wires are also used for very long cutters such as 8 or 10 feet.

The Tension Factor

All metals expand with heat so the nichrome wire at cutting temperature also expands and gets longer. Because of this, some method of keeping tension on the wire is needed in hot wire foam cutters. This is usually accomplished either with a springy frame that the wire is stretched between or a spring is used. It is also conceivable that a weight could be used with the wire over a pulley. Tension on the wire also helps keep it taut so when a little pressure is applied when cutting foam, the wire stays fairly straight which is necessary for a good quality and uniform cut.

Because of the need for tension, the smaller the wire is, the less tension can be applied without breaking or permanently stretching the wire. Using 40 gauge wire means very little tension is possible and it will be harder to keep the wire taut when cutting. The longer the wire is, the more pressure needs to be applied to the wire to keep it straight and taut. This is why as a general rule, the longer the wire, the thicker it needs to be. There is no length vs. gauge size standard since theoretically any size can be used at any length with the proper voltage applied and current capacity of the power supply.

Gauge/Current/Temperature Relationship

The temperature of a straight wire in room temperature calm air can be calculated. A given temperature will result in a specific current flowing through a specific diameter wire. It doesn't matter how long the wire is, a given current flowing through the wire will result in the same temperature. For example, a 26 gauge wire with 3.2 amps flowing through it will result in 1000 degrees F whether it is 2" long or 200" long.

The bigger the diameter, the more current is required to heat it to the same temperature. For example, only 0.43 amps will result in 1000F in 40 gauge wire, but 18.8 amps is required for 14 gage wire. In addition, the larger the diameter wire, the longer it will take to reach the equilibrium temperature.

Equilibrium Temperature.

The reason a strait wire reaches a given temperature and stays there in calm room temperature air is that the current continues to produce more heat as long as the current flows. At the same time, heat is being transferred away from the wire to the surrounding air. The hotter the wire is, the faster the heat is transferred away. The wire reaches its equilibrium temperature when the heat generated is equal to the heat transferred away.

If you coil the wire, in a tight coil like in heaters, transfer of heat away from the wire is reduced because there is more wire in a given volume of air and so the wire will get hotter.

In the same way, a wire in contact with any other material will change the rate of heat transfer away from the wire. If the material it is in contact with is a good conductor of heat such as copper, the equilibrium temperature will be lower because heat is transferred away faster. If the material it is in contact with is a poor conductor of heat (an insulator) the equilibrium temperature will be higher because less heat is transferred away. These situations result in complicated heat transfer equations that are not easily solved. In this case, experimentation is required to find the right wire and voltage to create the desired temperature.

When used in ovens, kilns and enclosed heated areas, resistance wire will get progressively hotter as the oven or kiln gets hotter if the voltage isn't changed. The equilibrium temperature is based on the surrounding air temperature and will be a fairly constant DIFFERENCE in temperature between the wire and air temperature. So if you started out with 28 feet of 22 gauge wire that was coiled such that the temperature was double that of a straight wire, it would be around 1200F (316C), a difference of 1130F between air and wire temperature, if the enclosure air temperature started at 70F. It the wire would just be turning red at that temperature. By the time you reached 1400F (760C) enclosure air temperature, the wire temperature would be 1400F plus the difference of 1130F or 2530F. The wire would melt. For kilns and other high temperature enclosures, the wire gauge, type, length, coil dimensions, and voltage applied need to be carefully designed to limit the wire temperature at the final achieved air temperature to be well below the melting point, and the apparatus must be designed to turn off at the target temperature or lower. This is not a trivial design process and should normally be left to an engineer trained in heat transfer and electrical design.

Current Created From Applied Voltage

As mentioned above, it doesn't matter what the length of wire is, a certain current flowing through a given wire diameter will result in a given temperature in free air. So how is that current created? A voltage applied across the two ends of the wire create that current. The longer the wire, the more voltage is required to create the same current. This is due to the difference in the total resistance of the wire in different lengths.

Ohms Law

Ohms law is required to figure out the current and voltage relationship. Ohms law states:

V = IR

V is voltage in volts (traditional E is used for voltage and stands for electromotive force instead of V), I is current in amps, and R is resistance in ohms. You can rearrange the formula to find the current:

I = V/R

From this you can see that is the resistance goes up, so does the required voltage to get the same current. The resistance of nichrome wire is specified in ohms per foot. The longer the wire, the more ohms resistance it has so the longer the wire, the more voltage is required to push the current through the resistance of the wire.

What Transformer Do I Need?

Power is calculated by the formula:

W = I²R or W = VI

A transformer is usually rated in watts or volt amps. For small transformers, they are essentially the same and interchangeable. You need to know the power required for your heated wire so you know what size transformer will be required. To calculate that, you first decide what gauge wire you will use and find the ohms per foot resistance of that wire. For example, 26 gauge wire has a resistance of 2.67 ohms per foot. If you are using the wire to cut foam with, a good rule of thumb is to heat the wire to just before it starts turning red which means just below 1112F or 600C. 1000F is a good initial target temperature. If you are using a dimmer or a variable voltage supply, you can turn the voltage up until you can just barely see it turning red and then turn it down a bit. You also need to know the length of the wire. Lets say you will use 2 feet. Now you can calculate the resistance, voltage, and power requirements.

I = 3.2 amps (from the calculator)

r = 2.67 ohms/ft

R = r*L = 2.67 X 3.2 = 5.33 ohms

V = IR = 3.2 X 5.33 = 17.1 volts

P = VI = 17.1 X 3.2= 55 watts

I = current in amps

r = resistance per foot of the wire in ohms

R = total resistance of wire

L = length of wire in feet

P = power in watts

The calculator actually calculates all of that for you. This is just to explain how it does that. It does not tell you what transformer you need.

To select the proper transformer, go to the transformer page and look in the table at the top for a voltage the same or higher than you (or the caclulator) calculated that is the same watts (VA) or higher. The closest voltage the same or higher is 18V. The same or higher VA is 100VA (50VA is too low). You have two choices of 100VA transformers; either the 9V/18V or the 18V/36V. Either can be wired for 18V. Click on the 100VA 9V/18V. Check the max rated amps at 18 volts. It is 5.5 amps which is higher than what you calculated so this will work. If you had chosen the next lower VA, the 50VA 9V/18V, the max rated amps at 18 volts is only 2.8 amps which is below the 3.2 amps we need. You could use that if you used a dimmer with it and turned the voltage down to about 14.7 volts which would give you 850F and 2.75 amps. That would still cut foam fine, just slower.

How do you know whether in this case you should pick the 9V/18V or the 18V/36V? If you know you will only use the length of wire you started with, it doesn't matter. If you think you might want to use a shorter length in the future, get a dimmer with the transformer so you can turn down the voltage. If you might use much shorter, then be sure to get the 9V/18V so you can rewire it for 9V. You can also get a DPDT switch so you can quickly switch between the 9V and 18V.

If you think you might want to use a longer wire, you can't just get the 18V/36V because when wired for 36V, you cut the max amps in half so that does not work. ALWAYS FIGURE THE LONGEST WIRE YOU MIGHT EVER USE and chose the transformer that can handle that at the temperature you will be cutting at. You can always turn the voltage with a dimmer and can also switch to the lower of the two voltages also if needed.

What if you really only wanted to use a 50 watt (VA) transformer because of the size, weight, or cost? As I already mentioned above, you can cut at a lower temperature. It isn't that much lower. But you have another option. You aren't stuck with just using 26 gauge wire. You can use a smaller gauge wire. Plug 28 gauge into the calculator keeping the temperature at 1000F and length at 24. You get 20.2 volts at 2.38 amps. Now you need to chose a transformer that can put out 24 volts. The 50VA transformer at 24 volts has a max rated amps of 2.1. Not quite enough. Try 29 gauge. It gives 2.1 amps and 22.4 volts. That works, barely, and you need a dimmer to turn the voltage down to 22.4 volts.

The difference in the sizes of wire is the strength. Obviously, the larger the wire, the stronger it is. If you are careful and don't try to push the foam through the wire faster than it can cut, smaller wire works fine. You don't gain anything by pushing harder anyway. These transformers are designed to only get warm at the rated amps but it is still a good idea to select a transformer that will be operating a little below the rated amps.

Transformers - Gauge And Max Lengths

Below are a couple examples from the 30 transformers I carry now. See the transformer page where each transformer has its own graph. The graphs show the minimum and maximum length that each transformer heat to 800F when used with a dimmer for foam cutting. For plastic bending, the wire should be hotter and so the maximum lengths would be shorter. The normal foam cutting temperature is 600F but figuring for 800F gives some room for adjustment. All but one are dual voltages outputs so the lower voltage handles higher current and so extends the range to larger diameter wires because the current capability is doubled when the voltage is halved. The higher voltage handles smaller gauge but longer wire. Dimmers do not go all the way to zero volts, they go to about 20%, so there is a minimum wire length that can be use.

This transformer can be used with short pieces of stiffer wire for shaped wire cutting.