Calculations

Calculations

• Phase spacing needed

  The spacing between phases a span needs, from its largest sag.

  need = k·√(sag + insulator length) + U ÷ 150 (U in kV)

  Overhead line checks: clearances, support loads and sizing powerline/checks.js

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• Loads on a support

  The transverse, longitudinal and vertical load on a support in each load case and the equivalent load at its nominal point.

  T = n·(w_h × wind span + (H_L + H_R)·sin(turn ÷ 2)); V = n·w_v × weight span + equipment; F_eq = √(T² + L²) × attach height ÷ nominal height

  Overhead line checks: clearances, support loads and sizing powerline/checks.js

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• Insulator swing angle

  The angle a suspension insulator swings to under the wind case.

  swing = atan2(T per conductor, V per conductor + insulator weight ÷ 2)

  Overhead line checks: clearances, support loads and sizing powerline/checks.js

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• Support strength check

  Whether the support's nominal load covers the worst equivalent load times the size factor.

  ok when worst F_eq × factor ≤ nominal × (1 + 1e−6)

  Overhead line checks: clearances, support loads and sizing powerline/checks.js

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• Foundation size

  The depth, diameter and volume of a support's foundation hole.

  depth = embedment, or height ÷ 10 + 0.5; diameter = max(0.6, foot diameter + 0.3) m; volume = π·d² ÷ 4 × depth

  Overhead line checks: clearances, support loads and sizing powerline/checks.js

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• Where a span crosses an obstacle in plan

  The positions along a span, from 0 to 1, where it crosses an obstacle's outline or passes a single point.

  t = ((p − a) × e) ÷ (d × e); u = ((p − a) × d) ÷ (d × e)

  Overhead line checks: clearances, support loads and sizing powerline/checks.js

  • CivilCraft
  64-bit

• Plant sizes in project units

  The factor that turns a plant's mature height and spread in meters into project units.

  project units per meter = 1 ÷ (1200 ÷ 3937) for feet

  Overhead line checks: clearances, support loads and sizing powerline/landscape-obstacles.js

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  64-bit

• Tree canopy as a ring

  The outline of a plant's canopy used to find where a span passes over it.

  12 points on the circle of radius r: (x + r·cos(2πk ÷ 12), y + r·sin(2πk ÷ 12))

  Overhead line checks: clearances, support loads and sizing powerline/landscape-obstacles.js

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• A plant as an obstacle

  A single plant's canopy radius, height and ground level as an obstacle under a line.

  radius = max(spread ÷ 2, 0.1); height = mature height

  Overhead line checks: clearances, support loads and sizing powerline/landscape-obstacles.js

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• Foundation volume shown in cubic yards

  The foundation volume in the support's properties, in cubic yards for a feet project.

  yd³ = m³ × 1.307951

  Overhead line checks: clearances, support loads and sizing powerline/powerline-ui.js

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• Length of a span in the network

  The electrical length of each overhead span.

  length = √(Δx² + Δy²) × m per unit

  Power network: load current and voltage drop powerline/network.js

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  64-bit

• Snapping to the nearest node

  Finds the support or equipment a route end or a piece of equipment connects to.

  nearest node with distance × m per unit ≤ snap + 1e−9

  Power network: load current and voltage drop powerline/network.js

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• Resistance, reactance and ampacity of an edge

  The electrical data of a span or cable route, with parallel cables counted.

  R = R₂₀ ÷ n; X = X ÷ n (0.08 or 0.35 Ω/km by default); ampacity × n

  Power network: load current and voltage drop powerline/network.js

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• Loads summed upstream

  The active and reactive power each edge carries, and the current each load draws.

  Q = P·tan(acos pf); I = √(P² + Q²) ÷ (√3·U)

  Power network: load current and voltage drop powerline/network.js

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• Current, voltage drop and node voltage

  The current and voltage drop in each edge and the voltage and cumulative drop at each node.

  ΔU = √3·I·(L ÷ 1000)·(R·cos φ + X·sin φ); drop % += ΔU ÷ (U × 1000) × 100; U node = U·(1 − drop ÷ 100)

  Power network: load current and voltage drop powerline/network.js

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• Route length

  The plan length of a cable route in project units.

  L = Σ √(Δx² + Δy²)

  Underground cable routes: cover, crossings, joints and trench quantities powerline/underground.js

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• Cover and cable band of a trench

  The cover over the cable and the thickness of the band the cable or its ducts occupy, in meters.

  cover = trench cover, or max(0, depth − bedding − band); band = duct diameter, or cable diameter

  Underground cable routes: cover, crossings, joints and trench quantities powerline/underground.js

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• Cable profile and cover check

  The ground and the top of the cable along the route, and whether the cover meets the minimum.

  cable = ground − cover ÷ m per unit; samples every L ÷ 100 by default

  Underground cable routes: cover, crossings, joints and trench quantities powerline/underground.js

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• Crossing of two plan segments

  Where two straight segments cross in plan, as a position along each.

  t = ((p − a) × e) ÷ (d × e); u = ((p − a) × d) ÷ (d × e)

  Underground cable routes: cover, crossings, joints and trench quantities powerline/underground.js

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• Crossings along the route

  Every place a segment crosses the route, with its chainage.

  ch = chainage of the vertex before + t × segment length

  Underground cable routes: cover, crossings, joints and trench quantities powerline/underground.js

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• Separation from a pipe at a crossing

  The clear vertical gap between the cable and a pipe where they cross.

  invert = (inv up + (inv down − inv up)·u) × m per unit; pipe top = invert + diameter; cable top = ground − cover; gap = max(cable bottom − pipe top, invert − cable top)

  Underground cable routes: cover, crossings, joints and trench quantities powerline/underground.js

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  64-bit

• Separation from another cable route

  The clear vertical gap between two cable routes that cross, each at its own cover under the same ground.

  gap between [−cover A − band A, −cover A] and [−cover B − band B, −cover B]

  Underground cable routes: cover, crossings, joints and trench quantities powerline/underground.js

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  64-bit

• Cables and pipes under an overhead line

  The cable routes and pipes an overhead line crosses in plan, with the line's chainage and the level of the top of each.

  cable top = ground − cover ÷ m per unit; pipe top = invert at the crossing + diameter

  Underground cable routes: cover, crossings, joints and trench quantities powerline/underground.js

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• Joints from the drum length

  How many joints each cable needs and where along the route they fall.

  run = length × (1 + slack %); joints per cable = ⌈run ÷ drum⌉ − 1; at = k × drum ÷ (1 + slack %)

  Underground cable routes: cover, crossings, joints and trench quantities powerline/underground.js

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• Trench quantities

  Trench length, excavation, bedding and backfill volumes, duct length and cable length of a route.

  excavation = width × depth × length; bedding = width × bedding × length; backfill = excavation − bedding − ducts × π(d ÷ 2)² × length; cable = (length × slack + 2 × depth) × count

  Underground cable routes: cover, crossings, joints and trench quantities powerline/underground.js

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• Numbers in the file

  Turns a value into the fixed-decimal text the file carries, and newtons into decanewtons.

  text = v.toFixed(d); daN = N ÷ 10, 2 decimals

  Line study file (.DON) export and import powerline/don.js

  • CivilCraft
  64-bit

• Signed line angle at each support

  The turn of the line at each support in degrees, counter-clockwise positive.

  turn = atan2 of the span ahead − atan2 of the span behind, wrapped to ±180°

  Line study file (.DON) export and import powerline/don.js

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  64-bit

• Support coordinates and heights written

  Each support's position, ground level, pole length, height above ground and line angle as written to the file.

  X = x × m per unit, 3 decimals; Hauteur = typed height × m per unit + embedment

  Line study file (.DON) export and import powerline/don.js

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  64-bit

• Section tension and catenary parameter written

  The reference temperature, horizontal tension and catenary parameter of each section as written to the file.

  Parametre = H ÷ w, 3 decimals; TensionIni = H ÷ 10 daN, 2 decimals

  Line study file (.DON) export and import powerline/don.js

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  64-bit

• Reading a number

  Turns a field's text into a number, accepting a decimal comma.

  Line study file (.DON) export and import powerline/don.js

  • CivilCraft
  64-bit

• Angles in grades

  Converts a line angle given in grades to degrees.

  degrees = grades × 0.9

  Line study file (.DON) export and import powerline/don.js

  • CivilCraft
  64-bit

• A study file into a line

  Turns the supports read from a file into a line in project units.

  x = X (m) ÷ m per unit; voltage kV = V ÷ 1000

  Line study file (.DON) export and import powerline/don.js

  • CivilCraft
  64-bit

• Cubic meters per cubic yard

  The factor used to give volumes in cubic yards in a feet project.

  1 yd³ = 0.764554857984 m³

  Power line tables, quantities and GIS export powerline/outputs.js

  • CivilCraft
  Exact

• Stringing table rows

  Tension, span length, sag and conductor length per section and temperature, in project units.

  length ÷ m per unit; force ÷ 10 for daN or ÷ 4.4482216152605 for lbf

  Power line tables, quantities and GIS export powerline/outputs.js

  • CivilCraft
  64-bit

• Stringing table CSV

  The stringing table as CSV text.

  lengths and sags round(v, 2); tension round(v, 1)

  Power line tables, quantities and GIS export powerline/outputs.js

  • CivilCraft
  64-bit

• Support table rows

  Ground, attachment, load, nominal load, foundation and swing per support, in project units.

  attach height = attach z − ground z; load = worst F_eq in daN or lbf

  Power line tables, quantities and GIS export powerline/outputs.js

  • CivilCraft
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• Conductor length to buy

  The conductor length of a line with an allowance for jumpers and waste.

  length = Σ catenary lengths × phases × circuits × 1.02 ÷ m per unit

  Power line tables, quantities and GIS export powerline/outputs.js

  • CivilCraft
  64-bit

• Lengths and volumes in project units

  Converts meters and cubic meters to feet and cubic yards for the quantity rows.

  LF = m ÷ 0.3048; CY = m³ ÷ 0.764554857984

  Power line tables, quantities and GIS export powerline/outputs.js

  • CivilCraft
  64-bit

• Quantities file for TakeoffCraft

  The quantity rows in the format TakeoffCraft reads.

  qty = round(qty, 2)

  Power line tables, quantities and GIS export powerline/outputs.js

  • CivilCraft
  64-bit

• Clear-sky beam and diffuse irradiance

  The irradiance outside the atmosphere, the beam transmittance, and the beam and diffuse irradiance at the ground.

  τ_b = a₀ + a₁·exp(−k ÷ cos Z); G_on = 1367·(1 + 0.033·cos(2πn ÷ 365)); G_bn = G_on·τ_b; τ_d = 0.271 − 0.294·τ_b

  Clear-sky solar irradiance pv/daylight-bim-sky.js

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• Meters per unit

  The length of each supported unit in meters.

  ft = 0.3048; US survey ft = 1200 ÷ 3937; in = 0.0254; yd = 0.9144; mi = 1609.344

  Placing a scanned sheet in the project scanstart/place.js

  • CivilCraft
  Exact

• Scale from two points

  Project units per pixel from two points on the scan and the true distance between them.

  units per pixel = distance ÷ √(Δpx² + Δpy²)

  Placing a scanned sheet in the project scanstart/place.js

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• Scale from a stated scale

  Project units per pixel from the scan's resolution and a scale such as 1 inch = 50 feet or 1:500.

  per ÷ dpi, or ratio × 0.0254 ÷ (m per unit) ÷ dpi

  Placing a scanned sheet in the project scanstart/place.js

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• Placement from a scale, origin and rotation

  The transform that puts the sheet's lower-left corner at a point, turned by an angle, at a given scale.

  c = s·cos θ, d = s·sin θ; X = x₀ − d·h + c·px + d·py; Y = y₀ + c·h + d·px − c·py

  Placing a scanned sheet in the project scanstart/place.js

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• Pixel to project coordinates

  The project position of a pixel.

  X = g₀ + g₁·px + g₂·py; Y = g₃ + g₄·px + g₅·py

  Placing a scanned sheet in the project scanstart/place.js

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  64-bit

• Inverse placement

  The transform from project coordinates back to pixels.

  det = g₁·g₅ − g₂·g₄; inverse = adjugate ÷ det

  Placing a scanned sheet in the project scanstart/place.js

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  64-bit

• Scale of a placement

  The project units per pixel a placement stands for, reported with every fit.

  scale = √|g₁·g₅ − g₂·g₄|

  Placing a scanned sheet in the project scanstart/place.js

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  64-bit

• Rotation of a placement

  The angle a placement turns the sheet by, in degrees.

  rotation = atan2(g₄, g₁) × 180 ÷ π

  Placing a scanned sheet in the project scanstart/place.js

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  64-bit

• 3 × 3 linear solve

  Solves the normal equations of the affine fit.

  Gauss-Jordan elimination with partial pivoting

  Placing a scanned sheet in the project scanstart/place.js

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  64-bit

• Least-squares fit to matched points

  The placement that best matches points picked on the scan to their project coordinates, with each point's residual and the root mean square.

  similarity: c = Σ(u·X + v·Y) ÷ Σ(u² + v²), d = Σ(u·Y − v·X) ÷ Σ(u² + v²); rms = √(Σ r² ÷ n)

  Placing a scanned sheet in the project scanstart/place.js

  • CivilCraft
  64-bit