How the slip casting calculator works

Jump to: Plaster · Consistency · Gravity · Correcting a batch · Casting time · The session · What it does not do

Slip casting runs on three quantities that most studios guess. How much plaster a mould needs. How much clay a bucket of slip carries. How long the slip stays in the mould before you drain it. Each guess has its own way of going wrong: a plaster batch that runs out halfway through the pour, a slip that casts slow and shrinks hard because it carries too much water, a wall that comes out thin on the first cast of the day and thick on the last. The slip casting calculator does the three sums in three columns, plus a fourth row for the session as a whole. This post walks through the arithmetic so you can check it by hand.

Plaster is mostly the space it fills

The sizing rule that works is the simplest one: set plaster takes up very nearly the room its ingredients took up in the bucket. The water keeps its volume, the powder keeps the volume of its solid, and the block that comes out of the cottle (the wall of boards, lino or plastic the plaster is poured inside) is the two added together. Plaster expands only slightly as it sets, so the mix you pour is, near enough, the mould you get. With the dry plaster at a solid density ρ_p of about 2.7 g/cm³:

V = m_p / ρ_p + m_w

The water is fixed by the mix. At a consistency C, meaning C parts of water to 100 of plaster by weight, m_w = C / 100 · m_p, so the plaster for a given volume is

m_p = V / (1 / ρ_p + C / 100)

The calculator’s default is a round cottle 18 cm across, filled to 16 cm, around a model that displaces 940 mL. The cylinder holds 4.07 L, the model takes 0.94 L of it, and 3.13 L is left for plaster. At consistency 70, each gram of plaster brings 1 / 2.7 + 0.70 = 1.07 cm³ of mix, so the mould needs 2.93 kg of plaster. Add the 10% spare and it is 3.22 kg of plaster into 2.25 L of water.

That spare deserves a word, because the studio rules hide it. The book’s rule is 1.4 L of mould per litre of water, mixed at 1.5 kg of plaster per litre, and in imperial 80 cubic inches per quart. Worked through the formula, a litre of water and 1.5 kg of plaster actually occupy 1.56 L, and a quart of water with three pounds of plaster about 88 cubic inches. The rule under-counts by about 10%, on purpose: plaster clings to the bucket and to your hands, the last of the slurry is too stiff to pour, cottles weep at their seams. Pitelka is more conservative still and sizes from the water alone, dividing cubic inches by 58 for quarts, then suggests knocking off about 20%, which lands near 72 cubic inches per quart. Anything from 72 to 88 cubic inches per quart is defensible, though 88 leaves no margin at all. The calculator computes the honest volume and adds the spare as a visible number, so you can see the margin instead of trusting a constant. At 10% and consistency 67 it reproduces the book’s 1400 cm³ per litre to within 1%.

Running short costs far more than running over. Surplus plaster becomes a drying slab for reclaim. A shortage halfway through means a second batch, and plaster poured onto a batch that has begun to set delaminates along the join.

Consistency, the dial that sets the mould

Consistency is the one setting that changes the mould itself, and the reason is chemistry. The powder in the bag is calcium sulphate hemihydrate, CaSO₄·½H₂O. Setting turns it back into gypsum, CaSO₄·2H₂O, which takes one and a half more molecules of water: 27 g of water for every 145 g of hemihydrate, or about 18.6 g per 100 g. That is all the water the plaster needs. Everything you add above it sits between the crystals and leaves when the mould dries, and the space it leaves is the pore network that pulls water out of the slip.

So the share of the dry mould that is pore space follows from the mix:

porosity = (C − 18.6) / (100 / ρ_p + C)

At consistency 70 that is 48% pore space by volume. At 67, the 3:2 mix many studios use, it is 47%; at 60 it falls to 43% and at 80 it rises to 52%. More pore space means faster absorption and a mould that casts more per session, and also a softer plaster that wears out sooner. Below about 60 the plaster is too dry to set properly; above about 80 it sets so soft it crumbles. The calculator takes any consistency and offers three presets: 67 for a harder, longer-lived mould, 70 for the manufacturer’s recommended mix, and 72 for production work where fast drainage is worth a shorter mould life.

Gravity, and the clay it carries

Specific gravity is the weight of a volume of slip divided by the weight of the same volume of water. Weigh 100 mL: if it weighs 178 g, the gravity is 1.78. Use a scale rather than a hydrometer, which floats wrongly in a deflocculated slip, one thinned with a deflocculant: a sodium compound, a few grams to the batch, that lets the clay flow at far less water.

Gravity tells you how much clay is in the bucket. Take a slip of specific gravity s whose solids have a density ρ, at a fraction x of the slip’s weight. A gram of slip occupies x / ρ cm³ of solid and 1 − x cm³ of water, so

1 / s = x / ρ + (1 − x)

and the solids fraction follows from the gravity alone:

x = (1 − 1 / s) / (1 − 1 / ρ)

This is Brongniart’s formula, which Cardew and Hamer give in the form potters used it: weigh an imperial pint, and the dry weight in it is (P − 20) × g / (g − 1), with P the pint weight in ounces, 20 oz the weight of an imperial pint of water, and g the specific gravity of the solids. Cardew’s own example, a china clay (kaolin) slip at 26.75 oz the pint with g = 2.5, carries 11.25 oz of dry clay. The formula above gives the same.

For ρ the calculator uses 2.6. Cardew’s table puts china clay at 2.5 to 2.6, the feldspars at about 2.55 to 2.62, quartz at 2.65 and plastic clays at 2.5 to 2.7, so 2.6 is the middle of a casting body. At a gravity of 1.78 that makes the slip 71% dry materials by weight, with water at 40% of the dry weight, which is exactly the water in Martin’s test batch.

Body	Gravity	Water, % of dry weight
Mixed studio body	1.75 to 1.80	44 to 38
High in ball clay	1.72 to 1.76	47 to 43
Kaolin or porcelain	1.78 to 1.82	40 to 37
High-iron red earthenware	1.72 to 1.78	47 to 40

Rhodes puts the ceiling at about 50 parts water to 100 of clay: past it, a casting slip is not likely to behave, and the calculator says so. That is a gravity of about 1.70 at these densities.

The default batch fills four moulds with a 940 mL cavity each, plus 15% for what stays in the bucket and the jug: 4.32 L of slip. At 1.78 that weighs 7.70 kg, of which 5.48 kg is dry materials and 2.22 L is water. Darvan at 0.3% of the dry weight is 16.4 g, stirred into the water before any of the dry materials go in.

Correcting a batch

A slip that has drifted off its gravity needs water or solids, and the amounts come from the same mass balance. To bring V litres at gravity s₁ down to s₂, add W litres of water:

W = V (s₁ − s₂) / (s₂ − 1)

Five litres at 1.84, brought to 1.78, take 385 mL of water. Going the other way, you can add m kilograms of dry materials of density ρ:

m = V (s₂ − s₁) / (1 − s₂ / ρ)

or, if the slip leaves clear water on top after a night’s rest, pour off W litres of it:

W = V (s₂ − s₁) / (s₂ − 1)

Five litres at 1.70 need 1.27 kg of dry materials to reach 1.78, with their share of deflocculant. Martin mixes the addition in and waits a couple of hours before he measures again. Pouring off would take about 515 mL, and that route depends on the slip giving up its water. A deflocculated slip is made to keep its particles apart, so it seldom drops a clear layer that size overnight. Pour off whatever clear water there is and make up the rest with dry materials.

What none of this fixes is flow. Gravity and flow are separate dials, and a slip can sit on the right gravity and still pour like yoghurt. That slip is under-deflocculated: it wants a few drops of deflocculant, not water. Water would thin it too, but it would pull the gravity below target and give you a wetter cast that builds slower and shrinks more. The starting doses the calculator offers are the cautious ones from the sources. Martin starts sodium silicate at 0.25% and stops at 0.5%. The book starts Darvan at 0.3% for light bodies and 0.5% for high-iron ones. Pitelka caps a silicate and soda ash pair at half a percent in total, with ⅛% silicate and ¼% soda ash as the recipe. Past the optimum a slip gels suddenly, and only a few drops of vinegar or magnesium sulphate bring it back.

The wall grows with the square root of time

A cast wall is a filter cake. The plaster pulls water out of the slip, the clay particles pile up against the plaster, and from then on every drop of water that reaches the mould has to cross the wall already built. The thicker the wall, the slower it grows. If the rate of growth is inversely proportional to the thickness, the thickness t goes as the square root of the time θ in the mould:

t = K √θ

K belongs to one slip in one mould, and a single test cast measures it. The default test is 3 mm after 12 minutes, so K = 3 / √12 = 0.87 mm per root minute, and a 3.5 mm wall needs (3.5 / 0.87)² = 16 minutes. A 4.5 mm wall would need 27. That is the diminishing return every caster feels: the first millimetre comes in under two minutes, and each one after it costs more than the last. Twice the wall takes four times the wait.

The figures sit where the sources put them. The book gives 10 minutes to half an hour for a normal wall. Martin leaves his tumbler moulds 6 to 10 minutes with a thin, fast slip, casts very thin cups in about 5 minutes, and gives solid-cast handles 10 to 25. After draining, a simple form shrinks away from the plaster and lets go in 15 to 30 minutes, which is the demould window the calculator adds on.

The session, as the mould wets

A mould does not cast at the same rate all day. Each cast leaves water in the plaster, and a wetter mould pulls water more slowly. The book’s figures are the anchor: a mould with 4 cm of plaster over its load-bearing walls runs six or seven casts before it needs a night to dry, and one with 7.5 cm runs ten to fifteen. Martin makes his tumbler moulds thick so that they take six or seven casts a day, and about ten with his fast slip.

It is tempting to compute the session from the mould’s pore volume, and it does not work. Three litres of plaster at 48% porosity hold well over a litre of water, and by that sum a mould would take dozens of casts. It takes six or seven because only the plaster near the casting face takes part on the timescale of one cast. The saturated layer at the surface is what slows the next wall, long before the mould as a whole is full.

No source gives the slowdown as numbers, so the calculator uses a stated model, not invented data. It lets the rate constant K² fall in a straight line with the casts already poured, so that the cast just past the session limit takes twice as long as the first:

θ_i = θ₁ / (1 − (i − 1) / (2N))

where N is the top of the book’s range for that plaster wall. With the defaults (4 cm, six or seven casts), N is 7 and the holds run 16, 18, 19, 21, 23, 25 and 29 minutes. The release time, taken at the middle of the 15 to 30 minute window, stretches by the same factor, since the same wet plaster is holding the cast, and the session comes to about six hours. The factor of two is the assumption most worth replacing with real numbers. If you time a full session, the casts you record are better than the model, and we would like to hear them at [email protected].

What it does not do

It does not measure flow. Viscosity and thixotropy need a flow cup or a viscometer, and the calculator only knows gravity. It only knows box and round cottles. For any other space, measure what it holds and use Known volume; the model always goes in as the water it displaces, whatever its shape.

Two constants carry real uncertainty. The plaster density, somewhere between 2.6 and 2.75 g/cm³, moves the yield by about 2%, and the spare absorbs it. The dry-materials density of 2.6 is right for clays, feldspar and quartz, and wrong for a body loaded with something much heavier: Cardew lists zircon at 4.7 and red iron oxide at around 5, so a slip heavy in either carries less solid than the gravity suggests.

The cast’s own shrinkage, the reason it lets go of the plaster, belongs to the clay body rather than to the mould. What makes clay plastic, and why it shrinks covers where it comes from.

Sources

• The Form of Clay, the moulds chapter. Plaster consistency and its 60 to 80 range, the 1400 cm³ per litre sizing rule and the reasoning behind its surplus, gravity targets by body family, deflocculant dosage, mould thickness and casts per session.
• Andrew Martin, The Essential Guide to Mold Making & Slip Casting. Casting times for cups, tumblers and handles, release times, sodium silicate dosage and his test batch, and casts per day.
• Vince Pitelka, Clay: A Studio Handbook. The water-only plaster sizing rule, and the silicate and soda ash deflocculant pair.
• Michael Cardew, Pioneer Pottery, Appendix 4. Brongniart’s formula, its worked example and the specific gravities of ceramic materials.
• Frank and Janet Hamer, The Potter’s Dictionary of Materials and Techniques. Brongniart’s formula and its use in measuring slips.
• Daniel Rhodes, Clay and Glazes for the Potter. The limit of about 50 parts water to 100 of clay for a casting slip that behaves.