What the nomograph computes, and why printed concrete needs a tighter limit

The evaporation rate is the ACI 305 value, computed exactly. There is no multiplier for printing; the severity of printed geometry enters only through the threshold.

ACI 305R, the Guide to Hot Weather Concreting, publishes this relationship as a four-panel nomograph: air temperature and relative humidity give a moisture level for the air, the concrete surface temperature gives the level the surface wants to reach, and air movement scales the difference into a rate. Uno (1998) fitted the nomograph with the single expression above. EvapMargin computes that expression at full precision and rounds only for display, so the chart and the number agree to the pixel.

A cold surface in humid air gives a negative bracket. Nothing evaporates in that condition, so the rate is clamped to zero and the verdict is Pass.

Four panels, read clockwise from the top left, exactly as ACI 305R is read. One construction line threads through all four and ends on the evaporation axis.

The equation separates into three steps, and each step is one hand-off between panels. The two quantities handed between panels are the carriers. They are indices, not measurements, so their axes carry a name and no unit.

• Ambient panel, top left. The line rises from the ambient temperature on the horizontal axis to the relative-humidity curve, then runs right. Its height is the air moisture level: how much water vapour the air already holds.
• Surface panel, top right. The line runs right until it meets the surface-temperature line, then drops. The distance it travelled is the moisture deficit: how much more vapour the warm surface wants to shed than the air already holds. A surface no warmer than the air's moisture level gives a deficit of zero.
• Air movement panel, bottom right. The line drops until it meets the air-movement line, then runs left. Its depth is the evaporation rate. The rate increases downward, as in ACI 305R, so the loop closes on itself.
• Evaporation panel, bottom left. The line ends on the evaporation axis with a marker, on a ramp that runs from the Pass colour at zero through the working threshold to the ACI limit and beyond. The panel is a narrow bar against the air-movement panel, which the line runs straight into: it carries an axis, a ramp and two lines, and needs no more width. Each threshold line carries its value beside the axis and its short name inside the bar. The readout stands straight under the chart, on its width, and gives the rate to three decimals, the verdict, the margin to the next threshold and the four values the line was drawn from.

The four hand-offs are numbered along the line in the order the chart is read: the ambient temperature at its foot on the temperature axis, the relative humidity where the line turns on its curve, the printing temperature where it turns on its diagonal, and the air movement where it turns on its line, named with its preset where one is set. The fifth reading is the rate itself, at the marker.

Threshold lines, threshold curves, verdict fills and the risk ramp

The evaporation panel carries two fixed threshold lines on the evaporation axis: the 3DCP working threshold and the ACI limit. Each is labelled with its value and name, so the two read correctly without their colour. They move only when the working threshold is edited.

Each of the other three panels draws the same two thresholds in its own input. In the surface panel a threshold is the surface-temperature diagonal at which this print, with its air and its air movement as set, would sit exactly on that threshold. In the air-movement panel it is the air-movement line at which the same is true. In the ambient panel it is the relative-humidity curve, and the reading is carried down to the ambient-temperature axis as well. Each of these threshold curves is dashed, in its threshold's colour, and labelled with the threshold's value and the value of the input, so a reader sees at once that the print crosses the working threshold at a surface of about 29 °C, at air moving at about 14 km/h, or at air drier than about 31 %. An operating point sitting exactly on a threshold has all three of that threshold's curves running through it.

Between the curves each panel is tinted for the verdict: Pass below the working threshold, Caution between the two, Risk above the ACI limit. The three tints are named outside the figure, by the verdict key under the chart, which carries each verdict in its own colour with the range of evaporation rates it stands for. Inside the panels a tint is bounded by two threshold curves labelled with their values, and that is what says which side of which threshold it is on; the colour is never the only signal, and no verdict word is written over the chart. The evaporation panel is the exception: the rate is a continuous quantity, not a side of a line, so the panel carries a continuous ramp along the evaporation axis instead of three tinted strips. The ramp is the Pass colour at zero, the Caution colour exactly on the working threshold and the Risk colour exactly on the ACI limit, deepening above it. The two threshold lines are drawn on it, so each threshold keeps a hard edge, and the key names the three tints the ramp runs through.

Where a threshold has no member on a panel the curve is not drawn and a label at the edge of the panel says why. A surface too cool to shed the moisture the threshold needs leaves no humidity and no air temperature that reaches it, and the ambient panel says the threshold is not reached at that surface temperature. A print already over the threshold in perfectly still air is noted as such on the air-movement panel. A surface temperature past the far corner of its panel is labelled off-scale with its value. Nothing is left out silently.

Axes and the Vertico envelope

The chart keeps the panel structure and reading order of ACI 305R but not its ranges. The original chart runs air and surface temperature from 5 to 40 °C, relative humidity from 10 to 100 %, air movement from 0 to 40 km/h and the evaporation rate from 0 to 4 kg/m²/h. On that scale the two thresholds occupy the bottom quarter and Vertico's whole ambient envelope is a small corner. EvapMargin sets the axes to that envelope: temperatures from 5 to 40 °C, relative humidity from 20 to 100 %, air movement from 0 to 25 km/h and the evaporation rate from 0 to 2 kg/m²/h, so both thresholds sit mid-scale and their curves are legible. An operating point whose rate exceeds 2.0 is off-scale: the line is pinned at the scale edge with an open arrowhead, and the readout still shows the numeric rate.

ACI 305 sets 1.0 kg/m²/h as the rate above which cast concrete risks plastic-shrinkage cracking. Printed layers reach that risk at a lower rate, so EvapMargin reads the same rate against a second, tighter line.

Plastic-shrinkage cracking occurs when water leaves the surface faster than bleed water can replace it. The surface dries, contracts, and cracks wherever the contraction is restrained. For a cast wall the exposed surface is a single top face, and ACI 305R's limit of 1.0 kg/m²/h reflects that geometry. It is fixed in EvapMargin and labelled the ACI limit.

A printed element differs in three ways, and each one makes the same evaporation rate more severe:

• Surface-to-volume ratio. Every layer exposes its top and both flanks while it is fresh. A printed wall loses water from far more surface per unit of material than a cast wall of the same volume.
• Thin walls. A single-bead wall is a few centimetres thick. The bleed water that would resupply the surface of a cast section is not there in the same quantity, so the surface dries through sooner.
• Restraint from the bed and earlier layers. Each new layer bonds to a layer below that has already stiffened, and the lowest layer to the print bed. The contraction of a drying layer is restrained along its whole length, which is the condition under which cracks open.

The 3DCP working threshold expresses this severity relative to the cast-concrete limit. Its default is 0.5 kg/m²/h, half the ACI limit, and it never exceeds 1.0. The evaporation rate itself is never multiplied: E stays the honest ACI 305 value, so the chart stays the ACI 305 nomograph and a reader who knows it from cast work recognises every line.

The control on the main page is labelled printing temperature: the temperature of the material as it leaves the nozzle. It stands in for the real surface temperature, which is the quantity the equation wants.

Within minutes of placement the real surface drifts toward the air temperature, or above it once hydration heat builds in the layer. Printing temperature is the value an operator knows before the print starts, which is why it is the primary control. It is always entered on its own; its default of 20 °C equals the default air temperature, so the chart opens with a surface at air temperature, and moving either control shows the surface-against-air differential. A measured surface temperature, where one is available, goes in the same control.

The equation is steep in this input. With 25 °C air, 55 % relative humidity and 8 km/h of air movement, a surface at 20 °C evaporates at 0.134 kg/m²/h and a surface at 30 °C at 0.558 kg/m²/h: a 5 °C shift either way changes the rate by a factor of roughly four across the pair. The surface temperature is the input most worth measuring. Where an infrared thermometer reading of the fresh surface is available, enter it; it is a better input than the printing temperature.

Air movement is the speed of the air over the concrete surface, in km/h. The equation does not distinguish its source: moving air on an open site, a fan, an extractor hood and an open door all count.

The Outdoor preset of 8 km/h is a little over 2 m/s: a light breeze, felt on the face, enough to move leaves. It is the representative condition on an open site with no shelter. The Outdoor, windy preset of 20 km/h is a moderate breeze that raises dust and moves small branches. The Indoor preset of 2 km/h is still air in a closed hall.

A print hall is rarely that still. A fan aimed at the print, an extractor hood above it or a door left open produces local speeds of several metres per second, which is 10 to 20 km/h at the surface. In those conditions the Outdoor preset, not Indoor, is the honest input, and a measured speed at the surface is better than either.

The term (V + 4) means still air still evaporates: at 0 km/h the rate is four fifths of the rate at 1 km/h, not zero. Moving air carries the water away; still air adds nothing, but it does not stop the loss.

The verdict reads the drying condition at one operating point. It does not prescribe a mitigation.

Pass means the evaporation rate is below the 3DCP working threshold. Caution means it is at or above the threshold and below the ACI limit. Risk means it is at or above the ACI limit for cast concrete. A value exactly on a threshold takes the more severe verdict. The margin states how far the rate sits from the next threshold above it, in the same unit, so the reader can judge how much room an input has.

The verdict says nothing about the mix, the layer time, curing compound, fogging, shading or screens. Those are the operator's decisions, and the chart is built so that their effect can be read: shade lowers the surface temperature, a screen lowers the air movement, and the construction line shows the new rate. The verdict also says nothing about strength, bond or buildability. It is one condition, plastic-shrinkage drying, at one moment.

The ACI limit rests on decades of field evidence for cast concrete. The equivalent evidence for printed geometry is not yet fixed, so the 3DCP working threshold is adjustable, with 0.5 kg/m²/h as its default.

The reasons printed layers are more sensitive are established; the magnitude is not. Surface-to-volume ratio, wall thickness and restraint vary with the mix, the bead geometry and the layer time, and no single field value yet covers them. The threshold is therefore exposed under Advanced on the main page, in the range 0.1 to 1.0, so that a site with its own evidence can set its own line. It never exceeds the ACI limit, because printed geometry is never less sensitive than cast.

The evidence that would fix it is direct: evaporation rates measured at the print, from air temperature, relative humidity, surface temperature and air movement at the surface, paired with observed plastic-shrinkage cracking on the printed element, across mixes, bead sizes and layer times. A threshold that separates cracked from uncracked prints in that record replaces the default. Until then, 0.5 is the working value.

• ACI 305R, Guide to Hot Weather Concreting. American Concrete Institute. Source of the nomograph and the 1.0 kg/m²/h limit.
• Uno, P. J. (1998). Plastic shrinkage cracking and evaporation formulas. ACI Materials Journal 95(4). The closed-form equation used here.