I’ve been pondering the same thing myself, and am probably in about the same stage of build as you are right now. I can’t speak for the amount of electricity that the compressor would need. I actually have a small air cylinder (about the size of a propane cylinder for a grill) that I have plumbed in. It’s plenty safe up to 100psi. Considering the low volume of air necessary for the Babington, I figure it will last for a long time before I need to refill it with the shop compressor. I wonder, too, if a compressor dedicated to the Babington might be inefficient, given the small volume of air needed. I suppose an on-demand compressor, with a storage tank, might be a little bit more efficient than a dedicated always-on compressor. This will likely have high current draw, though, and might be more than a Sterling could handle. Anyway, that’s my thoughts on it, having not completed one of these yet. I think I’ll add this to my research ideas though, and track it, to see how various setups compare!
As far as the oil pump goes, I don’t imagine it would take much of a pump for the flow of oil that a Babington needs. From what I’ve learned from this mailing list (I did browse through all of the archive), a flow rate of about 1GPM should be plenty. I’m still lacking coffee, so I don’t dare go calculating how much energy it would take to maintain this flow through a 1/8″ copper fuel line, with however much lift is necessary, but I can’t imagine it would be very much. I think I remember reading about some people using thermoelectric generators (like a Peltier junction, but to generate electricity from heat/cool, not heat/cool from electricity) on their burner tube to produce electricity for the pump. A quick search and I found some specs showing some that will produce about 0.5-3.5A at about 4VDC (2.6-14.7W), at 230C (hot side) and 50C (cold side). Not too big either, at 40cm^2, and 56cm^2… ought to be able to mount nicely along a burner tube. No mention of price on these exact modules, but the list of modules that do have prices range from $9.00US – $24.00US, for 5-10 pieces. Of course, they also have a minimum order of $100US. pf… I’m sure we can find another supplier, or a similar part from a different manufacturer, if we look hard enough.
One good thing about Stirling engines is that they often have unused sides to the pistons, which can be used for fluid pumping operations directly. I have a design for a small engine capable of about 20W which should be capable of generating sufficient pumping action directly to pump the oil and compress air for the burner. John Archibald should know how many CFM and psi is required at the atomiser to make it work. It would not be efficient to have to generate electricity and then convert back to drive a pump and a compressor, when these mechanical functions come almost for free on the Stirling. The engine was designed by me and Stirling guru, Roy Darlington, and Roy built it up a few years ago. One day we will get around to producing plans so that others can build it. By way of comparison, the water circulation pump used in most (European) central heating systems is rated at about 50W. A few watts can produce a lot of pumping action. I have a 12V peristaltic pump which can shift gallons of water a day on about 5W.