The historical drill for curved holes shown by Hiscox carries a rotary drill at the end of a curved guide tube. A flexible shaft transmits rotation through the tube, while a pivoted arm and worm gear advance the tube around its center of curvature. The bit therefore follows a circular path into the coal. This construction is different from a modern bent-sub or rotary-steerable downhole tool.
Drill for Curved Holes Interactive Calculator
Explore the historical curved guide-tube drill. Radius and sweep determine the path; worm gearing determines feed, while the flexible shaft supplies separate bit rotation.
Equation Used
- Guide tube centered on the fixed feed pivot.
- Rigid tube, no backlash or shaft torsional lag.
- Direct flexible-shaft to bit rotation.
- 155° illustrative tube arc; forward cutting followed by withdrawal.
Rigid circular guide tube and exact ideal worm speed ratio. No empirical formation factor or cutting-load model.
Separate cutting rotation from curved feed
The fixed pivot is at the center of the curved tube. Two arms support the tube and turn with the feed worm wheel. As the wheel rotates, the complete tube advances around that pivot without changing its bend radius. The drill tip moves tangentially along the same circular path.
Inside the tube, a flexible shaft spins the bit. The illustration separates that cutting rotation from the slower worm-driven feed. A cutaway reveals the shaft inside the grey guide tube; the bit’s flute markings rotate while the guide tube itself follows the feed arm.
The source drawing identifies the curved tube, flexible shaft, pivoted arm and worm gear but provides no dimensions. The animation uses a 155° tube arc and a stated circular-path model. The external power connection is outside this section; the flexible shaft is shown within the curved tube. Support details are explanatory geometry. Worm tooth profiles are schematic; their counts and angular ratio follow the inputs.
Compare reach, offset and feed time
Adjust the tube centerline radius and desired cutting angle to calculate the curved length, reach along the entry tangent and offset from that tangent. The worm-wheel tooth count, number of worm starts and worm speed determine feed turns, time and centerline speed.
The separate bit-speed input determines how many cutting revolutions occur during the forward feed. It does not change the geometric path. The model contains no empirical formation factor, penetration prediction, cutting force or torque estimate.
Circular-path and worm-feed equations
For radius R and feed angle α in radians, centerline length is L=Rα, entry-direction reach is x=R sin α and normal offset is y=R(1−cos α). These distances are measured from the bit’s entry point; the tube radius is measured from the fixed feed pivot.
For a worm with s starts driving a wheel with Z teeth, the wheel turns s/Z revolutions per worm turn. A forward sweep of αdeg therefore needs N=αdeg Z/(360s) worm revolutions. At worm speed n rpm, forward time is t=60N/n seconds. Centerline feed speed is L/t.
If the flexible shaft and bit rotate at nb rpm with no intervening ratio, bit revolutions during the forward feed are nb t/60. The animation uses these same speed relationships, displayed at least twice slower than actual motion, with a minimum eight-second forward-and-return cycle for readability. It shows forward feed followed by controlled withdrawal; withdrawal does not undo the previously cut channel.
Example: a 600 mm tube radius and 60° feed
The centerline cutting length is 600Ï€/3, or 628.32 mm. The tip reaches 519.62 mm along the initial direction and moves 300.00 mm away from that tangent.
A single-start worm and 40-tooth wheel require 6.67 worm turns for the 60° sweep. At 60 rpm that takes 6.67 seconds, with centerline feed speed 94.25 mm/s. A 300 rpm bit makes 33.33 revolutions during that forward feed. These are kinematic values for the entered example, not recommended coal-cutting settings.
What this model establishes
The guide tube retains its circular shape and turns about its curvature center. The illustration’s feed arms stay outside the work face over the supported angle range. Its cutting envelope is wider than the tube so the tube can follow the tip through the illustrated channel.
The model does not establish whether a selected flexible shaft can withstand the bend, transmit the necessary torque or survive a particular speed. Cutting performance, spoil removal, shaft stress, tube deflection, backlash and bearing loads are separate questions. The calculator describes a rigid circular guide path. Flexible-shaft durability and material-dependent cutting performance require separate engineering data.
Curved-hole drill questions
Does the guide tube spin like the drill bit?
No. The rigid curved tube advances about the feed pivot. The flexible shaft inside it transmits the separate bit rotation.
Why does a larger radius make a longer hole at the same angle?
Arc length is radius times angle in radians. Reach and offset also scale directly with radius.
Why do more worm-wheel teeth slow the feed?
At the same worm speed and start count, more wheel teeth require more worm turns for the same output angle.
Does a faster bit change the bore path?
Not in this rigid geometric model. It changes the cutting-revolution count while the feed mechanism defines the path.
Is this the same as a modern directional drilling calculator?
No. This page explains the historical curved-tube mining mechanism shown in the cited source, not formation-dependent steering with a bent sub or downhole motor.
Construction reference
Gardner D. Hiscox, Mechanical Movements, Powers and Devices, printed page 299, figure 1205, identifies a drill on a curved tube driven through a flexible shaft and fed by a pivoted arm and worm gear. The animation follows that arrangement with explicit illustrative dimensions.
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