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Red Seal Boilermaker practice questions

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Question 1Occupational Skills and Safety

Before a boilermaker enters a confined vessel that previously held hydrocarbon, which permit condition must be satisfied first?

  1. A second worker stands at the manway with a radio
  2. The vessel interior has been swept with a broom
  3. The vessel has been drained, purged, and tested to confirm acceptable oxygen and flammable-gas levels Correct answer.
  4. The vessel has been tagged out by the maintenance planner

Explanation

Entry into a confined space requires atmospheric testing after isolation, draining, and purging, confirming oxygen and flammable-gas readings are within acceptable limits before anyone enters. A standby attendant and lockout are also required, but they do not substitute for verified breathable atmosphere.

Question 2Occupational Skills and Safety

A boilermaker must cut a section from a steel plate using oxy-fuel cutting. Which practice protects the cut quality and the operator?

  1. Open the cutting oxygen fully before lighting the torch
  2. Set the preheat flame before opening the cutting oxygen and wear approved eye protection Correct answer.
  3. Cut with the tip dragged directly on the plate to steady it
  4. Point the torch upward so slag falls clear of the kerf

Explanation

Correct sequencing sets a neutral preheat flame first, then the cutting oxygen lever is engaged to start the cut, with proper filtered eye protection against the intense ultraviolet and infrared radiation. Dragging the tip or opening cutting oxygen before ignition produces poor cuts and unsafe flame conditions.

Question 3Occupational Skills and Safety

What is the primary purpose of a lockout/tagout procedure on a boiler feedwater pump before maintenance?

  1. To prevent unexpected energization or release of stored energy during the work Correct answer.
  2. To notify the control room that the pump is being serviced
  3. To record the pump's operating hours for the maintenance log
  4. To reduce the pump's discharge pressure gradually

Explanation

Lockout/tagout isolates energy sources and secures them so the equipment cannot be started or release stored energy while a worker is exposed. Notification and logs are secondary and do not by themselves protect the worker.

Question 4Occupational Skills and Safety

A boilermaker is rigging a tube bundle for lifting. Which factor most directly determines the required sling capacity?

  1. The load weight, sling angle, and number of legs sharing the load Correct answer.
  2. The color coding of the sling tags
  3. The experience level of the signal person
  4. The distance the bundle will travel

Explanation

Sling tension rises as the angle from horizontal decreases, so capacity depends on the load weight, the geometry of the sling legs, and how many legs share the load. Travel distance and tag color do not change the tension in the sling.

Question 5Occupational Skills and Safety

During a hydrostatic test of a newly built pressure vessel, what is the main reason for using water rather than compressed air as the test medium?

  1. Water prevents rust formation inside the vessel
  2. Water stores far less elastic energy, so a failure releases much less energy than a gas test Correct answer.
  3. Water is cheaper to obtain on site than compressed air
  4. Water allows the test to be run at a lower pressure

Explanation

A compressed gas test stores enormous elastic energy, so a rupture can be catastrophic; water is nearly incompressible and releases little energy on failure. Cost and corrosion control are not the governing safety reason.

Question 6Occupational Skills and Safety

A welder must join two sections of carbon steel boiler shell using shielded metal arc welding. What does the electrode classification E7018 indicate about the deposited weld?

  1. A minimum tensile strength of 70,000 psi and suitability for all-position welding with low-hydrogen deposit Correct answer.
  2. A Charpy impact value of 70 ft-lb at room temperature
  3. A minimum yield strength of 70,000 psi in the flat position only
  4. A minimum tensile strength of 70 ksi and a cellulose-based rutile coating

Explanation

In the E7018 designation the first two digits give minimum tensile strength in ksi (70,000 psi), the third digit indicates position (1 = all position), and the last two digits identify the coating and current type, with 8 indicating a low-hydrogen iron-powder coating.

Question 7Occupational Skills and Safety

A boilermaker is asked to roll a tube into a tubesheet. Which condition most affects achieving a proper tube-to-tubesheet joint?

  1. The length of the tube beyond the tubesheet
  2. Correct hole groove dimensions and controlled tube expansion Correct answer.
  3. The color of the tube marking paint
  4. The ambient humidity in the shop

Explanation

A sound rolled joint depends on proper hole size and groove geometry combined with controlled expansion so the tube fills the grooves without being over-rolled and thinned. Cosmetic and environmental factors do not govern joint integrity.

Question 8Occupational Skills and Safety

Which fire extinguisher class is appropriate for a pressurized flammable liquid fuel fire near a boiler front?

  1. Class A extinguisher rated for ordinary combustibles
  2. Class K extinguisher rated for cooking oils
  3. Class D extinguisher rated for combustible metals
  4. Class B extinguisher rated for flammable liquids Correct answer.

Explanation

Flammable liquid fires are Class B, so a foam, dry chemical, or CO2 extinguisher rated for Class B is appropriate. Class A covers wood and paper, Class D covers combustible metals, and Class K covers cooking media.

Question 9Occupational Skills and Safety

A boilermaker is working at height on a scaffold platform. Which fall protection rule applies at a working height of 3 metres?

  1. Fall protection is required only above 6 metres
  2. Fall protection is optional because the platform has guardrails
  3. Fall protection is required because the working height exceeds the jurisdictional trigger height Correct answer.
  4. Fall protection is required only when tools are being used

Explanation

Most jurisdictions require fall protection above a trigger height commonly set around 3 metres, and guardrails are one acceptable form of protection. Working above the trigger height without any protection is not permitted.

Question 10Occupational Skills and Safety

A boilermaker must enter a vessel that has been purged with nitrogen to inert it. What hazard does this create?

  1. A toxic atmosphere that causes immediate corrosion of the lungs
  2. A high-pressure atmosphere that can rupture the vessel
  3. An oxygen-deficient atmosphere that can cause rapid unconsciousness Correct answer.
  4. A flammable atmosphere that can ignite from static

Explanation

Nitrogen displaces oxygen, creating an oxygen-deficient atmosphere that can render a worker unconscious within seconds. Entry is prohibited until the space is ventilated and tested to confirm acceptable oxygen levels.

Question 11Occupational Skills and Safety

When performing a visual inspection of a completed weld on a boiler pressure part, which feature indicates a defect that must be evaluated?

  1. A slight discoloration of the heat-affected zone
  2. A uniform fine ripple pattern on the weld face
  3. Undercut along the weld toe that exceeds the code allowance Correct answer.
  4. A weld reinforcement that is uniform along its length

Explanation

Undercut reduces the effective throat and creates a stress concentration, so it must be measured against the code allowance and repaired if it exceeds it. Uniform ripples, heat tint, and even reinforcement are normal and acceptable.

Question 12Occupational Skills and Safety

A boilermaker is preparing to weld on a vessel that has been in service and may have contained flammable material. What must be done before hot work begins?

  1. The welder must simply wear a respirator during welding
  2. The vessel must be filled with water to the weld line only
  3. The work can proceed if a fire watch is present
  4. The vessel must be cleaned, purged, and tested to confirm no flammable atmosphere, with a hot work permit issued Correct answer.

Explanation

Hot work on equipment that held flammables requires cleaning, purging, and gas testing to confirm the absence of a flammable atmosphere, plus a formal hot work permit. A fire watch alone does not make an unsafe atmosphere safe.

Question 13Occupational Skills and Safety

In a shell-and-tube heat exchanger, what is the function of baffles in the shell side?

  1. To support the tubesheet against internal pressure
  2. To direct shell-side flow across the tubes and increase heat transfer Correct answer.
  3. To seal the shell-to-channel joint
  4. To prevent tube vibration only

Explanation

Baffles force the shell-side fluid to flow across the tube bundle, increasing turbulence and heat transfer, and they also support the tubes. Sealing the joint and resisting tubesheet pressure are functions of other components.

Question 14Occupational Skills and Safety

A boilermaker must remove a seized stud from a boiler manway cover. Which practice best reduces the risk of injury?

  1. Heat the stud with an oxy-acetylene torch until red hot before turning
  2. Apply penetrating oil, use the correct size wrench, and brace against the reaction force Correct answer.
  3. Strike the wrench with a hammer to break the stud free
  4. Use a pipe extension on the wrench and pull toward the body

Explanation

Correct wrench size, lubrication, and bracing against the reaction force reduce slipping and sudden release of stored energy. Heating a stud red hot near a boiler and pulling toward the body both create serious injury risk.

Question 15Occupational Skills and Safety

A boilermaker is welding inside a vessel. Which ventilation practice is most appropriate?

  1. Open the manway and rely on natural draft
  2. Provide mechanical ventilation that removes welding fume at the source and supplies fresh air Correct answer.
  3. Weld only in the morning when the vessel is cooler
  4. Wear a dust mask and weld in short bursts

Explanation

Confined-space welding requires mechanical ventilation that captures fume at the source and supplies fresh air to the worker, along with atmospheric monitoring. Natural draft and dust masks do not control welding fume in a confined space.

Question 16Occupational Skills and Safety

Which PPE is specifically required for a boilermaker performing overhead welding?

  1. A hard hat only
  2. Safety glasses only
  3. A dust mask and rubber gloves
  4. Leather sleeves, a flame-resistant jacket, and a welding helmet with the correct shade Correct answer.

Explanation

Overhead welding showers sparks and molten metal downward, so flame-resistant clothing, leather sleeves, and a properly shaded helmet protect against burns and arc radiation. A hard hat or safety glasses alone leave skin and eyes exposed.

Question 17Occupational Skills and Safety

A boilermaker is inspecting a pressure vessel for cracks using dye penetrant testing. What is the correct sequence?

  1. Clean the surface, apply developer, then apply penetrant
  2. Apply penetrant, then immediately inspect without developer
  3. Apply developer first, then penetrant, then clean the surface
  4. Clean the surface, apply penetrant, remove excess, apply developer, then inspect Correct answer.

Explanation

Dye penetrant testing requires a clean surface, penetrant dwell time, removal of excess penetrant, then developer to draw penetrant from defects so they become visible. Applying developer before penetrant or skipping developer prevents proper indication.

Question 18Occupational Skills and Safety

During a hydrostatic test, a boilermaker notices the pressure gauge fluctuating and a small leak at a temporary test connection. What is the correct action?

  1. Depressurize the vessel, repair the connection, and restart the test Correct answer.
  2. Tighten the connection while it is under pressure
  3. Continue the test and note the leak in the report
  4. Increase the test pressure to compensate for the leak

Explanation

Test connections must not be tightened under pressure because of the risk of sudden failure and injury; the vessel must be depressurized before repair. Continuing a test with a known leak invalidates the test result.

Question 19Occupational Skills and Safety

Two boilermakers must lift a heavy tube bundle by hand into position. Which lifting practice is correct?

  1. Bend at the waist and lift with the back muscles
  2. Lift with straight legs and locked knees while leaning forward
  3. Use a mechanical lifting device or team lift with coordinated communication Correct answer.
  4. Twist the torso while lifting to reach the position

Explanation

Mechanical aids are preferred; if a manual lift is unavoidable, a coordinated team lift with communication reduces strain. Bending at the waist, twisting, or locked knees all increase injury risk.

Question 20Occupational Skills and Safety

A boilermaker is laying out a nozzle opening on a cylindrical shell. Which method gives the correct developed opening shape?

  1. Use the intersection of the nozzle and shell geometry to develop the opening curve Correct answer.
  2. Draw a circle equal to the nozzle diameter
  3. Use the flat pattern of the shell only
  4. Use a square opening equal to the nozzle diameter

Explanation

The opening in a curved shell is not a simple circle; the intersection curve must be developed from the geometry of the nozzle and shell so the cut matches the mating part. A simple circle or square will not fit the curved surface.

Question 21Occupational Skills and Safety

What is the purpose of a safety valve on a boiler drum?

  1. To relieve pressure automatically before it exceeds the design limit Correct answer.
  2. To drain condensate from the drum during startup
  3. To regulate feedwater flow to the drum
  4. To indicate drum water level to the operator

Explanation

A safety valve is a pressure-relief device that opens automatically at a set pressure to prevent the drum from exceeding its design limit. Drain, feedwater regulation, and level indication are functions of other components.

Question 22Occupational Skills and Safety

A boilermaker is preparing to weld a pressure part and the ambient temperature is below the code minimum. What is the appropriate action?

  1. Preheat the part to the code-required temperature before welding Correct answer.
  2. Weld without preheat because the electrode is low hydrogen
  3. Reduce the welding current to compensate
  4. Weld only in short passes to avoid heat buildup

Explanation

Low ambient temperature increases the risk of cracking, so the base metal must be preheated to the temperature required by the applicable code before welding begins. Low-hydrogen electrodes and short passes do not replace required preheat.

Question 23Occupational Skills and Safety

A boilermaker is asked to select a welding process for field repair on a boiler where wind is a concern. Which process is most suitable for outdoor field welding?

  1. Submerged arc welding because the flux protects the arc
  2. Gas metal arc welding with a CO2 shield because it is unaffected by wind
  3. Flux-cored arc welding with no shielding gas because it needs no protection
  4. Shielded metal arc welding because the slag and gas shield resist wind better than gas-shielded processes Correct answer.

Explanation

Shielded metal arc welding uses a self-shielding electrode coating that resists wind better than gas-shielded processes, making it common for field repair. Gas-shielded processes lose shielding in wind, and submerged arc is impractical for field repair.

Question 24Occupational Skills and Safety

What is the primary purpose of a boiler's blowdown procedure?

  1. To add chemicals to the feedwater
  2. To increase the steam pressure in the drum
  3. To remove dissolved solids and sludge that concentrate in the drum water Correct answer.
  4. To cool the boiler shell after shutdown

Explanation

Blowdown controls the concentration of dissolved solids and removes sludge from the drum, protecting the boiler from carryover and scale. It does not raise pressure, cool the shell, or add chemicals.

Question 25Layout and Pattern Development

A boilermaker needs to divide a circle into 12 equal parts using dividers. Which chord length should be stepped around the circumference?

  1. The chord of a 45° central angle
  2. The radius of the circle
  3. The diameter divided by 12
  4. The chord of a 30° central angle Correct answer.

Explanation

Dividing 360° by 12 gives a 30° central angle for each sector, so the dividers must be set to the chord corresponding to 30°. Stepping any other chord will not close the circle exactly at 12 divisions.

Question 26Layout and Pattern Development

In triangulation of a developable surface, what does each triangle represent?

  1. A region left undeveloped
  2. A curved segment that must be rolled
  3. A flat plane whose true lengths can be found Correct answer.
  4. A line of intersection between two solids

Explanation

Triangulation approximates a curved surface as a series of flat triangles. Because each triangle lies in a single plane, its true side lengths can be determined and laid out flat in the development.

Question 27Layout and Pattern Development

On a drawing, a line is drawn at 30° to the horizontal and measures 80 mm along the drawing. What is its true horizontal projection?

  1. 40.0 mm
  2. 69.3 mm Correct answer.
  3. 80.0 mm
  4. 92.4 mm

Explanation

The horizontal projection equals the true length multiplied by the cosine of the angle: 80 × cos30° = 80 × 0.866 = 69.3 mm. The drawn length is the hypotenuse, so the projection must be shorter.

Question 28Layout and Pattern Development

What is the purpose of a stretch-out line in pattern development?

  1. To indicate the direction of rolling
  2. To locate the centre of gravity of the development
  3. To mark the seam allowance on the finished pattern
  4. To establish the baseline onto which true lengths are transferred Correct answer.

Explanation

The stretch-out line is a straight reference line representing the developed circumference or perimeter. True lengths taken from the elevation are stepped off along it to build the pattern.

Question 29Layout and Pattern Development

A right circular cylinder has a diameter of 200 mm. What is the developed width of its full pattern before seam allowance?

  1. 200 mm
  2. 400 mm
  3. 628 mm Correct answer.
  4. 314 mm

Explanation

The developed width equals the circumference, π × diameter = π × 200 ≈ 628 mm. This length is the stretch-out used to lay out the rectangular pattern.

Question 30Layout and Pattern Development

Which development method is appropriate for a truncated oblique cone?

  1. Parallel line method
  2. Triangulation method Correct answer.
  3. Rolling method
  4. Radial line method

Explanation

A cone with an oblique cut cannot be developed accurately by radial lines because element lengths vary. Triangulation divides the surface into triangles whose true lengths are found and laid out flat.

Question 31Layout and Pattern Development

On a pattern, what does a bend line indicate?

  1. Where the seam is welded
  2. Where the material grain runs
  3. Where the plate must be cut
  4. Where the plate is to be folded or formed Correct answer.

Explanation

Bend lines mark the locations where the plate is folded or formed to shape. They are reference lines for fabrication, not cut lines.

Question 32Layout and Pattern Development

A pattern is developed for a square-to-round transition. Which method is normally used?

  1. Single-curve development
  2. Parallel line development
  3. Triangulation Correct answer.
  4. Radial line development

Explanation

A square-to-round transition has no parallel elements and no common apex, so it is developed by triangulation. The surface is divided into triangles whose true lengths are determined.

Question 33Layout and Pattern Development

In a first-angle projection drawing, where is the top view placed relative to the front view?

  1. Above the front view
  2. Below the front view Correct answer.
  3. To the right of the front view
  4. To the left of the front view

Explanation

In first-angle projection the object is imagined between the observer and the plane, so the top view is projected below the front view. This is the reverse of third-angle placement.

Question 34Layout and Pattern Development

A line in a plan view appears as a point. What does this indicate about the line in space?

  1. The line is horizontal
  2. The line lies at 45° to the plan plane
  3. The line is perpendicular to the plan plane Correct answer.
  4. The line is parallel to the plan plane

Explanation

A line that projects as a single point is viewed end-on, meaning it runs perpendicular to the plane of projection. Its true length appears only in a view perpendicular to it.

Question 35Layout and Pattern Development

A right pyramid has a square base of 100 mm side and a vertical height of 120 mm. What is the true length of a corner edge?

  1. 156 mm
  2. 130 mm Correct answer.
  3. 170 mm
  4. 120 mm

Explanation

The horizontal distance from the base corner to the centre is half the diagonal, about 70.7 mm. The edge true length is √(120² + 70.7²) ≈ √(14400 + 5000) ≈ 130 mm.

Question 36Layout and Pattern Development

What is the developed length of the outer arc of a frustum sector if the large radius of the development is 250 mm and the included angle is 90°?

  1. 393 mm Correct answer.
  2. 500 mm
  3. 250 mm
  4. 196 mm

Explanation

Arc length equals radius × angle in radians: 250 × (π/2) ≈ 393 mm. This arc corresponds to the circumference of the large end of the frustum.

Question 37Layout and Pattern Development

In parallel line development of an oblique-cut cylinder, why are the element lines drawn at equal spacing around the circumference?

  1. To reduce the number of seam allowances
  2. To obtain a uniform set of ordinates for accurate transfer to the stretch-out Correct answer.
  3. To ensure the cylinder rolls straight
  4. To simplify the welding sequence

Explanation

Equally spaced elements provide a uniform set of ordinates whose heights are transferred to the stretch-out. This gives an accurate developed curve for the oblique cut.

Question 38Layout and Pattern Development

A cone has a base diameter of 300 mm and a slant height of 500 mm. What is the included angle of its radial development?

  1. 108° Correct answer.
  2. 180°
  3. 54°
  4. 216°

Explanation

The development radius equals the slant height of 500 mm, and the arc length equals the base circumference of π × 300 ≈ 942 mm. The angle is arc/radius in radians = 942/500 ≈ 1.885 rad ≈ 108°.

Question 39Layout and Pattern Development

When laying out a pattern for a rolled plate, why is the neutral axis used rather than the inside or outside surface?

  1. The neutral axis is the only surface that can be marked
  2. The neutral axis is always at the mid-thickness for every material
  3. The neutral axis simplifies the welding procedure
  4. The neutral axis length is unchanged by bending and gives the true developed length Correct answer.

Explanation

During bending, the inner surface compresses and the outer surface stretches, while the neutral axis retains its original length. Using it gives the correct developed length for the plate.

Question 40Layout and Pattern Development

A pipe intersection requires developing a hole in a header. What is the correct first step in the layout?

  1. Weld the branch in place and mark around it
  2. Draw the true shape of the branch and project intersection points onto the header surface Correct answer.
  3. Cut the hole to approximate size and grind to fit
  4. Roll the header to final diameter

Explanation

Accurate layout begins by drawing the true shape of the branch and projecting element intersection points onto the header. These points define the developed hole outline.

Question 41Layout and Pattern Development

In a development drawing, what is a 'true length diagram' used for?

  1. Choosing the plate thickness
  2. Calculating the weight of the finished part
  3. Setting the welding current
  4. Determining the actual lengths of foreshortened lines Correct answer.

Explanation

A true length diagram resolves foreshortened lines into their actual lengths using auxiliary views or rotation. These true lengths are then used to construct the development.

Question 42Layout and Pattern Development

A square-to-round transition has a round end of 400 mm diameter and a square end of 400 mm side. Which feature must be found for each triangulation triangle?

  1. The included angle at the apex only
  2. The radius of curvature of the round end
  3. The true lengths of all three sides Correct answer.
  4. The plate thickness

Explanation

Each triangle in the triangulation must be laid out from its three true side lengths. Without all three true lengths, the triangle cannot be constructed accurately.

Question 43Layout and Pattern Development

A pattern for a conical hopper is developed and the seam is placed along a line of symmetry. Why is this placement preferred?

  1. It reduces the developed area of the pattern
  2. It allows the seam to be formed without a joint
  3. It minimises distortion and simplifies fit-up of the joint Correct answer.
  4. It eliminates the need for a stretch-out line

Explanation

Placing the seam on a line of symmetry keeps the joint in a simple plane and reduces distortion during forming. This simplifies fit-up and alignment of the edges.

Question 44Layout and Pattern Development

A line is inclined to both the horizontal and vertical planes. How can its true length be found?

  1. By scaling the plan length by the drawing scale
  2. By rotating it parallel to a reference plane in an auxiliary view Correct answer.
  3. By measuring it directly in the front view
  4. By projecting it onto the horizontal plane only

Explanation

A line inclined to both principal planes is foreshortened in both views. Rotating it parallel to a reference plane in an auxiliary view reveals its true length.

Question 45Layout and Pattern Development

A right cone is cut by a plane parallel to one element, producing a parabola. Why can this curve not be developed by simple radial lines?

  1. Element lengths from the apex to the curve vary, so each must be found separately Correct answer.
  2. The apex is missing from the development
  3. The surface becomes a cylinder
  4. The base is no longer circular

Explanation

For a parabolic cut, the distance from the apex to each point on the curve differs. Each element must therefore be measured individually and transferred to the radial development.

Question 46Layout and Pattern Development

Two cylinders of different diameters intersect at 90°. Why must the intersection curve be developed on both members separately?

  1. The intersection curve is identical on both members
  2. The smaller cylinder cannot be developed
  3. Each cylinder has a different circumference, so the curve maps differently on each stretch-out Correct answer.
  4. Only the larger cylinder needs a developed hole

Explanation

Each cylinder has its own circumference and element spacing, so the same spatial intersection curve maps to a different developed shape on each stretch-out. Both must be developed for a correct fit.

Question 47Layout and Pattern Development

A development is made for a twisted square-to-square transition. What is the key challenge in its layout?

  1. All elements are parallel and equal
  2. Each face is a warped surface requiring triangulation with individually found true lengths Correct answer.
  3. The development is a simple rectangle
  4. The four faces are identical triangles

Explanation

In a twisted transition, corresponding corners are rotated, so each face is a non-planar surface. Triangulation with individually determined true lengths is needed to develop it accurately.

Question 48Layout and Pattern Development

A frustum development is laid out with two concentric arcs. If the small arc radius is 180 mm and the large arc radius is 300 mm, what is the slant height of the frustum?

  1. 480 mm
  2. 60 mm
  3. 240 mm
  4. 120 mm Correct answer.

Explanation

The difference between the large and small development radii equals the slant height of the frustum: 300 − 180 = 120 mm. This is the true slant length of the conical surface.

Question 49Layout and Pattern Development

When developing a pattern, why is it important to establish the true shape of the cut edge before transferring it to the stretch-out?

  1. The cut edge sets the welding position
  2. The true shape fixes the seam allowance
  3. The cut edge determines the plate thickness
  4. The true shape provides the ordinate heights that define the developed curve Correct answer.

Explanation

The true shape of the cut edge gives the ordinate heights at each element position. Transferring these heights to the stretch-out produces the correct developed curve.

Question 50Layout and Pattern Development

In triangulation development, why are the element lines between the top and bottom profiles of a transition piece divided into small, equal segments before true lengths are found?

  1. Because the number of divisions determines the plate thickness used in the layout
  2. Because the developed length of each segment equals its plan length regardless of inclination
  3. Because each small segment can be treated as a straight line whose true length is found from a right triangle Correct answer.
  4. Because equal spacing ensures the seam allowance is automatically included in the development

Explanation

Triangulation approximates a curved surface with a series of adjacent triangles. Dividing the profiles into small equal segments makes each chord short enough that it can be treated as a straight line, and its true length is then solved from a right triangle using the segment's plan length and vertical height. More divisions reduce the chordal error in the final pattern.