Size a sand-casting riser (feeder) so it stays liquid longer than the casting and feeds solidification shrinkage. Built on Chvorinov's rule t_s = K·M² and the Caine criterion M_r ≥ 1.2·M_c, the tool updates the modulus comparison, solidification times and volume yield in real time.
Parameters
Casting volume V_c
cm³
Net casting volume (exclude cored cavities)
Casting surface area A_c
cm²
Area in contact with the mold (excluding the riser interface)
Riser diameter D_r
cm
Riser height H_r
cm
Standard practice is H_r ≈ D_r (H/D = 1 cylinder)
Chvorinov constant K
min/cm²
Empirical constant for the mold material / pour temperature. ~2 for steel in green sand
Results
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Casting modulus M_c (cm)
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Riser volume V_r (cm³)
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Riser modulus M_r (cm)
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Modulus ratio M_r/M_c
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Solidification time t_c / t_r (min)
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Riser volume ratio V_r/V_c (%)
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Casting + riser solidification animation
Orange = liquid, dark = solidified. The thin casting freezes from the surfaces inward while the high-modulus riser stays liquid longer and feeds the casting through the runner.
Modulus comparison — M_c, M_r and 1.2·M_c safety target
Chvorinov's rule: the solidification time t_s [min] is proportional to the square of the modulus M = V/A [cm]. K [min/cm²] is an empirical constant for the mold material. The riser is sized so its modulus exceeds the casting's by at least 20% (Caine), so it stays liquid longer.
Cylindrical riser volume V_r and surface area A_r (side + top; the bottom face is in contact with the casting and excluded). M_r = V_r/A_r. While the casting freezes and shrinks, the riser feeds molten metal into it through the runner to prevent shrinkage cavities.
Designing the Casting Riser (Feeder)
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"Riser" is that lumpy extra blob of metal that sits on top of a sand casting, right? Why bother adding all that scrap on purpose?
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It looks like waste, but without it almost every casting comes out defective. The reason is simple: molten metal shrinks as it freezes. About 1-2% for cast iron, 4-5% for steel, 5-7% for aluminium. Pour one litre of steel, and once it solidifies you are short by 40-50 cubic centimetres. That missing volume has to come from somewhere — and that "somewhere" is the riser (or "feeder" in English, "押湯/oshi-yu" in Japanese, literally "pushing-hot-metal"). While the casting freezes and shrinks, liquid metal flows out of the riser, through the runner, into the casting and fills the shrinkage.
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Got it — it's a shrinkage refill tank. So the bigger the better, right?
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Not quite. The single most important condition is "the riser must freeze AFTER the casting". Obvious when you say it out loud — if the riser freezes first the feeding stops. What controls the freezing time? Chvorinov's rule: t_s = K·M², where M = V/A is the modulus. Anything with lots of surface relative to its volume cools fast; a chunky blob cools slowly. So risers are made as simple cylinders or spheres to maximise M. The working design rule is M_r ≥ 1.2·M_c (Caine's criterion) — the riser modulus must beat the casting's by at least 20%.
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With the default values I get a modulus ratio of 0.96 and the verdict is red. Does that mean the riser is too small?
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Exactly that case. M_c = 1.67 cm but M_r = 1.60 cm — the riser has a smaller modulus than the casting, so it freezes first. Try raising the riser diameter to about 10 cm. M_r climbs past 1.9 cm and the ratio shoots over 1.2. But also watch the volume ratio V_r/V_c. For steel you typically need V_r ≥ 10-20% of V_c. Even with the right modulus, a riser that is too small physically runs out of liquid metal to feed, and a tiny shrink void shows up at the very end of solidification.
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Making the riser huge sounds wasteful. How do real foundries get around that?
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Good catch — for many steel castings the yield (casting mass divided by total poured mass) sits at only 50-60%, with the rest being riser and runner scrap. Modern foundries wrap the riser in an exothermic sleeve or insulated sleeve. The sleeve cuts heat loss almost to zero, so the effective surface area drops and the apparent modulus jumps. Same M_r with half the metal. Yield often climbs to 70-80%, which is why sleeves are standard kit on steel today. On top of that, casting CFD packages like MAGMASOFT or ProCAST visualise the solidification front so engineers can place and size risers to the millimetre. Chvorinov's rule is still the go-to for the first-cut sizing though.
Frequently Asked Questions
Molten metal shrinks when it freezes — typically 3-7% by volume (cast iron 1-2%, steel 4-5%, aluminium 5-7%). Left uncompensated, this shrinkage forms internal shrinkage cavities, porosity and surface sinks that ruin the casting. The riser (also called a feeder) is a reservoir of extra molten metal attached to the casting. As the casting freezes and shrinks, the riser supplies liquid metal through a runner to fill the shrinkage and keep the part sound.
Chvorinov's rule states that the solidification time t_s of any region of a casting is proportional to the square of its modulus M = Volume/Surface-Area: t_s = K·M². K is the Chvorinov constant, an empirical value (~1-5 min/cm²) that depends on mold material, pouring temperature and superheat. Thin sections with lots of surface freeze quickly; blocky sections with high V/A freeze slowly. A riser is designed as a simple shape (cylinder or sphere) with a small surface area to maximise M, so it stays liquid longer than the casting.
For a riser to compensate shrinkage it must remain liquid longer than the casting. From t_s ∝ M² this becomes: the riser modulus M_r must exceed the casting modulus M_c. The common design margin (Caine criterion) is M_r ≥ 1.2·M_c. In addition, the riser must contain enough metal — typically 10-20% of casting volume for steel — to physically supply the shrinkage. This tool computes both M_r/M_c and V_r/V_c so you can check the size from both angles.
Too small: M_r falls below M_c, the riser freezes first, and shrinkage cavities form inside the casting. This is the worst case — internal defects only show up after machining, leading to scrap and remelt. Too large: the riser works, but melting, pouring, cutting and remelting waste a lot of metal — yields of 50-60% are common for steel castings. Modern foundries get around this with insulated or exothermic sleeves that raise the effective modulus of the riser so a smaller riser still does the job, pushing yield to 70-80%.
Real-World Applications
Large steel castings (valve bodies, turbine casings): Power-plant and chemical-plant castings weighing hundreds of kilograms to tens of tonnes live and die by riser design. Steel shrinks a lot, and any heavy section must have a riser placed where the last bit of metal freezes. Engineers compute the modulus of each section, identify the hot spot, and arrange one or more risers so each covers a feeding distance of roughly 4.5× section thickness. Multiple risers are common, sometimes augmented by chills to steer solidification toward the riser.
Cast iron parts (gray and ductile): Ductile iron (FCD/SG iron) graphitises during freezing and that graphite expansion partly cancels shrinkage, so risers can be smaller than for gray iron. But parts with mixed section thicknesses still risk having the thin sections freeze first and isolate the heavy section from its riser, leaving porosity. The modulus ratio from this tool is the starting point for working out which section freezes first and where to put the riser, chill, or feed neck.
Aluminium gravity and low-pressure casting: Aluminium shrinks 5-7%, so cylinder heads, wheels and structural castings depend heavily on riser/runner design for yield. Low-pressure casting uses the sprue itself as the riser, with the pressure held until Chvorinov solidification time has elapsed. Quick sizing with this tool gets the modulus into the right ballpark, then MAGMASOFT or FLOW-3D Cast nails down the details.
Yield improvement and cost reduction: Risers and runners can be 20-40% of the cast weight, so shrinking them is the foundry's perennial cost-down lever. Switching bare risers for exothermic or insulating sleeves typically pushes the effective M_r up by 1.4-1.6×, halving riser volume. Use this tool to size a "bare" riser first, then compare against the effective modulus with sleeves to justify the sleeve investment.
Common Misconceptions and Pitfalls
The biggest trap is treating the whole casting with a single average M_c. This tool takes one V_c and one A_c, but a real casting is a mix of thin and thick sections, each with its own modulus. What the riser really needs to feed is the modulus of the last region to freeze, not the average. In practice you split the casting into "region being fed" (the hot spot) and "region that has already frozen" (the thin walls) and apply the rule to the hot spot. The result here is a first-cut estimate; complex shapes should be broken into V/A pieces in CAD, or validated with a casting CFD package.
Next, treating the Chvorinov constant K as a universal number. K depends strongly on the mold material (green sand, no-bake, permanent mold), pour temperature, superheat, mold preheat and the surrounding sand mass. Even for the same steel, K ≈ 2 in green sand, K ≈ 3 in no-bake, K ≈ 0.5 in permanent mold. Borrowing a literature value blindly can swing the solidification time by 50-100%. Always use a value measured in your own foundry or from your internal database. The default K = 2 in this tool is representative for steel in green sand.
Finally, "M_r/M_c ≥ 1.2, so the casting is safe" is only half the story. Chvorinov + Caine guarantee the riser does not freeze first, but say nothing about feeding distance, runner geometry, or the need for chills. A heavy section far from the riser can still develop shrinkage even with the right modulus because liquid metal simply cannot reach it. For steel the feeding distance is around 4.5× section thickness; beyond that you need a second riser or a chill placed to drive directional solidification. The final check today is almost always a solidification simulation in a dedicated casting CFD package.
How to Use
Enter casting volume (cm³) and surface area (cm²) to define geometry—for a steel pulley, typical values are 450 cm³ and 280 cm².
Input riser diameter and height (cm) to configure the cylindrical feeder—start with diameter 8 cm and height 12 cm for medium castings.
Review output metrics: ensure riser modulus M_r exceeds casting modulus M_c by 1.2–1.5x, and solidification time t_r should exceed t_c by at least 10–15% to guarantee feeding until casting solidifies.
Worked Example
Cast ductile iron housing: casting volume V_c = 520 cm³, surface area A_c = 310 cm². Riser: diameter 9 cm, height 14 cm. Calculated casting modulus M_c = A_c/(V_c/5) ≈ 3.0 cm. Riser volume V_r ≈ 890 cm³ (ratio 1.71%). Riser modulus M_r ≈ 4.2 cm (M_r/M_c = 1.4). Solidification time scales as t ∝ M²; t_c ≈ 8.5 min, t_r ≈ 16.8 min. Riser stays liquid ~8.3 min longer, feeding shrinkage adequately.
Practical Notes
Target M_r/M_c ≥ 1.2 for gray iron, ≥ 1.5 for steel castings to prevent premature riser freezing and loss of feeding pressure.
Exothermic sleeves around risers can extend solidification time by 20–30%, reducing required riser volume by similar percentage in aluminum alloys.
Check riser-to-casting volume ratio: 2–4% typical for iron, 5–8% for aluminum—oversized risers waste metal and energy; undersized risers fail to feed shrinkage cavities.
Casting modulus accounts for shape: thick sections (high M_c) require proportionally larger risers to maintain thermal advantage.