I brainstormed a few ideas and having a second or even third barrel is definitely doable if size allows. However in the Mirage itself, if it was possible to have 2x the power of the main chamber (so basically twice the shot power, no pumping) instead of the pump, which one would you think would deliver the most power?
Not sure I can answer your questions that precisely, I will try.
But I don't think I even understand the first one, hehe. Can you try to explain that one again?
In the meantime, I will share some thoughts on the general constraints of the Mirage classic platform. You have figured out most or all if it already but here we go:
As we know by now, the bigger the difference in cross area between the two barrels, the bigger the "Mirage Effect" becomes - the easier the preloading becomes.
So, you would want that delta to be as large as possible. The ratio on a stock Mirage is ~1:1.7 (10mm pumping piston vs. 13mm shooting piston).
On a Mirage, the smallest you can make the pumping barrel depends on the shaft size and the OD of the tang (tail end). So, the Mirage was designed to accomodate an 8mm shaft with a 9mm tang and then you need a bit of a flange at the end of the pumping barrel so the piston doesn't fly out - hence the barrel ID of 10mm.
Now, on this shorter Mirage I am working on right now, I have dropped the ID to 9mm - I just have to stick with a 7mm shaft. And yes, that gets me to around a ~1:2.1 ratio. So, x2 the power/force acting on the shooting piston.
From this, the logical thinking is that for a bluewater Mirage shooting a thicker spear (8-9mm) where I will need a 10-11mm pumping barel, I will also need to go up in the shooting barrel ID to having enough of a difference between the two.
If I go to a 15mm shooting barrel I can get a ratio of 1:1.86 with a 11mm pumping barrel (for max 9mm shafts) or as much as 1:2.25 with a 10mm pumping barrel for 8mm shafts.
The difficulty is finding the right material for a a bigger ID shooting barrel
and having it smooth enough on the inside. Alu is probably out of the question but I have shorter samples of stainless and titanium tubes on the way that I will try to see if I can polish well enough to make them work. The problem then becomes one of mass and having enough buoyancy. Which leads me to the dream - a custom made, carbon fiber cuttlefish shaped high pressure reservoir. Or the stepping stone of adding a bit of a belly/wings to a normal tube.
Now, I should mention that there is one 'cheat code' you could easily make. If you switch to what we call
free/nude shafts without sliders where the tang has the same OD as the shaft itself (the shooting line is tied to the front of the shaft), then you "gain" 1mm. Meaning you can now use an 8mm shaft in a 9mm pumping barrel. Or even a common 7mm shaft in an "small" 8mm pumping barrel.
The latter is something I am considering for my girlfriend who is not only less physically strong but is also, like I am, battling with an injured wrist.
That would result in a ratio of 1:2.6 meaning that to load, say, a 23bar gun she would only need to put in about 12kgf of peak loading force. And a 23bar gun would still be a formidable thing on the reef. Again, remember, the original Mirage came with a 10mm secondary barrel and a 1:1.7 ratio

.
Anyhow, all this above can possibly start to explain why I sometimes try to make a little lever pump idea work in the CAD. Then no worry at all about the size of the pumping barrel and the limitations on shaft sizes. Also, one thing a full length pumping barrel inevitably results in is the need for a large enough nose to house both the shooting and pumping barrel. I would love to slim down the nose for easier tracking. I also have some CAD work done where the pumping barrel ends halfway up the gun and then the reservoir can taper from there on forward. Again, that would need a fancy custom made reservoir.
Anyways, that was the thoughts on the constraint of the Mirage platform as I see them
And in terms of kgf where are the secondary barrel's pumps hovering around? (I know they decrease with each pump so I'm already expecting that) Let's say for 4 pumps
Let's assume we are after max power and haven't yet been able to overpower a shaft to the point where it hurts accuracy and penetration. In that case, the approach would likely be to just pump up the gun to the point where the secondary piston sees the same force on it as you can physical push it with. So, for me, let's call that 30kgf. I think it's that simple. (Remember, the
pressure on the secondary piston is the same as on the main one.)
And then, of course, the more you can increase the delta/ratio/Mirage Effect - the more force you end up with on the main piston for the shot.
Anyways, I think that's evident to you already. But yes, the pumping/secondary piston can/should start at your max possible peak loading force (well, a tad lower to allow for the slight increase in kgf due to compression during the stroke).
And then you are asking what the pressure drop is like. That one depends on a few things. The length and diameter of the pumping barrel (how much air is being moved) as well as the volume of the smaller air chamber that you are "emptying out". I think Mares' old manual for the Mirage 80 stated that 5 pumps would get you down to ~5 bar (can't recall if that's from 30 or 40 bar but the manual is uploaded here somewhere). The original Mares handle and the bulkhead really don't have much internal volume at all, just about enough to let the air flow whereas I am using a more modern Mares handle not made to be a Mirage so it has a larger volume and so does my custom DIY bulkhead. The upside is that my low power shot has "more air in it" whereas on a Mirage the low power shot can be quite "weak". Somewhere in the middle would be good, I think. The downside, as explained is needing more pump strokes. But the rear volume is one of the things I would reduce on a custom handle. And for a BW gun, I would reduce it even more as you wouldn't need a low power shot at all so having less pump strokes would be preferable.
Actually, my goal this year is to make a custom handle in alu. And am thinking I can reduce the internal volume by inserting 3D printed plastic (or silicone) blocks into the handle for the BW version.
On my present gun, since I dropped the piston diameter
and have a larger rear volume I have to pump more. I
feel like I have to pump perhaps 10-12 times to get to the same as on the Mirage. But it's not a big deal as each pump is just a few seconds and as you say, they get easier and easier. Also, I could stop at five and just load the gun in the bigger barrel with a bit more effort. But at around 10, it doesn't take much effort at all to do final loading.
Basically, the pressure drop curve is one of diminishing returns. Like the first stroke may reduce the pressure by e.g. 7 bar whilst the 10th stroke may only drop it less than 1bar.
I am not smart enough to explain it to others but it has to do with Boyle's law, the remaining air expanding and that you are moving molecules of air and not just a simple volume. But the math is pretty simple for the right people once you have the chamber and pump volumes established.
An example of a pressure drop table could look like this:
A simple way to check this is to measure the pressure in the gun at the end of the pumping routine as the pressure is being read at the rear chamber. Also, a factor in how efficient the air transfer is, is how much dead space you have in your one way valves where the pump can't compress the air.
Now, back to a hybrid type gun. Unless I am missing something, you could get a huge delta/ratio on those as their main pistons are so much larger than a pumping piston would need to be. If you can somehow keep the smaller part of the air chamber really tiny, you could make an incredibly powerful gun which wouldn't even take many pumping strokes.