LFSD 2004 West Coast Challenge
Long Flights On Short Days
Original posting 11/3/04
Updated 11/4/04 Rev A superseded by Rev B
Updated 11/6/04 Rev B superseded by this current Rev
Updated 11/7/04 Current

Our South Coast Flying is some of the best to be had on short days.  To demonstrate, we offer a challenge to all unpowered foot launched aircraft on the West Coast.  The winner will be determined by the formula:

miles times x

• Where
  • Miles = Total straight line miles between two points over-flown by an unpowered aircraft that was foot launched from anywhere in one of the USA states that borders the pacific ocean (California, Oregon, and Washington)
  • x = (cos(d/2)²
    • where d is calculated by subtracting 6 from the calendar day of the year and clamping d so that d is not less than zero. (subtract 5 for non leap years)

• Rules:
  • Aircraft: any unpowered aircraft, but the launch method for the flight must be unassisted foot launch (no wheeled launches or towing, but you may use people to assist without the aid of mechanical devices)
  • Entry Fee: None
  • Registration or prior declaration: None Required
  • Documentation:  A reasonably descriptive article must be posted to the SCPA flight discussion forum under the thread titled Challenge (thread date:11/3/04).  Flight articles must be posted by the end of January, 2005.
  • Contest Period: From Jan 1st 2004 through Dec 31st, 2004

• Prizes: To be awarded by The Sundowner at the February SCPA general membership meeting (attendance not required)
  • 1st place flight $100
  • 2nd place flight $50
  • 3rd place flight $25

• The formula is not as bad as it looks
  • Calculate "d" by taking the day of the year (counting up from Jan 1) and subtracting an offset of 6.  Clamp the calculated difference so that d is not less that zero.  (this equalizes the ends and shifts the surplus toward seasonal lag)
  • Divide "d" by 2 and take the cosine of that number (in degrees) (dividing by 2 scales the cycle to track the seasons)
  • Squaring the cosine causes the curve to fall off more aggressively in the midrange and then curve again the other direction toward rounded apex at the bottom rather than a cusp.  It also forces the result to be positive

Examples

1. a 50 mile flight on Jan 1st
   • d computes to 0
   • x computes to 1
   • 50 times x = 50 points
      
2. 50 mile flight on Dec 21st
   • d computes to 350
   • x computes to 0.9924
   • 50 miles times x = 50 points
      
3. a 50 mile flight on Feb 15th
   • d = 40
   • x computes to 0.8830
   • 50 miles times x = 44 points
      
4. a 80 mile flight on April 1st
   • d = 86
   • x computes to 0.5349
   • 80 miles times x = 43 points
      
5. a 180 mile flight on May 1st
   • d computes to 116
   • x computes to 0.2808
   • 100 times x = 51 points
      
6. a 180 mile flight on Sept 21st
   • d = 259
   • x computes to 0.4046
   • 180 miles times x = 73 points
      
7. a 500 mile flight on July 4th
   • d = 0
   • x computes to 0.0
   • 500 miles times x = Zero points

• Formula Adjustment Notes:
  • We'll see what happens for 2004 and likely run again in 2005.  We may choose to make some adjustments in future years.  This years formula will be fixed once the first flight is posted.
  • We may need to increase the exponent in future years if late spring and early fall flight scores are better than those in the middle of the year.  If we increase the exponent, we will also need to take the square root of the square of the cosine prior to raising the cosine to an uneven power because we rely on the even power to force the result to be positive.  If we raise the exponent, we would likely select something between 2.2 and 3.
  • We can also tune the offset if deemed necessary, but it would result in a bump at the end of the curve.  Another 10 or 15 days of offset would better approximate the seasonal lag, but I didn't like the minor bump on New Years Day.
  • 2004 is a leap year.  In 2005 we will use an offset of 5 rather than 6, so 2005 values will be slightly different (365-360=5).