Thermal Expansion

Going through our latest obstacle – releasing our CF tube off the Aluminium mandrel – it made me to do some thinking and recap some calculations on what should we actually expect in this field.

So let’s start with Wikipedia again – Aluminium’s Thermal expansion coefficient (CTE) (α) comes as 23.1 ×10-6/°C

All credits to Wikipedia!

Now, our Al tube comes with 60mm in diameter, which makes our initial circumference of 3.14 * 60 -> 188.4 mm.

Case #1: ΔT – 40C

Our initial test was reaching max 70 C for 90 minutes. While starting on beautiful Queensland summer’s 30 C, that makes our total temperature change (ΔT) of 40C. Using our tube’s diameter, AL CTE and delta we get the circumference change.

188.4×0.0000231×40 -> additional 0.1740816 mm (174 μm) to our original circumference value

Going back to our diameter

188.5740816÷3.14 -> 60.0554 mm

Just for reference, Hair’s breadth comes ranging anywhere from 17 μm to 181 μm [millionths of a meter] – yep, it would be very thin hair gap there!

Case #2: ΔT – 70C

While case #1 temperature change (ΔT) was 40 C, because of Queensland, we’ll now improve our chances by reducing the base line to 0 C. That ramps up our total temperature change (ΔT) of 70 C. In this case we’ll get following change.

188.4×0.0000231×70 -> additional 0.3046428 mm (304 μm) to our original circumference value

Going back to our diameter

188.7046428÷3.14 -> 60.09702 mm

Coming back to our hair’s breadth comparison, we are still within a limit of a single hair (17 μm to 181 μm) here.

Crayion’s response when asking to draw me two strands of thin hair

Case #3: ΔT – 150C

Let’s go wild and aim for our final ΔT of 150 C. This is going to be achieved by heating our mold to 150 C, while cooling it to 0 C afterwards with a common ice.

188.4×0.0000231×150 -> additional 0.652806 mm (652 μm) to our original circumference value

Going back to our original diameter again

189.052906÷3.14 -> 60.2079 mm

Doing our final hair’s breadth comparison – we finally made it over the single hair (17 μm to 181 μm) limit here – let’s be humble and say we’ll have “two hairs” space there. Would it be enough? No idea.

One thought on “Thermal Expansion

  1. Nice math! Do you have a micrometer? A nice check would be to chuck a bit of tube in the freezer, measure, then stick it in the hot sun, measure again, and see if the numbers align with the math?

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