Fulcrum on a Circle Dock: Calculate Distance from Bulkhead

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SUMMARY

The discussion focuses on calculating the horizontal distance a dock retreats towards a bulkhead as it rises or falls with the tide. The dock, measuring 30 feet in length, swings up and down by +/- 7 feet. The key formula derived is based on the cosine function, where the horizontal distance at an angle x from the horizontal plane (HP) is given by the equation: distance = 1 * cos(x). At 45 degrees, the dock's horizontal distance is reduced to 1/sqrt(2) of its maximum extension. This calculation is essential for determining the size of slots needed for lateral stabilization posts on the dock.

PREREQUISITES
  • Understanding of basic trigonometry, specifically the cosine function.
  • Familiarity with the concept of angles and their measurement in degrees.
  • Knowledge of dock mechanics and how they interact with tidal movements.
  • Ability to apply mathematical formulas to real-world scenarios.
NEXT STEPS
  • Research the application of trigonometric functions in engineering design.
  • Learn about the principles of buoyancy and stability in floating structures.
  • Explore the use of CAD software for designing dock components and slots.
  • Investigate the effects of tidal forces on marine structures and their design considerations.
USEFUL FOR

Marine engineers, dock builders, and anyone involved in the design and maintenance of floating structures will benefit from this discussion, particularly those looking to optimize dock stability and functionality in tidal environments.

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I have a dock. It is mounted to my bulkhead and "swings" up and down with the tide (+/- 7ft). The total length of the dock is 30ft.

Intro:

When the dock is at it's maximum "extension" out into the water I know, intuitively",that, along a horizontal plane (HP), the dock at it's furthest length edge wise (LEW) and is furthest from the bulkead upon which it is attached...HORIZONTALLY.

It SEEMS, intuitively, that if the dock rises or falls 45 degrees above or below a horizontal plane (HP) that at 45 degrees (theoretical) that the above mentioned LEW is now 1/2 the distance that it was at HP.

Further, at 90 degrees, (theoretical...it is standing on end) if a bob weight were to be dropped from the LEW it would point to it's attachment point and bulkhead.

What formula I need:

The formula I need is one that gives me for ever foot the dock ascends or descends past HP what is the distance that it retreats back toward the bulkhead? (Degrees of ascent/descent do no good as I don't have a protractor).

I need this because the dock free floats and on one side I want to put in post that stabilize the float laterally. I am trying to figure out how big of slots I will need on the side of the float so that as the dock rides up and down with the tide the slots will allow the posts freedom of movement within the slots along the HP.

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If at maximum extension the end of the dock is at distance 1 (measured horizontally), at 45 degrees the dock will be at distance 1/sqrt(2), measured horizontally.

If x is the angle the dock makes with the horizontal, the formula for horizontal distance is cosine(x)
 

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