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Mathematics of the Mares "Mirage" Speargun's Pumping Barrel Operation

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popgun pete

Well-Known Member
Jul 30, 2008
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Although the Mares “Mirage” pneumatic speargun uses the principle of loading via a smaller ID inner barrel of 10 mm, and shooting from another larger ID inner barrel of 13 mm, that is not strictly speaking how it operates. The hydropneumatic auxiliary hydropump spearguns do work that way, e.g. Aquatech “Black Sea”, Alcedo “Hydra” and “Hydra Sprint”, because the spear can be inserted without pushing any resistive medium behind it when the spear is moved to the rear of the gun’s main barrel, ready for shooting, as the gun’s interior can be bypassed by a water valve being left open to the environment.

How the "Mirage" works is that it progressively shifts air from the partitioned off rear section of the gun by using the 10 mm diameter pumping barrel and transfers that air into the front tank, the gun being split into two sections by the partitioning bulkhead located between the large volume and nearly full length front tank, Vft, and the balance of the gun. The rear section is a combination of the volumes of the pumping barrel Vpb, the main barrel Vmb and the pre-chamber Vpc at the rear of the gun. The pumping barrel operates as a gas molecules shuttle as the proportion of gas being shuttled across is the same each time, but the amount differs as for each pumping barrel stroke there is less gas being left in the rear end of the gun. After each pumping barrel stroke is completed the pump refills from the main barrel and pre-chamber which are always connected, but each time that refill pressure is lower, hence less gas molecules are transferred as the number of pumping barrel strokes increases. The pumping barrel has a very high compression ratio, so it can squeeze even small gas quantities down to a pressure which can move across into the front tank. The pumping barrel stroke is shorter than the main barrel stroke, or working course of the piston, because the former terminates at the partitioning bulkhead, whereas the main barrel piston travels further back to latch on the sear lever's tooth which pivots inside the main barrel tube.

The proportion of gas transferred by the pumping barrel is given by Vpb/(Vpb + Vmb + Vpc) which will be denoted here by K, which is a ratio or a percentage.

Therefore K = Vpb/(Vpb + Vmb + Vpc)

K can be calculated by measuring the respective gun internal volumes, but it can also be obtained from the original version of the “Mirage” speargun's pressure reduction table by using the first pumping barrel stroke result where the numbers are larger. (Mares kept using this table without recalculating it for the longer guns and those with a well type bulkhead, which increases Vpc, in place of the original flat face bulkhead). As the initial start pressure is 30 Bar and the pumping barrel stroke has reduced the rear section’s pressure to 22 Bar by removing 8 Bar, then K must equal 8/30 or 0.266666 repeating. The first pumping barrel stroke leaves the rear section with (1 – K) gas molecules (note proportions are being used here, not the absolute values), the second stroke with (1 – K)^2 gas molecules, the third stroke with (1 – K)^3 gas molecules and so on. As the pumping barrel refills by gas travelling through a ball type inlet valve, at a certain pressure the ball valve’s biasing coil spring will start to shut off the gas flow, hence the calculations will be slightly out at very low pressures, but by then the effort required to push the pumping barrel piston back will be minimal given the small cross-section of the pumping barrel and its piston.

Using the value of 0.26666 for K the values for (1 – K)^n for values of n from 1 to 5 have been calculated and the results shown below. Note that Mares probably rounded the results shown in their own table, hence the value of K may be slightly different and reverse calculating it, as I have done here, may introduce some mathematical error.

Pumping barrel stroke 1 - 0.7333; stroke 2 - 0.5378; stroke 3 - 0.3944; stroke 4 – 0.2892; stroke 5 - 0.2121.
If we multiply the above numbers by 30 Bar then we should obtain the numbers shown in the “Mirage” pumping barrel table.
Pumping barrel stroke 1 – 21.99 Bar; stroke 2 – 16.13 Bar; stroke 3 – 11.83 Bar; stroke 4 – 8.68 Bar; stroke 5 – 6.36 Bar.
If we multiply those same numbers by 40 Bar then we obtain the numbers for a “Mirage” speargun operated at 40 Bar.
Pumping barrel stroke 1 – 29.33 Bar; stroke 2 – 21.51 Bar; stroke 3 – 15.78 Bar; stroke 4 – 11.57 Bar; stroke 5 – 8.48 Bar.

As the pressure in the rear of the gun is progressively decreased by using the pumping barrel as a "gas molecules" transport shuttle, the pressure in the front tank goes up, in fact it will be pushed higher than the gun's "cocked to shoot" pressure. When the power selector switch is subsequently moved back to the "full power" shot position the front tank can refill the rest of the gun's internal volumes and the pressures throughout the gun then equalize.

Note that longer “Mirage” type guns will have different values for K, as while the main barrel and pumping barrel volumes will increase with their additional barrel lengths, the volume of the pre-chamber, Vpc, will remain the same. For a super version “Mirage Evo” with a 14 mm diameter main barrel the value of K will be smaller as Vmb will be larger and K is inversely proportional to Vmb (refer to above mathematical expression for K).
 
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To be easier to understand:
o8ard1.jpg
 
The main and pumping barrel volumes are defined by the volumes swept by the pressure seals on the pistons, rather than the length of the barrels themselves. It does not matter which seal you choose, as long as it is the same one and the measurement is taken from its position at either end of the respective piston's travel. Any other open space rearward of the partitioning bulkhead is part of the pre-chamber, including the unswept rear end of the main barrel. Mares tried to minimize the pre-chamber volume by reducing the size of any gaps around the main barrel where it fits into the plastic rear handle molding, but left the blind ended holes seen from the front end of the handle unplugged. The only reason those holes are there is to allow the plastic component to cool after its ejection from the molding die without causing sinks in the plastic if the sections were too thick, which they are not thanks to the presence of those holes. Mares did not bother to do so, but they could have filled the blind ended holes with grease and reduced Vpc even further as those holes are not isolated by any seal from the other voids inside the rear handle body.
 
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How the pumping barrel operates to transfer gas in the gun from one section to another, the pumping barrel using its high compression ratio to force air into the front tank even as the gas enters the pumping barrel at ever lower pressures as it transfers from the back end of the gun with each operating stroke of the pump. This capability is conferred by the rubber sleeve valve which has a ring of exit holes very close to the rear end of the pumping barrel resulting in next to no dead space in the pumping barrel to front tank connection.
mares-mirage-operations-jpg.57821
 
I suppose this was the disappeared image from my post #2. Positions of power regulator are:
1 - preparing for lowering the pressure in main barrel having the piston,
2- 1/2 of full power shot,
3- full power shot.

1647171499271.png
 
I suppose this was the disappeared image from my post #2. Positions of power regulator are:
1 - preparing for lowering the pressure in main barrel having the piston,
2- 1/2 of full power shot,
3- full power shot.

1647171499271
In position 2 and 3 the hole on bulkhead is open, so the main chamber contact with the pre chamber, I don't see how in position 2 we have reduced power.
 
In position 2 and 3 the hole on bulkhead is open, so the main chamber contact with the pre chamber, I don't see how in position 2 we have reduced power.
Mares intention was to use a throttling of the transfer port by just leaving a small annular gap around the piston that fully plugs the bore when in the loading position. They had done this with the Titan series guns which also have a three position selector gate, but the Titan has a brass cup like prechamber unlike the smaller prechamber in the Mirage. With the power regulator opened up after loading and then reclosed back to position 1 the Mirage would have a low power shot maybe less than a third which is what the Eskwad guns are designed for. As for the power of the Mirage's throttled shot in position 2 it depends how far back the piston sits in the slightly larger diameter at the rear of the transfer port.

In the later versions of the Mirage using a hollowed out and slightly longer regulator bulkhead they actually cut a section out of the transfer port bore in the larger diameter entrance to the port.
MIRAGE later bulkhead rear view.jpg
 
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One way to check out a Mirage would be to screw a pressure gauge into the inlet valve port and watch the pressure fall as you operate the pumping barrel as the gauge will only be looking into the rear of the inner barrel, not the tank.
 
On this image you can see that a cut-out in the side of the transfer port on the original flat bulkhead would be of no use as the opening would not go anywhere as there is no void to open out into. It needs to be remembered that the main barrel occupies much of the open space we see here in these photos when the gun is assembled. Judging by the part numbers all guns use the same power regulator shaft in the various Mirage models.
Mirage bulkhead rears.jpg
 
Theoretically the 2 position has less power from 3 due to throttled transfer port, practically I think this is not half the power, maybe is like 80% of the full power.
Also theoretically position 1 is the lowest power if after loading you put the lever on 1 again. But practically this maybe isn't even functional due to incredible low power so no need for such a slow shaft speed.

The conclusion is, I think (maybe I am wrong) that mirage has full power 100%, power 80% and power 15%. Not handy at all.
 
The throttle on position 2 in the Titan withdraws a brass piston which has a tapered cone nose and that creates a flow path around that taper which has a short pin on its front end to act as a guide. This is needed because the piston is on a very long control rod that runs rearwards from the mid-handle unlike the very short control rod in the rear handle guns. It would appear Mares changed the bulkhead and hence the prechamber volume to try and give the later Mirage gun more power in low power settings, but the Mirage is really about loading a high pressure gun and the low power settings are an afterthought.

A gun could have been designed with a larger prechamber as is used in the Sten, but this would shorten the length of the pumping barrel and more strokes would have been required to pump down the man barrel and a now larger prechamber. So they could use the existing Mirage parts such as pumping barrels and control rods they could only add a small amount of prechamber by shortening the front boss on the rear handle and giving that space over to the bulkhead extension.
 
A way to check the prechamber volume is to load a Mirage with a pressure gauge screwed in the inlet port and then release the spear after the power regulator is set to position 1. The pressure in the barrel and prechamber after a low power shot is lower than the gun's start pressure as for the shot only the pressure in those volumes has been used. You can use the pressure readings before and after the shot to calculate the volumes. This experiment would need to be conducted by loading and releasing the gun against a block of wood and using a start pressure that was manageable as the experiment is not without its dangers. My Mirage never lasted long enough to conduct such experiments and back then I never had a pressure gauge for any of my guns. My Mirage is still in pieces as I cannot be bothered rebuilding it after so many times fixing it.
 
Yes only with practical experiments we can say for sure the power on each position. But I think is 100-80-15.
My Mirage never lasted long enough to conduct such experiments and back then I never had a pressure gauge for any of my guns. My Mirage is still in pieces as I cannot be bothered rebuilding it after so many times fixing it.
Why your mirage didn't last long Pete ? its not a problematic gun if all the orings placed in right positions.
 
Yes only with practical experiments we can say for sure the power on each position. But I think is 100-80-15.

Why your mirage didn't last long Pete ? its not a problematic gun if all the orings placed in right positions.
The "O" ring on the power regulator shaft leaks oil and air, a problem with all the early models. I remember seeing a number of brand new Mirages in a store which were all covered in thin oil. I bought mine in a different location in one of their suburban branches, they only had the one gun and it seemed OK until I pressurised it and oil flowed from it as well. I bought a kit afterwards by going into the Mares distributor (Airdive) and spending half an hour talking around the woman behind the counter who initially said they had nothing, then finally relented and got the kit, they only had two Mirage kits left. She told me they had to repair many Mirages and decided to drop them.

The Mirage lasted for a few dives and then I put it aside until I next retrieved it from its storage spot and it was leaking again. This process was repeated a number of times until I decided I had better guns to use.
 
I recall that I had a similar experience with my Mirage about leaking oil and air at power regulator. I had fixed it temporarily for the time being on vacation on the sea for about two weeks. But the solution using some higher cross section O-ring was not the final (optimal) solution It was maybe 10 years ago...
 
yes on the early mirage with power regulator shaft with two brass cylinders the gun was leaking, bad design. but in later mirages they fixed this with better design with one -always pressed- oring. You can even put a new design shaft and your early mirage will not leak ever again Pete.

ps* have any of you guys has the later mirage with the white trigger or even the mirage 100 which was only in white trigger ?
 
yes on the early mirage with power regulator shaft with two brass cylinders the gun was leaking, bad design. but in later mirages they fixed this with better design with one -always pressed- oring. You can even put a new design shaft and your early mirage will not leak ever again Pete.

ps* have any of you guys has the later mirage with the white trigger or even the mirage 100 which was only in white trigger ?
I would be surprised if the parts were interchangeable. When Mares changed the Mirage rear grip moulding by shortening the front boss they most likely reduced the size of the tunnel in the handle to just large enough for the regulator shaft to pass through, which is something that was done with the earlier Sten models and the Titans. Why they used a larger diameter tunnel for the metal sleeves is a bit of a mystery, but my guess as I have written on another thread is originally they planned to withdraw the piston plug further back in the tunnel. However to do that the power regulator gate would need to be longer and there was not enough room to fit it, so the piston plug’s head sat in the airflow with gas having to swirl around it in that short curved recess that was originally in the front boss. Unable to withdraw the piston any further back Mares just filled up the tunnel with two metal sleeves and moved the shaft seal to the gap between the sleeves, the rearmost sleeve now being a part of the rear handle and omitted from the parts diagram. There is no other reason for the larger diameter tunnel being so long otherwise, it really only needs to be slightly larger than the diameter of the power regulator shaft for most of its length.

With the changes in the later gun they pushed the back wall of the bulkhead forwards to move it away from the piston plug's head when it was retracted, simultaneously moving the front wall of the handle boss rearwards and that improved the airflow slightly, but it still had to pass through the rectangular duct running rearwards under the barrel tube to the large opening at the rear of the main barrel.
 
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With the changes in the later gun they pushed the back wall of the bulkhead forwards to move it away from the piston plug's head when it was retracted, simultaneously moving the front wall of the handle boss rearwards and that improved the airflow slightly, but it still had to pass through the rectangular duct running rearwards under the barrel tube to the large opening at the rear of the main barrel
that's only the in 2 position.. the throttled one. the full power position has wide open the transfer port so the air can pass easily,
 
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