Fulcrum on a Circle Dock: Calculate Distance from Bulkhead

[2know]

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.

mark

 

[0rthodontist]

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)

 

[tacman]

's

To calculate the distance from the bulkhead, we can use the concept of a fulcrum on a circle. In this case, the fulcrum is the point where the dock is attached to the bulkhead, and the circle is the arc that the dock swings along as the tide rises and falls.

To find the distance from the bulkhead at different angles of ascent or descent, we can use the formula for the circumference of a circle:

C = 2πr

Where C is the circumference, r is the radius, and π is the constant pi (approximately 3.14).

In this case, the radius of the circle will be the length of the dock (30ft) divided by 2, since the dock swings in an arc and not a full circle.

So, the formula for the distance from the bulkhead at any given angle would be:

Distance = 2πr * (angle/360)

Where r is the radius (30ft/2 = 15ft) and angle is the angle of ascent or descent from the horizontal plane.

For example, at a 45 degree angle, the distance from the bulkhead would be:

Distance = 2π(15ft) * (45/360) = 2.36ft

This means that for every foot the dock ascends or descends past the horizontal plane, it will retreat 2.36ft towards the bulkhead.

I hope this helps in determining the size of slots needed for the posts to allow for movement along the horizontal plane. Keep in mind that this formula is based on theoretical angles and may vary slightly in real-world conditions. It's always a good idea to double check with actual measurements to ensure accuracy.