Bench Degree·REFRIGERATIONchapter

Chapter 15: Load, Tons, and Airflow

Cooling is sold by the ton, which is a unit invented for melting ice and has nothing to do with weight. This chapter works out how big a machine a real room needs, and why the rule of thumb everyone uses is wrong.

Everything so far has been about how a machine works. This chapter is about how big it should be, which is a different question and the one most often got wrong in practice.

Chapter 14 showed that oversizing is actively harmful. So the size has to be calculated rather than guessed, and calculating it requires knowing what a “ton” is, where the heat is coming from, and how much air has to move to carry it.

Section 1: The Ton, and Its Genuinely Odd History

Cooling capacity in North America is measured in tons, and the unit is a fossil of the ice trade of Chapter 3.

Before mechanical refrigeration, cooling was bought as ice. So when machines arrived, the natural way to rate them was by comparison: how much ice would this machine replace?

The answer was standardised as the heat required to melt one short ton (2,000 lb, 907 kg) of ice at 0 °C (32 °F) over twenty-four hours.

The arithmetic, using the latent heat of fusion from Chapter 5:

2,000 lb × 144 Btu/lb = 288,000 Btu per 24 hours 288,000 ÷ 24 = 12,000 Btu/h

One ton of refrigeration = 12,000 Btu/h = 3.517 kW.

So a “three ton” air conditioner would melt three tons of ice a day. It weighs perhaps 90 kg (200 lb) and contains no ice whatsoever. The unit describes a duty, not a mass, and every confused customer who has asked why a three-ton unit does not weigh three tons has been misled by an eighteenth-century sales comparison.

The rest of the world uses kilowatts, which is cleaner. Both appear throughout this chapter.

That last row is the pair of machines in the installation of Chapter 21, which works them in detail.

Section 2: Where the Heat Actually Comes From

A cooling load is the sum of every source of heat entering the space, plus every source generated inside it. Nine of them, and the list is worth internalising because a load calculation is nothing but this list with numbers attached.

From outside:

Conduction through walls, roof and floor. Driven by the temperature difference and resisted by insulation. Q = U × A × ΔT, where U is the assembly’s heat transfer coefficient and A its area.

Solar gain through glass. Usually the largest single item in a house with any real glazing, and it depends enormously on orientation and shading. A square metre of unshaded west-facing glass can admit 500 to 700 W in late afternoon, which is more than the wall it replaced by a factor of twenty.

Solar gain on opaque surfaces. A dark roof in sun runs far above air temperature, so the effective ΔT for conduction is much larger than the thermometer suggests.

Infiltration. Outdoor air leaking in through gaps, and this one carries both sensible and latent load, because the incoming air brings its moisture with it. In a humid climate infiltration is often the dominant latent load.

Ventilation. Outdoor air brought in deliberately for air quality. Same physics as infiltration but intentional and therefore designable.

From inside:

People. A seated adult rejects roughly 75 W sensible and 55 W latent, about 130 W total (445 Btu/h). Active people much more. The latent part is breathing and perspiration, which is why a crowded room gets humid.

Lighting. Every watt becomes heat. LED lighting cut this dramatically; an older office at 20 W/m² of lighting was a genuine load.

Equipment. Every watt of electricity consumed inside the space becomes heat inside the space. Computers, motors, kettles, televisions.

Cooking and moisture sources. Kitchens, showers, indoor pools, wet processes. Mostly latent.

IN PLAIN ENGLISH: Every watt of electricity used inside a room ends up as heat in that room, and a cooling system has to remove all of it. A 500 W gaming computer is a 500 W heater. This is not approximately true; it is exactly true, because the energy has nowhere else to go.

Section 3: The Rule of Thumb, and Why It Fails

Contractors commonly size residential cooling at one ton per 45 to 55 m² (500 to 600 ft²) of floor area.

It is quick, it is sometimes close, and it is wrong often enough to matter, because floor area is a poor proxy for load. Two rooms of identical size can differ by a factor of three.

What the rule ignores:

• Glazing area and orientation. A room with one small north window and a room with a wall of west-facing glass are not comparable.
• Insulation. A 1920s uninsulated wall and a modern one differ by a factor of five in U-value.
• Ceiling height. Area says nothing about volume, and infiltration and ventilation scale with volume.
• Internal gains. A bedroom and a server room of the same footprint differ by ten times.
• Climate. Phoenix and Seattle need different machines for the same house.
• Shading and thermal mass.

The proper method is a room-by-room calculation, standardised in North America as ACCA Manual J. It is tedious rather than difficult, and any competent contractor should produce one on request. If a contractor sizes a system from floor area alone, that is the moment to ask for the calculation, because Chapter 14 established what oversizing costs in comfort.

Section 4: A Worked Load Calculation

A real room, worked start to finish. Numbers rounded for legibility.

The room. A home office, 4 m × 5 m (13 × 16 ft), so 20 m² (215 ft²), ceiling 2.7 m (9 ft). One west-facing window 2 m² (21.5 ft²), double glazed, unshaded. Insulated modern construction. Two occupants. A desktop computer and two monitors. Design conditions 35 °C (95 °F) outdoors, 24 °C (75 °F) indoors, so ΔT = 11 °C (20 °F).

Walls. Exterior wall area after subtracting the window, about 24 m². Insulated assembly at U = 0.35 W/m²·K. Q = 0.35 × 24 × 11 = 92 W

Ceiling. 20 m² at U = 0.20 W/m²·K, with an attic ΔT of 20 °C rather than 11 because the attic is far hotter than outdoor air. Q = 0.20 × 20 × 20 = 80 W

Window conduction. 2 m² at U = 1.8 W/m²·K. Q = 1.8 × 2 × 11 = 40 W

Window solar gain. 2 m² unshaded west glass in late afternoon, solar heat gain coefficient 0.6, incident about 600 W/m². Q = 2 × 600 × 0.6 = 720 W

Infiltration. Say 0.5 air changes per hour. Volume is 54 m³, so 27 m³/h, which is 0.0075 m³/s. Air density 1.2 kg/m³, specific heat 1.0 kJ/kg·K. Q = 0.0075 × 1.2 × 1000 × 11 = 99 W sensible Plus latent, for the moisture that air brings: roughly 60 W in a temperate climate.

People. Two at 75 W sensible and 55 W latent each. 150 W sensible, 110 W latent

Equipment. Computer and monitors, measured at the wall: 250 W

Lighting. LED, 20 m² at 5 W/m²: 100 W

Totals. Sensible: 92 + 80 + 40 + 720 + 99 + 150 + 250 + 100 = 1,531 W Latent: 60 + 110 = 170 W Total: 1,701 W, and SHR = 1,531 / 1,701 = 0.90

1,701 W is 5,800 Btu/h, or 0.48 tons.

Now compare against the rule of thumb. At one ton per 50 m², a 20 m² room gets 0.4 tons, which is 1,400 W. Close, and closer than it deserves to be.

But look at what dominates the calculation: the window, at 720 W, is 42 percent of the entire load. Change one thing, an external blind or an awning cutting solar gain by seventy percent, and the load falls to 1,197 W, a thirty percent reduction from a piece of fabric.

That is the real lesson of load calculation. It is not that the arithmetic gives a better number than the rule of thumb, though it does. It is that the arithmetic tells you which term to attack, and it is almost never the equipment.

SLOW DOWN. Check Your Understanding: The same room, but the window faces north instead of west, with solar gain of 100 W/m² instead of 600. What is the new total load, and what has happened to the SHR? Work it out before reading on.

Solar becomes 2 × 100 × 0.6 = 120 W, a reduction of 600 W. Sensible falls to 931 W, total to 1,101 W, which is 3,760 Btu/h or 0.31 tons. The same room needs a machine a third smaller because the window points a different way. And SHR falls to 931/1,101 = 0.85, because the latent load did not change while the sensible load shrank, so the water is now a larger fraction of the job. Orientation changed both the size and the character of the machine required.

Section 5: Airflow, and the 400 CFM Rule

A machine’s capacity is only realised if enough air passes over the coil. Too little airflow and the coil gets too cold, the split gets too large, and eventually it ices. Too much and the coil never gets cold enough to dehumidify.

The rule of thumb is 400 CFM per ton, which is 680 cubic metres per hour per ton, or about 190 litres per second, or 24,000 cubic feet per hour.

Where it comes from is worth seeing, because it is the same Q = m c ΔT from Chapter 4 rearranged.

One ton is 12,000 Btu/h. Aim for a temperature split of 20 °F. Air’s specific heat is 0.24 Btu/lb·°F and its density about 0.075 lb/ft³.

mass flow = 12,000 / (0.24 × 20) = 2,500 lb/h volume flow = 2,500 / 0.075 = 33,333 ft³/h = 556 CFM

That gives 556, not 400. The difference is latent load: on a typical residential system some of the capacity goes into condensing water rather than dropping temperature, so less airflow is needed for a given sensible duty. 400 CFM/ton assumes an SHR around 0.75.

Which immediately tells you when the rule is wrong:

Lower airflow means a colder coil and more dehumidification. Higher airflow means a warmer coil and more sensible cooling. Airflow is therefore not merely a plumbing detail: it is the knob that sets the sensible-latent split, and it is the single most commonly maladjusted item in the field.

ON THE BENCH: Measure your own airflow

Parts: an anemometer, $35; a tape measure; two thermometers. Cost: about $50. Time: 30 minutes. Method: measure the free area of a supply register in m² or ft². Take several velocity readings across its face with the anemometer and average them. Multiply average velocity by free area to get volume flow. Sum across all registers. Then cross-check with the temperature split. Measure return and supply air temperature. With the machine’s nameplate capacity, rearrange Q = m c ΔT to solve for the airflow the temperatures imply. What you should find: the two estimates within perhaps twenty percent of each other, and both often well below the design figure, because real duct systems leak and restrict. A system nominally moving 1,200 CFM frequently moves 900. What that means: the machine is delivering less than its rating, and no amount of refrigerant will fix it. This is why Chapter 12 insists on checking airflow before touching the charge. More systems are ruined by technicians adding refrigerant to compensate for an airflow problem than by any other single error.

Section 6: Duct Sizing, Briefly

Airflow has to get there, and the constraint is friction.

Velocity limits exist for noise as much as for pressure. Residential main trunks run at 4 to 6 m/s (800 to 1,200 ft/min); branches at 3 to 4 m/s (600 to 900 ft/min). Above that, ducts whistle.

Friction loss is expressed as pressure drop per unit length, and residential design typically targets 0.1 inch of water column per 100 feet, or about 0.8 Pa per metre.

Fittings dominate. A sharp elbow can cost as much pressure as many metres of straight duct. Flexible duct with slack in it is far worse than the same length pulled taut, and a compressed flex duct behind a joist is a common and invisible cause of a system that cannot deliver.

And the whole point: the fan has a static pressure it can work against, published on its curve. Exceed it and airflow collapses. This is exactly why SEER2 replaced SEER in 2023 with a higher assumed external static pressure: the old test flattered machines by assuming ductwork better than anyone actually builds.

Section 7: Sizing the Server Room

Now apply all of it to the room this book is walking toward.

A server room’s load is unusual in three ways.

It is almost entirely internal. Walls, roof and glazing barely matter because the room is interior and the load is the equipment. Every watt drawn from the rack PDUs is a watt of cooling required. If the racks draw 15 kW, the cooling load is 15 kW plus a small allowance for envelope and lighting. Nothing else in this chapter’s nine-item list contributes much.

It is nearly all sensible. SHR approaches 1.0 as Chapter 14 established, so the full nameplate capacity is available for temperature change and the airflow should be at the high end.

And it is constant. A house peaks in late afternoon and falls at night. A server room’s load is the same at 4 a.m. as at 4 p.m., which changes the machine selection completely: no diversity, no peak, no coasting. That is why the units in Chapter 21 are two identical machines with lead-lag control rather than one large machine sized for a peak that never falls away.

The sizing arithmetic is therefore refreshingly simple: measure the electrical draw, add ten to twenty percent for the envelope and for growth, and that is the load. A clamp meter on the feed does more than any Manual J.

Section 8: What This Chapter Bought You

A ton is 12,000 Btu/h or 3.517 kW, and it comes from melting a short ton of ice in a day using Chapter 5’s latent heat of fusion.

Nine load sources, and every watt of electricity used inside a space is a watt of cooling required, exactly.

The floor-area rule of thumb is sometimes close and structurally wrong, because it ignores glazing, orientation, insulation, internal gains and climate.

The value of a real calculation is not the total, it is knowing which term dominates. In the worked example the window was 42 percent of the load, and a blind cut the whole load by thirty percent. The cheapest fix is almost never the equipment.

400 CFM per ton assumes an SHR of about 0.75, and airflow is the knob that sets the sensible-latent split. Lower for humidity, higher for dry sensible loads.

And most real systems move less air than they were designed to, which is why airflow gets checked before charge, always.

Chapter 17 takes the simplest complete machine there is and dismantles it entirely.

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