btrettel's Nerf blog

random thoughts about the ballistics of foam darts

Archive for the ‘Pneumatics’ Category

Nerf test gun

Posted by btrettel on May 23, 2013

I am developing a Nerf gun purely for test purposes. My main goal is to get consistent performance. I am using a few methods to do this: regulated pressure, reducing the effect of the speed of opening the trigger valve by piloting my QEV with another smaller QEV (that is in turn piloted by a smaller trigger valve), and using stiff aluminum barrel to reduce the effect of barrel vibrations.

The first major set of tests I want to do will examine fishtailing and dart stability. I want to determine when darts fishtail. I have some some simple theoretical analysis, but the results have been trivial: darts possibly are unstable when the center of gravity is behind the center of pressure. That doesn’t say that much. The center of pressure moves as a function of the dart velocity. It’s commonly reported that faster darts fishtail more easily. Is the movement of the center of pressure the main effect causing the instability here? Or does the speed cause other effects?

Towards this, I have done some dimensional analysis. Hopefully this analysis will help me decide how to conduct my experiment. I have determined that the important parameters are fineness ratio, Reynolds number, a dimensionless distance difference between the dart center of pressure and center of mass, a dimensionless mass, a dimensionless moment of inertia, and the fractional location of the dart center of gravity (or pressure)

Unfortunately, there is one effect which is hard to characterize: muzzle blast. If there’s some extra pressure when the dart leaves the barrel, then this pressure could knock the dart off balance. I can’t measure muzzle blast at the moment, but I know that muzzle blast should be approximately minimized when the optimal barrel length is used. Thus, the first part of my tests is to find the optimal barrel lengths for a variety of different pressures. I figure this is a good restriction as we’d all want to use the optimal barrel length anyway.

I intend to finish the test gun this weekend and do some preliminary tests to help figure out what gas chamber volume, barrel lengths, etc., are appropriate for future tests.

This likely will be the first test gun I build. I plan to use what I learn from this test gun to develop a second test gun. The second test gun will use higher precision regulators and pressure gauges.

Posted in Experiments, Pneumatics | 1 Comment »

Notes about valves and flow rates

Posted by btrettel on March 20, 2013

Comparing valves for compressed gases can be difficult for several reasons. Even if you are familiar with how valve performance is specified, you can easily make mistakes. Valve performance is specified in several different sloppy and confusing ways, almost always in non-metric units. The worst part is that valve performance can be specified in obvious ways, but people working in the industry don’t do that.

Flow rates

The confusion starts immediately with the definition of the flow rate. Rather than specifying a mass flow rate (i.e., something like g/s), most valve manufacturers instead specify a volumetric flow rate (i.e., something like m3/s). Why? I’m not entirely sure. It’s probably a combination of tradition (e.g., “that’s all I was taught”), familiarity, laziness (e.g., the flow meter gives volumetric, and they don’t want to convert), or ignorance (e.g., they don’t realize it matters). I suspect the practice was held over from liquid valve flow, where the fluid density doesn’t vary much and the volumetric flow rate is just proportional to the mass flow rate.

This is problematic because volume can vary considerably over a range of temperatures/densities for the same mass flow rate. To use a volumetric flow rate (by converting it to a mass flow rate to use in a mass conservation equation) requires an engineer to know the temperature and pressure at which it applies.

With this in mind, some engineers developed the unit called “standard cubic feet per minute” or SCFM for short where the temperature and pressure are supposed to be standard, i.e., known. Unfortunately, there is no standard, though usually the reference pressure is 1 atm and the reference temperature is 70F.

Unfortunately, some companies simply treat SCFM as if it were the actual measured flow rate! It’s as if they don’t understand what the point of the standardization was or even that the S stands for standard. Clippard is one of these companies (I asked by email. Their reference pressure is the pressure they did the test at and their reference temperature is 70F.). If you are using a company’s valve, I suggest asking what their reference conditions are. If they don’t know, then don’t assume anything about their products. I’ve found that some companies are completely ignorant about the performance of their products. Some companies have no idea where the numbers they print on their spec sheets come from. They sometimes don’t even know the units to the numbers. This is extremely sloppy and it’s rather scary that a large number of engineers work this way.

The relationship between volumetric flow rate and mass flow rate is \dot{m} = \rho Q where \dot{m} is the mass flow rate, \rho is the mass density, and Q is the volumetric flow rate.

We can find \rho with the ideal gas law (\displaystyle P = \rho \frac{\overline{R}}{M} T) and convert between volumetric and mass flow rates. P is the pressure (in absolute units), T is the temperature (again, absolute temperature), \overline{R} is the universal gas constant, and M is the molecular mass of the gas (for us this is air). So, rearranging the equation above yields \displaystyle \rho = \frac{P M}{\overline{R} T}.

The standard uses the standard temperature and pressure. So, for example, for convert from a volumetric flow rate of 20 SCFM to a mass flow rate in g/s, we can do the following:

\displaystyle \dot{m} = \rho Q = \frac{P_\text{s} M Q}{\overline{R} T_\text{s}}
\displaystyle = \frac{101325~\text{Pa} \cdot 28.97~\text{g/mol} \cdot 20~\text{ft}^3\text{/min}}{8.3145~\text{J/(mol K)} \cdot 293.15~\text{K}} \left(\frac{3.28~\text{ft}}{\text{m}}\right)^3 \frac{1~\text{min}}{60~\text{s}} = 11.4~\text{g/s}

Valve flow coefficients and flow models

Often valve performance is specified with a valve flow coefficient. In the US, this usually is called C_\text{v} where v refers to valve. (This is not the heat capacity at constant volume. Again, this is another confusing point.)

Like the valve flow rate, C_\text{v} is defined in terms of liquid, not gas flows. C_\text{v} is defined as the volumetric flow rate in gallons per minute (GPM) for a pressure drop of 1 psi. There are some mainly empirical equations (scroll down to the section “Flow Coefficient – Cv – for Air and other Gases”) that can be used to calculate the volumetric flow rate (and mass flow rate from there). The “derivation” of this model is available in this book.

For more information on this subject, I suggest reading my notes about Nerf engineering, which contain many references to other materials. In particular, I detail a more accurate empirical valve model that can be used in computer simulations.

Accuracy of manufacturer data

You should always question the accuracy of valve manufacturer data (assuming that you understand what it means, which, as I’ve explained, isn’t always clear). In my experience, the flow rates given seem to be optimistic. It’s not easy to quantify how optimistic they are, but you should keep this in mind.

An aside

I could insert a long rant about how some engineers don’t understand what they are doing and treat some equations like magic black boxes which give them “the answer”. They don’t understand the assumptions or development of the equation. They don’t try to improve the equation to be more general, more useful, or less confusing, e.g., by eliminating confusing “standard” volumetric flow rates and moving to obvious mass flow rates. This practice creates a lot of confusion for people who do know what they are doing. If you are in engineering, please, don’t be one of these folks.

Posted in Interior ballistics, Math, Misconceptions, Pneumatics | Comments Off on Notes about valves and flow rates

Nerf Engineering notes

Posted by btrettel on July 8, 2012

I’ve started organizing my writings and thoughts on Nerf ballistics into a set of notes (link corrected). Readers of my blog might be interested.

For the moment my notes are very rough and incomplete. I’ll update the PDF as I make changes. I’d appreciate any feedback, especially corrections and ideas.

Edit (2012-10-02): I’ve removed the notes because they need a lot of work before I’m comfortable distributing them.

Edit (2013-01-19): I’ve readded the notes as I’ve revised them somewhat. They are still a work in progress.

Posted in Design, Exterior ballistics, Interior ballistics, Math, Pneumatics, Safety, Springers, Terminal ballistics | 2 Comments »

Approximate expansion diameter of latex tubing

Posted by btrettel on June 5, 2011

I previously wrote about how to estimate the expansion diameter of latex tubing, but I made no measurements to verify that the formula I suggested, 8.5 D_i + 2 t where D_i is the unexpanded inner diameter of the tube and t is the unexpanded tube wall thickness, was accurate.

Back in 2010, I made some measurements for tests that were aborted as the tubes continually burst. I was testing higher pressure tubes. These tubes have a tendency to burst and they are extremely loud when they burst if you fill them with air. I do not suggest testing latex tubes with air for this reason.

So, I have three data points and a reasonable understanding of the geometry of these tubes. I’ll make a better estimate for expansion diameter.

I’ll start with a few assumptions. When the tube expands, it is assumed to stop expanding when its expanded inner diameter equals a certain multiple of the unexpanded diameter. This is justifiable based on the observed behavior of the rubber. The Gent hyperelastic model makes the same assumption. My second assumption is that when the tube is fully expanded the cross sectional area of the expanded tube is a multiple of the cross sectional area of the unexpanded tube. I originally anticipated these areas would be equal as I know for small deformations, rubber is approximately incompressible (i.e. the volume is preserved). But that’s only applicable for volume, not area; the tube is expanding in length too. Also, it is only applicable for small deformations. I do not know how the rubber will act for large deformations.

D_o is the outer diameter of the tube. D_i is the inner diameter of the tube. t is the tube wall thickness. The superscript e refers to the expanded state. A variable or constant without e is in the unexpanded state or it does not refer to any state (like the constants).

A = \tfrac{\pi}{4} (D_o^2-D_i^2) is the equation for the cross sectional area of the unexpanded tube.

A^e = \tfrac{\pi}{4} [(D_o^e)^2-(D_i^e)^2] is the equation for the cross sectional area of the expanded tube.

D_i^e = C_1 D_i is my assumption about when the tubes stop expanding.

A^e = C_2 A, where C_2 is my assumption about the cross sectional areas of the tubes when they stop expanding.

Plugging all these equations together and solving for D_o^e, I find that D_o^e = \sqrt{C_1^2 D_i^2 + 4 t C_2 (D_i + t_i)}.

The data points I have available:

  • Unexpanded ID: 3/8″, wall thickness: 3/16″, expanded OD: a bit more than 3″ (from memory)
  • Unexpanded ID: 1/8″, wall thickness: 3/16″, expanded OD: 1.25″
  • Unexpanded ID: 1/8″, wall thickness: 7/32″, expanded OD: 1.375″

A linear regression leads toC_1 = 7.35 andC_2 = 3.33 (R^2 = 0.9999, which would definitely be lower if there were more data points). These constants seem reasonable given my understanding of the phenomena, so it is reasonable to accept that the tubes’ inner diameters expand to about 7.35 times their original inner diameter and the cross sectional area increases by 3.33 times.

The equation above with these constants can be used to find the expanded outer diameter. The equation with C_1 can find the expanded inner diameter. The definition D_o^e = D_i^e + 2 t^e can find the expanded wall thickness.

Further tests are necessary, but this formula is the best I can do with the data I have on hand.

An equation for the inner diameter of a tube if the outer diameter is restricted (i.e. does not fully expand) follows. This is based on the assumption that the area ratio scales linearly with the inner diameter ratio.

D_i^e = (C_1 D_i)^{-1} [\sqrt{4(t C_2)^2 (D_i + t)^2 + (C_1 D_i)^2 (D_o^e)^2} - 2 t C_2 (D_i + t)]

Posted in Design, Math, Pneumatics, Uncategorized | Leave a Comment »

Electro-Pneumatic Revolver by PVC Arsenal 17 build log

Posted by btrettel on February 20, 2011

Check out this interesting project by PVC Arsenal 17.

For those who were wondering, I’m still alive, but I am kept extremely busy with school work. Two grad. classes (one mech. eng., the other applied math), two advanced undergrad. classes (one math, the other mech. eng.), and the senior design course will keep you busy!

Unfortunately, due to my extremely busy schedule, I’ll be posting here less often over the next few weeks, and I’ll be basically impossible to find on IRC and at NerfHaven. You can email me if you want to contact me.

Posted in Pneumatics | 1 Comment »

Banding rubber bladders

Posted by btrettel on January 30, 2011

When a Nerfer wants to increase the pressure of a bladder, they generally turn to “banding,” the layering of rubber bands on the bladder. I came into this hobby from the similar water gun hobby, and I’ve often wondered why this method is so prevalent in Nerf but not water guns.

It’s not that layering rubber bands doesn’t work. I’m sure it works fine. It’s that layering rubber bands is surely far more difficult than the alternatives that will work even better. In water guns people generally layer bike tubes over bladders to increase the pressure. This is not a new idea—it probably originated in 2000 or 2001. (Water gunners generally call this modification “Colossus” as that’s what it’s traditionally called. See SSC for more information.)

When I asked about this on #nerfchat, the only salient point I heard was that kids are more likely to find rubber bands than bike tubes. I’d like to contest that point. Old bike tubes are not difficult to come by. My father had a ton of them that he kept for various odd projects. Many bike shops give them away for free. Consider the number of tubes needed too. One or two 26 inch bike tires should be more than enough to increase the pressure of a bladder substantially. But to get a similar amount of rubber over a bladder with rubber bands would require tens, maybe even hundreds, of rubber bands. How many rubber bands are people likely to have at home?

Additionally, I previously mentioned that banding is more difficult and time consuming than using bike tubes. Bike tubes generally can be rolled up and slid on a bladder quite rapidly unless one has many layers on the bladder (at which point the modifier should probably stop anyway). Banding requires a lot more effort and time, especially if one wants to ensure that the rubber bands are applied evenly over the bladder so that one part does not inflate while the remainder does not.

I hope my point is clear: Banding should be avoided as layering bike tubes is far easier. Why bike tubes are so foreign to Nerfers but well known to water gun people is not completely clear, but I suspect tradition and a lack of creativity from most people in the hobby has a lot to do with it.

Of course, there are other alternatives as well. Someone could layer latex tubing over the bladder or simply use latex tubing as a bladder. Someone could use a homemade hard pressure vessel with a regulator. There are many options.

Posted in Interior ballistics, Misconceptions, Pneumatics | 2 Comments »

Unfinished Nerf gun with semi-auto valve from 2007

Posted by btrettel on January 27, 2011

Back in 2006 I had an idea to improve a pneumatic Nerf gun my brother made. This Nerf gun had a semi-auto valve. At the time I was interested in semi-auto Nerf guns, but I saw the valve as a more daunting task than an advancement system. Like my brother, I started focusing on only the valve as the advancement system could come later.

I eventually started building the Nerf gun, but I ended the project after I found that one seal I used was too small and leaked. I later decided to end the project, but still, I did not see this as a waste of time as I learned a number of things in the process of planning and building (partly, at least) this Nerf gun.

I called the gun NAM, which stood for Nerf Assault Musket. You can view some images of the Nerf gun in construction here:

Problems with my brother’s Nerf gun

  • The valve was difficult to construct. It required the use of properly sized O-rings, and quite a bit of tinkering was necessary to get it to seal. But when it worked, it worked very well.
  • The valve was difficult to service. To replace the seals (which seemed to be necessary on occasion) you had to basically take apart the entire valve. I didn’t intend to make servicing easier, rather, I wanted to make it unnecessary.

My solution

I replaced the O-rings with rubber sheets. This made sealing easier as the sheets did not have to be any precise size to seal. The rubber sheets basically sealed against the flat part of a 2 inch to 1 inch PVC bushing. I made the following animation to help explain this when I would get around to posting it.

The grey is pressurized air. The left end is the barrel. The right end is the air source. Basically, the valve cycles between filling the gas chamber (when the seal is against the left end) and evacuating the chamber (when the seal is against the right end).

I do not remember much more about the project aside from what I have detailed and linked to here. As I said, I considered this project to be a learning experience, and I kept many of the issues I had with this in mind when making FANG1.

Problems with NAM

Around the time I learned that one part would not seal correctly, I started thinking about the design and realized it had a few problems. Not all of what was listed below necessarily was on my mind back in 2007, but I see these problems now:

  • Size – NAM was going to be a very long Nerf gun. Look at some of my photos; I couldn’t even fit the entire layout in one frame!
  • Weight – PVC pipe was used extensively, and PVC pipe is not a lightweight material.
  • Pressure source – If I recall correctly, I intended to fill NAM up with an air compressor. This is not practical for a Nerf war, and I made no plans to use a human powered pump of any variety (though, strictly speaking, this is perfectly possible with the air coupler swapped for a schrader valve).
  • Lack of dart advancement mechanism – NAM was going to have a simple coupler for a barrel. This may have been okay for a test, but I wanted to go further.

Other things that caused me to change my design

  • CaptainSlug’s ABP5K – This completely changed how I approached designing Nerf guns. Previously I limited myself to mostly PVC components as that was the norm. I did not really consider using components with only a structural purpose, even though that seems to be obvious now. You can definitely see CaptainSlug’s influence in FANG1.
  • Reading more about spud guns – Over the next few months I would read a great deal about spud guns and how spud gunners designed them. Until 2008, I was basically ignorant about what a QEV was. I had assumed it would not have been something I would have been interested in even though I was familiar with them going back to perhaps 2005.

All in all, NAM was an interesting learning experience that definitely was not a waste of time. I need to get back into just tinkering like I did here.

Posted in Pneumatics, Unfinished projects | Leave a Comment »

How far in does a pipe fitting thread?

Posted by btrettel on January 17, 2011

When drawing up homemade pneumatic Nerf guns in a CAD program, I used to wonder how deep a fitting would go in. Eventually I learned that technical drawings from McMaster-Carr and many other places offer this information in the listed “thread engagement”. See the drawing from McMaster-Carr below.

Click on the image to view the full sized version.

This information has finally allowed me to start making accurate drawings of my Nerf guns. See the little icon on the top left for an example. (I admit I was a little lazy and I didn’t cover up the threads in the overlap. This actually is somewhat useful, though, so it’s not a problem.)

Posted in Design, Pneumatics | Leave a Comment »