Anchor Rode Scope and Swing Radius
The bow-height-and-high-tide scope that keeps an anchor set.
Example
You enter
- Water depth at high tide (ft) 15
- Bow-roller height above water (ft) 3
- Desired scope (7 for rope with chain, 5 for all-chain; 3 is a calm-weather lunch stop) 7
- Boat length overall (ft, for swing radius) 30
You get
- True vertical (depth + bow height) 18.0 ft
- Rode (ft) 126
- Swing radius 154.7 ft
Checked against published worked examples from: The Ensign (America's Boating Club, J. Schwab).
Details, formula, and sources
ScopeScope is rode paid out over the VERTICAL rise from the seabed to the bow roller -- depth PLUS bow-roller height, at HIGH tide, not the sounder depth. In 15 ft of water with a 3 ft bow roller the true vertical is 18 ft, so a 7:1 scope needs 126 ft of rode (a 154.7 ft swing radius for a 30 ft boat); anchoring on 15 ft alone pays out only 105 ft = an actual 5.8:1, the quiet error that drags at 2 a.m. All-chain holds at about 5:1 (90 ft rode, a 118.2 ft swing) -- a tighter circle, why it is favored in a crowded anchorage. A planning aid; conditions, bottom type, and skipper judgment govern.
Formula or tablevertical = depth + bow_height (at high tide); rode = scope x vertical; actual_scope = rode / vertical; swing_radius = sqrt(rode^2 - vertical^2) + boat_length.
Source and editionAnchor rode scope and swing-radius relations (seamanship convention -- Chapman Piloting, US Sailing, ABYC ground-tackle references), by name; local conditions, bottom type, and skipper judgment govern.
Free accessThe scope and swing-radius relations are standard seamanship geometry; the depth, tide, and ground-tackle choice come from the chart and the vessel.
What governsEstimate. AHJ and licensed professional govern.
API field nameswater_depth_ft, bow_height_ft, scope_ratio, boat_loa_ft, vertical_ft, rode_ft, swing_radius_ft
- True vertical scope uses depth + bow-roller height at high tide, not the sounder depthseamanship convention
- Ground tackle all-chain holds at ~5:1 or 3:1; rope-and-chain wants 7:1Chapman Piloting / US Sailing
- Swing radius assumes the boat pivots on a set anchor; governs spacing to neighborsgeometry