The dynamics of how a ~5.95mm plastic sphere travels down a ~6.1mm 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 think this is not the case, and I’m here to debunk this myth and find out what is really happening.
The basic principle:
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.
The Myth: The hopup/magus effect/backspin, causes the BB to travel down the barrel rubbing against the top surface.
“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 no air passing around the BB. The pressure in front is atmospheric, the pressure behind is 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.
- Fourth, 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.
The Pursuit of Proof
It’s all very well and good me sitting here behind a keyboard and postulating. But I have no interest in opinions. 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!
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:
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, the air is moving over it.
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.
Next I model the BB in the barrel. In this case, the BB is stationary, The pressure at the opposite end of the barrel is atmospheric. and the pressure at the close 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.
This shows that the Magnus effect does move the BB off centre in the barrel. But down rather than up.
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 center.
The vertical force is larger than even 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.
This Begs the question… is wide bore to the same tolerance better? Less sensitive to small displacements from the axis. more air to do the centralisation. I assume it will reach some equilibrium with the now negative Magnus effect pushing the BB down and the Bernoulli/Coanda pulling it into centre.
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.
Maybe in the case of the wide bores, the BB could be minutely lower than the barrel axis due to reverse Magnus Effect. I suspect that this distance is perceivably small, and ultimately not of significance.
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’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.
I’ve duplicated this on instructables here:http://www.instructables.com/id/Mythbusting-Airsoft-Hopup-and-Barrel-Dynamics/