Calculations

Calculations

• GSI word to a length or angle

  The value of a GSI data word from its digits and its unit code.

  millimeters ÷ 1000; 1/10 mm ÷ 10⁴; 1/100 mm ÷ 10⁵; gon or degree counts ÷ 10⁵; sexagesimal digits split into D, M, S

  Data collector files and polar reduction collector.js

  • CivilCraft
  64-bit

• Polar reduction

  Northing, easting and elevation of every shot from its setup.

  orientation = atan2(ΔE, ΔN) to the backsight − circle reading; hd = sd·sin(vz)·scale; N = N₀ + hd·cos(az), E = E₀ + hd·sin(az); Z = Z₀ + sd·cos(vz) + hi − hr

  Data collector files and polar reduction collector.js

  • CivilCraft
  64-bit

• Shots as adjustment observations

  Directions and horizontal distances with their standard deviations, and starting coordinates for the free points.

  σ(direction) = 5″ = (5 ÷ 3600) × π ÷ 180; σ(distance) = 0.005

  Data collector files and polar reduction collector.js

  • CivilCraft
  64-bit

• Section stations

  The stations at which the corridor is built.

  s = ⌈from ÷ step⌉·step, then s += step; each rounded to 6 decimals

  Corridor cross sections and pavement quantities corridor.js

  • CivilCraft
  64-bit

• Lane edge and shoulder point (simple assembly)

  The edge of pavement and the shoulder's outer edge on one side of one section, with any width or elevation target applied.

  edge z = z₀ − lane width × slope; shoulder z = edge z − shoulder width × shoulder slope

  Corridor cross sections and pavement quantities corridor.js

  • CivilCraft
  64-bit

• One side of a section from its parts

  Every point of a side from the centerline out: lanes, gutter, curb, strip, walk, then the daylight point.

  t += width; z −= width × slope (curb: z += height)

  Corridor cross sections and pavement quantities corridor.js

  • CivilCraft
  64-bit

• Where a section meets a target line

  The distance out along a section to the first crossing of a 3D polyline, and the line's elevation there.

  t = (w × d) ÷ (u × d); z = z_a + s·(z_b − z_a)

  Corridor cross sections and pavement quantities corridor.js

  • CivilCraft
  64-bit

• Do two sections cross

  Whether neighboring sections intersect, which happens inside a curve tighter than the corridor is wide.

  Corridor cross sections and pavement quantities corridor.js

  • CivilCraft
  64-bit

• Pavement course area and volume

  The plan area and the volume of each pavement course along the corridor.

  area = Σ (w₁ + w₂) ÷ 2 × Δstation; volume = area × thickness

  Corridor cross sections and pavement quantities corridor.js

  • CivilCraft
  64-bit

• Systems the coordinates fit

  The catalog systems in which a project point falls inside the system's area of use.

  Coordinate system helpers crs-pick.js

  • CivilCraft
  64-bit

• Latitude and longitude as degrees, minutes, seconds

  The status bar text for a latitude or longitude.

  seconds = round(|v| × 360000) ÷ 100, then split into D, M, S

  Coordinate system helpers crs-pick.js

  • CivilCraft
  64-bit

• Latitude and longitude as decimal degrees

  The status bar text in decimal degrees.

  Coordinate system helpers crs-pick.js

  • CivilCraft
  64-bit

• Typed latitude or longitude

  A typed angle, decimal or in degrees, minutes and seconds, with a sign or a hemisphere letter.

  value = ±(D + M ÷ 60 + S ÷ 3600)

  Coordinate system helpers crs-pick.js

  • CivilCraft
  64-bit

• Local fit: project to grid

  Grid coordinates of a project point through a scale, rotation and shift.

  grid = to + scale · R(rotation) · (p − from)

  Coordinate system helpers crs-pick.js

  • CivilCraft
  64-bit

• Misclosure of a third control point

  How far a two-point fit puts a third known point from its grid coordinates, as a distance and in parts per million.

  ppm = distance ÷ span × 10⁶

  Coordinate system helpers crs-pick.js

  • CivilCraft
  64-bit

• Converting a project's coordinates

  Every stored x and y of the project (points, breaklines, boundary, alignment PIs, pads, structures) passed through a conversion.

  Coordinate system helpers crs-pick.js

  • CivilCraft
  64-bit

• Runoff depth by curve number

  The depth of runoff from a depth of rain.

  S = 25400 ÷ CN − 254; Q = (P − 0.2S)² ÷ (P + 0.8S) for P > 0.2S

  Detention pond hydrology and routing detention.js

  • CivilCraft
  64-bit

• Runoff hydrograph (triangular unit hydrograph)

  Flow against time from a catchment for a storm, with its peak and volume.

  Tp = Δt ÷ 2 + 0.6·Tc; qp = 0.208·A ÷ Tp; base = 2.67·Tp; Q(t) = Σ ΔQₖ·u(t − k·Δt)

  Detention pond hydrology and routing detention.js

  • CivilCraft
  64-bit

• Runoff hydrograph (rational method)

  A trapezoid hydrograph from the rational method peak.

  Qp = C·i·A ÷ 360 (i in mm/h, A in hectares, Q in m³/s)

  Detention pond hydrology and routing detention.js

  • CivilCraft
  64-bit

• Stage and storage table

  Water surface area and stored volume at each level of the pond.

  slopes: area = A₀ + P₀·m·h + π·m²·h²; storage = A₀·h + P₀·m·h² ÷ 2 + π·m²·h³ ÷ 3; table: V += h ÷ 3·(A₁ + A₂ + √(A₁·A₂))

  Detention pond hydrology and routing detention.js

  • CivilCraft
  64-bit

• Storage of a low place in the ground

  Area and volume below each level inside a polygon on the ground surface.

  storage(z) = Σ cells below z of (z − ground) × cell area

  Detention pond hydrology and routing detention.js

  • CivilCraft
  64-bit

• Flow through one outlet

  Discharge of an orifice, pipe, weir, spillway, V-notch or riser at a water level.

  orifice: Cd·A·√(2g·(h − D/2)); weir: Cw·(L − 0.2·n·H)·H^1.5; V-notch: (8 ÷ 15)·Cd·√(2g)·tan(θ/2)·H^2.5

  Detention pond hydrology and routing detention.js

  • CivilCraft
  64-bit

• Table interpolation

  A value read from a table between two rows, used for storage, level and outflow.

  Detention pond hydrology and routing detention.js

  • CivilCraft
  64-bit

• Modified Puls routing

  Storage and outflow at each time step from the inflow hydrograph.

  2S₂ ÷ Δt + O₂ = I₁ + I₂ + (2S₁ ÷ Δt − O₁)

  Detention pond hydrology and routing detention.js

  • CivilCraft
  64-bit

• Pond routing results

  Peak inflow and outflow, the highest level, the greatest storage, attenuation, draw-down time and the volumes in and out.

  attenuation = 1 − peak out ÷ peak in; volume = Σ (q₁ + q₂) ÷ 2 × Δt

  Detention pond hydrology and routing detention.js

  • CivilCraft
  64-bit

• Orifice diameter for a target outflow

  The orifice diameter at which the peak outflow just reaches the allowed flow.

  Detention pond hydrology and routing detention.js

  • CivilCraft
  64-bit

• Pond checks

  Overtopping, peak above the target, no attenuation, slow draw-down and a dry pond.

  Detention pond hydrology and routing detention.js

  • CivilCraft
  64-bit

• A saved pond in project units

  Converts a saved pond to SI, runs it, and converts the results back for display.

  1 ft = 0.3048 m; 1 ft² = 0.09290304 m²; 1 acre = 4046.8564224 m²; 1 in = 25.4 mm; 1 ft³/s = 0.028316846592 m³/s

  Detention pond hydrology and routing detention.js

  • CivilCraft
  64-bit

• Sun azimuth and altitude

  The sun's direction and height above the horizon at a moment and a place.

  JD = ms ÷ 86 400 000 + 2 440 587.5; T = (JD − 2 451 545) ÷ 36 525; cos Z = sin φ·sin δ + cos φ·cos δ·cos H

  Sun position drive.js

  • CivilCraft
  64-bit

• Atmospheric refraction

  The lift of the sun's apparent altitude by the atmosphere, added to the geometric altitude.

  h > 5°: 58.1 ÷ tan h − 0.07 ÷ tan³h + 0.000086 ÷ tan⁵h seconds of arc

  Sun position drive.js

  • CivilCraft
  64-bit

• Unit vector toward the sun

  The sun's direction as east, north and up components.

  (cos h·sin a, cos h·cos a, sin h)

  Sun position drive.js

  • CivilCraft
  64-bit

• Ground samples inside the area

  A grid of ground elevations inside the polygon, each standing for one cell of ground.

  cell = √(bounding box area ÷ 20 000) unless given

  Earthwork balance and haul plan earthwork.js

  • CivilCraft
  64-bit

• Cut and fill volumes

  Cut, fill, usable cut and the net at a design level.

  fill = area × Σ max(design − ground, 0); cut = area × Σ max(ground − design, 0); net = cut × factor − fill

  Earthwork balance and haul plan earthwork.js

  • CivilCraft
  64-bit

• Balanced level

  The design level at which usable cut equals fill.

  Earthwork balance and haul plan earthwork.js

  • CivilCraft
  64-bit

• Design plane

  The design elevation at a point for a level and two grades.

  z = z₀ + gx·(x − cx) + gy·(y − cy)

  Earthwork balance and haul plan earthwork.js

  • CivilCraft
  64-bit

• Free-haul moment

  The volume moved times the distance between the centroid of cut and the centroid of fill.

  moment = min(cut × factor, fill) × |centroid(cut) − centroid(fill)|

  Earthwork balance and haul plan earthwork.js

  • CivilCraft
  64-bit

• Best tilt

  The level and tilt, within the grade limit, that balance with the least haul moment.

  Earthwork balance and haul plan earthwork.js

  • CivilCraft
  64-bit

• Blocks of cut and fill

  Cells grouped into blocks, each with its volume and its volume-weighted center.

  center = Σ (p × v) ÷ Σ v

  Earthwork balance and haul plan earthwork.js

  • CivilCraft
  64-bit

• Minimum-cost transport

  How much goes from each block of cut to each block of fill at the least total volume times distance.

  Earthwork balance and haul plan earthwork.js

  • CivilCraft
  64-bit

• Haul plan totals

  Volume moved on site, total haul, average haul distance, and what is left to take away or bring in.

  haul = Σ volume × distance; average = haul ÷ moved

  Earthwork balance and haul plan earthwork.js

  • CivilCraft
  64-bit

• Earthwork balancer run

  The volumes at the pad's present level, the balanced level, the tilt and the haul plan for one pad.

  factor = 1 + percent ÷ 100; cell area = cell²

  Earthwork, route and pond tools: values stored and exported eg-ui.js

  • CivilCraft
  64-bit

• Balanced level written to the pad

  The pad's level, and its corner elevations when it tilts, as stored in the project.

  z stored = Number(z.toFixed(3))

  Earthwork, route and pond tools: values stored and exported eg-ui.js

  • CivilCraft
  64-bit

• Haul plan CSV

  The haul flows exported as a CSV file.

  Earthwork, route and pond tools: values stored and exported eg-ui.js

  • CivilCraft
  64-bit

• Alignment from a found route

  The PIs of a new alignment from the route's points, with a curve radius at each bend.

  r = min(R, min(l₁, l₂) ÷ (2·tan(Δ/2))), stored to 2 decimals

  Earthwork, route and pond tools: values stored and exported eg-ui.js

  • CivilCraft
  64-bit

• Route ends picked in the plan

  The start and end of a route search as taken from two picked points.

  x, y = Number(v.toFixed(3))

  Earthwork, route and pond tools: values stored and exported eg-ui.js

  • CivilCraft
  64-bit

• Sized orifice written to the pond

  The orifice diameter found for the target outflow, as stored in the pond.

  diameter stored = Number((d ÷ L).toFixed(3))

  Earthwork, route and pond tools: values stored and exported eg-ui.js

  • CivilCraft
  64-bit

• Pond hydrograph CSV

  Inflow, outflow and stage against time exported as a CSV file.

  Earthwork, route and pond tools: values stored and exported eg-ui.js

  • CivilCraft
  64-bit

• Survey points for progress checks

  Ground points read from a LAS, LAZ, CSV or text file and turned into a surface.

  LAS thinning cell = max(0.5, √(extent area ÷ 400 000)) unless a spacing is given

  Earthwork, route and pond tools: values stored and exported eg-ui.js

  • CivilCraft
  64-bit

• Three-decimal rounding of tool results

  The rounding applied to nearly every number a tool returns to an assistant or script.

  r3(v) = round(v × 1000) ÷ 1000

  Earthwork, route and pond tools: values stored and exported eg-agent.js

  • CivilCraft
  64-bit

• Volumes in report units

  Volumes converted to cubic yards or cubic meters for a tool's answer.

  cubic yards = cubic feet ÷ 27; from cubic meters: ÷ 0.028316846592 ÷ 27

  Earthwork, route and pond tools: values stored and exported eg-agent.js

  • CivilCraft
  64-bit