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Thursday, July 7, 2011

Math Secrets in Sports: Archery

This week in the Excel Math Blog we reveal a few of the inside mathematical secrets of popular sports. After dealing with tennis and bowling, we've come to Archery. If you take up this activity, you may have to learn new math or relearn the old math you learned in elementary school (possibly with our Excel Math curriculum).

In archery you need to understand distances, weight, straightness, keep track of time, learn to wait your turn, and add numbers rapidly and accurately. And count your pennies!

In some ways, archery sounds easy, doesn't it? No running. No tackling. You pull a string, shoot an arrow, hit a target. But it's not so easy. You need calm nerves, strength, speed, good eyesight, ability to repeat the same motion over and over and over ...

On Father's Day, I watched my brother-in-law explaining archery technique to my nephew.

To avoid any problems, he was pretty close to the hunting target, that square black box back by the horse barn. The horses were elsewhere, for safety.

I'll review a bit of the math details of archery. Some details will vary depending on whether you are doing target archery or field archery (hunting).

LEAGUE - a seasonal group of meetings where many archers and teams can shoot
   TOURNAMENT - a competition with many archers or teams shooting to win
      ROUNDS - this term describes shooting a batch of 2 to 6 dozen arrows for each target distance in competition
       ENDS - an end is a 2-minute interval time, during which an archer must shoot a group of 3 or 6 arrows, after which they are scored and retrieved. There are often 20 ends in a round
         POINTS - scores depend on where the arrows hit within 10 evenly-spaced concentric rings. The values range from 1 to 10 increasing towards the center (these values may vary from country to country). Some have an inner 10 ring:
  • 1 ring and 2 ring - white
  • 3 ring and 4 ring - black
  • 5 ring and 6 ring - blue
  • 7 ring and 8 ring - red
  • 9 ring, 10 ring and inner 10 ring - gold

After each end, archers add the scores for their arrows - if an arrow touches a line, you can claim the higher value. Scores for each arrow in an end are written in descending order on the score card (10, 9, 4, 4, 3, 3). No one may touch the arrows until the scoring is complete, in case a referee wants to inspect one. If you count wrong and shoot too many arrows, the highest scoring arrows are subtracted from your score.

Target sizes and distances vary, depending on the competition:
  • 16 inch (40cm) for 60 feet (18m) indoors
  • 24 inch (60cm) for 80 feet (25m) indoors
  • 32 inch (80cm) for 100 feet (30m) and 160 feet (50m)
  • 48 inch (122cm) for 240 feet (70m) and 300 feet (90m)
  • All target backings must be at least 48 inches round or square, regardless of target size
  • The center of the gold must be 51 inches (130cm) above the ground +/- 2 inches (5cm)
  • Targets must slope backwards, within 10-15° from vertical
  • Arrows range from 26-31 inches in length, measured from the bottom of the nock on the back to the front (not including the tip) and must be less than .27 inches (9.3mm) in diameter; good arrows are within +/- .001-.006" in straightness
  • Arrow weight is measured in grains (1/7000th of a pound); most weigh between 200 to 400 grains - you might have 5 grains weight of arrow per pound of draw on the bow
  • Arrows travel at speeds from 200 to 300 feet per second (fps) and so they reach a 160 foot (50m) target in about half a second (you can do the math)
Here's an on-line course on arrows, with lots of math details, charts and diagrams.

  • Bows are made of different kinds of materials and may have sights, but must have no electronic features
  • The power of a bow is expressed in pounds of draw weight or effort it takes to pull the string back
  • Both compound and recurve bows are used, but not mixed in the same events
Scoring is done in different ways; in target archery many countries follow FITA rules:
  • The top archery score in FITA competition is 1440
  • Archer Brady Ellison recently shot a 1368 score in competition - the highest recorded score in competition by a non-Korean archer.
  • Koreans dominate archery with 90% of the world records. They have used bows and arrows since before recorded history. Korean archers aggressively pursue excellence in competition - some shoot over 1000 arrows a day, 6 days a week!
If only we all were so diligent in learning math!

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