Wednesday, January 4, 2012
Poor Man's Ballistic Chronometer - Part 1
Many people who participate in paintball, archery, or other shooting sports have a desire to ascertain the velocities of their arrows, bullets, ... Usually this is done with a chronometer. Such devices can be rather pricy, and they are not something you can just walk into any hardware store or Wal-Mart and buy. Readers of this blog might recall that I enjoy archery and also have recently been shooting a primitive blowgun. See my post -
After shooting the blowgun a bit, I wanted to have at least a 'ballpark' idea of how fast the darts were flying. This information helps in comparing the performance of various dart designs, as well as giving an idea of how one's lung power is developing. I did NOT want to spend a lot of money on a chronometer, though. Some Google-searching turned up several pages suggesting the use of a computer's sound card as a data acquisition unit for ballistics measurements.
By far the best article I found on this was James Sluka's site at
http://www.inpharmix.com/jps/Jims_chrono.html. He apparently is a spudgun and BB gun enthusiast who, like me, decided to build his own chronometer.
How It's Done
From the basic concept he outlined, I designed a circuit using a photodetector to trigger when the dart leaves the blowgun and a microphone attached to the target to record the dart's impact. I use the sound card in my computer to record the signals, and some free audio editing software - Audacity - to measure the time from when the dart exits the muzzle to when it hits the target. With this time of flight data, and the distance from muzzle to target, one can calculate the average velocity of the dart. Here is the formula: distance = velocity x time, or
velocity = distance / time
While this formula gives the average velocity, a pretty good approximation of muzzle velocity can be had by simply shooting with the muzzle close (in this case, within 2 or 3 feet) to the target. Using such a short distance effectively minimizes the slow-down of the dart due to air friction. Comparing these approximate muzzle velocity measurements with 'time of flight' data at the distances you normally shoot from could yield some good insights into the darts' performance.
The circuit I designed, shown above (REVISED 02/04/2012), uses Mr. Sluka's basic idea with some modifications. I redesigned the "optical gate" to better suit a blowdart's geometry. I wanted to use the dart's airseal cone to start the time measurement just as the dart leaves the muzzle of the blowgun. So I oriented the photodetector setup somewhat off-center with respect to the tube so the shaft of the dart wouldn't prematurely trigger it. The detector is made from a 2" piece of 3/4" PVC schedule 40 pipe. I cut 1/2 way through the tube at the 1" mark, then split one of the sections lengthwise. This provides a spring-loaded 'expando' ring for clipping the device to the blowgun's muzzle. You can see the design and use in the photos below.
NOTE: These dimensions are for a blowgun made from 1/2" PVC schedule 40 pipe. If you are using a different size or type of tubing for your blowgun, you will need to use a different diameter tube for the detector housing, and quite possibly modify the mounting of it to the blowgun. The detector LED and phototransistor leads are 22 gauge stranded, twisted pair wire, approximately 10' in length. The same kind of wire can be used for the mic as well, since the mic impedance is fairly low.
The actual circuit consists of an Op Amp coupled to both a microphone and the phototransistor trigger circuit. When the light from the sensor LED to the phototransistor is interrupted, the 1 uf capacitor produces a pulse that is sent to the Op amp. Note that the phototransistor trigger circuit is coupled to pin2 of the OP amp through a 330K resistor - the same value as the feedback resistor on the amp. This provides essentially a voltage gain of 1. A voltage divider consisting of a 100K and a 15K resistor is used to provide about a 1.6 volt supply to the phototransistor trigger circuit. The mic, actually a noise maker out of an old PC modem, is also coupled to pin 2 of the OP amp through a 4.7K resistor. This provides the gain needed for the mic to work properly. Note that the 330K and 4.7K resistors, coupled to pin 2 of the OP amp, form a crude audio mixer. Power and ground are provided to the OP amp via a voltage divider comprised of a pair of 10K resistors. These are bypassed by capacitors to keep everything at AC ground and help prevent oscillation. The voltage divider is powered by a 12 volt battery. A diode protects everything from getting zapped if the battery is ever connected backward. I also provided a red LED to indicate when the power is 'on'.
The output of the OP amp is connected to the PC's sound card via a 0.1 uf capacitor followed by a voltage divider. The voltage divider, comprised of a 22K and a 2.2 K resistor, was determined by experimentation to work with my sound card's microphone input. If you have a 'line level' input on your sound card, you could probably eliminate these two resistors. Depending on your sound card, you may need to slightly adjust the ratio of these values, but the total resistance value should NOT be made significantly smaller, or circuit performance could be hindered.
The completed circuit assembly, built on a piece of experimenter's perf board measuring 1.75" x 3", is shown in the photo below:
With the detector, the mic, and the battery connected, use an audio amplifier or your PC to monitor the output. A tap on the mic should produce a clear sound; inserting your finger into the detector and pulling it back out should produce a click or pop sound. If these tests pass, the unit is ready to be used.
My follow-up post, "Poor Man's Ballistic Chronometer - Part 2", will explain how to use Audacity to record and interpret the data.