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Air Passages - Cross Area (When is enough enough...?)

Diving Gecko

shooter & shooter
Jun 24, 2008
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Thought I would start a bit of a thread and compilation about the size of the air transfers in pneumatic spearguns.
There has always been talk about how some guns' transfer ports in the bulkhead throttle the airflow too much and limit the ultimate power of the gun. To the point where - supposedly - a popular mod amongst the mediterranean spearos was to yank out the bulkhead as soon as you bought your gun and also sometimes open up the transfers at the rear of the barrel.

For now, I don't have any answers, I will just share some measurements as I do them or find them in my "archives". (I am still without most of my speargun parts as I am now based in the Philippines but a lot of my stuff is still in storage in China).

I will be focusing on 13mm guns but the real problem is, I have no way to model how much you can reduce any orifice the air has to pass through before it starts hurting the gun's performance. Also, does the shape of the ports matter? Is the flow laminar or turbulent and to which extent does that matter. There are so many things we don't actually know here but maybe someday we will have an expert in fluid dynamics here who can chime in:)

But air, of course, is extremely malleable in lack of a better word, so it might be a fair assumption that not all openings have to match the 133mm² cross area of a 13mm piston. But how much smaller can we go...?

Anyhow, let's get started in the next post with the PredaThor which is one of the guns I do have on hand.
 
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Air Passages of the Salvimar PredaThor

I am a bit rusty, so Pete can correct me if I get this wrong but as far as I recall, the Predathor is basically - by way of the Vintair - a facelifted, classic Scubapro Magnum with a vacuum muzzle. Not a bad run for that design;)

Anyhow, I haven't measured or guesstimated the open area around the trigger sear at the bottom of the barrel but the top of the barrel has a single transfer hole with a 10mm diameter. Which amounts to a cross area of 79mm² versus the 133mm² of the 13mm piston. I think that size of transfer may even be an increase as I have measured a few other guns to only be 8mm (more on those later).

Now, the interesting part is the bulkhead:
PredaThor Bulkhead Transfer_01_1200pix.JPG


It has what looks to be quite a substantial "valve cover" but when we look underneath, the transfer openings are perhaps less impressive:
PredaThor Bulkhead Transfer_03_1200pix.JPG


I flatbed scanned the bulkhead, imported it into Fusion and traced the port outlines:
PREDATHOR BULKHEAD_1200pix_1200pix.JPG

PredaThor Bulkhead Transfer_07_1200pix.JPG


I think I was quite generous, e.g. I left out the bridge in the middle of each port and also, the ports actually reduce to a smaller orifice at their bottom, which I also ignored yet, the cross area total is "just" ~57mm².
Now, I say "just" as at this point, this is still all very speculative and I really don't know if 57mm² is enough or whether it hinders performance at full power but I wanted to share the data.

Also, the cross area of the Predathor transfer ports would equate to a circular transfer bore with a diameter of 8.5mm - which I think is actually more than most other guns. And more than the 8mm transfer bore in the barrel - which may have been an older standard(?). Still it's 2.3 times less than that of the piston but maybe air doesn't care to be squeezed and expand like that...

The most practical way of testing this would be to shoot the gun, say 10 times, on a thick foam target and measure penetration, then pull out the bulkhead and take the gun up to the exact same pressure and redo the test which is something I may actually do that someday fairly soon. I have the pool access - just need the time...

And yes, I have - for years - fantasized about a target with load sensors to measure impact or audio sensors on the target and the gun to measure the average speed. But I badly need to cut down on the fantasies and focus on making actual spearguns.
 
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Air Passages of the Salvimar PredaThor

I am a bit rusty, so Pete can correct me if I get this wrong but as far as I recall, the Predathor is basically - by way of the Vintair - a facelifted, classic Scubapro Magnum with a vacuum muzzle. Not a bad run for that design;)

Anyhow, I haven't measured or guesstimated the open area around the trigger sear at the bottom of the barrel but the top of the barrel has a single transfer hole with a 10mm diameter. Which amounts to a cross area of 79mm² versus the 133mm² of the 13mm piston. I think that size of transfer may even be an increase as I have measured a few other guns to only be 8mm (more on those later).

Now, the interesting part is the bulkhead:
View attachment 60632

It has what looks to be quite a substantial "valve cover" but when we look underneath, the transfer openings are perhaps less impressive:
View attachment 60633

I flatbed scanned the bulkhead, imported it into Fusion and traced the port outlines:
View attachment 60634
View attachment 60635

I think I was quite generous, e.g. I left out the bridge in the middle of each port and also, the ports actually reduce to a smaller orifice at their bottom, which I also ignored yet, the cross area total is "just" ~57mm².
Now, I say "just" as at this point, this is still all very speculative and I really don't know if 57mm² is enough or whether it hinders performance at full power but I wanted to share the data.

Also, the cross area of the Predathor transfer ports would equate to a circular transfer bore with a diameter of 8.5mm - which I think is actually more than most other guns. And more than the 8mm transfer bore in the barrel - which may have been an older standard(?). Still it's 2.3 times less than that of the piston but maybe air doesn't care to be squeezed and expand like that...

The most practical way of testing this would be to shoot the gun, say 10 times, on a thick foam target and measure penetration, then pull out the bulkhead and take the gun up to the exact same pressure and redo the test which is something I may actually do that someday fairly soon. I have the pool access - just need the time...

And yes, I have - for years - fantasized about a target with load sensors to measure impact or audio sensors on the target and the gun to measure the average speed. But I badly need to cut down on the fantasies and focus on making actual spearguns.
Speed of sound = speed of free air flow = 330 m/s. The speed of the harpoon at the exit from the gun barrel is 33 m/s. The longer the gun, the longer the harpoon will accelerate and the smaller the bypass holes can be made! For a full shot from a short gun, 2/3 of the barrel cross-section is enough, for a long gun, 1/2 of the barrel cross-section is enough!
 
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Speed of sound = speed of free air flow = 330 m/s. The speed of the harpoon at the exit from the gun barrel is 33 m/s. The longer the gun, the longer the harpoon will accelerate and the smaller the bypass holes can be made! For a full shot from a short gun, 2/3 of the barrel cross-section is enough, for a long gun, 1/2 of the barrel cross-section is enough!
This is way above my knowledge level but happy you chimed in:)

I did what I swore not to do years ago and asked the AI lords to help me out and they agree there's a distinct relation between the flow or air and the speed of sound when it comes to restrictions through orifices and compressible gasses.
It may also make sense that if the travel length of the piston is long enough, there's enough time to get the shaft up to speed even with a reduced air flow - I think that's what you're saying?

But @Zahar here's the interesting thing, I don't think there's a single mass manufactured Italian gun that adheres to your 1/2 - 2/3rds ratio guideline.
Possibly the LG Revolution but I have never seen one in the flesh or taken apart so I don't know. Maybe the Eastern European pneumatic guns generally have larger openings?

The Mares Evo/Cyrano 1.3/Force has a bulkhead air passage cross section of 9 mm but most others have less. My notes has both the Seac Hunter and Mares Sten at 7mm and from memory the Mirages are 7mm or actually a little bit less by a design quirk where there's a smaller lip at the front of the bore, IIRCC. I would assume the Asso are 7mm, too.

So, best case scenario is the Mares Evo/Cyrano 1.3/Force which would have a total cross section passage in the bulkhead of 64mm² which at 48% is close to your 50% ratio for longer guns (13mm piston is 133mm²) but still doesn't reach the 67% "rule" for a shorter gun.
The Predathor bulkhead transfer port is ~43% of the piston area. And all the guns with a 7mm bulkhead opening have a cross section area of ~29% of the piston area.

In the spirit of transparency, this design element interests me as I am setting out to build my own gun from scratch bar the shooting barrel and reservoir for now. And one of my goals was to have no discernable throttling but it's quite the design challenge to make the power regulator transfer bore much larger in a 40mm classic reservoir. But I am up to 84% of the piston area now;). I was aiming for a 1:1 ratio but by Zahar's account, even 84% is much better than I would ever need:)
 
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Correct understanding of the ratio of speed 330 m/s to 33 m/s, as well as taking into account the inertia of the piston + harpoon + water in the barrel system, made it possible to make valve guns with ratios of 2/3 or less! Fighting force regulators, which reduce this ratio due to throttling through small sections, have shown in practice imperceptible
by efficiency
reduction in combat force at 1/2 flow area! There are 3 types of combat force regulators: Hydraulic, Cut-off part of the receiver, Throttle! In Ukraine, craftsmen underwater guns use combat force regulators, mainly throttling ones! The best Masters manage to reduce the strength of the battle to 15 - 20% of the Maximum! Throttling force regulators are effective only when the harpoon is completely released from the barrel! If the harpoon is partially in the barrel after the shot, then in a short period of time the entire force of the receiver pressure across the cross section presses on the piston! In fact, the best firepower regulators are the cut-off part of the receiver, like in Italian guns! All that remains is to make a variable volume by moving the partition between the parts of the receiver! This problem is eligible for a patent for the inventor!
 
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Correct understanding of the ratio of speed 330 m/s to 33 m/s, as well as taking into account the inertia of the piston + harpoon + water in the barrel system, made it possible to make valve guns with ratios of 2/3 or less! Fighting force regulators, which reduce this ratio due to throttling through small sections, have shown in practice imperceptible
by efficiency
reduction in combat force at 1/2 flow area! There are 3 types of combat force regulators: Hydraulic, Cut-off part of the receiver, Throttle! In Ukraine, craftsmen underwater guns use combat force regulators, mainly throttling ones! The best Masters manage to reduce the strength of the battle to 15 - 20% of the Maximum! Throttling force regulators are effective only when the harpoon is completely released from the barrel! If the harpoon is partially in the barrel after the shot, then in a short period of time the entire force of the receiver pressure across the cross section presses on the piston! In fact, the best firepower regulators are the cut-off part of the receiver, like in Italian guns! All that remains is to make a variable volume by moving the partition between the parts of the receiver! This problem is eligible for a patent for the inventor!
Here is Bernoulli Equation Calculator: And here is a skatch of our speargun. v3 is a approximate speed of air in main (outer) barrel during shot. I took that it is ID = 38 mm and the shoting barrel to be 16/13 mm, for 13 mm piston. As I see there is no significan reduction of pressure in shoting barrel at speed of 30 m/s even with 30 % of choking.
1738692225261.png
 
Tomi - Thanks so much!

It's funny how I used to be good at math but then I went and did something entirely different - photography - and for decades never exercised the math part of my brain and now, it's hard for me.

So, the last few days, I have asked ChatGPT the same thing but it considers this heavy math (like me, haha) so restricts itself to just 1-2 calculations in a day unless I pay.
A disclaimer: While I have caught the AI in some logical weirdness a few times, when it comes to the math below I haven't set out to check it.

I did my prompts for a 13mm piston, 40 bar pressure (Mirage) and started with comparisons between 8, 10 and 12mm bores - which was a roundabout way of doing it. But that's when it told me about Bernoulli's law, choked flow and mass flow rate.

It calculated the mass flow rate required for this system (13mm piston @ 40bar) to be 0.253 kg/s.
Here are its values for the flow rate for the three valve bores I asked for:
  • 8mm bore0.427 kg/s
  • 10mm bore0.668 kg/s
  • 12mm bore0.961 kg/s
The numbers show that they can all flow more air than needed without the pressure dropping behind the piston as i understand it.
I then did what I should have done the first time around and asked what the minimum bore would be that could sustain the flow rate required and the bot spat out the following:
"The required orifice diameter to achieve 0.253 kg/s mass flow at 40 bar is approximately 6.16 mm."

So, 6.16mm - there we have it. BUT that's for a gun with 40 bar in it which not many have. For 20 bar - a more common proposition - the bore has to be larger to let the same amount of air through in the same amount of time as there's less "push" behind the air.
At 20 bar, the required opening is 8.71mm
But I don't think the AI took into account that the piston will be moving slower at 20 bar. I didn't give it any speed prompts or any loads/mass of the shaft, so the needed opening would be a bit smaller than the 8.71mm but still larger than at higher pressures.

So, maybe at, say, 25 bar with a slower shaft speed we end up around 7mm or so - just a guess at this point.

Anyhow, IF the bot math can be trusted, the real engineers had it right a long time ago as I think one of the early standards was a 7mm opening. That said, you will have some losses due to the sharp edges and depth of the bore. Maybe that's why some manufacturers increased it later on. Or it's purely bling to fool uneducated buyers like me...

But for my own use case, I can stop obsessing about squeezing every mm² out of my valve design. Currently, it's at an equivalent of almost a 12mm bore. Way overkill, haha.
 
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Tomi - Thanks so much!

It's funny how I used to be good at math but then I went and did something entirely different - photography - and for decades never exercised the math part of my brain and now, it's hard for me.

So, the last few days, I have asked ChatGPT the same thing but it considers this heavy math (like me, haha) so restricts itself to just 1-2 calculations in a day unless I pay.
A disclaimer: While I have caught the AI in some logical weirdness a few times, when it comes to the math below I haven't set out to check it.

I did my prompts for a 13mm piston, 40 bar pressure (Mirage) and started with comparisons between 8, 10 and 12mm bores - which was a roundabout way of doing it. But that's when it told me about Bernoulli's law, choked flow and mass flow rate.

It calculated the mass flow rate required for this system (13mm piston @ 40bar) to be 0.253 kg/s.
Here are its values for the flow rate for the three valve bores I asked for:
  • 8mm bore0.427 kg/s
  • 10mm bore0.668 kg/s
  • 12mm bore0.961 kg/s
The numbers show that they can all flow more air than needed without the pressure dropping behind the piston as i understand it.
I then did what I should have done the first time around and asked what the minimum bore would be that could sustain the flow rate required and the bot spat out the following:
"The required orifice diameter to achieve 0.253 kg/s mass flow at 40 bar is approximately 6.16 mm."

So, 6.16mm - there we have it. BUT that's for a gun with 40 bar in it which not many have. For 20 bar - a more common proposition - the bore has to be larger to let the same amount of air through in the same amount of time as there's less "push" behind the air.
At 20 bar, the required opening is 8.71mm
But I don't think the AI took into account that the piston will be moving slower at 20 bar. I didn't give it any speed prompts or any loads/mass of the shaft, so the needed opening would be a bit smaller than the 8.71mm but still larger than at higher pressures.

So, maybe at, say, 25 bar with a slower shaft speed we end up around 7mm or so - just a guess at this point.

Anyhow, IF the bot math can be trusted, the real engineers had it right a long time ago as I think one of the early standards was a 7mm opening. That said, you will have some losses due to the sharp edges and depth of the bore. Maybe that's why some manufacturers increased it later on. Or it's purely bling to fool uneducated buyers like me...

But for my own use case, I can stop obsessing about squeezing every mm² out of my valve design. Currently, it's at an equivalent of almost a 12mm bore. Way overkill, haha.
Here are results for 13 mm barrel in two cases of choking 6 mm and 8 mm. I took for the pressure to be 20 bar and the speed of the shaft to be 30 m/s.
Izrezak1.JPG
 
Thanks again Tomi,
If I read your numbers correctly, it states that even with a tiny 6mm opening, there's only a pressure drop behind the piston of~ 0.1 bar.

That's really interesting. I mean, if you explained the setup - to squeeze a bunch of air through a small hole in almost no time - to most regular people (like me) many would probably assume the air would slow down to an extent it would impact the shot.

But maybe a small "but"...
I definitely tend trust your numbers more than the AI but I had to go look at the AI again as your mass flow number is ~50 times lower. (Also, when I did that, I realized that I hadn't prompted the AI with a speed number as I was too stupid/lazy to look in to the formula to notice it was a parameter. But the AI didn't ask me for a speed and just assumed one... I looked into its analysis and it had used 40m/sec.)

Anyhow, it had also used the pressure in its Mass Flow Rate which I had stated at 40 bar. I guess that's why its mass flow rate is so much higher, right? Your Mass Flow Rate is for 1bar, I think.
But I can't figure out if you have adjusted for that in the pressure change calculations or if it matters?
 
Thanks again Tomi,
If I read your numbers correctly, it states that even with a tiny 6mm opening, there's only a pressure drop behind the piston of~ 0.1 bar.

That's really interesting. I mean, if you explained the setup - to squeeze a bunch of air through a small hole in almost no time - to most regular people (like me) many would probably assume the air would slow down to an extent it would impact the shot.

But maybe a small "but"...
I definitely tend trust your numbers more than the AI but I had to go look at the AI again as your mass flow number is ~50 times lower. (Also, when I did that, I realized that I hadn't prompted the AI with a speed number as I was too stupid/lazy to look in to the formula to notice it was a parameter. But the AI didn't ask me for a speed and just assumed one... I looked into its analysis and it had used 40m/sec.)

Anyhow, it had also used the pressure in its Mass Flow Rate which I had stated at 40 bar. I guess that's why its mass flow rate is so much higher, right? Your Mass Flow Rate is for 1bar, I think.
But I can't figure out if you have adjusted for that in the pressure change calculations or if it matters?
Davide, I only used the online Bernuolli equitation calculator. I also niticed a huge diference in flow rates... Neither me trust very much to AI calculation. But it could be useful, somethimes. This calculations using Beruolli for air is usable for speeds 0.1 to 0.3 Mach where the density of the air does not changle a lot. That calculation with Bernuolli is simple so I did it in excel myself too.
Just a litle axplanation to the image with results: Numbers in black are input values and in blue calculated by the calculator. Position number parameters are as per my sketch p1, v1, p2, v2.
 
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Davide, I only used the online Bernuolli equitation calculator. I also niticed a huge diference in flow rates... Neither me trust very much to AI calculation. But it could be useful, somethimes. This calculations using Beruolli for air is usable for speeds 0.1 to 0.3 Mach where the density of the air does not changle a lot. That calculation with Bernuolli is simple so I did it in excel myself too.
Just a litle axplanation to the image with results: Numbers in black are input values and in blue calculated by the calculator. Position number parameters are as per my sketch p1, v1, p2, v2.
For fun I ask a question to AI Leo in Brave web browser. Here is our coversation:
Me
What is the smallest diameter of the constriction at the end of a 13 mm pipe if the air velocity in the pipe is 30 m/s and the pressure is 20 bar?

Leo
To calculate the minimum diameter of the constriction, we can use the Euler number equation:
V = √((2 * p) / ρ)
However, the velocity in the pipe is given as 30 m/s, which is lower than the critical velocity. In this case, we can use the Fanno flow equation to calculate the minimum diameter of the constriction.
Since the velocity in the pipe is lower than the critical velocity, we can use the equation:
d2 = d1 / (V2 / V1)
However, to find the minimum diameter of the constriction, we need to find the velocity V2 at the constriction.
Using the isentropic flow equation:
V2 = V1 * √((2 * k * p1 / (k + 1)) / (p1 / p2))
Substituting the values:
V2 = 30 m/s * √((2 * 1.4 * 20 * 10^5 Pa / (1.4 + 1)) / (20 * 10^5 Pa / 1))
V2 ≈ 67.6 m/s

Now we can use the equation:
d2 = d1 / (V2 / V1)
d2 = 13 mm / (67.6 / 30)
d2 ≈ 13 mm / 2.253
d2 ≈ 5.78 mm

So, the minimum diameter of the constriction should be approximately 5.78 mm.
 
We must learn to ask the right questions! The speed of 30 m/s is not a constant value, but a final value at the exit! That is, it is necessary to enter data on the duration of the shot in time from 0 m/s to 30 m/s! This time is spent accelerating the harpoon in the barrel!
 
We must learn to ask the right questions! The speed of 30 m/s is not a constant value, but a final value at the exit! That is, it is necessary to enter data on the duration of the shot in time from 0 m/s to 30 m/s! This time is spent accelerating the harpoon in the barrel!
Yes, Zahar thats right. To AI you must ask the right questio or you can get wrong answers. The speed of 30 m/s is the max speed and it is the worst case regarding the constriction diameter. For lower speds you will get even smaller diameter of the constriction.
 
Yes, Zahar thats right. To AI you must ask the right questio or you can get wrong answers. The speed of 30 m/s is the max speed and it is the worst case regarding the constriction diameter. For lower speds you will get even smaller diameter of the constriction.
That's not all I meant! You completely ignore the mass of the harpoon and the length of the barrel! You can accelerate a heavy harpoon up to 30 m/s in a certain time, and you will need an even smaller hole than for a light harpoon!
 
That's not all I meant! You completely ignore the mass of the harpoon and the length of the barrel! You can accelerate a heavy harpoon up to 30 m/s in a certain time, and you will need an even smaller hole than for a light harpoon!
Yes, that is not relevant for this calculation.
 
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