Distance from Anchor = Rhode Length

[ost]

Well within 3.2% that is.

So taking the Pythagorean Theorem and right triangle stuff...

a^2 + b^2 = c^2

a = Keel Depth + Draft + Height of Bow Roller + Tide
b = Distance from Anchor
c = Rhode Length

We want c to equal a*scope (such as 4:1, 5:1, 10:1...) so:

c=scope*a

Going back to the original equation and fill in with the data from thus far:

(Keel Depth + Draft + Height of Bow Roller + Tide)^2 + b^2 = (scope*(Keel Depth + Draft + Height of Bow Roller + Tide))^2

Solving for b:

b = [(scope*(Keel Depth + Draft + Height of Bow Roller + Tide))^2 - (Keel Depth + Draft + Height of Bow Roller + Tide)^2]^1/2

blah blah blah so what does all this mean?

For my boat:
Draft = 5ft
Bow Roller Height = 5 ft.
Tide = 3ft

A Keel Depth of 10 feet and a scope of 5:1 would yield a distance from the anchor (b) equal to 113ft.

If you do the traditional calculation of scope*(Keel Depth + Draft + Height of Bow Roller + Tide) you end up with 115ft.

A difference of 2%. The greater the scope the less error.

Scope - Error
4:1 3.2%
5:1 2.0%
7:1 1.0%
8:1 0.8%
10:1 0.5%

The moral of the story is if you place a waypoint (or MOB button) on your chartplotter when you drop anchor, the distance from your boat to that waypoint as you are laying out rhode is equal to the length of the rhode (or close enough). Or if the distance from the waypoint is greater than the rhode you are dragging or have drug.

Of course, if your anchor does not set immediately (like my CQR...) it would do you well to have your rhode marked.

This also does not take into effect any catenary. Using this method in a low wind/current situation, would have you playing out more rhode than your distance to anchor (waypoint) would suggest. However, it could prove to be a quick check when things pipe up.

Standing by to be out mathed.