Horizontal directional drilling
Laying out a bore path profile
A depth profile is not a depth. It is the vertical gap between two curves — the ground, which is uneven, and the bore, which is made of arcs and tangents. Getting it right means fixing the geometry of the entry and exit curves first, then checking that gap against every clearance rule that applies along the line.
The entry curve sets almost everything
A bore leaves the surface at an angle, curves to horizontal, runs at depth, and curves back up. The entry curve is a circular arc, and three exact relations describe it. With R the bend radius and γ the entry angle in radians:
Turn that around: to reach depth H at entry angle γ, the radius must be R = H / (1 − cos γ).
The pullback example in the PPI Handbook of PE Pipe, Chapter 12, uses the small-angle form of the same geometry:
How good is the approximation? Against the exact relations, 2H/γ² understates the radius the curve really needs and 2H/γ overstates the horizontal run, each by 0.25 per cent at a 10° entry and 1.0 per cent at 20°. Fine for planning, and both errors fall on the safe side: the radius you check against the rod limit is slightly tighter than the real one, and the ground you allow for the curve is slightly longer.
What the small-angle form makes obvious is the cost of depth. Rearranged, the radius needed is 2/γ² per foot of depth and the horizontal run is 2/γ per foot of depth:
| Entry angle | Radius per ft of depth | Horizontal run per ft of depth |
|---|---|---|
| 10° | 65.7 ft | 11.5 ft |
| 15° | 29.2 ft | 7.6 ft |
| 20° | 16.4 ft | 5.7 ft |
A steeper entry buys depth in far less ground but demands a far tighter radius — and radius is the thing that is already constrained by the drill rod and the product pipe. That is the whole tension in profile design. In the PPI example, 35 ft of depth at a 10° entry needs a 2,298 ft radius and 401 ft of horizontal run before the path is level; the 15° exit needs 1,021 ft and 267 ft. Of an 870 ft crossing, 668 ft — 77 per cent — is curve, and only 202 ft is flat at depth. (PPI names its angles from the product pipe’s side: its 10° “entry” is where the pipe goes in, which is the end where the drill came out.)
Published angles sit in a narrow band. The PPI river crossing uses 10° and 15°. The PRCI steel example uses 20° and 14° with 1,000 ft and 1,200 ft radii. Owners write limits into their specifications too: the City of Ocoee, Florida, for example, caps the entry angle at 15° and sets the exit angle at 6° to 12° to make the pullback easier.
Work out the curves
Enter the depth and the two angles. The calculator gives each curve’s radius, horizontal run and drilled length from the exact relations, the small-angle figures beside them, and what is left of the crossing for the flat run at depth. Enter the governing minimum bend radius and it checks both curves against it.
Depth is measured from a surface that moves
Everything above is measured from the entry point. Cover is not. Cover is the gap between the top of the pipe and the ground directly above it, and the ground has its own profile. Draw a bore against a level datum and the plan will show cover the job does not have, at whatever station the ground happens to rise.
So the profile needs two elevation series on the same horizontal chainage — ground surface and bore centreline — and the check is done station by station:
Note the last term. The borehole is reamed to 1.2 to 1.5 times the carrier pipe diameter (PPI Chapter 12), so the void that has to clear everything above it is larger than the pipe being installed. A 24 in pipe is a 29 to 36 in hole. Measuring to the top of the hole rather than the top of the pipe is the conservative choice, because the pipe can sit anywhere in the hole — a buoyant one rides the crown.
Where the ground elevation comes from
In the United States the public source is the USGS 3D Elevation Program. Its lidar quality levels set point density and accuracy, and most 3DEP lidar collected since 2014 meets quality level 2 (QL2): at least 2 pulses per square metre, nominal pulse spacing no worse than 0.71 m, vertical accuracy of 10 cm RMSEz, and a 1 m digital elevation model. QL1 and QL0 collect at least 8 points per square metre at 0.35 m spacing and produce a 0.5 m model; QL0 tightens vertical accuracy to 5 cm.
RMSEz is root-mean-square error in elevation — the typical vertical disagreement between the model and surveyed check points. Ten centimetres is about 4 in. Set that against a 12 in minimum clearance and the surface model consumes roughly a third of the margin before drilling starts. That is a real number, but not the dangerous one: the dangerous one is the depth of what is already buried, which is why the rule below is to expose it rather than model it.
The model must also be the bare-earth surface, not the first return. First return is whatever the pulse hit first — canopy, rooftops, vehicles. Under trees the two surfaces are nowhere near each other. The 3DEP elevation models are the bare-earth surface derived from the lidar point cloud.
The constraints that set the depth
Cover over the installed pipe
For gas pipelines, 49 CFR 192.327 sets minimum cover between the top of the pipe and the surface. The first three rows are paragraph (a), which covers transmission lines; the navigable-water row is paragraph (e), which applies to all gas pipe, mains included, and is measured to the underwater natural bottom:
| Location | Normal soil | Consolidated rock |
|---|---|---|
| Class 1 | 30 in | 18 in |
| Class 2, 3 and 4 | 36 in | 24 in |
| Drainage ditches of public roads, railroad crossings | 36 in | 24 in |
| Navigable river, stream or harbour (below the natural bottom) | 48 in | 24 in |
Elsewhere, gas mains need at least 24 in under paragraph (b) of the same section. For hazardous liquid pipelines, 49 CFR 195.248 requires 36 in in industrial, commercial and residential areas and in drainage ditches at public roads and railroads, and 48 in where the line crosses an inland body of water at least 100 ft wide.
Under water, the datum is the bottom the river will have, not the bottom it has. Scour during a flood cuts the bed down and then refills it with silt, so a survey taken in normal flow reads the deposited surface and not the scoured one. The PPI HDD chapter notes that river-crossing pipes are typically installed at least 20 ft below the expected future river bottom, considering scour — far below any regulatory minimum.
Clearance from what is already there
The INGAA Foundation’s Natural Gas Pipeline Crossing Guidelines define the crossing clearance distance as the vertical separation between the new line and the existing facility, and set the recommended value at 24 in with a minimum of 12 in. The excavation tolerance zone — where soil may only be removed by hand digging, potholing or vacuum excavation — is 24 in from the existing pipeline in those guidelines, against the 18 in tolerance zone of CGA Best Practice 5-19.
The Trenchless Best Practices for Damage Prevention published by the Gas Technology Institute turn that into a rule about what must be dug up before drilling starts. Positively identify, by potholing, every crossed utility expected to be:
- above and within 5 ft of the proposed vertical alignment, or
- below and within 3 ft of it.
Running parallel to an existing utility has its own table: within 3 ft, expose the utility at least every 25 ft and track the drill head at least every 5 ft; within 5 ft, expose every 100 ft and track every 10 ft. In all cases the head is tracked every half to full rod length through the pilot bore, tooling is not operated inside the tolerance zone of an unexposed utility, and the backreamer size, not just the pilot bit, has to be considered when placing the pilot bore.
Bend radius
The radii in the table at the top of this page are demands, not choices. Each has to be checked against the minimum bend radius of the drill rod and the product pipe. If the required radius is tighter than any of those limits, the entry angle or the depth has to give.
Putting the profile together
The order that works is from the constraints inward, not from the entry point outward:
- Fix the deepest point first. It is set by the deepest clearance requirement on the line — usually the crossed utility with the least headroom, or the scoured river bottom.
- Choose the flattest entry and exit angles the available setback allows. Setback is the horizontal run from the table above, and it is the ground the entry curve needs before the path is level.
- Check the resulting radii against the rod and pipe limits. A radius that fails here is fixed by a shallower angle or a shallower bore, not by drilling it anyway.
- Extend the tangent at depth rather than adding bends when more clearance is needed. Straight length adds pull load linearly through μ wb L; every extra bend multiplies it through the capstan term eμθ, by the angle it turns.
- Re-run the cover check station by station against the ground surface, with the reamed hole diameter, not the pipe diameter.
BorePlanner Coming soon lays the profile out on an Android phone at the jobsite. It can cache USGS 3DEP ground elevation around the site so the profile works without a signal, fits the bore through the depth points you enter, reports the entry and exit pitch and the tightest radius along the path, and flags every known utility where clearance to the reamed hole falls short of the figure you require.
Sources
- Plastics Pipe Institute, Handbook of PE Pipe, Chapter 12 — path geometry, reaming oversize, scour depth, worked river crossing.
- 49 CFR 192.327 and 49 CFR 195.248 — cover requirements.
- Gas Technology Institute, Trenchless Best Practices for Damage Prevention (2016, hosted by the Common Ground Alliance) — potholing and tracking tables.
- INGAA Foundation, Natural Gas Pipeline Crossing Guidelines (2013) — clearance and tolerance zone.
- USGS 3DEP topographic data quality levels and 3DEP products and services — point density, vertical accuracy, bare-earth models.
- City of Ocoee, Florida, Article 33: Horizontal Directional Drilling — an owner’s entry and exit angle limits.