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Old 12-23-2016, 05:46 PM   #1
popgun pete
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Mathematics of the Mares "Mirage" Speargun's Pumping Barrel Operation

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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Last edited by popgun pete; 12-24-2016 at 06:11 PM.
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Old 12-24-2016, 05:52 PM   #2
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Re: Mathematics of the Mares "Mirage" Speargun's Pumping Barrel Operation

The Mares "Mirage" pneumatic speargun pumping tables. After 5 spear strokes using the spear as a pump rod in the lower 10 mm ID pumping barrel the spear is then transferred to the main 13 mm ID shooting barrel. This allows the spear to be pushed back with next to no effort with the piston being latched on the sear tooth. Once that is done the power regulator switch is flipped up from the "loading" position and air pressures then rapidly equalize throughout the gun, whereas before the compressed air had virtually all been squeezed into the front tank by the loading action using the pumping barrel. The "Mirage" speargun is much easier to load this way, especially with a start pressure of 40 Bar being used in the gun, however it takes a lot longer than muzzle loading the gun via the main 13 mm ID barrel. At 40 Bar that is not so easy to do!

Mares re-released the "Mirage" pneumatic speargun at least twice with updates being implemented to make the gun perform better, but never really solved its airflow problems that resulted from trying to cram too much into the rear handle interior and at the same time keep Vpc small.

That is the reason why I created this thread: http://www.spearboard.com/showthread.php?t=191702
as the basic idea is good, but the gun needs to be redesigned with a new rear handle without being too concerned with Vpc being somewhat larger as the gun will then still work OK, but may require more pumping barrel strokes to load it.
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Last edited by popgun pete; 12-25-2016 at 03:47 PM. Reason: further comment
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Old 12-25-2016, 02:21 PM   #3
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Re: Mathematics of the Mares "Mirage" Speargun's Pumping Barrel Operation

Mares had a few tries at fixing the "Mirage" by shortening the front boss on the pistol grip rear handle which then also decreases the length of the rectangular channel, but that still left a choke in the only pathway for air to flow into the main barrel during the shot. Pneumatic spearguns usually have two air pathways, the second being a large port drilled in the roof of the inner barrel tube just behind where the "cocked to shoot" piston sits.

A detail from the exploded parts diagram for the later versions of the "Mirage" speargun is shown here. Note the shortened front boss on the rear pistol grip handle and the lengthened power regulator block which now has a well recess incorporated into its rear face (but hidden in this view). This modification also removed the dogleg in the airflow path as shown by the white line with arrow indicators in the photograph of the original production gun handle's long front boss.
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Last edited by popgun pete; 12-28-2016 at 06:07 AM.
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Old 12-25-2016, 06:56 PM   #4
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Re: Mathematics of the Mares "Mirage" Speargun's Pumping Barrel Operation

The "Cyrano Evo" rear handle has been designed with increased airflow ports as can be seen here and would be a possible handle for use in a new "Mirage", but Mares may wish to give the gun a new name rather than call it a "Mirage" as such. Maybe honor one of the company's founders or some milestone in the company's growth to a full line manufacturer of diving equipment.

Mares was founded in 1949 by Ludovico Mares in Rapallo, Italy.
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Last edited by popgun pete; 12-26-2016 at 04:35 PM. Reason: added name of Mares Sub founder
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Old 12-28-2016, 12:42 AM   #5
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Re: Mathematics of the Mares "Mirage" Speargun's Pumping Barrel Operation

The various volumes used in the "Mirage" are defined here.
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Old 03-11-2022, 05:57 PM   #6
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Re: Mathematics of the Mares "Mirage" Speargun's Pumping Barrel Operation

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.
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