My electrical experience is very limited. I poked around many different sources to find a clear answer as to how the DC voltage changes when three phase AC is rectified to DC. I got many answers. The previous video and the video attached here provided a clear answer. The specs for the alternator I want indicates "24 VAC at 2000 RPM". But "VAC" is vague. Do they mean Root Mean Square (RMS), peak, line to line, line to neutral, etc.? Turns out they must have meant RMS line to line. Well, the DC voltage is about 1.8X the VAC in this case. NOTE: Of course, this is just an empirical estimate.
Example 1) The previous video show 53vdc at 1520 rpm. The alternator specs for that unit show "48 VAC at 2500 RPM". So, at 2500 RPM, the DC voltage will be about 1.8(48) = 86.4v. Therefore, 53v will correspond to about (53/86.4)(2500) = 1530 RPM. Actual speed was 1520 RPM. That checks out.
Example 2) The attached video shows about 14v RMS VAC. So, the expected DC voltage from the rectifier at the same RPM should be about 1.8(14) = 25.2. It checks out as well.
So, if the alternator provides 24v VAC at 2000 RPM, then the DC voltage would be about 1.8(24) = 43.2v. The RPM for 28v (which is about right for the charging conditions I want) would be about (28/43.2)(2000) = 1300 RPM. If I were to use the alternator ME1603 shown in the previous video, then charging a 48v battery at 56vdc would require about 1620 RPM. So, it seems my engine would operate at 1300 RPM for the 24v version, and about 1600 RPM for the 48v version. Again, assuming the damned thing ever works at all.
ALTERNATOR DISCUSSION: Just sharing a recent experience. I'm engaged in a discussion with someone who sells alternators designed primarily for wind turbines. He sells what are essentially automotive alternators with the rotors replaced with neodymium magnets. These have three phase windings, and the rectifier is either internal or external depending on the model. I'm sharing the details of the discussion because the details might help someone to understand more about how these alternators work. Anyway, the specs available on these alternators are limited. So, I contacted the seller asking about the stator resistance and the DC voltage output as a function of RPM. However, rather than provide the specs, he replied with questions about my application. This was frustrating because I don't need anyone to do the engineering. I just need the specs. The seller argued that knowing the voltage as a function of RPM is not useful because the actual RPM while battery charging will be A LOT higher than the cut in voltage.
MY REPLY: This is precisely why I want to know the stator resistance! The effect he describes is a consequence of HIGH stator resistance which is typical with automotive alternators. These alternators show LOW efficiency typically 50-60%. The primary loss is in the stator windings (especially at high amperage because the loss is equal to the square of the amperage X the resistance in Ohms - I^2R). Other losses include friction, windage, and rectification losses (which are higher at lower voltage). But the seller argues on his website that his alternators are highly efficient because using a permanent magnet rotor prevents having to use some of the electricity to energize the rotor, and there are no brushes which introduce a loss. Yeah, this avoids some losses. But the fact remains that the lion's share of the losses are from the stator windings which (I suspect) are unchanged in his units (and why I asked). So, naturally I'm a little skeptical of his "high efficiency" claims. MORE IMPORTANTLY, the effect that he describes where his alternators have to rotate at significantly higher RPM after cut in speed for charging is a consequence of VOLTAGE DROP ACROSS THE STATOR AS AMPERAGE INCREASES (i.e. low efficiency). Automotive alternators are NOT designed to be highly efficient. They are designed to deliver high amperage in a compact and low-cost package. Automotive alternators with higher efficiency are available. But notice they are LARGER because getting higher efficiency requires reducing the resistance of the stator windings (this means MORE copper!).