Insulation & ablative liners

In one lineThickness = what the flame takes (erosion + char), with margin, plus enough virgin material to keep the bondline cool — including after burnout.

Before thisPropellant grain (exposure comes from burn-back) · Case sizing

Why this matters

Combustion gas is around 3000 K. High-strength case steels lose strength quickly above a few hundred °C, composite case resins soften at around 120–200 °C, and the adhesive bonding insulation to case may be limited lower still. The insulation is all that stands between them. Too thin, and the case or bond overheats or burns through — a catastrophic failure. Too thick, and it is inert mass, which costs performance just like case mass. Insulation can be a significant share of a motor’s inert mass, so it is sized region by region, not with one blanket thickness.

Two jobs at once

Inside an ablating wall — section, not to scale

The insulator does two jobs: it gives up its surface slowly (erosion and charring carry heat away), and the virgin material left behind insulates the case. Thickness must cover the affected depth with margin and leave enough virgin material to keep the bondline cool — including after burnout.

An ablative insulator protects the structure in two ways:

1. It gives up its surface on purpose. Heat decomposes the rubber or resin (pyrolysis), leaving a porous carbon char. The decomposition absorbs heat, and the gases it releases percolate out through the char and thicken the boundary layer, blocking some of the incoming heat (“blowing”). The flow scours the char away slowly — erosion.
2. The virgin material behind it insulates. Low conductivity keeps the heat near the surface, so the bondline and case stay cool.

Think of it like…

A log in a campfire

A thick log burns for hours because its outside turns to charcoal, and charcoal is a good insulator: the wood inside stays brown and cool while the surface glows. Poke the log and knock the char off, and it burns much faster. Motor insulation is the same: the char layer protects what is behind it, and anything that strips the char — fast gas, impinging aluminium-oxide droplets — speeds up the attack.

Material affected depth (MAD) is everything the flame has used up: eroded material plus char. It is the number measured by sectioning insulation after a firing, and the basis of most insulation design rules.

Think of it like…

An oven glove versus a cast-iron pan

A cast-iron pan doesn’t burn on the hob, but its handle gets too hot to hold: it resists the flame and passes the heat on. An oven glove chars if you hold it in the flame, but your hand stays cool. Graphite and carbon-carbon behave like the pan — superb surface resistance, poor insulation — and rubbers and phenolics like the glove. That is why a graphite throat insert always has an insulator behind it.

Exposure time sets the thickness

Insulation only works while hot gas touches it, so the first question for any location is how long is it exposed? That comes straight from the grain design.

Insulation thickness follows exposure — half-section, thickness exaggerated

1. 1
   Forward domeExposed early in the burn, but the gas is slow here. Moderate thickness.
2. 2
   Cylinder under the grainCovered by propellant until the web burns through, so it only sees the tail-off. Usually the thinnest insulation in the motor.
3. 3
   Aft dome and nozzle entranceExposed for the whole burn to fast, turning flow and impinging aluminium-oxide particles. Thickest, in an erosion-resistant grade.
4. 4
   Stress-relief flapAn unbonded insulation flap at the grain end that lets the grain shrink without tearing the bond. Insulated on both faces.
5. 5
   NozzleGraphite or carbon-carbon throat insert, always backed by an insulator; carbon phenolic at the entrance; silica or glass phenolic in the exit cone.

Insulation is not one thickness. Each region is sized for how long it is exposed and how aggressive the flow is there — which is why the thickness map is drawn from the grain burn-back and the internal flow, not chosen once.

• Under the grain, the cylinder insulation is covered by propellant until the web burns through. Exposure is only the tail-off, so this is usually the thinnest insulation in the motor.
• Domes and grain ends are exposed from ignition, so their exposure is close to the full burn time.
• The aft dome and nozzle entrance add the fastest, turning flow and aluminium-oxide particles hitting the surface, so erosion dominates. This is where the thickest, toughest grades go.

With a star or slotted grain, the flame reaches the case under the star tips long before it reaches the case under the valleys. Exposure — and the thickness needed — therefore varies around the circumference, not just along the motor:

Where the case is exposed firstcylinder section · from the grain burn-back

Grain (from the propellant grain page)

150 mm grain, 600 mm long, generic AP/HTPB-like propellant, peak pressure 7 MPa.

Insulation

Erosion rate (mm/s)Safety factorEffective surface (°C)Char front (°C)

EPDM properties (k 0.25 W/m·K, ρ 1100 kg/m³, c_p 2000 J/kg·K). Thickness here is SF × affected depth at burnout only — check the bondline with the calculator above.

Burn time (incl. tail-off)

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Exposure min / max

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Thickness min / max

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Ring shade: exposure time (darker = longer). Ring width: required thickness, exaggerated. Red dot: thickest point; blue dot: thinnest. Inner outline: the port at ignition.

The physics of charring

Heat soaks in as the square root of time

Treat the insulation as a thick slab whose surface is suddenly held at a high temperature. Heat spreads in by conduction, and the temperature rise at depth $x$ after time $t$ is

$$\frac{T - T_0}{T_s - T_0} = \operatorname{erfc}\!\left(\frac{x}{2\sqrt{\alpha t}}\right), \qquad \alpha = \frac{k}{\rho\,c_p}$$

where $\alpha$ is thermal diffusivity. Every depth scales with $\sqrt{\alpha t}$: double the time and the heat reaches only about 1.4 times deeper.

Think of it like…

Roasting a joint of meat

Cooking time goes with the square of thickness, which is why a joint twice as thick takes about four times as long, not twice. The same √t law sets how far heat reaches into insulation. For insulation it is good news: a long burn is less punishing per second than simple arithmetic suggests.

Erosion changes the shape of the problem

If the surface also recedes at a steady rate $v$, the exact solution for a semi-infinite solid with its surface held at $T_s$ is:

$$\theta(\xi, t) = \tfrac{1}{2}\left[\operatorname{erfc}\!\left(\frac{\xi + v t}{2\sqrt{\alpha t}}\right) + e^{-v\xi/\alpha}\,\operatorname{erfc}\!\left(\frac{\xi - v t}{2\sqrt{\alpha t}}\right)\right]$$

where $\xi$ is depth below the current surface. The char front is where $\theta$ falls to the pyrolysis level $\theta_p = (T_p - T_0)/(T_s - T_0)$. Two limits make it easy to read:

• No erosion ($v = 0$): char grows as $\sqrt{t}$ indefinitely.
• Long times: the profile settles into $\theta = e^{-v\xi/\alpha}$, which travels with the surface. The char layer stops growing at a steady thickness

$$\delta_{\text{char}} = \frac{\alpha}{v}\,\ln\frac{1}{\theta_p}$$

and the affected depth then grows linearly with time, $\text{MAD} \approx v\,t + \delta_\text{char}$.

So short burns are char-dominated and long burns are erosion-dominated. That is why the erosion rate — which depends on the local flow, not just the material — is the number insulation designers argue about most.

After burnout: soak-back

When the motor stops, the hot char and insulation still hold a lot of heat. With no gas flow to carry it away, much of it flows inward, the only way left to go. The bondline often reaches its peak temperature minutes after burnout, long after the insulation surface has started to cool.

Think of it like…

A stone pizza oven

Rake the fire out of a stone oven and it keeps cooking for hours, because the heat stored in the stone keeps flowing into the bread. The insulation layer is that stone; the bondline and case are the bread.

How much of the stored heat goes inward depends on how the motor cools after burnout: radiation to the cold nozzle opening, venting, and heat absorbed by continuing pyrolysis. The calculator brackets it with two bounds: insulated face (all stored heat soaks inward — conservative) and radiating face (the surface radiates to cold surroundings — optimistic for most of a closed case).

Sizing rule

Two requirements, and the thicker wins:

$$t \;\ge\; SF \times \text{MAD} \qquad\text{and}\qquad T_\text{bond,peak}(t) \;\le\; T_\text{limit}$$

plus a minimum gauge for manufacture and handling. Safety factors of around 1.5–2.0 on measured affected depth are common in the open literature. Your programme sets its own, often higher in the aft dome and other regions with large uncertainty.

Calculator

Insulation thickness at one location1-D transient · erosion + char + soak-back

Insulator

k (W/m·K)Density (kg/m³)c_p (J/kg·K)Char front temp (°C)

Exposure

Erosion rate (mm/s)Exposure time (s)Effective surface temp (°C)Initial temp (°C)

Erosion rates and the effective surface temperature are calibration values. Defaults are illustrative; fit them to char and erosion depths measured on your own firings.

Behind it

Wall (mm)Bondline limit (°C)Safety factor on MADMinimum gauge (mm)

Check an as-designed thickness (mm, optional)

Required thickness

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Governed by

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Mass per area

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Material affected depth

Eroded

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Char at burnout

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MAD incl. soak-back

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SF × MAD

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Bondline temperature

Thickness for limit — insulated face

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…radiating face

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Peak at this thickness

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Bondline temperature at this thickness. Shaded band: between the radiating-face and insulated-face assumptions after burnout.

1-D implicit conduction through insulation and case, hot face held at the effective surface temperature and receding at the erosion rate; char = material that reached the char-front temperature. Neglects pyrolysis heat absorption and gas blowing (both lower the bondline temperature), property changes in the char, and 2-D effects.

Worked example — EPDM over a thin steel case

Aramid-filled EPDM ($k = 0.25$ W/m·K, $\rho = 1100$ kg/m³, $c_p = 2000$ J/kg·K) on the 1.4 mm D6AC case from the case-sizing example, in a low-velocity region exposed for 20 s. Effective surface temperature 1200 °C, char front 450 °C, erosion 0.025 mm/s, bondline limit 150 °C, safety factor 1.5. These are the calculator’s defaults.

1. Diffusivity. $\alpha = 0.25 / (1100 \times 2000) = 1.14 \times 10^{-7}$ m²/s, so $\sqrt{\alpha t} = 1.51$ mm at 20 s.
2. Char front level. $\theta_p = (450 - 20)/(1200 - 20) = 0.364$.
3. Without erosion the char would reach $2\sqrt{\alpha t}\;\operatorname{erfc}^{-1}(0.364) = 3.02 \times 0.64 = 1.93$ mm.
4. With erosion, 0.5 mm of surface is removed, and the moving-surface solution puts the char front 1.64 mm below the new surface. Affected depth at burnout is $0.5 + 1.64 = 2.14$ mm. The calculator’s transient model gets the same 1.64 mm, and the automated tests check that agreement.
5. Soak-back pushes the char front a little deeper after burnout: MAD ≈ 2.4 mm, so $1.5 \times \text{MAD} = 3.6$ mm.
6. Bondline. Keeping the peak bondline temperature below 150 °C needs about 8.9 mm with the insulated-face assumption (peak about 6 minutes after burnout), or 6.7 mm with the radiating face.

The bondline governs, by a wide margin. The affected depth alone suggests 3.6 mm, but a 1.4 mm steel case has very little heat capacity to absorb soak-back. Try the carbon/epoxy case, a 60 s exposure, or the high-velocity regime, and watch which requirement takes over. The steady char thickness, $(\alpha/v)\ln(1/\theta_p) = 4.6$ mm, shows that at this erosion rate the char layer would never exceed about 4.6 mm, however long the burn.

Choosing the material

Material	Where it’s used	Strengths	Watch out for
EPDM, aramid-fibre filled	Case insulation, most regions	Lowest density and conductivity, good ageing, good bond	Lower erosion resistance in high-velocity, particle-laden flow
EPDM, carbon-fibre filled	Aft domes, high-flow regions	Tougher, more adherent char	Higher conductivity than aramid grades
NBR, silica filled	Case insulation (older and some current designs)	Good propellant compatibility, tough char	Denser; historically asbestos filled — phased out
Silicone, silica filled	Flexible joints, wide-temperature service	Silica-rich char, flexible when cold	Bonding needs special primers
Carbon phenolic	Nozzle throat region, entrance (large motors)	High erosion resistance, good insulation	Precursor supply; delamination and pocketing if made badly
Silica / glass phenolic	Exit cones, insulation behind inserts	Cheaper, lower conductivity than carbon phenolic	Lower erosion resistance; silica melts at high heat flux
Carbon-carbon	Throats and exit cones	Very low erosion, light, strong when hot	Conducts heat — needs backing insulation; cost; oxidation
Bulk graphite	Throat inserts in small motors	Cheap, low erosion	Thermal shock cracking; very conductive

How to choose, in order:

1. Exposure and flow first. Long exposure in fast, particle-laden flow needs an erosion-resistant grade. Short, gentle exposure is driven by conductivity and density.
2. Then mass. Density × thickness is the cost. A slightly less erosion-resistant but much lighter insulator often wins in low-velocity regions.
3. Compatibility with the propellant. Plasticiser and burn-rate catalysts can migrate from the propellant into the liner and insulation over years of storage. That weakens the bond and changes the propellant next to it. The liner is formulated partly as a barrier against this migration.
4. Bond and processing. How the insulation is laid up (calendered sheet, cured in place or co-cured with a composite case), and how it bonds to the case and the propellant liner, are as important as its thermal numbers.
5. Ageing. Insulation has to keep its properties and its bonds for the motor’s whole service life.

Where this model stops

Screening model, not a qualified thermal analysis

The calculator holds the surface at one effective temperature, uses constant virgin properties throughout, and ignores pyrolysis heat absorption, gas blowing and the char’s different properties. That makes the bondline result conservative in some ways and optimistic in others. Real insulation is sized with charring-ablation codes calibrated against material-affected depths from sectioned motors, and bondline thermocouple data from firings.

• Erosion is an input, not a prediction. It depends on local velocity, particle impingement, pressure, propellant aluminium content and the material’s char strength. Use measured rates.
• 2-D effects at joints, flaps, grain terminations and the nozzle entrance can dominate locally.
• Nozzle throats erode much faster than case insulation and change chamber pressure as they do — covered on the planned nozzle page.

On the drawing

• Thickness map — insulation thickness by zone, with tolerances. Show where it is measured and with what method.
• Material and process specifications — compound, lay-up and cure, bond surface preparation and primers.
• Bond inspection — NDT of the case-to-insulation and insulation-to-liner bonds, with acceptance criteria.
• Stress-relief flaps — geometry, and the release agent that lets them open.

References and further reading

• NASA SP-8093, Solid Rocket Motor Internal Insulation (1976).
• NASA SP-8115, Solid Rocket Motor Nozzles (1975).
• G. P. Sutton & O. Biblarz, Rocket Propulsion Elements, 9th ed., Wiley (2017) — chapters on solid motor components and nozzles.
• H. S. Carslaw & J. C. Jaeger, Conduction of Heat in Solids, 2nd ed., Oxford (1959) — semi-infinite and moving-boundary solutions.
• A. Davenas (ed.), Solid Rocket Propulsion Technology, Pergamon (1993).

Note

Screening and educational material. Insulation design and qualification are governed by your programme’s requirements, material data from your own firings, and sign-off by the responsible thermal and safety authorities.