Double boiler power: is it safe?

So, here’s an interesting thought experiment. Before I go on, I should say that actually implementing this idea would possibly be very stupid. So, let’s just keep it as a thought experiment for now.

[Update: I've done it. It's great. It's documented here.]

Having said that, let’s wonder together: what would happen if we doubled the heating power of a Gaggia coffee machine? (You’re wondering how we might do that? It’s easy if you have a 240VAC model: put a big fat diode across both elements so that the diodes end up back-to-back. Then in each mains half-cycle, the entire 240VAC will be across just one element rather than two elements in series. This effectively halves the resistance and doubles the power.)

So, getting back to the idea: what could possibly go wrong? If you’re thinking the whole thing might overheat, this is not a worry: it’s got a thermostat. We’re talking upping the rate of heating, not the maximum temperature.

So what could go wrong? Well, for starters, the diodes might fail and when diodes fail, they short. So, in addition to the diodes, a fast blow fuse would be a good idea. And, given the temperature inside the boiler enclosure, both fuse and diodes are more likely to fail. So careful attention must be given to placement of these components.

That’s cool. I can manage those caveats. What else might go wrong? Well, now, an element designed with 120V RMS (i.e. peak voltage 170V) in mind will need to be electrically safe at 240V RMS (i.e. 340V peak). Actually, this is fine. One side of the pair of elements gets connected to full mains voltage and the boiler itself is connected to mains ground. So the whole assembly must be able to safely insulate 340V.

What else? Wires: they would need to carry twice the current. Then again, on the 120VAV models of the machine, the boiler elements are wired in parallel and the current is double that of the 240VAC models. At a guess, Gaggia use the same wire Gauge for both models. Or maybe not: to be on the safe side, we might want to rewire the affected wires. Okay, I can do that.

And then there’s the switches. The built-in ones are almost certainly the same as the 120VAC models. I could check this by looking at parts diagrams, but I won’t bother because I am not using the switches to carry the heater current. I’m using a triac. So, my triac needs to be specced and heat-sinked appropriately. Check.

The disk thermostats? They’re rated for 10A. It doesn’t say whether that’s DC or AC (breaking high-current DC is much harder because of arcing). It also doesn’t say whether that’s a limit on the current breaking capacity or on the current carrying capacity. The resistance of the device is less than 0.1Ω and with 5.6A running through it, voltage across it is negligible. So it is dissipating basically no power and doubling the current won’t hurt. So I think the 10A refers to breaking capacity. The load is essentially non-inductive and 2700W results in a current of 11.25A. We’re walking the line here. Then again, so, it seems, are Gaggia. All the parts diagrams I can find specify the same part number for the thermostats even when they specify voltage-specific part numbers for the wiring loom. So it looks like Gaggia uses this for the half-voltage/double-current USA version of the machine.

Mains fuse? It’s 5A. Need to change it to 13A.

That leaves the heater elements themselves. Can they handle twice the power? I don’t know for certain how the elements are constructed, but it is very likely they are standard tubular heating elements. These are very common in all sorts of heating appliances and they are pretty much always made of a nichrome heating coil packed in a magnesium oxide insulator inside a metal sheath. The metal sheath’s temperature is going to be controlled by the coffee machine’s thermostat because it is in contact with the boiler shell. So we need to ask whether the nichrome wire and MgO insulator can take the heat. According to some googling, it seems that MgO’s maximum working temperature is over 2000K, whereas nichrome is best kept below 800°C to keep its rate of oxidisation low enough for a reasonable working life. (Sorry about different units – but if I use the ones I found on the web my numbers are easier to verify). So no need to worry about the MgO: we just need to keep the heater wire below 800°C. How hot will the nichrome wire get at double the power, i.e. at 1350W per element?

Let’s make some simplifying assumptions. The element cross-section is square, which is annoying so let’s do our calculations for a circular cross-section that entirely encompasses the square. That way, we’re getting an upper bound. The corner-to-corner diameter of the element is 14mm (i.e. radius 7mm). What is the diameter of the heating wire? No idea: it’s probably a coil a few mm wide. But let’s assume a worst-case scenario: which is that the wire is not coiled but is just a straight piece of wire. This is the shortest length the wire can have and so will also have to correspond to the smallest diameter the wire can have (length and diameter are directly related because the resistance of the wire must be the 21Ω I measured for each element). So, no coiling and minimal wire diameter mean the largest distance for the heat to travel through the MgO. Nichrome’s resistivity is around 1 x 10-6Ω.m and the element is about 150mm long. So the wire’s radius is 0.048mm.

The last thing we need to know is the thermal conductivity of MgO. Sources vary but 40 W/m/K seems to be a lower bound. I won’t bore you with the derivation, but my analysis shows that the difference in temperature between the wire and the sheath will be:

ΔT = P/(2.π.l.k) x ln(r1/r2)

Where P=1350W is the power of the element, l=0.15, is the length, k=40W/m/K is the thermal conductivity of MgO and r1=7×10-3m and r2=4.8×10-5m are the outer and inner radii, respectively. That gives ΔT = 178.5K.

Actually, only 3 of the four sides of the heating element are in contact with the boiler shell. So let’s assume the entire quarter of the element facing outwards conducts no heat. This means the ΔT must be multiplied by 4/3, for a value of just under 260K. The hottest temperature I’ve managed to measure on the sheath of the heating element (full power in steam mode, measured on the outer surface at the top) is 180°C, which is 50°C hotter than the shell generally. At double the power, that’s likely to be 100°C above the shell temperature – which I limit to 140°C, so we’re talking 240°C. Add ΔT=260K and we have 500°C – well below the 800°C limit. Result!

So maybe we can do this. But what if I destroy the heating element? That’ll be £40ish for a new boiler. Okay, I can live with that. Maybe I’ll have a go with the controller set to deliver a maximum of 1500W (i.e. well below full duty cycle) and see what happens. Wish me luck…

[Another update: I laugh airily now at a mere 1500W. My present most daringest is to use 2000W for about 40s and then switch to 1600W for another 30s, by which time I have injected all the energy I need.]

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