A drill for curved holes is a borehole-cutting tool that follows a non-straight path through rock or coal by using a flexible or articulated drill string and a steerable bit. The Valley Longwall in-seam directional drill rig uses one to push boreholes that arc along a coal seam for hundreds of metres. The mechanism solves the problem of reaching targets a straight hole cannot — gas drainage zones, ore lenses, or obstructions overhead — by controlling the build rate of the curve. Modern in-seam tools routinely hold a planned path within ±1 m over a 1500 m run.
Drill for Curved Holes Interactive Calculator
Vary bent-sub angle, formation build factor, and drilled length to see build rate, turn angle, curve radius, and borehole offset.
Equation Used
The bent-sub angle alpha is converted to an estimated build rate BR using the empirical factor k. The borehole is then treated as a constant-radius circular arc, so drilled length L gives turn angle theta and the offset from the original straight path.
- Soft-coal empirical build factor is constant over the drilled interval.
- Borehole follows a circular arc with constant dogleg severity.
- Bit walk, toolface drift, formation changes, and rod fatigue are not included.
How the Drill for Curved Holes Works
A drill for curved holes works by deliberately biasing the cutting face sideways while the drill string flexes to follow. The two common approaches are a bent sub — a short housing with a 1° to 3° kink between the motor and the bit — and a fully articulated head with a hinge driven by mud pressure or an embedded actuator. Either way the bit cuts slightly off the string axis, and over each metre of advance the hole curves by a known build rate, expressed in degrees per 30 m (or degrees per 100 ft if you are reading American logs). The drill string itself uses non-magnetic drill collars and thin-walled rods that bend elastically without yielding — typical in-seam rods take a 60 m radius of curvature without permanent deformation.
The reason for this design is geometry. You cannot push a rigid pipe around a corner. The flexible drill string, the steerable bit, and the downhole motor work together so the bit rotates without the whole string rotating — that is the point of the mud motor or PDM (positive displacement motor). With the string held still and oriented, the kink in the bent sub points the bit in the desired direction and the hole curves toward that point. Roll the string 180° and the curve reverses. Operators monitor toolface angle with an MWD (measurement while drilling) probe — usually a magnetometer-and-accelerometer pack reading inclination and azimuth every few seconds.
When tolerances drift the hole misbehaves fast. If the bent sub angle is too aggressive — say 3° in a formation that needed 1.5° — the dogleg severity exceeds what the drill rods can elastically follow and you get rod fatigue cracks, usually at the box-end thread root, within 200 m to 400 m of run. If the toolface drifts because the MWD probe loses sync, the hole spirals and the planned target is missed by tens of metres at depth. And if the build rate is set too low for the geology, the hole runs out of the seam and into rock — common in coal seam methane drilling when the seam dips faster than the build rate can track.
Key Components
- Steerable Bit: A polycrystalline diamond compact (PDC) or tricone bit sized 96 mm to 152 mm for in-seam work. The bit cuts slightly off-axis when the bent sub is held stationary, generating the curve. Gauge protection on the bit shoulder must be within 0.5 mm tolerance — worn gauge causes the hole to spiral.
- Bent Sub: A short housing with a built-in 1° to 3° angular offset between the motor output and the bit. The angle is fixed at manufacture and selected to match the planned build rate. A 1.5° bent sub typically gives a build rate of 6°/30 m in soft coal.
- Positive Displacement Motor (PDM): A Moineau-style mud motor that converts drilling fluid pressure into bit rotation while the drill string itself stays oriented. Output is typically 100 to 300 RPM at 5 to 25 kN·m torque depending on stator lobe count.
- Flexible Drill Rods: Thin-walled non-magnetic rods, often 73 mm OD with 9 mm wall, that bend elastically through the planned curve. Yield strength must exceed the bending stress at the minimum radius — for a 60 m radius and 73 mm rod, that means 80 ksi grade minimum.
- MWD Probe: Measurement-while-drilling instrument package. Reads inclination ±0.1°, azimuth ±0.5°, and toolface ±1°. Pulses data up the mud column to surface every 10 to 30 seconds. Without it, steering is blind.
- Surface Steering Control: Driller's console showing real-time toolface, hole inclination, and projected target intercept. The driller rotates the entire string in 5° to 15° increments to set toolface and adjust the curve direction.
Where the Drill for Curved Holes Is Used
Curved-hole drilling shows up wherever a straight hole cannot reach the target or where one surface setup needs to cover multiple downhole positions. The technique started in oil and gas directional drilling in the 1930s and has since spread across mining, civil works, and utility installation. The reasons people choose it over straight drilling come down to access, surface footprint, and target geometry — you would be amazed how often a single curved hole replaces three or four vertical ones, cutting setup time and surface disturbance dramatically.
- Coal Mining: In-seam directional drilling for methane drainage at Anglo American's Grosvenor and Moranbah North longwall mines in Queensland, where holes follow the coal seam for 1000 m to 1500 m ahead of the longwall face.
- Oil & Gas: Horizontal wellbores in the Permian Basin drilled with Schlumberger PowerDrive rotary steerable systems, building from vertical to horizontal over a 150 m to 300 m radius.
- Hard Rock Mining: Boart Longyear's directional core drilling tools used for ore body delineation at deep base-metal projects, where a single mother hole branches into multiple daughter holes off a wedge.
- Civil Tunnelling: Horizontal directional drilling (HDD) for utility crossings under rivers and highways — a Vermeer D550 rig regularly arcs a 600 mm pilot hole 1200 m under the Mississippi for fibre-optic installs.
- Geothermal: Directional geothermal wells at the Eden Project deep geothermal site in Cornwall, where curved holes target specific fracture zones in granite at 4500 m depth.
- Underground Construction: Curved cable bolting holes drilled with Atlas Copco Boomer rigs in deep metal mines, allowing a single drill setup to install bolts across a wide stope back.
The Formula Behind the Drill for Curved Holes
The most useful formula in curved-hole drilling is the relationship between build rate, radius of curvature, and the bend angle of the bent sub. At the low end of typical build rates — 2°/30 m — the hole curves gently, the radius is large (around 860 m), and rod fatigue is minimal but you need a long run to reach a deep horizontal target. At the nominal 6°/30 m, the radius drops to about 285 m and the rods see manageable bending stress. Push to the high end at 15°/30 m and the radius collapses to about 115 m — a tight build that gets you horizontal fast but stresses the rods near their fatigue limit and risks key-seating. The sweet spot for in-seam coal drilling sits at 4°/30 m to 8°/30 m.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| R | Radius of curvature of the hole | m | ft |
| L | Course length over which build is measured | m (typically 30) | ft (typically 100) |
| BR | Build rate (degrees of curve per course length) | °/30 m | °/100 ft |
| π | Pi, geometric constant | dimensionless | dimensionless |
Worked Example: Drill for Curved Holes in an in-seam methane drainage hole
A bituminous coal operation in West Virginia is planning an in-seam horizontal hole for pre-mine methane drainage ahead of a longwall panel. The plan calls for a 1200 m horizontal reach inside a 2.4 m thick seam, starting from a cross-cut where the tool is already nearly horizontal but needs a small 12° course correction to align with the seam dip. The crew is choosing between a 1° bent sub and a 2° bent sub, and they need to know the radius of curvature and where rod fatigue becomes a concern.
Given
- L = 30 m
- BRnom = 6 °/30 m
- BRlow = 2 °/30 m
- BRhigh = 15 °/30 m
- Rod OD = 73 mm
Solution
Step 1 — at the nominal 6°/30 m build rate (typical for a 1.5° bent sub in soft coal), compute the radius of curvature:
That radius is comfortable for 73 mm in-seam rods. Bending stress sits around 35% of yield, well below the fatigue threshold, and the 12° correction takes about 60 m of hole — barely a dent in the 1200 m total reach.
Step 2 — at the low end of the typical operating range, 2°/30 m (a 1° bent sub running gently):
The hole curves so gradually you need 180 m of drilling to complete the 12° correction. That eats 15% of the planned reach and you may run out of seam before the build is complete — a real risk if the seam dips at more than 1° per 30 m.
Step 3 — at the high end, 15°/30 m (a 3° bent sub pushed hard):
The 12° correction now finishes in 24 m of hole — fast and tight. But at a 115 m radius, 73 mm rods see bending stress around 85% of yield. Run them through that curve more than 30 times (which happens fast in a back-and-forth tripping cycle) and you will see fatigue cracks at the box-end thread root. This is where key-seating starts too — the rotating string wears a slot in the high side of the dogleg, and recovery gets ugly.
Result
The nominal radius of curvature is 286 m at a 6°/30 m build rate, completing the 12° correction in 60 m of hole. Practically, that means the driller sees the toolface settle quickly, MWD inclination tracks within 0.2° of plan, and the bit stays in the seam without scraping the roof or floor. Compare that to the 860 m radius at the low-end build rate (slow and hungry for hole length) and the 115 m radius at the high-end (fast but rod-fatigue territory) and the 6°/30 m sweet spot is obvious. If your measured build comes in 30% below the predicted rate, the most common causes are: (1) a worn bent sub where the elastomer stator has lost its 1.5° set angle, (2) excessive weight on bit pushing the assembly straighter than the bent sub wants to point it, or (3) a harder coal band forcing the bit to wander toward the path of least resistance instead of holding the planned toolface.
Choosing the Drill for Curved Holes: Pros and Cons
Curved-hole drilling is one option among several when you need to reach a non-vertical target. The realistic alternatives are a straight hole drilled from a different setup location, or a multi-hole pattern of straight holes covering the same target volume. Each has a clear engineering profile, and the choice depends on surface access, target geometry, and budget.
| Property | Drill for Curved Holes | Multiple Straight Holes | Single Long Straight Hole |
|---|---|---|---|
| Reach to off-axis target (m) | Up to 1500 m horizontal from one setup | Limited to direct line-of-sight from each setup | Limited to drill-rod length, no off-axis reach |
| Build rate / steering control | 2°/30 m to 15°/30 m, MWD-controlled | None — fixed by setup angle | None |
| Positional accuracy at 1000 m depth | ±1 m to ±3 m with MWD | ±0.5 m per hole, but multiple setups multiply error | ±2 m to ±5 m, drift accumulates |
| Surface footprint | Single pad, minimal disturbance | Multiple pads, large disturbance | Single pad |
| Cost per metre (USD) | $180 to $450 (in-seam coal) | $80 to $150 per straight hole, but you drill more | $80 to $150 |
| Rod fatigue / failure mode | Bending fatigue at box-end thread, key-seating | Minimal — straight loading only | Buckling on long horizontal runs |
| Setup complexity | High — MWD, mud motor, steering crew | Low — re-rig and drill | Low to medium |
| Best application fit | In-seam methane, ore lenses, under-river utility crossings | Shallow exploration, multiple parallel targets | Vertical exploration, single deep target |
Frequently Asked Questions About Drill for Curved Holes
This is almost always a weight-on-bit (WOB) issue compounded by friction. As the hole gets longer, more drill string lies in the curve and on the low side of the hole, and the friction on the string eats the WOB you're applying at surface. The bit ends up running with less effective WOB than the bent sub needs to bite directionally, so the hole straightens out.
Check the differential pressure across your mud motor — if it has dropped 20% to 30% from early in the run while your surface WOB is unchanged, friction is stealing the load. The fix is usually a friction reducer in the mud, or rotating the entire string in short bursts to break static friction without losing toolface.
Bent sub angle and build rate are not 1:1 — geology mediates the relationship. A 1.5° sub typically gives 5°/30 m to 7°/30 m in soft coal and 3°/30 m to 5°/30 m in harder mudstone. A 2° sub gives 7°/30 m to 10°/30 m in soft coal but can be excessive in hard rock, where it overloads the rods without hitting the planned build because the bit can't cut sideways fast enough.
For a planned 8°/30 m in soft coal, the 2° sub is the right call. In harder formations, go with the 1.5° sub and accept that you will need a longer run to complete your build — pushing a 2° sub through hard rock is how you snap rods at the bent sub box thread.
Spiralling usually comes from gauge wear on the bit, not from steering input. When the gauge protection on the bit shoulder wears unevenly — even by 1 mm to 2 mm — the bit develops a preferred lateral cutting direction that fights your toolface command. The MWD reads the toolface you set, but the bit is no longer cutting in that direction.
Pull the bit and inspect the gauge. If you see asymmetric wear on the shoulder pads, that's the culprit. The other cause is a bent rod just above the motor — sometimes a previous trip put a slight permanent set in the first or second rod, and it acts like a second, uncontrolled bent sub.
For utility installation under 200 m, a dedicated horizontal directional drilling (HDD) rig like a Vermeer D24 or D40 is the right tool — they're built for soft ground, use bentonite mud, and the entire workflow is optimised for pipe pullback. Adapting a mining-style in-seam rig to that work is mechanically possible but operationally wasteful. The mining rig is built for hard rock cutting at low penetration rates and high mud pressures, which is mismatched to soft soil.
The exception is rocky river crossings or pilot holes through bedrock where the soft-ground HDD rig stalls. There, a hard-rock directional rig with a PDC bit and mud motor pays off.
Azimuth drift on a tangent section is almost always magnetic interference. MWD probes use magnetometers referenced to magnetic north, and any nearby ferrous mass throws the reading off. The first place to check is your non-magnetic drill collar count — you need enough non-mag spacing above and below the probe (typically 9 m above and 5 m below) to isolate it from the steel BHA components.
The second cause is local geology. Magnetite-bearing formations or nearby cased holes from earlier drilling can pull the magnetometer reading by several degrees. If you're drilling near old workings, run a gyro survey instead of an MWD-only survey at key checkpoints to verify true azimuth.
Published rod fatigue numbers assume the rod sees the rated bending cycles at the rated radius. In practice, two things shorten life. First, the actual hole curvature is not uniform — micro-doglegs from steering corrections produce localised radii much tighter than your average build rate, and fatigue scales roughly with the inverse cube of radius, so a 30% tighter local radius cuts life by more than half.
Second, rod-on-rock contact in the dogleg wears the OD asymmetrically, and once the wall thins by 10%, bending stress at that section jumps 25% to 30%. Pull rods at the recommended interval and inspect for OD wear with a calliper at multiple points along each rod, not just the ends.
References & Further Reading
- Wikipedia contributors. Directional drilling. Wikipedia
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
