# Back of the envelope calculations, with no actual envelope

A project log for Coin cell battery powered spot welder

Wait overnight and do your welding job!

While commuting in tram from one end of Bratislava to another one, I noticed massive sparks on collector head of pantograph when tram crossed via crossroads. That could be handy for welding the tabs to 18650 cells, I thought, but quickly came to conclusion that it would be somehow unpractical - especially in my small home laboratory - so I have to search for smaller energy source. Fortunately, the time it takes to travel to destination gives me plenty of contemplating time. In order to not look like rainman in public transport, I tend to make simple "order of magnitude" calculations in my head. Kind of back of the envelope calculations, but performed from memory, like this.

I remembered seeing videos, where folks did some basic spot welding discharging supercapacitors with capacity of around 100F, with modest, but lovely sound and visual effects. The energy stored in capacitor is proportional to capacity and square of voltage, with constant of 0,5. The voltage is usually limited to ~ 2,5V, because that's how supercaps are made, but it seems to be OK for small welding jobs. So, 0,5*100*2,5^2, when performing such as calculations, I like to round the numbers to get simpler math operations. 2,5 is close to 2,56 - being beautiful round number: 2,56*2,56 is 6,5536. Half of it is 3,2768 (again well known number), multiplied by 100 is 327,68. So energy stored in 100F capacitor is 327,68J. So far so good.

Energy stored in CR2032 cell is a bit different matter, but still within reach of elementary school physics. Energy is power by time, where power is current by voltage. Average discharge voltage of cell is around 2,5V and capacity of 240mAh (0,24Ah) tells me current of 240mAh (0,24A) can be drawn for one hour. So I have to multiply 2,5 by 0,24 by 3600 to get the desired result. To simplify the math I divided first number by ten and multiplied the second one by ten, so 0,25 * 2,4 * 3600. Quarter of 2,4 is 0,6; 0,6 * 3600, uhm, that is one tenth of 3600 more than half of 3600... 360+1800, that is 2160J of energy stored in CR2032. At first I was surprised and expected mistake in my calculations, but it looks like CR2032 is much that more powerful than 100F supercap, when comparing raw energy stored in given volume.

So, why can't you do welding with CR2032? Because of internal resistance. Short circuit of CR2032 is in order of dozens of miliamps, let's say 30mA. At 3V it's 90mW, that is power that barely heats up quarter of watt carbon resistor, being hell far away from welding. But the battery can do the heating for long hours, while welding is made done in fraction of second and supercapacitor is here to help.

By slowly charging the supercapacitor I can build up the energy to the point it is ready to dump quick into piece of metal to be welded. The charging of capacitor has to be done slowly, though. As the discharge current increases, losses in battery do increase too and I can get less of the energy stored in battery.

Details to be discussed later.

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