In this day and age, I believe Lindsay still makes compressors using existing gasoline engines. Notably, they use a V-4 air cooled Wisconsin engine, with one bank of 2 cylinders being the engine, and the other bank fitted with a cylinder head having compressor valves.
A company named Smith used to sell conversion heads for Model A engines, and later on, flathead Willys engines. The arrangement was one pair of cylinders being the compressor and one pair being the engine. At the recent old engine and machinery auction in Hudson, NY, there was a "Smith" compressor built on a converted Willys 4 cylinder short block. Years ago, when I worked in Wyoming, I was friendly with a ranching family. They had a line of old vehicles, tractors and farm machinery along a fence and there were all sorts of interesting things to be found. Amongst them were a compressor made on a Model A chassis, with a "Smith" conversion on the engine. Another interesting item was a home made DC welder. As the patriarch of the family (then 78 years of age) explained: after WWII, the interurban lines in California were being phased out. Some enterprising soul bought up DC traction motors from the interurban cars and converted them into welding generators. A control box with a big rheostat to set the heat was furnished with the converted traction motor. It was up to the buyer of this "welding generator" to come up with some means of mounting it and driving it. The old rancher had taken a V-12 Lincoln Zephyr as a wreck from a junkyard and built his welder on the chassis. The sheet metal up to the firewall was intact, enclosing the engine. The dash panel was intact with the instruments. The bell housing and transmission were left in place on the chassis. The driveshaft had been cut off and a "rag joint" type of shaft coupling used to couple the driveshaft to the welding generator's shaft. No governor was used, just a hand throttle. The old rancher said it worked well enough for what they needed it to do. It was one of those situations where if you asked about buying or trading to get anything out of that iron pile, you'd likely have been turned down. I was somewhat nomadic at that point in my life, and had no interest in accumulating "someday" projects, nor did I even own a place of my own to pile up those "projects".
A buddy of mine has a welder that was a homebuilt job. It is a Hobart welding generator, ordered new by a local man in 1939. The local fellow is the grandfather of a mechanic I know, and in passing, the mechanic had told me about his grandfather's welder. It was a powerful brute and they used it to weld up their construction and well drilling equipment. The mechanic said he had no idea where that old welder had gotten off to, as his father had sold it some years earlier. In the meanwhile, another mechanic friend had a "mystery" welder in his boneyard. His boneyard is maybe 5 miles from the shop where the mechanic's grandfather had built and used that welder. The mechanic described it as a 300 amp machine, home built and powered with a '32 Ford flathead V-8, and said he remembered-and liked- the sound of that old flathead when an arc was struck with a hefty electrode. A third friend bought the "mystery welder" from the 2nd mechanic's boneyard. I took a good hard look at it. At first glance it looked like a factory built unit. Closer looking revealed the Ford auto chassis had been modified into a trailer while retaining the engine mounts. The instrument cluster, minus the speedometer, was from the dash of the Ford car. The sheet metal enclosure was very neatly made using oxyacetylene welding and nice braking work. The friend who bought the welder got it running again and is burning rod with it. The mechanic whose grandfather had built that welder dug up the paperwork and gave it to me- the order from 1939 and correspondence with Hobart. I gave the paperwork to my friend who now owns the welder. The mechanic who had it sitting in his boneyard said he was routinely pestered by people wanting that flathead V-8. Apparently it is an early Ford flathead V-8 and the antique car restorers and builders of "retro" street rods want that engine. My friend who now owns the welder keeps it as it is and uses it. I believe he put a couple of "cherry bomb" hot rod mufflers on the engine, and it really snorts when an arc is struck and settles into a nice throaty sound.
There were plenty of companies years ago who started with auto or industrial engines and did compressor conversions. If I recall correctly, Schramm and several other outfits whose names escape me did this as well. Recently enough, I saw a blue tow-behind air compressor. It was an unfamiliar machine, but on closer examination, consisted of a Ford V-8 (modern version, not a flathead). One bank of cylinders was the engine, the other had the compressor conversion. The manufacturer had their own name on the unit and stuck with the "Ford Blue" paint.
Sandblasting service is rough service for a lot of compressors. The sandblasting crews often work in close proximity to the compressor and it eats a lot of airborne grit. Another item came from my mechanic friend's boneyard in the form of an ancient Ingersoll-Rand engine driven compressor. I believe this has a Continental flathead 6 cylinder engine coupled to a water-cooled recip compressor. Unfortunately, this unit was used by a sandblaster, and apparently, the air cleaners clogged and were removed. The compressor was then run minus the air cleaners. The result is the engine has almost no compression and the compressor does not build much pressure.
I was at our congregation's cemetery a couple of weeks back, doing repair welding on the ca 1920 ornamental steel fence- frost heaving and hits by snow plows and wayward hearses took their toll over the past 100 years. As I worked, a young fellow with a pickup towing an I-R compressor drove up. He asked me where a certain grave was located. I showed him, and he was there to abrasive blast the "vital statistics" into an existing headstone for one of our congregants who had died recently. The fellow had a rubber stencil that he squared up and glued to the headstone, and a small pressure pot sandblast rig. I asked him what abrasive he was going to use, and he said it was silica sand, bought as "playground sand". He said it would be the last job they did with silica sand and would be going over to some other abrasive. I was surprised when this fellow did not have an air supplied mask. He had a half face respirator with cartridge filters, which he wore under his sandblast hood. I wasted no time in rolling up my leads and picking up my tools and clearing out. I did notice that he parked the truck and compressor within about 25 feet of the headstone he was going to work on. With that kind of working environment, air filter life has to be quite short, though the newer generations of air cleaners on engines and compressors have a "precleaner" to knock out heavier particulates.
Nowadays, I think almost all the tow-behind compressors are diesel driven, and almost all are rotary screw compressors. The compressor pictured in this thread looks like a hard-used machine and probably dates to the 40's or 50's when flathead Ford V-8's were a common item. Interesting to look at and appreciate for what it is, but nothing I'd want to own or try to use. The Lindsay units built on the V-4 Wisconsin engine are quite popular with heavy equipment mechanics needing enough air to run a 1" drive impact or other hefty air tools. Some monument sandblasters also use these Lindsay compressors as they can be hauled on a light pickup truck, no trailer needed.