I shot an arrow into the air, It fell to earth, I knew not where; For, so swiftly it flew, the sight Could not follow it in its flight. I breathed a song into the air, It fell to earth, I knew not where; For who has sight so keen and strong, That it can follow the flight of song? Long, long afterward, in an oak I found the arrow, still unbroke; And the song, from beginning to end, I found again in the heart of a friend. - Henry Wadsworth Longfellow
The Arrow and the Accelerometer
Why Engineers don't do well in English Literature
When Henry Wadsworth Longfellow penned those words in 1845 he wasn't contemplating the flight dynamics of arrows. But what if he could today? He would learn that the X250-1 impact data recorder made by Gulf Coast Data Concepts can capture some interesting data regarding arrows.
GCDC is a high-tech electronics company but occasionally we like to work it "old school". What better way than use a longbow carved from the very oak trees hurricane Katrina fell in 2005. The bow provides a 48lb draw force at 28" and can launch an arrow at approximately 140 feet per second.
Using basic physics (a=(v-v0)/t), the average launch acceleration of about 130 g's was expected. However, there were several significant limitations to this experiment that must be noted. A normal arrow weighs about 3/4oz but the X250-1 added another 1-1/8 oz to the mass of the test arrow. Furthermore, the addition of the X250-1 limited the draw to 24" or about 38lb draw. The reduced draw force and the additional weight dramatically reduced the flight speed and tragectory characteristics.
The X250-1 was mounted to the arrow using zip-ties and a rubber pad between the X250-1 enclosure and the arrow. The rubber pad helped maintain the grip between the case and arrow shaft, which eliminated slippage during release. The longer machine screw in the enclosure provided an anchor point for the forward zip-tie.
The oak longbow
X250-1 mounted to arrow
While Longfellow suggested shooting arrows blindly into the air, it's safer to keep arrows more earthbound and aimed at a target. Our tests shot the arrow approximately 50 feet and into a cardboard box filled with packing peanuts. As mentioned earlier, the increased mass of the arrow due to the X250-1 caused a significant reduction in flight speed. It required several tries to zero in on the target.
Try #1: Oops. Too low and skipped off the concrete.
Try #2: Oops again. Hit the ground. Hey, we never promised a Robin Hood performance!
Try #3: Oops, into the trees. Maybe this is how Longfellow started his poem.
Try #4: Bingo! Finally, a good release and impact into the box.
The average peak launch acceleration was 199 g's. Excluding shot 2, which bounced off the ground badly, the average speed was 87 ft/sec. The average speed was nearly half the speed of a normal arrow but this was expected due to the extra weight. The acceleration profiles for the four shots were very similar and occured over a period of about 25 msec. The impact of the arrow into the carboard box peaked at 310 g's, which saturated the sensor (exceeded the sensor limit). The dramatic impact was caused by the X250-1 enclosure pentrating the cardboard box.
The X250-1 was able to detect the vibrations of the arrow during flight. This is apparent in the acceleration-vs-time plots above. In each case, the frequency was approximately 78Hz.
This experiment certaintly was not scientific poetry. The act of measuring the test is not supposed to radically influence the test. As a general rule, the accelerometer sensor should be at least an order of magnitude lighter than the test subject. However, the experiment illustrated the data collecting capabilities of the X250-1 and was good fun as well.