Who remembers their Trigonometry ? (related to OffCourse Calibration)

swbcaswbca Posts: 867 Crazy Baller
edited July 14 in Technique & Theory
The factory instructions for calibrating the width settings of the OffCourse system use field measurements including a skier observing the results of a series of gun angle adjustments until the angle appears to shoot the marker the correct distance from the boat. They provide a method for the skier to ski a path 37.5 feet from the boat centerline to make this observation.

To confirm those results, I want to start with one single field measurement and then use "Trig" to set the downward angle of the two paint-ball markers.

I have measured the vertical peak of the OffCourse gun trajectories at 4'11" above the lake surface with the boat traveling at 32mph.

Its a compound Trig problem because the Guns are angled down (calibrated by the user) to set the course width and are also aimed forward 30 degrees, requiring a longer flatter trajectory to hit the 37.5 foot course width.

Known Values
1. The trajectory of the left and right barrel intersect in the middle of my boat at 4'11" above the lake surface at 32mph.
2. The guns have a fixed angle to shoot 30 degrees forward of a straight sideways shot - - lengthening the shot's distance to reach the 37.5' course width.

Calculated Value
Disregarding normal projectile drop, what angle from horizontal should the guns be set to hit 37.5 from the boat centerline ? Rounded to the nearest .1 degree.

I believe you start by calculating the distance of the shot with the guns angled forward 30 degrees. Then calculate the guns vertical angle to hit the water at that distance.

Using Trig calculators on the web I couldn't figure out those 2 simple problems.

Reward for best correct answer(s) 5 "likes" on your 5 most recent posts :).

The guns aim forward 30 degrees and should aim down (derived)
Home of the world's first submersible slalom course.

Comments

  • swbcaswbca Posts: 867 Crazy Baller
    edited July 14
    @UWSkier
    There are a lot obsessions possible in slalom skiing or any other competitive sport. The more the merrier. I've learned from experience that Sail Boat Racing, Car Racing and Competitive Skiing success depends on perfecting everything you can with your equipment and your skills, then sailing, driving or skiing as much as you can. Both my drivers are out of town.

    Your question about fuel level applies to any method of maintaining your calibrating OffCourse. I always have less than 10 gallons in the tank and then don't worry about it. Knowing the OffCourse gun angles makes it easy to adjust for the 60lb difference in my driver's weights without stumbling over additional weights that aren't permanently stowed somewhere.
    Home of the world's first submersible slalom course.
  • lundberglundberg Posts: 130 Solid Baller

    first triangle to get the horizontal distance. cos(30 degrees) = 37.5/x x = 43.3 feet
    second triangle to get downward angle. tan(a) = 43.3/4.92 a = 83.52 degrees (angle from vertical)

    angle from horizontal = 90 - 83.5 = 6.5 degrees
    swbcaIntheday
  • swbcaswbca Posts: 867 Crazy Baller
    edited July 14
    @lundberg Thanks a lot; my method using the manufacturer's instructions are a little narrower than that, measured at 7.0 degrees. I am learning that real-time variables, like wind and skier pull tend to swamp the decimal points. Every .5 degree swing changes the marker width by about 2.5 feet.
    Home of the world's first submersible slalom course.
    Intheday
  • DragoDrago Posts: 1,823 Mega Baller
    The boat is blue
    SR SL Judge & Driver (“a driver who is super late on the wheel and is out of sync”)
    liquid dScarletArrowslow
  • swbcaswbca Posts: 867 Crazy Baller
    @Drago save your trolling for twitter
    Home of the world's first submersible slalom course.
    Drago
  • GloersenGloersen Posts: 1,293 Mega Baller
    refraining from comment; it would be too obtuse
    DragoigkyaHucklefin
  • swbcaswbca Posts: 867 Crazy Baller
    @Gloersen "Obtuse" is that the Trig answer you are refraining from offering to answer my original question ? Asking a high school math question on this forum seems to really get people bent out of shape ? Go for it see what kind of insults you can come with.
    Home of the world's first submersible slalom course.
  • GloersenGloersen Posts: 1,293 Mega Baller
    actually quite a trig nerd here afflicted with puns
    dvskier
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