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).

    The post was edited 1 time, last by popgun pete: typo ().

  • The "Mirage" in component form, this example being repaired more often than it actually being used. In forty years this gun has spent more time in pieces as the "Mirage" is very prone to leaking air at the power regulator shaft's pressure seal and many other places depending on "O" rings being nicked or scratched during assembly at the Mares Factory. I purchased this gun brand new, but it was already leaking oil and was sold at a discount price, $50.00. They could not even give them away once the word had got around.

  • This is where the real problem lies, air has to travel up the long rectangular channel under the main barrel when the gun shoots. In Mares desire to keep Vpc as low as possible there was only this one way in for air to flow into the main barrel. A revised bulkhead with a small well replaced the flat wall version and straightened out the previous dogleg in the airflow, but that channel was still there and it restricted the power of the shot. However the shortening of the front boss on the rear handle, which resulted in the power regulator piston/plug (that closes off the gun's power regulator air transfer port) projecting outwards rather than sitting flush also shortened the front end of the rectangular channel. That modification improved the "Mirage" gun's airflow, but still left only one way in for the compressed air during the shot to enter the main barrel.


    In most pneumatic spearguns, such as the Mares "Sten", the compressed air can enter the main barrel via the sear lever slot in the main barrel (underneath) and a port hole drilled in the top of that inner barrel tube, thus providing two airflow pathways. The "Mirage" only has the sear lever slot which is opened out towards the rear end to be much wider, but air can only reach it by going through the choke point of the rectangular channel. That was a consequence of lifting the main barrel upwards in the gun and setting it up to be off-axis in order to allow room for the fitting of the pumping barrel underneath. The much later Mares "Cyrano Evo" also has an off-axis inner barrel tube, but there the designers have created two extra ports on the sides of the inner barrel, in fact there are two on each side, bringing the number of ports up to five, including the sear lever slot under the main barrel. At some stage that rear handle, fitted with a 13 mm, or even 14 mm diameter main barrel, instead of the current 11 mm diameter version, could be the basis for a new "Mirage" speargun.

  • A detail from the exploded parts diagram for the later versions of the "Mirage" speargun. 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).

  • Coincidentally, to try to better the airflow, I just did a small modification on one of my barrels. I, surprisingly got away with it on a shitty, cheapo Chinese bench drill with a likewise "milling bed";-).


    Here are some snaps:



    More of a write-up over here in case you feel like it (so far, five pages on my fun with my old Mirages, haha):
    https://forums.deeperblue.com/…102586/page-5#post-963681

    The post was edited 1 time, last by Diving gecko ().

  • The Mares "Cyrano Evo" with its high mounted inner barrel with two side airflow ports located on either side of the gun as indicated.


    The Predathor barrels also have an inlet hole on the very top of the barrel. I will try to take a snap and measure the bore one of these days.

  • Thanks Peter, one of the guns my sons collection needs some day.


    Cheers, Don


    If it is to be used (and it is a great gun - I think I remember you having used one before) then go for a V2 version, as the leaking power regulator rod that Pete mentions is not an issue on those. Luckily, it seems like the very vast majority of Mirages out there are V2s.


    PM me if you start looking for a gun in anger, I have a contact I can share that tends to come across them once in a while:-)

  • The various volumes used in the "Mirage" are defined here. The only airflow port, or breather hole, in the main barrel is shown in this detail photo which I have now added. Air can only access this "window" by travelling along the rectangular channel shown earlier which runs underneath the main barrel and is in line with the mechanism slot. In actual use the sear lever occupies the front end and most of the slot length as can be seen from the position of the sear lever pivot pin mounting hole.

  • If anyone is interested the conversion of a Mares "Cyrano 1.3" to a "Mirage Evo" speargun type is taking place here:-


    https://forums.deeperblue.com/…ng-speargun-parts.113094/


    The use of 3D Printing has made this all possible, although the porous nature of printed parts has required them to be filled or sealed. In a commercial development once 3D printed components had been checked for fit and function then permanent molds would be created to injection mold the required parts.

    The post was edited 1 time, last by popgun pete ().

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