This blog has moved to NerfHaven and is now titled Nerf Engineering. That is all.
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Blog moved to NerfHaven
Posted by btrettel on February 25, 2014
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NY Times Magazine Interview
Posted by btrettel on August 7, 2013
I was interviewed for the New York Times Magazine about my other toy gun hobby: homemade water guns. I haven’t worked on homemade water guns for several years now, but I’ll eventually get back into the hobby.
Edit: To be clear, I am not Lonnie Johnson. He was interviewed first in the article. The section with me is at the end.
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Drag coefficient of Nerf darts
Posted by btrettel on May 31, 2013
The drag coefficient tells you how much drag affects an object moving in a fluid. A higher drag coefficient means that the drag force is larger, which’ll slow down an object more. Lower drag darts will have more range and travel faster.
What’s the drag coefficient of a Nerf dart? Many tests have been done on cylinders. I’ve plotted the results of these tests below. The data comes from this paper and this book.
This is a plot as a function of fineness ratio (
), which is the ratio of the dart’s length to its diameter. This’ll allow the results to scale up for any size dart.
Nerf darts seem to be much closer to the flat nose curve above than the smooth nose one. Tests done by Daniel Beaver have shown that Nerf darts with a length of 1.25 inches have a drag coefficient of about 0.67.
This plot shows that darts have the least drag in the range of = 1.75 to 3. The increase in drag for darts shorter than that is much steeper than the increase for longer darts. The variability also increases for shorter darts, which could reduce accuracy. Based on this information, we should make our darts about 2.5 times as long as their diameter to have low drag and good accuracy.
The curve fits I developed above use this equation:
For the flat nose, 
= 1.104, 
= -0.988, 
= 0.402, and 
= 0.413. For the smooth nose, = 0.427, = -0.579, = 0.060, and = 0.248. is the drag coefficient of a cylinder with effectively zero length.
Typical darts were longer at one time. Perhaps Nerfers have slowly have figured out that shorter darts perform better. In 2004, the average Nerf dart was 2.1 inches long ( = 4.0). In 2008, the average dart was 1.7 inches long ( = 3.2). Now I’d say darts are even shorter. Daniel Beaver’s tests used darts with a fineness ratio of 2.4, which is about what I suggest based on this data.
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Goals for the end of 2011
Posted by btrettel on November 19, 2011
I’ve been too busy to accomplish what I want to in this hobby, but I do have a few plans for the end of this year:
- I will write a NerfHaven article about misconceptions in Nerf physics. I have already written a few things along these lines. The goal here is to make a summary of many misconceptions.
- I will write another NerfHaven article about basic theoretical ballistic engineering. The point here is to offer those with a high-school algebra background some equations they can use to design Nerf (or even potato) guns. Whenever possible I’ll try to offer empirical data to compare to and calibrate these models.
- I will buy a drill press, a vise, and some other tools so that I will have my own machine shop.
Early next year I hope to finish an initial version of my Lagrangian gas gun simulation (LGGS). This is mean mostly for spud gun work, but I’ll use it for Nerf too.
I also have some plans for FANG 4, but I will not start FANG 4 until after LGGS is functional. This is after when I had hoped to finish FANG 4, but that’s fine. I complete things as I can. I have already detailed some of my plans for FANG 4 on the Nerf Engineering forum.
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Improving accuracy and precision
Posted by btrettel on September 11, 2011
I wrote a long post at NerfHaven on improving accuracy and precision of guns back in April.
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I’m not entering Ryan’s contest
Posted by btrettel on July 2, 2011
To answer a question that I’m sure will be asked, I will not be entering Ryan’s contest. I do not have easy access to anything resembling a machine shop or much money to buy components with. This is unfortunate.
I have, however, explained my ideas elsewhere. Others are free to implement these ideas as they please.
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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, 
where 
is the unexpanded inner diameter of the tube and 
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.
is the outer diameter of the tube. is the inner diameter of the tube. is the tube wall thickness. The superscript 
refers to the expanded state. A variable or constant without is in the unexpanded state or it does not refer to any state (like the constants).
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]](http://btrettel.nerfers.com/wp-content/latex/909/909be35771d66b437b608f0c88395eca-ffffff-000000-0.png "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.
is my assumption about when the tubes stop expanding.
, where 
is my assumption about the cross sectional areas of the tubes when they stop expanding.
Plugging all these equations together and solving for 
, I find that 
.
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 to
= 7.35 and = 3.33 (
= 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 can find the expanded inner diameter. The definition 
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)]](http://btrettel.nerfers.com/wp-content/latex/3db/3db2081ce5e683bdf4bfe9f16bddbd22-ffffff-000000-0.png "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)]")
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Next two months
Posted by btrettel on June 1, 2011
Sorry all, but I’ll be basically inaccessible for the next two months. At the moment I’m working at NIST with Randy McDermott and I’m staying at a hotel with terrible internet. I’ll see what I can do on weekends.
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Nerf Engineering forum
Posted by btrettel on April 7, 2011
The Nerf Engineering forum is now open. I’m receptive to suggestions, so let me know at the forum if you have any ideas, especially with regard to its organization.
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Temporary NerfHaven archive
Posted by btrettel on April 6, 2011
I have made a temporary NerfHaven archive for those who wish to browse threads while NH is down.
Also, would anyone be interested in a small forum for this blog? I am thinking I’d like to discuss some topics not typically covered at Nerf forums, like, for example, “concept” threads (where the merits of a concept are discussed), ballistic modeling, engineering, and advanced pneumatic Nerf guns. I basically just want a place where like-minded folks can discuss some things not typically covered elsewhere.
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