Fill limits are a thermal and mechanical rule, not a packing one
A conduit carrying more than two conductors is considered full at about forty per cent of its cross-sectional area. Far more cable than that will physically fit, and the limit is not about whether it fits.
It is about two things the extra cable would prevent. HEAT generated in the conductors has to reach the conduit wall and leave; a tightly packed raceway insulates its own core and the middle conductors run hottest. And the cable has to be INSTALLED — pulled through, around bends, without its insulation being scraped, stretched or crushed — and a full conduit makes that impossible without damage nobody will see afterwards.
The permitted percentage changes with the number of conductors for the same reason. One cable may occupy more than half the bore because it has the whole wall to shed heat to and a clear path to be pushed along; two are limited more tightly because a pair can jam against each other in a bend; three or more settle at the familiar forty.
Bundling adds a second, separate penalty. Conductors grouped in a raceway each carry less current than they could alone, because their heat is shared — so a conduit at legal fill can still oblige every cable in it to be derated. Fill and ampacity are two different checks and passing one says nothing about the other.
- T_in, T_out
- pulling tension entering and leaving a bend
- μ
- coefficient of friction — what lubricant reduces
- θ
- bend angle in RADIANS, accumulated over the whole pull
- R
- bend radius; a tighter bend crushes the cable at the same tension
Tension multiplies through bends, so the order of the bends matters
Pulling a cable along a straight run adds tension in proportion to length and weight. Pulling it around a bend MULTIPLIES the tension already present, by a factor that grows exponentially with the angle turned.
The numbers are startling. At a friction coefficient of a half, a single ninety-degree bend multiplies tension by about two point two; two of them by about four point eight; three by more than ten. A run with four right angles can arrive at its end needing more than twenty times the force it started with, and a cable that would pull easily through any one of those bends cannot be pulled through all four.
Because the effect is multiplicative, the SEQUENCE changes the answer. A bend near the start of a pull multiplies a small tension; the same bend near the end multiplies a large one. Pulling the same run from the opposite end — so that the bends come early while the cable is still light and slack — can reduce the peak tension substantially without changing a single fitting.
That is why an experienced installer's first question about a difficult pull is which way to pull it, and why a design that adds a pull box in the middle of a long bent run is not conceding anything: it resets the tension to zero and turns one impossible pull into two easy ones.
Sidewall bearing pressure is the limit tension alone does not show
A cable under tension going around a bend is pressed against the outside of that bend, and the force per unit of length pressing it there is the tension divided by the RADIUS. That is sidewall bearing pressure, and it is a separate limit from tension.
It is the reason a tight bend is dangerous at a tension a gentle bend would tolerate. Halving a bend radius doubles the crushing force at the same pull, and the damage it causes — flattened insulation, a displaced conductor, a compromised shield — is invisible from outside and shows up as a fault months later.
There is also a static minimum bend radius that applies whether or not anything is being pulled, set by the cable's construction and quoted as a multiple of its diameter. Armoured, shielded and large cables have the largest multiples, and a cable bent tighter than its minimum is damaged at the moment of installation.
The two limits interact in the obvious way. A pull designed to stay within its tension limit can still fail on sidewall pressure at one tight bend, so both are checked, and the fitting that governs is usually the last bend before the end of the pull.
Tray is a beam, and the load arrives after the design
Cable tray is a structural member. It spans between supports, carries a distributed load, and deflects — and deflection goes with the fourth power of the span, exactly as it does for a joist, which is why halving a support spacing reduces sag by a factor of sixteen.
The awkward part is that the load is decided later. A tray is installed early and filled by whoever comes afterwards, often by several trades over months, and the weight per metre at the end of a project frequently exceeds what anybody calculated at the start. A tray designed to its predicted load with no margin is a tray that will be overloaded by the second cable that was not in the schedule.
So the load figure is the sum of the cable weights the tray will EVENTUALLY carry, plus an allowance, plus a concentrated load representing a person standing on it — which is not a design intent but is a thing that happens and which manufacturers' load tables include for that reason.
Tray fill is expressed differently from conduit fill — as a depth or a cross-sectional allowance rather than a single percentage — but it is answering the same question. Cables piled deep in a tray insulate the ones underneath, so the derating that applies to a bundled raceway applies to a deep tray too, and a single layer with spacing between cables carries far more current than the same cables heaped.
Heating cable is a power balance, and the length is the easy part
A heat trace on a pipe is not sized by length. Its length is the pipe's length, and the design quantity is the POWER PER METRE needed to replace the heat the pipe loses at the design condition — which follows from the pipe's diameter, its insulation, the temperature to be maintained and the coldest ambient expected.
Get that balance wrong in either direction and it fails differently. Too little and the pipe freezes despite having a heater on it; too much on a self-limiting product wastes energy, and too much on a constant-wattage product can exceed the temperature rating of the pipe's contents or its insulation.
SELF-REGULATING cable changes the problem in a way worth understanding. Its conductive core increases resistance as it warms, so each centimetre independently reduces its output where the pipe is already warm and increases it where it is cold. That makes it forgiving of overlap and of being cut to length on site — but it also means its rated output is quoted at a stated pipe temperature, and its actual output at the design condition is lower or higher than the headline figure.
Start-up is the case that catches designs out. A self-regulating cable draws a large inrush when energised cold, several times its running current, so the circuit protection is sized for that inrush rather than for the steady load — and a circuit sized on running watts will trip every time it is switched on in winter.
Snow melting is a latent problem, and that is why it needs so much power
Heating a driveway is not like heating a room, and the installed power per square metre is far higher than any building surface would need. The reason is that most of the energy does not go into raising a temperature.
The load has three parts. Melting the snow is a LATENT load — changing ice to water at constant temperature — and latent heat dominates it. Then the meltwater and the slab have to be kept above freezing, which is sensible. And the slab loses heat downwards into the ground and upwards by evaporation and convection to a cold, often windy, sky the whole time.
The design case is a snowfall RATE together with an air temperature and a wind speed, not a total depth, because the system has to keep up with snow as it arrives. A system sized for a gentle fall at a mild temperature will be overwhelmed by the same total depth delivered faster or colder.
It also takes time to respond, because the slab has to be warmed before any melting happens. That is why these systems are controlled by moisture-and-temperature sensors that start them BEFORE the snow arrives rather than by a thermostat that reacts to it, and why an idling setpoint that keeps the slab just below freezing costs energy continuously and is nevertheless the way a responsive system is run.
Radiant cable spacing is an output density with a temperature ceiling
Cable in a floor delivers a fixed power per metre of cable. What the room experiences is power per square metre of FLOOR, and the conversion between them is the spacing: halve the spacing and you double the output density.
So the spacing is chosen from the heat the floor must deliver, and then checked against two limits that have nothing to do with the heating requirement. There is a maximum floor SURFACE temperature for comfort and for the covering — timber, vinyl and some adhesives have their own ceilings — and there is a minimum spacing below which the cable itself overheats.
Uniformity is the constraint that decides the layout. Cable laid at varying spacing produces warm stripes and cool stripes that are detectable underfoot, and a cable must never cross itself, because the crossing point has twice the local output and no extra path for it to escape. Both are laying rules rather than calculations, and both are why a cable's length has to be planned onto the actual floor rather than ordered from an area.
The final constraint is that the length is fixed. A cable set cannot be cut to fit — cutting changes its resistance and therefore its output and its load — so the room has to be laid out to consume exactly the length supplied, which is why the spacing is adjusted to fit the cable rather than the cable ordered to fit the spacing. That inversion is the single most useful thing to know before ordering one.
Calculators that use this method
Basis
- NFPA 70 (National Electrical Code) Chapter 9 tables and Annex C for conduit fill percentages, and 310.15 for ambient and bundling adjustment of ampacity.
- NFPA 70 Article 392 for cable tray installation, fill and support; manufacturers' published load-span tables for tray deflection under distributed and concentrated loads.
- The capstan equation for tension around a bend, and IEEE Std 1185 / NECA pulling guidance for friction coefficients, lubricant effects and sidewall bearing pressure limits.
- Cable manufacturers' published maximum pulling tension per unit of conductor area, minimum bend radius multiples, and sidewall pressure limits by construction.
- IEEE Std 515 and IEC 62395 for electrical resistance heat tracing: power balance against pipe heat loss, self-regulating behaviour and cold start-up inrush.
- ASHRAE Handbook, HVAC Applications, Snow Melting and Freeze Protection — the latent, sensible and loss components and the snowfall-rate design condition.
- IEC 60800 and floor heating manufacturers' guidance for cable spacing, maximum floor surface temperature by covering, and the fixed-length constraint on factory-terminated sets.