Calculations

Calculations

Electrical Power

If you’ve been considering the electrical theories at play, a battery is a fixed voltage power supply which is very similar to the solid-state fixed voltage power supplies (like computer battery chargers, etc). You can use this same process when retrofitting a steady-state fixed voltage power supply to your circuit.

Generally speaking, I would not normally recommend attempting to retrofit the supply to match the circuit... BUT when dealing with batteries you have to alter your circuit’s resistance to account for the fixed voltage if you wish to maintain battery life.

I doubt that many of you would actually require a battery to supply the power your foam cutters, as most of you are going to be indoors where a wall sockets are available. But if you have an application where it may be outdoors, at a remote location, or at a demonstration, you might think about using a battery as your source of power.

Before we proceed, you need to know I’m not talking about hooking up a pair of AA batteries. To realistically gain any longevity with foam cutting, the battery supplies need to be physically larger, with a higher capacity, and be between 6-12 volts. Check out the purchasing section for more information.

As you may well know, in reading from our Electrical Theory Discussion Page, power supplies put out a constant voltage while the current drawn is dependent upon wire resistance. Batteries are no exception to this rule.

Just to recap the information listed above (incase you got lost), all batteries have a rated capacity which is essentially how long a battery can run based upon how much current is drawn from the battery. It would also be proper to state that this rating pertains to the duration and intensity of the battery power output.

This capacity rating is given as Amp-Hours (Ah)

A battery rated at 10Ah may theoretically provide 10 amps for 1 hour, or 1 amp for 10 hours.

When it comes to choosing a high power battery, there are basically two voltage rating to choose from but a ton of different capacities. Your options in fixed voltage are typically 6 volts & 12 volts.

Most applications only require 6 volts, but 12 volts will give you much more length on your cutting wire if your design demands it. But if you use 12 volts and intend on switching between devices, just mind the applied voltage to the circuit’s resistance. You may need to add resistance to your shorter cutting devices to account for this higher voltage. Visit the Adding Resistance Page for more information.

Here is an example ::

6V / 12Ah

This battery can supply a constant output of 6 volts

The output amperage will depend upon the resistance of your circuit, but the battery can theoretically supply :

12 amps for 1 hour

or

1 amp for 12 hours

or

2 amps for 6 hours

etc..

Please note that 1 amp = 1000mA

So a battery rated at 700mAh is really only 0.7Ah

26 Gauge NiChrome Wire Chromel C

Because we know that voltage is constant, temperature is dependent upon amperage, and amperage is dependent upon resistance, I have outlined the necessary circuit resistance to obtain a variety of temperatures for the two more common wire gauges.

Scroll down to use the Jacobs Online Calculator and manually calculate your own requirements.

6.3 Amps

5.1 Amps

7.6 Amps

Required Circuit Resistance

20 Gauge NiChrome Wire Chromel C

Necessary

Amperage

600°F / 316°C

Desired

Temperature

800°F / 427°C

1000°F / 538°C

6 Volt

12 Volt

1.9 Ohms

1.2 Ohms

2.4 Ohms

0.79 Ohms

1.6 Ohms

0.95 Ohms

0.6592 Ohms / Foot

2.67 Ohms / Foot

What if you want a 26 gauge wire at 600°F, on a 6 volt battery, and only 10 inches (0.8 feet)?

Required Length

6 Volt

12 Volt

2.9 Feet

1.8 Feet

3.6 Feet

1.2 Feet

2.4 Feet

1.4 Feet

2.6 Amps

2.1 Amps

3.2 Amps

Required Circuit Resistance

Necessary

Amperage

600°F / 316°C

Desired

Temperature

800°F / 427°C

1000°F / 538°C

6 Volt

12 Volt

4.6 Ohms

2.9 Ohms

5.7 Ohms

1.9 Ohms

3.8 Ohms

2.3 Ohms

Required Length

6 Volt

12 Volt

1.7 Feet

1.1 Feet

2.1 Feet

0.7 Feet

1.4 Feet

0.9 Feet

Well you know that in order to achieve 600°F you need 2.1 amps, and because the battery is a 6 volt supply, you NEED to have 2.9 ohms. But a 26 gauge wire, at 2.67 ohms per foot, at 0.8 feet is only 2.1 ohms. This means that you have to account for 0.8 ohms...

If you do not provide 0.8 ohms, there is less resistance in your circuit, which means a higher amperage, which in turn creates a higher temperature (close to 700°F)

All-in-all this higher temperature may not mean a lot when cutting foam, but because you are not drawing a higher amperage, you will decrease the duration that your battery can supply power.

Remember Amp-hours...

Retrofitting a Supply

It is possible to place some of these batteries in series and others in parallel.

Remember these two key points...

Placing batteries in parallel,

the voltage remains the same but capacity is added

Placing batteries in series,

the capacity remains the same but voltage is added

Please visit this help page for more explanation of this calculator.

Batteries are an excellent source of storable, and easily accessible electrical power. Each single unit of a battery is called a cell, and battery is a combination of cells joined together. Each cell will have a characteristic voltage range between charged and discharged states which are set by the electrochemical nature of the internal metals. Simply put, the chemistry determines the voltage of a cell and the number of cells determines the voltage of a battery.

Within each battery is a set of chemical reactions that occur at the anode and cathode which drive electrons and ultimately the electrical gradient from which a direct current of power is derived.

Some non-rechargeable batteries contain chemicals to absorb waste materials and byproducts from the chemical reaction. Should the byproducts build up, they will ultimately poison the cells.

Alkaline batteries contain other chemicals to absorb waste byproducts from this reaction which allows them to last longer than most other batteries. But once discharged, these batteries cannot be recharged. In fact attempting to recharge can be quite dangerous.

Rechargeable batteries function the same as any other battery, but when charged the flow of electrons is forced backwards against the anode and cathodes to reverse the electrochemical reactions.

Many large cell batteries (like car batteries) can produce large amounts of output amperage, but also can therefore be quite dangerous. In fact, a car battery can produce up to 300 amps if it is short circuited!

One caveat to car batteries though is that while they have enough capacity to electrocute a human many times over, it does not have enough voltage to penetrate dry (and even damp) human skin. It takes about 48 volts to puncture the dry skin resistance of the human body. Still, one should be careful when handling any high capacity electrical power circuit regardless of its voltage.

Many large cell batteries are rated in Cold Cranking Amps or Reserve Capacity. CCA is approximately equal to the RC of a battery times five.

Amp-Hours = (RC / 2) + 16

Battery Charging

Battery charges are usually straight forward devices that has a transformer and a few large diodes. Some of them have circuit breakers and amp meters. While others allow manual control of both amperage and voltage.

Proper battery charging demands that you apply a voltage that causes current to flow at 1/10th the amp-hour rating of the battery to a maximum of about 1/4th the amp-hour rating of the battery.

Exercising Batteries

All lead/acid batteries should be completely discharged at 1/10th to 1/4th of their amp-hour rating. Once the battery is loaded, monitor the voltage output on the battery. When the voltage drops below rated voltage, it is ready for recharge. For reference a 12.6v battery will be ready to recharge when the voltage drops below 11 volts while loaded.

Reference ::

You can certainly discharge a battery at a higher amperage rating than this, but do not expect it to be able to maintain a mathematically consistent time frame. The higher current demand will cause extra losses, and the internal resistance of the battery will then increase. When the internal resistance goes up, it decreases the output voltage and ultimately decreased capacity.

Many will note that when a battery is discharged at a higher rate than it is designed for the more power that is lost as heat. In some circumstances the battery will become dangerously hot and may explode.

While the 1/10th rule is a safe estimate, as good rule of thumb some say to divide a battery's amp-hour rating by 4 to estimate the maximum current the battery can deliver and still have a reasonable life expectancy before it is fully discharged.

For the maximum capacity of a battery, do not pull more amperes than 1/10th of its amp-hour rating.

20 amp-hour should not supply more than 2 amps for maximum capacity

A battery that is rated as 5 amp-hours can theoretically supply 5 amps for 1 hour, or 1 amp for 5 hours. Sometime the capacity may be rated as miliamp-hours, which is the same concept just a different measurement of amperage.

1 amp = 1000 miliamps

Valve Regulated Lead Acid (VRLA) batters are also known as Sealed Batteries which is a lead-acid rechargeable battery. A subclass of VRLA batteries are known as AGM or Absorbed Glass Mat batteries.

These batteries typically supply 6 or 12 volts, and have a wide selection of capacities. Most are available through local retailers, but you can also search them online.

Please follow the provided link to the Battery Supply Section for further recommendations on styles and suppliers.