The dynamics of how a ~5.95mm plastic sphere travels down a 6.01mm-6.23mm barrel, accelerated by environmental pressure difference.
It's commonly thought that the BB travels down the top of the barrel due to the hop up. I'm here to debunk this myth.
This is a duplication of the post on my website here: https://letsbuildone.wordpress.com/mythbusting-airsoft-hopup-and-barrel-dynamics/
Step 1: The Basic Principles of Airsoft
Projectile pneumatic acceleration:
Atmospheric pressure on the open end of the barrel, compressed air on the other end of the barrel. The pressure difference across the BB which is on the boarder of the high pressure end of the barrel, accelerates the BB down the barrel.
It's important to note, that the pressure difference across the BB reduces on it's journey down the barrel, because as it moves, the volume behind the BB increases. Since the volume of compressed air is set, the pressure must decrease accordingly. This acceleration starts high, and reduces.
Hop up is a device used to correct the projectiles parabolic trajectory to something more flat. This extends/increases the range of the Airsoft gun. Conventional projectile weapons do not use this, they just have much higher projectile speeds so the drop is less noticeable. Hop up is only possible in Airsoft because the projectile is spherical. Applying a backspin allows us to utilise the Magnus Effect to apply an aerodynamic vertical force to the projectile to oppose gravity.
The Magnus Effect:
The Magnus Effect is when a spinning sphere or cylinder has air moving over it transverse to the axis of rotation. One side opposes the flow of air, slows the air via skin drag, and causes a higher pressure region. The other side is rotating in the same direction of the air, and either has no effect, or speeds it up via skin drag, lowering the pressure of the air, leading to a low pressure region. This creates a pressure difference across the sphere/cylinder, which in turn, imparts a force upon it.
Bernoulli Principle states that restrictions cause the working fluid to move faster, and faster fluids have lower pressure. Diversions spread the fluid out, slowing it down, causing low pressure. This is important to understand the effects of air passing around the BB within the Barrel.
The Coanda Effect is the tendency for a fluid to be attracted to nearby surfaces, and by extension; to follow a curved surface. This is important because the BB is curved. So the Coanda effect is prevalent in this application.
Step 2: The Myth: the BB Goes Down the Barrel, Rubbing Against the Top Due to Hopup
"So if the Magnus effect causes a vertical force to be applied to the BB accelerating it upwards, then, since the spin is imparted in the first inch of the barrel, for the rest of the barrel, it must scrape down the top of the barrel."
I'm afraid not my misinformed friends. Here are four simple reasons why:
- Firstly, if the BB is scraping down the top of the barrel, there is no air going over the top, so there is no Magnus effect, so there is no vertical force to hold it against the top of the barrel. So at best, the BB would be bouncing off the top of the barrel.
- Secondly, there is (in comparison to flying through free air) almost no air passing around the BB. The pressure in front is roughly atmospheric, the pressure behind is significantly higher than atmospheric, the pressure difference accelerates the BB, which has relatively low mass, and is unrestrained, so is accelerated quickly. The amount of blow by is very small. With such little airflow over the BB, it experiences little vertical force due to the Magnus Effect.
- Thirdly, Bernoulli Principle states that restrictions cause the working fluid to move faster, and faster fluids have lower pressure. Diversions spread the fluid out, slowing it down, causing low pressure. If the BB becomes off centre, then Bernoulli will re-centre it. This also means any blow by lowers the pressure just in front of the BB.
- Fourthly, finally, and maybe most importantly, let's imagine for a moment that the BB is unrealistically heavy, or for some reason is fixed in place within the barrel, still with massive backspin. It has atmospheric pressure air in front of it, higher pressure air behind it, the air forces it's way past the stationary BB. Relative to the airstream now moving over it. The BB now has "forward spin", not backspin. So any Magnus effect it experiences while within the barrel, would be down rather than up.
Step 3: Backing It Up
It's all very well and good me sitting here behind a keyboard and postulating. I want to take opinion and belief out of the matter, and talk about cold, hard, facts. I am a scientist and an engineer after all. And I believe in utilising Newton's Flaming Laser Sword where applicable.
This being the case; there are two ways to check if I'm right:
- Build a test rig with a high frame rate camera and a glass barrel to video the BB travelling down the barrel and observe the reality of the situation.
- Do a Computational Fluid Dynamics (CFD) study to model it.
Building option one would take significant time, effort, and money. Maybe I could use a plastic barrel, and borrow the camera from the Slo-Mo Guys or something. Observing the boundary of the barrel and air could prove difficult. This could be solved with using smoke, or other coloured gas to propel the BB. Unfortunately all coloured gasses I know of are toxic. Could use smoke. I have a smoke machine. Or steam/ water vapour. All of these solutions have the same problem; They are not air. So their dynamics will be different due to their variance in density, viscosity, and a plethora of other issues. The Barrel and BB would also probably need to be marked to get any useful information out of the experiment. I'll happily do this, if someone provides the components, and does the filming.
This leaves CFD. This is a method of using a computer to calculate the physical model mathematically using base principles. It is essentially free if you have a capable computer and the right software. It will just take a little time to generate the 3D geometry and set up the model. CFD it is!
Step 4: The CFD Results: Free Flow
So, generate the CAD, set up the model. Leave the computer for a few hours.I won't bore you with the exact model parameters, if you ask I shall tell. Otherwise, here are the important bits:
I've assumed and applied a surface roughness of 0.4um for the polished plastic BB and Barrel ID. If you have a measured value for either of these, then please let me know so I can improve the model.
Y is Vertical, Z is the axis of the barrel, X is lateral.
Firstly I tested that the program models Magnus effect properly. to do this I modeled a BB in free flow of air. The BB has backspin about the X axis of 115,000 rpm, the air is moving over it at 106.68m/s.
Force (X) [N] -0.000143715
Force (Y) [N] 0.074027023
Force (Z) [N] 0.07616237
This shows that there is minimal lateral movement, and that in this case; the drag on the BB is roughly equal to the Magnus lift.
Step 5: 6.01mm Tight Bore Results
Next I model the BB in the barrel. 5.95mm BB, 6.01mm Barrel. In this case, the BB is stationary, The pressure at the opposite end of the barrel is atmospheric. and the pressure at the closed end is 827371Pa.
Force (X) [N] -0.000197728
Force (Y) [N] -0.007692067
Force (Z) [N] 20.24816055
Here you can see that the lateral force is roughly the same, there is a large accelerating force as expected, and that the vertical component is an order of magnitude lower, and negative. This means that the Magnus effect is reversed, and 1/10th as strong as in free flow.
This is as expected. Though it is important to note, that this computer program cannot model induced movement. As such, this is a model of steady state. This is to say, the amount of air passing over the BB is much higher than in reality because it is artificially fixed in the computer model. In reality, this Magnus and Lateral Force would be far less. For interest, the mass flow rate out of the barrel muzzle at atmospheric pressure was 0.001219999 kg/s. i.e. naff all. Since the BB in this model isn't moving, all this air is coming out of the muzzle after blowing around the BB.
This shows that the Magnus effect does move the BB off centre in the barrel. But up, rather than down.
It is important to note that any variation from the exact centre of the barrel is countered with the Bernoulli Principle and the Coanda effect, to bring the BB back to the centre. To test this, I modeled the BB off centre down as if the magnus effect had moved it down. These are the results:
Force (X) [N] 0.00212832
Force (Y) N] 0.142694822
Force (Z) [N] 20.27990608
The lateral force is 20x larger, I suspect this is due to flow detachment on the other side of the BB causing turbulence which in turn creates off centre pressure centre. The vertical force is now up and much larger. Even larger than the Magnus effect in free flow. This shows that the BB would self centre and self correct. The axial force is roughly the same as before, as expected.
Step 6: How Long Range Barrels (LRB) Fit Into This...
sypher told me about how they use S-Bent barrels in paintball to impart spin on the ball. I didn't know about that, but it reminded me about LRB mods, which are the Airsoft equivalent:
LRB in airsoft is where the barrel is bent down to impart spin on the BB by making it rub down the top of the barrel on it's way out.
LRB's work. So how do they work if the BB is kept central by a cushion of air? Simply put, the force pushing it to the top surface, must be larger than the force keeping it central.
Lets do the maths to work it out what's going on and how this works:
Take a barrel length 0.3m, muzzle velocity of 350fps= 106.68m/s.
SUVAT gives us an acceleration of 18967.7 m/s^2, but more importantly, a 0.0056s in the barrel.
Assume BB weight of 0.2g for that 350fps shot.
Regardless of weight, the aerodynamic self centering force is ~0.15N. This would be different for different BB to bore ratios and magnitude it is off centre. F=ma means this leads to an acceleration of 750m/s/s.
Back to SUVAT to find that the vertical displacement would be 11.86mm over that 0.3m barrel.
Therefore, if your 0.3m long barrel is bent by more than 11.86mm and you're firing a 0.2g BB at 350fps, then the BB will contact the Barrel.
This might suggest a reason why they are not very common too: For a different weight BB, or different muzzle velocity, you'd need a different barrel. For example, at 0.2g, 500fps, 509mm barrel, would be 16.73mm.
It would be a very rigid set up. Manufacturing tolerances would make each gun shoot consistently to itself, but different to any other. Each may have a slight left/right lean, which may be difficult to correct due to the lack of adjustment in the set up. Perfect for technically capable modders maybe. A bit too restrictive for others.
I imagine you get a much more consistent hop from this method, because there are no moving parts. Modern hop up is deformed slightly differently with each BB that passes through it, which will lead to some variation between shots. Steel doesn't yield... Well... When compared to silicone rubber...
Step 7: What About Wide Bore Barrels? (6.23mm ID)
Good question. No point in guessing, here are the results:
Force (X) [N] 0.001410775192
Force (Y) [N] -0.01125947496
Force (Z) [N] 20.16382565
Off centre down, by the same amount (0.025mm) as the 6.01 barrel model:
Force (X) [N] -0.004697257464
Force (Y) [N] 0.06429097636
Force (Z) [N] 20.158691
What this means:
The first thing to note is that the Z axis force is less than the 6.01mm barrel in both cases. This is expected, and ties up well with the experimental results of a drop in FPS that a wide bore barrel is known to give. The magnitude of the drop in force is less than explains the magnitude of FPS drop. But this is because this is a steady state model. In reality, the force would diminish to almost zero as the BB accelerates down the Barrel. With a wide bore, the pressure drops off faster than a tight bore, due to the increased blow by. The blow by in 6.01mm was 0.001219999 kg/s. For 6.23 it was 0.005544020306 kg/s. That's 4.5x more air passing around the BB.
The X force is not really relevant to the purpose of this investigation. It is noted that it's still pretty small.
The Y force is the focus of this investigation. 6.01mm centred resulted in a reverse Magnus force of -0.0077N. For 6.23mm Centred, the Y force is -0.01126N. This is a ~30% increase in reverse Magnus force. This makes sense because it has more air moving over the BB in the reverse direction.
Off centre down, the 6.01mm got 0.143N pulling it back to centre. For 6.23mm it got 0.0643N. This is a ~45% drop in force. This means that the force attempting to return the BB to centre in a wide bore barrel is less than that of a tight bore barrel,for the same pressure, and displacement. This makes sense, because Bernoulli works on relative aperture difference:
In a 6.01mm Barrel, The BB, when centralised, is 0.03mm off the barrel all around. When you move it down by 0.025mm, it is 0.005mm from the bottom surface, and 0.055mm from the top. That's an 11:1 ratio.
For a 6.23mm Barrel, it has 0.14mm gap to the Barrel when centralised. When moved the same 0.025mm down, it has 0.115mm below, and 0.165mm above. Giving a ratio of 1.44:1. Significantly lower. So Bernoulli principle and Coanda effect are decreased proportionately.
To put another perspective on this: For 6.01mm, the vertical force went from -0.01126N down, to 0.0643N up. A swing of 0.07566N. The 6.23mm went from -0.0077N to 0.143N. A swing of 0.1507N. That's almost double.
It would seem that for the same pressure, the BB is held more central by a 6.01mm barrel than a 6.23mm barrel. For the same FPS, a higher pressure would be required, which would increase the force swing. This may change things. More investigation is necessary. In order to bottom this out, I need to know what the pressure increase, to get the same fps on a 6.23 as you got on a 6.01 would be.
At this point the results are inconclusive. All that can be said, is that all other things being equal, a tight bore should hold the BB more consistently central on it's journey down the barrel, than a wide bore.
Step 8: Wide Bores Further Investigation...
What about increasing the pressure?
To be fair, you wouldn't run the gun with the fps drop associated with a wide bore, you'd tune it up to your class limit again. Higher fps is achieved with higher pressure air. Or, to a limited extent; a larger volume of the same pressure air.
I have no real world numbers for this, so I'm going to take a guess. If you have numbers, please give them me, and I'll re-run these tests.
I up the pressure by 15% and re-run it. The results are:
Force (X) [N] -0.006858518
Force (Y) [N] 0.013336395
Force (Z) [N] 23.4898044
The pressure is increasing the fps roughly proportionately: 20.158691N to 23.4898044N. It is important to not that this is not a directly proportional relationship. The wide bore experiences more blow by, so the pressure drops off faster as the BB progresses down the length of the barrel. So although the initial force is higher, it may soon drop lower than the tight bore.
The interesting thing is the vertical component: It was 0.06429097636N, but the increased pressure has lowered it to 0.013336395N. This is most likely because the Magnus effect is increasing more than the Bernoulli proportionally to the pressure difference.
So increasing the pressure doesn't necessarily move the BB more central.
What about proportional displacement?
Ok, so moving a BB 0.025mm down in a 6.01mm bore barrel, makes a bigger relative difference to the air gap than moving it the same distance down in a 6.23mm barrel. Bernoulli states that the forces shouldn't be equivalent.
0.025mm down in a 6.01mm barrel gives an air gap on top of 0.055mm, and one below of 0.005mm. This is a ratio of 11:1. Applying the same ratio to a 6.23mm barrel makes the move 0.116666666666667mm down.
Remodel and back to standard pressure. Here are the results:
Force(X) [N] 0.00075039
Force (Y) [N] 0.346269096
Force (Z) [N] 20.23075439
Now that's much more like what I was expecting. The Z component is roughly the same, X is still very small. Y is now of an important magnitude.
- You will lose fps with a wide bore.
- The BB will still self centralise in a wide bore.
- Increasing fps/pressure is likely to move the BB slightly down in the bore rather than up.
- For the same pressure, and proportional displacement from the barrel axis, to the barrel ID wall, the wide bore will have a larger force, self centering the BB.
- For the same displacement from the Barrel axis, the tight bore has a larger force holding it central.
- BB's in tight bores follow a more stable path than wide bores.
- The difference is microns and likely irrelevant.
This is not definitive. This is not saying that tight bores are more accurate than wide bores. It may be that the larger bores allow for more dampening of oscillations between interactions with the barrel walls, thus producing a more stable flight at the end of the barrel. It may be that something else I haven't discovered or thought of yet it also going on and making a much bigger difference.
Step 9: Conclusion
From the previous results. it should be evident that the BB is very unlikely to travel down the top of the barrel.
The evidence suggests that the BB should self centralise.But reverse Magnus effect would cause it to be slightly lower than central.
In the case of the wide bores, the BB would be minutely lower in the barrel due to an increased reverse Magnus Effect. In addition to this, The Bernoulli and Coanda effect are reduced due to a lower change in relative gap proportion for a given displacement. This is to say, the same vertical displacement in a wide bore, produces a smaller change in gap ratio, than in a tight bore. As such, the Bernoulli and Coanda effects are both also reduced. Meaning that the BB will ride marginally lower in the barrel than in the tight bore, and will wobble around the centre by a larger displacement.
This is all assuming that the same pressure is used. In reality, you would up the pressure to maintain the same FPS. This would increase the Bernoulli and Coanda forces that centralise the BB. In order to model this, I need to know what pressure a 6.23mm barrel needs to achieve the same fps that a 6.01mm barrel does at a given pressure, preferably the pressure I used in this model.
This model doesn't have a fixed volume input like an airsoft gun. But the BB also doesn't move in the Z axis down the Barrel so it wouldn't change within the snapshot of this model. This is because of software limitations, it cannot move components dynamically. The model should be indicative of real world results though.
I acknowledge that this is a purely theoretical investigation, and no physical, real world tests have been conducted. Although this does leave room for doubt, as "the map is not the territory", it is entirely plausible that the reality of the matter is quite different. All the scientific principles, thought experiments, and computational modelling, suggest that this is the case. Until it is observed in a physical experiment, it cannot be said for certain that this isn't the case, and at this point in time all that can be said, is that this is our best understanding.
In future I'd like to corroborate these results with the aforementioned test using a transparent barrel and high speed camera. Then this matter can be put to bed once and for all. I suppose another alternative would be to take a photo down the barrel while the BB is on it's way down it. Maybe with a light behind it to highlight the gaps around it. I've heard that this has been done several times, but can't find any videos, photo's or results online. If you have seen them, and could send me a link, I'd be most appreciative.
I'm in this for the knowledge. I want us, as a collective, to understand the world better. Which will enable us to make improvements that benefit everyone. I am likely blind to my own flaws. It is only through identifying faults that we can improve. If you have any recommendations, improvements, or further insights, I'd love to hear them. As a collective we are stronger and more capable than any one individual alone.