Calculations

Calculations

• Block grid

  The block index, block center and block volume of a regular grid.

  center = origin + (i + 0.5) × size; volume = dx × dy × dz

  Block model, ultimate pit and mine schedule mining.js

  • CivilCraft
  64-bit

• Grade by inverse distance weighting

  Each block's grade from the drill-hole samples around it.

  grade = Σ (g_s ÷ d_s^p) ÷ Σ (1 ÷ d_s^p)

  Block model, ultimate pit and mine schedule mining.js

  • CivilCraft
  64-bit

• Block value

  The money each block is worth if mined: ore margin less mining cost, or the cost of waste.

  t = volume × density; ore = t × (grade × recovery × price − process cost); value = ore − t × mining cost, or −t × waste cost

  Block model, ultimate pit and mine schedule mining.js

  • CivilCraft
  64-bit

• Maximum flow

  The maximum flow from which the ultimate pit is read.

  Block model, ultimate pit and mine schedule mining.js

  • CivilCraft
  64-bit

• Ultimate pit

  The set of blocks to mine for the highest total value within the slope, with its value, ore and waste tonnes.

  reach per layer = dz ÷ tan(slope); blocks above within round(reach ÷ dx), round(reach ÷ dy) and hypot ≤ reach

  Block model, ultimate pit and mine schedule mining.js

  • CivilCraft
  64-bit

• Grade and tonnage curve

  The tonnes and mean grade of everything at or above each cut-off grade.

  tonnes = Σ t; grade = Σ (t × g) ÷ Σ t

  Block model, ultimate pit and mine schedule mining.js

  • CivilCraft
  64-bit

• Bench report

  Ore and waste tonnes, mean grade and strip ratio for each bench.

  strip = waste ÷ ore; z = origin_z + (k + 1) × dz

  Block model, ultimate pit and mine schedule mining.js

  • CivilCraft
  64-bit

• Ramp length

  The length of ramp needed to climb a number of benches at a grade.

  per bench = H ÷ grade; total = per bench × benches

  Block model, ultimate pit and mine schedule mining.js

  • CivilCraft
  64-bit

• Production schedule and net present value

  Assigns blocks to periods within ore and movement capacities and discounts each period's cash flow.

  PV_t = cash_t ÷ (1 + discount)^t; NPV = Σ PV_t

  Block model, ultimate pit and mine schedule mining.js

  • CivilCraft
  64-bit

• Angle from degrees, minutes and seconds

  Reads an angle typed as degrees, minutes and seconds or as decimal degrees.

  degrees = d + m ÷ 60 + s ÷ 3600

  Parcels: deed calls, closure, area and legal description parcels.js

  • CivilCraft
  64-bit

• Bearing to direction

  Turns a quadrant bearing or an azimuth into a direction in radians from east, counter-clockwise.

  direction = (90° − azimuth) × π ÷ 180, wrapped to 0…2π

  Parcels: deed calls, closure, area and legal description parcels.js

  • CivilCraft
  64-bit

• Central angle of a curve call

  The central angle of a deed curve from its arc length, or as typed.

  Δ = L ÷ R

  Parcels: deed calls, closure, area and legal description parcels.js

  • CivilCraft
  64-bit

• Traverse and misclosure

  The corners reached by the calls, the gap back to the start, the total length and the precision ratio.

  p ← p + d·(cos θ, sin θ); chord = 2R·sin(Δ ÷ 2); misclosure = |end − start|; precision = length ÷ misclosure

  Parcels: deed calls, closure, area and legal description parcels.js

  • CivilCraft
  64-bit

• Curve from a bulge

  The radius, length, central angle, chord, tangent directions and center of a curved course.

  Δ = 4·atan|b|; R = chord ÷ (2·sin(Δ ÷ 2)); L = R × Δ; center = start + R·(cos, sin)(dir_in ± 90°)

  Parcels: deed calls, closure, area and legal description parcels.js

  • CivilCraft
  64-bit

• Courses of a parcel

  Each side of the parcel as a line (direction and distance) or a curve.

  direction = atan2(Δy, Δx); distance = hypot(Δx, Δy)

  Parcels: deed calls, closure, area and legal description parcels.js

  • CivilCraft
  64-bit

• Parcel area

  The area of the parcel, with curved sides counted exactly.

  2A = Σ (x_i·y_j − x_j·y_i) + Σ ± R²·(Δ − sin Δ); area = |2A| ÷ 2

  Parcels: deed calls, closure, area and legal description parcels.js

  • CivilCraft
  64-bit

• Perimeter

  The length round the parcel.

  perimeter = Σ line distances + Σ curve lengths

  Parcels: deed calls, closure, area and legal description parcels.js

  • CivilCraft
  64-bit

• Area in words

  The area as square units with acres or hectares.

  acres = sq ft ÷ 43560; hectares = sq m ÷ 10000

  Parcels: deed calls, closure, area and legal description parcels.js

  • CivilCraft
  64-bit

• Legal description

  A draft description: the point of beginning, each course, and the area.

  Parcels: deed calls, closure, area and legal description parcels.js

  • CivilCraft
  64-bit

• Course and area labels

  The bearing and distance text along each side and the area text at the middle.

  Parcels: deed calls, closure, area and legal description parcels.js

  • CivilCraft
  64-bit

• Bulge from a typed radius

  Turns a radius typed for one side of a parcel into the stored curve.

  bulge = ± tan(asin(chord ÷ 2R) ÷ 2)

  Parcels: deed calls, closure, area and legal description parcels-ui.js

  • CivilCraft
  64-bit

• Does the traverse close

  Decides whether typed deed calls return to the start, in which case the last point is dropped and the parcel closes on its first corner.

  closes when misclosure ≤ 0.0005 × max(1, length ÷ 1000)

  Parcels: deed calls, closure, area and legal description parcels-ui.js

  • CivilCraft
  64-bit

• Pipe slope, cover and structure levels

  Length, slope and least cover of each pipe; rim and sump of each structure; and the list of rule problems.

  slope = (inv_up − inv_dn) ÷ L; crown(t) = inv_up + (inv_dn − inv_up)·t + D; cover = min over samples (ground − crown); sump = lowest invert − sump depth

  Gravity pipe network: slopes, cover and automatic inverts pipes.js

  • CivilCraft
  64-bit

• Automatic inverts

  Sets each pipe's upstream and downstream inverts from the ground, the minimum cover, slope and drop.

  up = min(ground − cover − D, lowest incoming invert − drop); dn = min(up − s·L, min over samples (up + (ground − cover − D − up) ÷ t))

  Gravity pipe network: slopes, cover and automatic inverts pipes.js

  • CivilCraft
  64-bit

• Rounding an invert down

  Rounds a computed invert down to two decimals.

  ⌊v × 100 + 1e-7⌋ ÷ 100

  Gravity pipe network: slopes, cover and automatic inverts pipes.js

  • CivilCraft
  64-bit

• Bench outlines, area and perimeter

  The closed outlines of the mined area at one level, each with its area and perimeter.

  point = origin + index × block size; area = Σ (x_i·y_j − x_j·y_i) ÷ 2; perimeter = Σ edge lengths

  Open pit benches, haul ramp and pit surface pit-geom.js

  • CivilCraft
  64-bit

• Pit floor per column

  The bottom elevation of the lowest mined block in each column.

  floor = origin_z + k × dz

  Open pit benches, haul ramp and pit surface pit-geom.js

  • CivilCraft
  64-bit

• Overall slope with a ramp

  The overall wall angle when every bench carries a ramp lane.

  OSA′ = atan(H ÷ (H ÷ tan(OSA) + w))

  Open pit benches, haul ramp and pit surface pit-geom.js

  • CivilCraft
  64-bit

• Outline moved inward

  The bench outline moved inside by half the ramp width.

  vertex shift = (n₀ + n₁) × d ÷ (1 + n₀ · n₁)

  Open pit benches, haul ramp and pit surface pit-geom.js

  • CivilCraft
  64-bit

• Haul ramp route, length and drop

  The ramp's 3D line down the pit, its length, its drop, and how many laps each bench needs.

  run = dz ÷ grade; z = z_top − dz × min(1, walked ÷ run); length = Σ 3D segment lengths; laps = run ÷ lane perimeter

  Open pit benches, haul ramp and pit surface pit-geom.js

  • CivilCraft
  64-bit

• Pit cut into the ground and volume dug

  The ground surface with the pit cut in, and the volume between the ground and the pit floor.

  node z = min(ground, mean of the 4 columns round it); dug = Σ max(0, ground − floor) × dx × dy

  Open pit benches, haul ramp and pit surface pit-geom.js

  • CivilCraft
  64-bit

• Depth of cut and fill by cell

  The depth at every cell, the cut and fill volumes, and the deepest cut and highest fill.

  dz = design − ground at ((i + 0.5)·c, (j + 0.5)·c); fill = Σ dz·c² (dz > 0); cut = Σ −dz·c² (dz ≤ 0)

  Cut and fill map, spot levels, sloped pads and free sections platform.js

  • CivilCraft
  64-bit

• Depth classes

  Equal steps of depth for shading the map, with a level band around zero.

  n = ⌈depth ÷ step − 1e-9⌉; level when |dz| < step ÷ 20

  Cut and fill map, spot levels, sloped pads and free sections platform.js

  • CivilCraft
  64-bit

• Spot levels

  Ground level, design level and their difference on a grid, with the deepest cut and highest fill marked.

  Cut and fill map, spot levels, sloped pads and free sections platform.js

  • CivilCraft
  64-bit

• Sloped pad as a plane

  The elevation of each pad corner on a plane through a point, rising in a direction at a grade.

  z = z₀ + grade × ((x − x₀)·cos θ + (y − y₀)·sin θ)

  Cut and fill map, spot levels, sloped pads and free sections platform.js

  • CivilCraft
  64-bit

• Ramp strip

  The four corners of a ramp between two points, its length and its grade.

  L = hypot(Δx, Δy); grade = (z_b − z_a) ÷ L; corners = ends ± normal × width ÷ 2

  Cut and fill map, spot levels, sloped pads and free sections platform.js

  • CivilCraft
  64-bit

• Free section

  Ground and design cut along a polyline, with cut and fill areas and the distance of each vertex.

  Cut and fill map, spot levels, sloped pads and free sections platform.js

  • CivilCraft
  64-bit

• Stretches of a line inside the graded regions

  The distances along the section line where it runs inside a graded region.

  t = ((p − a) × e) ÷ (d × e); inside tested at the middle of each piece

  Cut and fill map, spot levels, sloped pads and free sections platform.js

  • CivilCraft
  64-bit

• Section CSV

  Writes the section as distance, ground level and design level rows, then the cut and fill areas.

  value = round(v × 100) ÷ 100

  Cut and fill map, spot levels, sloped pads and free sections platform.js

  • CivilCraft
  64-bit

• Plot scales

  The list of scales and the millimeters on paper per project unit for each.

  mm per foot = 25.4 ÷ n (1 in = n ft); mm per meter = 1000 ÷ n (1:n)

  Plan sheets and plan-and-profile sheets as PDF plot.js

  • CivilCraft
  Exact

• Scale that fits

  The largest standard scale at which the drawing's extents fit the sheet.

  Plan sheets and plan-and-profile sheets as PDF plot.js

  • CivilCraft
  64-bit

• Drawing window in project coordinates

  The part of the project that a sheet shows at a scale.

  half width = frame width ÷ 2 ÷ mm per unit; window = center ± half

  Plan sheets and plan-and-profile sheets as PDF plot.js

  • CivilCraft
  64-bit

• Project coordinates to paper

  Where each point of the plan lands on the sheet, in millimeters.

  x_mm = x·s + o_x, o_x = frame middle − c_x·s

  Plan sheets and plan-and-profile sheets as PDF plot.js

  • CivilCraft
  64-bit

• Scale bar length

  A round length about 50 mm long on paper for the scale bar.

  want = 50 ÷ s; length = largest of {1, 2, 5, 10} × 10^⌊log₁₀ want⌋ not over want

  Plan sheets and plan-and-profile sheets as PDF plot.js

  • CivilCraft
  64-bit

• Arcs as Bézier curves

  Turns a circular arc into cubic Bézier pieces for the PDF.

  n = ⌈|sweep| ÷ 90° − 1e-9⌉; d = sweep ÷ n; k = 4 ÷ 3 × tan(d ÷ 4); control = end ± k·r·tangent

  Plan sheets and plan-and-profile sheets as PDF plot.js

  • CivilCraft
  64-bit

• A number in the PDF

  Formats every coordinate and width written to the page.

  text = v.toFixed(4) with trailing zeros removed

  Plan sheets and plan-and-profile sheets as PDF plot.js

  • CivilCraft
  64-bit

• Millimeters to PDF points

  The page transform that makes the content's units millimeters.

  72 ÷ 25.4 points per millimeter

  Plan sheets and plan-and-profile sheets as PDF plot.js

  • CivilCraft
  64-bit

• Stations per sheet

  The stretch of alignment each sheet shows and where each sheet starts and ends.

  fits = plan window width ÷ mm per unit; length = ⌊fits ÷ round⌋ × round; sheet k starts at start + k × length

  Plan sheets and plan-and-profile sheets as PDF pp-sheets.js

  • CivilCraft
  64-bit

• Design profile points on a sheet

  The stations at which the design profile is drawn within a sheet's range.

  Plan sheets and plan-and-profile sheets as PDF pp-sheets.js

  • CivilCraft
  64-bit

• Vertical exaggeration

  The largest standard exaggeration (10, 5, 4, 2 or 1) at which every sheet's elevations fit the profile window.

  fits when range × mm per unit × exaggeration ≤ available height; vertical scale = s × exaggeration

  Plan sheets and plan-and-profile sheets as PDF pp-sheets.js

  • CivilCraft
  Exact