What is the speed of a Nerf dart? The short answer is, on average, anywhere from about 30 to 45 MPH.
My son and his buddies are Nerf gun fans so I get to hear a lot of talk about which gun shoots the farthest and therefore is the best. He also plays hockey so I get to hear more nattering on about who has the fastest slap shot. One day as I was contemplating various ways of measuring the speed of a hockey puck it occurred to me that a break beam detector, while not well suited for a hockey puck, might be ideal for measuring the speed of a Nerf dart. I did some estimates of the time of flight as a dart traveled past the detector and concluded the nominal 3-5 millisecond time interval was ideal for the Propeller to measure.
I did some online research on how to make a break beam detector and it seemed relatively straightforward and the circuit seemed easy to assemble too. I found some inexpensive IR emitters and photodiodes in a tiny T1 (3 mm) LED package so I ordered a few of each and built a simple prototype detector to see how well it would work. I drilled a 1/8" diameter hole through a short section of 3/4" PVC pipe and stuffed the IR emitter in one end of the hole and the photodiode in the other end. I hooked up a quick circuit on a breadboard and sure enough it functioned as a simple break beam detector. I used an LM393 voltage comparator to convert the analog signal from the photodiode current onto an "on/off" signal as the input to a Propeller pin. I attached a few files below with the circuit schematic and a few photos.
I fashioned this little detector onto the end of some 1/2" EMT which has an ID well suited to a Nerf dart. I grabbed one of my son's guns, shot a few darts through it and had the Propeller measure the amount of time the photodetector was blocked as the darts traveled past (about 4.8 msec). From this and the length of the dart (72 mm) I calculated a speed of about 35 MPH. This result was comparable to the Nerf dart speed values I found online which were measured using either high speed video, a commercial projectile chronograph or a radar speed detector.
My son found this amusing enough to donated one of his unloved Nerf barrel attachments so I could mount the detector in it. This would make it easy to measure the speed of darts fired from a variety of guns. Such a device would thus enable the Nerf gang to determine just who had the fasted gun. Game on!
I was curious to know how accurate and consistent the detector was so after a little more thinking I figured out that a second photodetector might yield some insights. The donated barrel was about 10" long so there was enough room to add a second detector. Since the current in the photodiode is in the µA range and thus likely to be susceptible to EMI noise, I decided to stuff the voltage comparator circuit into the barrel so only the logic level voltages needed to travel through the 8 foot cable to the Propeller. After much Dremeling out of the barrel innards and soldering resistors, headers and a dual comparator onto a small prototype circuit board I had a working dual break beam detector system built into a detachable Nerf gun barrel.
When a dart is fired through the barrel each detector is triggered on then off as the dart passes by. Knowing the time intervals between these four trigger events, the length of the dart and the distance between the photodetectors you can calculate up to six speeds from a single dart firing. With the detectors nicely packed into a barrel I wrote some SPIN code to measure the photodetector time events, calculate the six speeds for each dart fired and log these data to a micro SD card so they could be further analyzed in Excel. So now it was time to put the homemade break beam chronograph to work measuring the speed of Nerf darts.
Already knowing that some darts travel farther than others we picked six "like" darts and numbered them 1-6 so we could keep track of them individually. Using his "Recon CS-6" Nerf gun (aka the "yellow" gun) we shot the six darts in the same sequence 21 times to get our first set of data for analysis. It was pretty apparent looking at the data on the computer screen that dart #3 was consistently slow compared to the others. Out of the 126 test shots the fastest speed recorded was 43.13 MPH while the slowest was 25.41 MPH. It also appeared that for each dart fired the first speed value was slightly greater than the last speed value which suggested that the darts were already decelerating as they traveled through the barrel (more on this later).
Next up was to see how much difference there was between gun types. So my son grabbed his "Longshot" ("blue") and "Modulus" ("white") guns and we put the same six darts through each gun ten times. The next experiment was primarily for me because I was interested in applying some elementary statistics on these data to see what other information could be teased out. The data from the "blue" gun seemed to be more consistent than the other two guns so I used it to fire a single dart 60 times to get a fairly large set of data for analysis.
The measurement data stored on the micro SD card was then imported into a pivot table in Excel for analysis. For me analyzing the data is just as fun as building the detector. Here is a brief summary what we found:
On average the "blue" gun shot the darts the fastest with an average speed of 38.12 MPH. In second place was the "white" gun at 37.48 MPH and the slowest was the "yellow" gun at 34.67 MPH. I attached the Excel file for anyone wanting to see all the data.
I then analyzed the 60 shot data and using a paired-data t-Test on the first speed versus the last speed confirmed that the dart was indeed decelerating. On average the speed of the dart decreased by about 1 MPH over the 125 mm distance between the first and second detectors. A plot of the average dart speed as a function of time between the two detectors shows the deceleration trend nicely. Wow, what fun!
Next weekend the neighborhood "Nerf gang" will be using this little device so we can finally and definitive resolve the burning question of "Who has the best Nerf gun?". -QED
It seems to me that this is Nerf gun experiment could be easily adapted to a fun learning/educational project for a variety of age groups. The younger kids would probably just like shooting the guns and seeing how fast and how far the darts go (muzzle velocity is a good predictor of range). An older more curious group of kids might be interested in building their own detectors (components are cheap) and seeing how a microprocessor can measure the trigger event times and calculate speeds. Once you get to high school aged students this type of project would bring together various elements of physics and statistics. The ease and speed of data collection makes it ideal for teaching the concepts of experimental design, data analysis and using elementary statistics confirm or reject hypotheses. There is a multitude of variables that could be investigated by different subgroups, e.g. exploring individual darts, dart types, guns, gun types, etc. Of course for the mechanically inclined there is the whole area of modifying the gun firing mechanism to produce faster dart speeds! And for the truly geeky types there is the whole area of detector accuracy and precision that can be explored (the attached Excel file has some detector response curves for you!).
I bet Parallax could put together a variety of kits ranging from a box of individual components for the hackers all the way up to assembled Nerf gun barrels for those more focused on the physics and data analysis.
I hope this inspires others to go forth and build fun stuff!
Oh, by the way, I am already putting together a shopping list of components needed to modify the assembly so all of the electronics fit inside the barrel and the data is transmitted via Bluetooth LE to an iPhone! Hey Hasbro, call me! :-))