Calculations

Calculations

• Curve to bulge

  The bulge of a feature-line arc from its start, center and end.

  sweep = (a₁ − a₀) mod 2π; bulge = ± tan(sweep ÷ 4)

  LandXML export and import landxml.js

  • CivilCraft
  64-bit

• Sump depth of a structure

  The depth of a structure's sump below its lowest pipe invert.

  sump depth = max(0, lowest invert − sump elevation)

  LandXML export and import landxml.js

  • CivilCraft
  64-bit

• Joining feature-line pieces

  Joins consecutive lines and curves of a plan feature into one line.

  LandXML export and import landxml.js

  • CivilCraft
  64-bit

• Scaling an import to project units

  Multiplies every coordinate, elevation, station, radius and length of an import by one factor.

  LandXML export and import landxml.js

  • CivilCraft
  64-bit

• Mass ordinate

  The running total of earth along the alignment, and the cut and fill totals.

  m_i = m_(i−1) + cut_i × factor − fill_i

  Mass-haul diagram masshaul.js

  • CivilCraft
  64-bit

• Balance points

  The stations where the mass ordinate crosses zero.

  sta = sta_a + (sta_b − sta_a) × m_a ÷ (m_a − m_b)

  Mass-haul diagram masshaul.js

  • CivilCraft
  64-bit

• Volume moved and average haul

  For each balanced stretch, the volume moved and the average distance it travels.

  volume = |peak| − |end level|; haul = ∫ (|m| − |end level|)⁺ d(sta) ÷ volume

  Mass-haul diagram masshaul.js

  • CivilCraft
  64-bit

• Totals and what is left over

  Total cut, adjusted cut, fill, the end ordinate, and whether the job wastes, borrows or balances.

  balanced when |end| < 1e-6 × max(1, cut + fill)

  Mass-haul diagram masshaul.js

  • CivilCraft
  64-bit

• CSV export

  Writes the stations, ordinates and spans as a CSV file in cubic yards or cubic meters.

  cubic yards = cubic feet ÷ 27

  Mass-haul diagram masshaul.js

  • CivilCraft
  64-bit

• Footprint and floor area of an option

  The footprint area and gross floor area of each alternative, in square meters.

  area (m²) = |A| ÷ 10⁶; gross = area × floors

  Massing options placed on a lot massing-options.js

  • CivilCraft
  64-bit

• Is the footprint a simple polygon

  Refuses a footprint whose edges cross.

  Massing options placed on a lot massing-options.js

  • CivilCraft
  64-bit

• Turning and moving a footprint

  Rotates a footprint about its centroid and moves it to a position.

  x′ = t_x + (x − c_x)·cos a − (y − c_y)·sin a; y′ = t_y + (x − c_x)·sin a + (y − c_y)·cos a

  Massing options placed on a lot massing-options.js

  • CivilCraft
  64-bit

• Placing an option in the envelope

  The position and rotation at which as much of the footprint as possible lies inside the buildable envelope.

  k = 0.001 ÷ meters per project unit; inside = area(envelope ∩ footprint) ÷ area(footprint)

  Massing options placed on a lot massing-options.js

  • CivilCraft
  64-bit

• Option to a mass

  Makes a project mass from a placed option, with its floor height in project units.

  floor height = mm × 0.001 ÷ meters per project unit

  Massing options placed on a lot massing-options.js

  • CivilCraft
  64-bit

• Envelope file

  Writes the buildable envelope in millimeters, turned so its longest edge lies along x.

  mm = meters per project unit × 1000; value = round(v × 10) ÷ 10

  Massing options placed on a lot massing-options.js

  • CivilCraft
  64-bit

• Footprint area

  The signed area of a mass outline.

  A = Σ (x_i·y_j − x_j·y_i) ÷ 2

  Building mass areas, levels and base earthwork massing.js

  • CivilCraft
  64-bit

• Gross floor area and height

  The floor area of all floors and the height of the mass.

  GFA = |A| × floors; height = floors × floor height

  Building mass areas, levels and base earthwork massing.js

  • CivilCraft
  64-bit

• Centroid

  The center of area of the outline.

  c_x = Σ (x_i + x_j)·k_ij ÷ 6A, k_ij = x_i·y_j − x_j·y_i

  Building mass areas, levels and base earthwork massing.js

  • CivilCraft
  64-bit

• Ground under a mass

  The lowest, highest and mean ground elevation under the footprint, and the samples used for earthwork.

  sample (i, j) at x₀ + (i + 0.5)·dx, y₀ + (j + 0.5)·dy; dA = |A| ÷ samples; mean = Σ z ÷ n

  Building mass areas, levels and base earthwork massing.js

  • CivilCraft
  64-bit

• Ground floor level

  The level the mass is set at: the mean ground, the highest ground (podium) or the lowest (cut in).

  Building mass areas, levels and base earthwork massing.js

  • CivilCraft
  64-bit

• Cut and fill under a mass

  The earth to remove above the ground floor level and to place below it.

  fill = Σ (z₀ − z)·dA where z < z₀; cut = Σ (z − z₀)·dA otherwise

  Building mass areas, levels and base earthwork massing.js

  • CivilCraft
  64-bit

• Floor levels

  The elevation of each floor and its top.

  z_i = z₀ + i × floor height

  Building mass areas, levels and base earthwork massing.js

  • CivilCraft
  64-bit

• Floors for a pulled height

  The floor count nearest to a height set by push and pull.

  floors = clamp(round(H ÷ floor height), 1, 200)

  Building mass areas, levels and base earthwork massing.js

  • CivilCraft
  Exact

• Triangles of a footprint

  Splits a simple polygon into triangles for the pad top and the roof.

  Building mass areas, levels and base earthwork massing.js

  • CivilCraft
  64-bit

• Mass prism mesh

  The triangles of the walls and roof of a mass.

  Building mass mesh for the 3D view massing.js

  • CivilCraft
  32-bit, display only

• Lengths, bearings, grades and area

  Every number the Measure tool shows for a picked line or shape.

  L = hypot(Δx, Δy); bearing = atan2(Δy, Δx); grade % = Δz ÷ L × 100; L₃ = hypot(L, Δz); area = |Σ (x_i·y_j − x_j·y_i)| ÷ 2

  Measure tool measure.js

  • CivilCraft
  64-bit

• Between two points on a profile

  The horizontal distance, height difference, straight-line distance and grade between two profile points.

  dx = |ch_b − ch_a|; dz = z_b − z_a; slope distance = hypot(dx, dz); grade % = dz ÷ dx × 100

  Measure tool measure.js

  • CivilCraft
  64-bit

• Overall slope angle

  The overall pit slope from bench height, face angle, berm width and ramp.

  OSA = atan(H ÷ (H ÷ tan α + B + ramp × share))

  Block model, ultimate pit and mine schedule mining.js

  • CivilCraft
  64-bit

• 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

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  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