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).