Calculations

Calculations

• Elbow area and angle

  The sheet-metal area of an elbow and the angle in its name.

  area = perimeter × centerline length; name angle = round(θ × 180 ÷ π)

  Duct runs, fittings and schedule addons/hvac/lib/duct.js

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• Transition area

  The sheet-metal area of a transition between two sizes.

  rectangular: bottom + top + two sides as trapezoids over their slant lengths; other: (pₐ + p_b) ÷ 2 × slant length

  Duct runs, fittings and schedule addons/hvac/lib/duct.js

  • CadCraft
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• Straight pieces

  The length and area of each straight piece of a run.

  du = s₁ − s₀; length = lenOut(du); area = perimeter × du

  Duct runs, fittings and schedule addons/hvac/lib/duct.js

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• Schedule totals

  The total duct length, total sheet-metal area and number of fittings.

  length = Σ rows; area = Σ duct areas + Σ fitting areas

  Duct runs, fittings and schedule addons/hvac/lib/duct.js

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• A run in the other unit system

  Converts a run's sizes and airflows between inches with cfm and millimeters with L/s.

  size × 25.4 or ÷ 25.4; airflow × 0.47194745 or ÷ 0.47194745

  Duct runs, fittings and schedule addons/hvac/lib/duct.js

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• A typed duct size

  Reads a size such as 24x12 or Ø14.

  Duct runs, fittings and schedule addons/hvac/main.js

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• A point pulled onto a run's centerline

  Moves a point picked inside a duct's outline onto its centerline, to start or end a branch there.

  inside when distance ≤ W ÷ 2 + 1e-9

  Duct runs, fittings and schedule addons/hvac/main.js

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• Schedule table in the drawing

  The rows of the duct schedule placed in the drawing.

  shown length and area = value.toFixed(1), trailing zeros removed

  Duct runs, fittings and schedule addons/hvac/main.js

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• Schedule CSV

  Writes the duct schedule as CSV.

  length, perimeter, area: 3 decimals; velocity: 0 decimals (inch units) or 2; friction rate: 4 decimals

  Duct runs, fittings and schedule addons/hvac/main.js

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• Liters per second in one cfm

  The factor that converts airflow from cubic feet per minute to liters per second.

  1 cfm = 0.3048³ ÷ 60 × 1000 L/s = 0.4719474432 L/s exactly

  Duct network pressure: drawing adapter addons/hvac/lib/ductnet.js

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• Millimeters per drawing unit

  The factors that take a run's coordinates, sizes and airflow to millimeters and L/s.

  draw = k × 25.4 (inch) or k; size = 25.4 or 1; lps = CFM_LPS or 1

  Duct network pressure: drawing adapter addons/hvac/lib/ductnet.js

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• Turn at a corner

  The angle a run turns through at a corner, in degrees.

  turn = acos(u·v ÷ (|u| |v|)) × 180 ÷ π

  Duct network pressure: drawing adapter addons/hvac/lib/ductnet.js

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• Runs handed to the engine

  Each run's vertices in millimeters, its section size in millimeters, and its free ends with their airflow.

  vertex mm = p × draw; w mm = w × size; z mm = z × draw

  Duct network pressure: drawing adapter addons/hvac/lib/ductnet.js

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• Fan point matched to a run end

  Finds the run end the fan sits on and takes its height.

  nearest end by √(Δx² + Δy²); accepted when ≤ 60 mm

  Duct network pressure: drawing adapter addons/hvac/lib/ductnet.js

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• Terminal airflows

  The airflow in L/s at each free end of the network.

  L/s = q × lps factor of the run

  Duct network pressure: drawing adapter addons/hvac/lib/ductnet.js

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• Pascals to inches of water

  Converts a pressure in pascals to inches of water gauge.

  in. w.g. = Pa ÷ 249.08891

  Duct network pressure: drawing adapter addons/hvac/lib/ductnet.js

  • CadCraft
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• Network result CSV

  Writes the result rows as CSV.

  length 2 decimals; airflow 1; velocity 2; rate 3; pressures 1

  Duct network pressure: drawing adapter addons/hvac/lib/ductnet.js

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• Numbers read from an IES file

  Splits the numeric part of an IES file into numbers.

  Luminaire files and point-by-point illuminance addons/lighting/lib/mep/photometry.js

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• IES candela values and luminaire size

  Scales the candela table and converts the luminous opening to millimeters.

  cd = value × multiplier × ballast factor; lumens = lamps × lumens per lamp; size mm = value × 304.8 (feet) or × 1000 (meters)

  Luminaire files and point-by-point illuminance addons/lighting/lib/mep/photometry.js

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• Full set of horizontal planes

  Mirrors the horizontal planes of a symmetric IES file to cover 0 to 360 degrees.

  quadrant: a, 180 − a, 180 + a, 360 − a; bilateral: a, 360 − a

  Luminaire files and point-by-point illuminance addons/lighting/lib/mep/photometry.js

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• EULUMDAT lamp flux and watts

  Adds up the lamp flux and wattage of the lamp sets in an EULUMDAT file.

  lumens = Σ |count| × flux; watts = Σ watts

  Luminaire files and point-by-point illuminance addons/lighting/lib/mep/photometry.js

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• EULUMDAT candela scale

  Turns the file's cd per 1000 lm values into candela.

  cd = value × (lumens ÷ 1000) × (LORL ÷ 100) × conversion factor

  Luminaire files and point-by-point illuminance addons/lighting/lib/mep/photometry.js

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• Position in an angle table

  Finds the two table angles on either side of an angle and the fraction between them.

  f = (x − a_lo) ÷ (a_hi − a_lo)

  Luminaire files and point-by-point illuminance addons/lighting/lib/mep/photometry.js

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• Candela in a direction

  The luminous intensity at a vertical and horizontal angle, interpolated from the table.

  I = (1 − f_h) (I₀₀ (1 − f_v) + I₀₁ f_v) + f_h (I₁₀ (1 − f_v) + I₁₁ f_v)

  Luminaire files and point-by-point illuminance addons/lighting/lib/mep/photometry.js

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• Luminaire axes

  The nadir, C0 and C90 directions of an aimed and rotated luminaire.

  n = aim ÷ |aim|; r₀ = axis − (axis·n) n, normalized; r = r₀ cos t + (n × r₀) sin t

  Luminaire files and point-by-point illuminance addons/lighting/lib/mep/photometry.js

  • CadCraft
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• Illuminance at a point

  The direct illuminance in lux at a point on a surface from all luminaires.

  E = LLF × Σ I(γ, C) × scale × cos θ ÷ d², d in meters

  Luminaire files and point-by-point illuminance addons/lighting/lib/mep/photometry.js

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• Calculation grid

  The points the illuminance is computed at: cell centers inside the area at the working height.

  nₓ = max(1, round(width ÷ spacing)); x = x₀ + (width ÷ nₓ) × (i + 0.5)

  Luminaire files and point-by-point illuminance addons/lighting/lib/mep/photometry.js

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• Minimum, average, maximum and uniformity

  The statistics of the grid values.

  avg = Σ E ÷ n; uniformity = min ÷ avg; min ÷ max

  Luminaire files and point-by-point illuminance addons/lighting/lib/mep/photometry.js

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• Area and lighting power density

  The area in square meters, the total lumens and watts, and the watts per square meter.

  area m² = |Σ (xᵢ yᵢ₊₁ − xᵢ₊₁ yᵢ)| ÷ 2e6; LPD = watts ÷ area

  Luminaire files and point-by-point illuminance addons/lighting/lib/mep/photometry.js

  • CadCraft
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• Checks against typed targets

  Compares the average, minimum, uniformity and power density with the targets the person typed.

  avg ≥ target; min ≥ target; min ÷ avg ≥ target; LPD ≤ limit

  Luminaire files and point-by-point illuminance addons/lighting/lib/mep/photometry.js

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• Grid CSV

  Writes each grid point and its illuminance.

  x, y, z = round(mm); lux = value.toFixed(1)

  Luminaire files and point-by-point illuminance addons/lighting/lib/mep/photometry.js

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• Lighting report CSV

  Writes one row per area with its totals and statistics, then every grid point.

  area and lux 1 decimal; lumens and watts 0; W/m² and min ÷ avg 2

  Luminaire files and point-by-point illuminance addons/lighting/lib/mep/photometry.js

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• Inputs of an illuminance run

  The mounting height, working height, grid spacing and light loss factor asked for a run.

  mount ≥ 100 mm; work ≥ 0; spacing ≥ 50 mm; 0.05 ≤ LLF ≤ 1

  Luminaire files and point-by-point illuminance addons/lighting/main.js

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• Result printed in the command line

  The summary line of an illuminance run.

  min, avg, max: whole lux; uniformity 2 decimals; area and W/m² 1 decimal

  Luminaire files and point-by-point illuminance addons/lighting/main.js

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• Length of a position

  The length of a pipe, truss or floor line along its points.

  L = Σ √(Δx² + Δy²)

  Stage lighting plot: positions, fixtures and loads addons/lighting/lib/model.js

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• Where a point is on a position

  The distance along a position to the point nearest a fixture, and the fixture's distance from the line.

  u = clamp((p − a)·(b − a) ÷ |b − a|², 0, 1); s = length before + u × |b − a|; off = |p − q|

  Stage lighting plot: positions, fixtures and loads addons/lighting/lib/model.js

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• Position a fixture belongs to

  The nearest named position within reach of a point.

  nearest with off ≤ tol

  Stage lighting plot: positions, fixtures and loads addons/lighting/lib/model.js

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• Fixture data checked

  Checks a fixture's stored data: scale, wattage, DMX footprint and aim angle.

  aim = ((aim mod 360) + 360) mod 360

  Stage lighting plot: positions, fixtures and loads addons/lighting/lib/model.js

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• Wattage of a fixture

  The watts of a fixture: its own value, or its type's typical value.

  Stage lighting plot: positions, fixtures and loads addons/lighting/lib/model.js

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• Point at a distance along a position

  The drawing point a given distance along a position's line.

  u = clamp((s − run) ÷ l, 0, 1); p = a + (b − a) × u

  Stage lighting plot: positions, fixtures and loads addons/lighting/main.js

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• Fixtures spread along a position

  Places n fixtures evenly along a position.

  sᵢ = L × (i + 0.5) ÷ n

  Stage lighting plot: positions, fixtures and loads addons/lighting/main.js

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• A position moved, turned or scaled

  Applies a move, rotation or scale to a position's points and its scale.

  k′ = k × √(m₀² + m₁²); p′ = M · p

  Stage lighting plot: positions, fixtures and loads addons/lighting/main.js

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• Fixture symbol turned to its aim

  Rotates a fixture's symbol by its aim angle.

  x′ = x cos a − y sin a; y′ = x sin a + y cos a

  Stage lighting plot: positions, fixtures and loads addons/lighting/lib/draw.js

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• Position length in millimeters

  The length of a position for the schedule and the capacity warning.

  mm = length in drawing units ÷ k

  Stage lighting plot: positions, fixtures and loads addons/lighting/lib/draw.js

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• Legend totals

  The total number of fixtures and total watts at the foot of the legend.

  total = Σ count; total watts = Σ watts

  Stage lighting plot: positions, fixtures and loads addons/lighting/lib/draw.js

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• A drawing object as a nest loop

  Turns a circle or closed polyline into a loop of points with bulges.

  circle = (cx + r, cy) and (cx − r, cy), each with bulge 1

  Nesting add-on: outlines in, placed copies out addons/nesting/lib/parts.js

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• Outline as chords for containment

  Points along an outline, with each arc as 8 chords, used to test which outline contains which.

  θ = 4 atan(b); r = c ÷ (2 sin(θ ÷ 2)); center = chord middle + normal × r cos(θ ÷ 2)

  Nesting add-on: outlines in, placed copies out addons/nesting/lib/parts.js

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• Parts and their holes

  Groups outlines into parts with holes and moves each part to its own corner.

  parent = smallest larger outline containing the first point; shifted point = p − (x₀, y₀)

  Nesting add-on: outlines in, placed copies out addons/nesting/lib/parts.js

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• A part's object placed on the sheet

  Moves and turns one object of a part to where the engine placed it.

  q = at + (x, y) + R(rot) · (p − origin)

  Nesting add-on: outlines in, placed copies out addons/nesting/lib/parts.js

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• Sheet rectangles and labels

  A rectangle for each sheet, side by side, and the part names over the copies.

  xₖ₊₁ = xₖ + w + gap, gap = max(20, 0.1 × h) by default; label at the mean of the outline's points

  Nesting add-on: outlines in, placed copies out addons/nesting/lib/parts.js

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