A Great Curve Delineator is a draughting device that traces a circular arc of very large radius without needing access to the actual centre point. Naval architects and shipwrights rely on it for lofting hull stations and deck camber where the arc centre would sit metres off the drawing board. It works by sliding two straight rails through two fixed pins while a pencil at the rail intersection traces the arc. The result is a fair, geometrically true curve where a beam compass would be impossible to swing.
Great Curve Delineator Interactive Calculator
Vary the pin chord, locked angle, and angle drift to see the traced arc radius, sagitta, and apex error.
Equation Used
The delineator uses the inscribed angle relationship: for pin spacing L and locked angle theta, the traced circular arc has radius R = L / (2 sin(theta)). The apex rise is the sagitta of that same circle, and the drift result estimates how much the arc apex moves if the set angle increases by the entered error.
- Pins define an exact straight chord.
- Rails remain rigid and in continuous contact with both pins.
- Theta is entered in degrees and converted to radians for the sine calculation.
- Rail thickness, pencil offset, and pin clearance are ignored.
Inside the Great Curve Delineator
The principle behind the Great Curve Delineator is the inscribed angle theorem — any point on a circular arc views the arc's chord at the same angle. Lock that angle into a rigid frame, slide the frame around two pins set at the chord endpoints, and the vertex of the angle traces a perfect arc. You never need the centre. That's the whole trick, and it's why pattern lofts have used these tools for two centuries to draw arcs with radii of 5, 10, even 30 metres on a flat floor.
The practical build is two straight rails (sometimes called arms or blades) joined rigidly at a fixed angle. Two pins go into the board at the chord endpoints — these are the arc's two known points. The third known point sits at the vertex where you start the pencil. As you slide the frame, each rail must stay in continuous contact with its pin. If a rail lifts off, the angle constraint breaks and the curve goes off-fair instantly. This is why the rails on a quality delineator have a hardened bearing edge and the pins are precision-ground — typically 6 mm dowel pins with a tolerance better than ±0.02 mm on diameter.
What goes wrong? Three things, mostly. If the included angle between the rails drifts even half a degree, the radius of the traced arc changes by a noticeable amount over a long sweep — on a 10 m radius arc that's a 25 mm error at the apex. If the pins are loose in their holes, the chord length wanders and you get a non-fair curve that looks right at the ends but bulges in the middle. And if the rail edges develop wear notches from years of pin contact, the frame catches and skips, leaving visible kinks in the pencil line. A naval architect inspecting a lofted station for fairness will spot a 0.5 mm kink across a 4 m sweep.
Key Components
- Rigid Angle Frame: Two straight rails fixed at a precise included angle, typically between 30° and 150° depending on the arc radius being drawn. The angle must hold to within ±0.05° across the working temperature range, which usually means a steel or aluminium frame rather than wood for arcs above 5 m radius.
- Chord Pins: Two precision-ground dowel pins set into the drawing board at the chord endpoints. Standard sizes are 6 mm or 8 mm hardened steel, with a board-hole fit of H7/g6 so the pin sits without play but can be removed cleanly. Pin spacing defines the chord and therefore the arc.
- Bearing Edges: The inner edges of the two rails that ride against the pins. These must be straight to within 0.05 mm over their full length and hardened to resist wear notches. On heavily-used shop tools, these edges get re-ground every few thousand sweeps.
- Tracing Point: A pencil socket, scribe, or cutter mounted at the vertex where the two rails meet. For lofting work this is usually a 0.5 mm pencil lead held in a sprung socket so it tracks the paper without scoring it. Alignment to the angle vertex is critical — an offset of 1 mm at the tip translates to roughly 1 mm error along the whole arc.
- Counterweight or Handle: A grip positioned to keep the operator's hand pressure evenly distributed across both rails. If you press harder on one rail than the other, that rail bears harder against its pin and the other can briefly lift off, breaking the angle constraint.
Real-World Applications of the Great Curve Delineator
Anywhere a draftsman needs a long-radius fair curve and the centre point is inaccessible, the Great Curve Delineator earns its place. It's particularly common in trades where the arc radius runs into multiple metres — far beyond what any beam compass can swing. The tool also wins where the arc must pass through three known points and the centre is simply not interesting to the worker, only the curve itself.
- Naval Architecture: Lofting deck camber and sheer lines on the mould loft floor at yards like Brodosplit in Croatia, where deck arcs have radii of 15-40 m and the centre point would sit beyond the loft wall.
- Bridge Engineering: Drawing arched truss chords for restoration work on structures like the Iron Bridge at Coalbrookdale, where a full-scale template needs a 23 m radius arc on a 6 m chord.
- Architectural Drafting: Setting out segmental window heads in heritage restoration — Georgian shopfronts often need arcs with radii of 3-8 m drawn on a 1:1 plywood pattern.
- Furniture Pattern Making: Marking long, shallow curves on table aprons and chair rails at workshops like Robinson House Studio, where a 4 m radius pattern has to fit on a 2.4 m bench.
- Stone Masonry: Templating segmental arches for stone-cut voussoirs in cathedral repair work — York Minster's stoneyard uses the same three-point geometry to set out arches matching original 13th-century radii.
- Boatbuilding: Drawing wineglass transom curves and toe-rail sweeps on traditional builds, where a 12 m radius is common and the loft floor is too small to swing a trammel.
The Formula Behind the Great Curve Delineator
The radius of the arc traced by a Great Curve Delineator depends on the chord length set by the two pins and the included angle locked into the frame. Knowing this relationship matters because a designer typically wants a specific radius, and they need to set up the chord and angle to deliver it. At the low end of the working range — small included angles approaching 30° — the tool draws very large radii from a short chord, but small errors in angle blow up into large radius errors. At the high end — angles approaching 150° — the tool draws shallow arcs with tight radii, the geometry is forgiving, but the frame has to be physically large to span the chord. The sweet spot for most lofting work sits between 60° and 120°, where errors stay bounded and frame size stays manageable.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| R | Radius of the arc traced by the delineator | metres (m) | feet (ft) |
| L | Chord length — distance between the two fixed pins | metres (m) | feet (ft) |
| θ | Inscribed angle — supplement of the included rail angle (θ = 180° − rail angle) | degrees (°) | degrees (°) |
Worked Example: Great Curve Delineator in a heritage timber-framed barn restoration
A timber-frame restoration crew in the Cotswolds is drawing a full-scale plywood template for the curved tie-beam of an 18th-century cart barn. The original beam was an arc with a 1.8 m chord and a 50 mm rise at the apex. They need to reproduce that arc on a 2.4 × 1.2 m plywood sheet using a Great Curve Delineator with adjustable rails. They want to know the implied radius, set the rail angle, and understand what happens if their angle setting drifts.
Given
- L = 1.8 m
- h (rise) = 0.050 m
- θ (target inscribed angle) = to be calculated °
Solution
Step 1 — calculate the radius from the chord and rise using the standard sagitta relationship:
Step 2 — at the nominal radius, solve the delineator formula for the inscribed angle θ:
The rail included angle is therefore 180° − 6.36° = 173.64°. That's a very shallow frame — the two rails are nearly parallel, which is exactly what you'd expect for an 8 m radius drawn from a 1.8 m chord.
Step 3 — at the low end of a likely setup error, suppose the crew sets the rail angle 0.5° too tight, giving θ = 6.86°:
That's a radius error of nearly 600 mm — the apex rise climbs from 50 mm to about 54 mm across the 1.8 m span. On a heritage match, that's visibly wrong.
Step 4 — at the high end, if the angle drifts 0.5° the other way to θ = 5.86°:
Now the apex sits about 46 mm — too shallow. The lesson: at shallow inscribed angles, the radius is wildly sensitive to angle error. Half a degree changes the radius by ±8% on this geometry.
Result
The implied radius is 8. 125 m, set with a rail included angle of 173.64°. The tie-beam will trace as a barely-perceptible curve — a passenger walking under it would not register it as curved, but the eye reads it as straight-and-true rather than sagging. Across the typical 0.5° angle-setting tolerance the radius wanders from about 7.54 m to 8.81 m, which moves the apex rise by ±4 mm — visible on a heritage match. If the crew measures the apex of their finished template and finds it off by more than 2 mm, the likely causes are: (1) the rail-fixing screw slipping during sweep, letting the included angle open progressively as the pencil moves, (2) one pin sitting in an oversized hole and walking sideways under rail pressure, or (3) the pencil socket worn off-axis from the rail vertex by more than 0.5 mm, which biases the entire arc toward one chord endpoint.
Great Curve Delineator vs Alternatives
The Great Curve Delineator earns its keep on long-radius arcs, but it isn't always the right call. For short radii a beam compass is faster. For irregular curves a spline beats it. Here's how the three stack up on the dimensions a draftsman actually cares about.
| Property | Great Curve Delineator | Beam Compass / Trammel | Spline & Ducks |
|---|---|---|---|
| Practical radius range | 1 m to 50+ m | 0.1 m to ~3 m (limited by beam length) | Any — but no true circular arc |
| Geometric accuracy on a fair circular arc | ±0.5-1 mm over a 4 m sweep with a quality frame | ±0.2 mm — best in class for true circles | Not a circular arc — fair curve only |
| Setup time | 5-10 min (set pins, lock angle) | 1-2 min (set beam length) | 10-20 min (place ducks, adjust) |
| Need for accessible centre point | No — three points only | Yes — centre must be on the board | No |
| Tool cost (typical 2024 UK shop) | £80-300 for a quality steel frame | £25-90 | £40-150 for a set with ducks |
| Best application fit | Long-radius arcs in lofting, naval, heritage work | Small to mid-radius circles where centre is accessible | Free-form fair curves like hull buttocks |
| Skill required | Moderate — even rail pressure matters | Low | High — eye for fairness |
Frequently Asked Questions About Great Curve Delineator
This is almost always uneven hand pressure on the two rails. If you grip closer to one rail, that rail bears harder against its pin and the opposite rail momentarily lifts off — when it lifts, the angle constraint breaks and the pencil tracks toward the loaded side. The arc looks fair on the loaded half and slightly flattened on the unloaded half.
Fix it by gripping at the vertex itself, not on either rail, and pulling the frame rather than pushing it. A pull keeps both rails loaded against their pins by geometry. If asymmetry persists, check whether one pin hole is slightly oversized — even 0.1 mm of pin slop on one side biases the whole arc.
You don't need to calculate the radius at all. Set the two outer points as the chord pins, then position the frame so the pencil sits exactly on the third (middle) point with both rails touching the pins. Lock the rail angle right there. By the inscribed angle theorem, that locked angle will reproduce the same arc through all three points as you sweep.
This is actually the original use case — three-point arc generation without ever computing a radius. Naval architects use it constantly because their stations are defined by offsets at three or more waterlines, not by a centre and radius.
Honestly, no — not at hand-set precision. At those very shallow inscribed angles (below about 5°), a 0.1° error in the rail angle shifts the radius by 2-3%. On a 25 m arc that's hundreds of millimetres of radius drift, which means visible apex error.
For arcs that long, lofters traditionally switch methods. Either use the ordinate method — calculate offsets from a chord at known stations and connect them with a spline — or build a one-off fixed-angle frame with the angle machined to ±0.02°. The Great Curve Delineator's practical radius ceiling on hand-set work is around 15-20 m for ±2 mm fairness.
Three usual suspects, in order of frequency. First, check whether the rail-locking thumbscrew is actually holding — if it slips even slightly during the sweep, the angle opens and the arc flattens, which produces exactly that shallow-apex symptom. Tighten and re-test on scrap.
Second, check the pencil-tip wear. A pencil that started sharp and rounded off mid-sweep traces a slightly smaller arc on the second half, pulling the apex down. Use a fixed-diameter scribe or a clutch pencil with hardened lead for long sweeps.
Third, verify the chord measurement. A pin spacing 5 mm shorter than nominal on a 2 m chord shifts the apex by roughly 2-3 mm at typical radii — easy to overlook if you eyeballed the pin holes from a tape rather than a stop block.
You can, but the failure mode shifts. On a horizontal board, gravity holds the rails flat against the pins. On a vertical surface, gravity pulls the frame downward, which loads the lower rail against its pin and unloads the upper rail. The upper rail then tends to drift off its pin under any sideways hand movement, breaking the angle constraint.
If you must work vertical, add a light spring or bungee between the frame and a third point above the chord to keep both rails preloaded against their pins. Stonemasons templating segmental arches in situ use this trick routinely.
Use the delineator when the station genuinely is a circular arc — common on traditional working-boat hulls, deck cambers, and many transom shapes. The delineator gives you a geometrically exact circle that any other lofter can reproduce later from the same three points.
Use a spline when the curve is non-circular — buttock lines, diagonals, modern yacht stations. A spline gives a fair curve with continuous curvature, which a circular arc cannot. The decision really is: is this geometry a circle or not? If yes, delineator. If no, spline. Mixing the two on the same hull is normal practice.
References & Further Reading
- Wikipedia contributors. Inscribed angle theorem. Wikipedia
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