# Torpedo tube analogy

On the show I heard today you were explaining to “The Chief of the Boat” that his master cylinder heating up was like a heated torpedo tube expanding, and therefore the torpedo would fit looser in the tube. Actually the opposite is true. The heated tube would expand in ALL directions; making the inside diameter of the tube smaller, not larger. The torpedo would fit tighter in the tube, not looser.

That is unless this paticular submarine happened to have the “symetrical tube expansion update kit” installed. The Navy started installing these kits in 1940 I believe, they also estimate that all subs will have the update by 2050.

I think you’ll find that if the circumference of the tube expands, it expands over 3 times faster (the value of PI) than the thickness - ergo, the tube grows in diameter = looser fit.

Kicking myself for not thinking of that.

Easy science experiment: Take a metal ring, find a marble that just barely goes through the ring. Heat the ring. The marble will no longer fit through. The outside diameter of the ring will get bigger, but the inside diameter will get smaller.

So you’ve changed your position? You wrote: “The heated tube would expand in ALL directions”. The direction tangent to the circumference is a direction.

It appears that Dr. Ali Khounsary of Argonne National Laboratory doesn’t agree with you.

Now you tell us! For years and years I have been using an induction bearing heater that heats ball bearings to about 200 degrees F so that I could simply slip then onto the shafts instead of having to use a hydraulic press to force them onto the shaft.

Micbou, you are mistaken. Heating rings is a time-tested way to make the holes in them bigger, it’s used all the time to make the hole in an object bigger so they can be slipped over something (a shaft, a barrel, a wooden wheel, you name it). Think of it this way - take a copy of a washer on a Xerox machine. Now take a copy with the Xerox machine set to 110% enlargement - everything is bigger, including the hole.

I had the same arguement with my 11th grade science teacher. He showed me the error of my ways…

Parts expand “photographically” when heated as suggested by Texases. Holes get bigger.

The assembly technique mentioned by B.L.E. and texases is a very, very common method in the manufacturing industry for press fits.

The Xerox analogy does not hold. The ring is not expanding in all directions as a 3 dimentional mass, it is enlarging symetrically outwardly 110%. In the case of the ring, it is expanding outwardly, 3 dimentionally in all directions, from the center of the mass. Thus, the inner diameter gets smaller. In the case of heating metal to expand it over something, you are still pressing (hammering, pushing) it in place. The heated metal expands under this force, not because the inside diameter got bigger.

But, having said all this, I will bow to The Department of Energy scientists. Do I have to tell Tom and Ray they are probably right?

First, can we agree to be nice and respectfully disagree? I believe Micbou is incorrect, but I am open to a counter-proof or video counter-demonstration.

What I will show:
? The correct answer: Hole gets larger.
? The common though experiment that leads people to the wrong answer
? The exception

## The correct answer: Hole gets larger.

Skipping all the math, just watch the video where a teacher heats a metal ring. Q.E.D. __ http://www.youtube.com/watch?v=V0ETKRz2UCA
Tom and Ray were correct; heating a metal ring or tube will make the inner open-space diameter larger.

Explanation (no math):
When you heat a metal toroid (metal donut) the entire toroid expands. The expansion is along the circular centerline of the ring. The question is not related to the inner and outer diameter of the ring. The question is actually:
What moves faster–the outward change in the toroid centerline, or the inward change of the inner diameter?

The answer is known by many expert mechanics, such as Tom and Ray(*). You can slip a tight bushing on a shaft by heating it first to expand the inner diameter. When it cools (and the inner diameter shrinks), it’s locked on.

## The common though experiment that leads people to the wrong answer

This is like the Monty Hall trick that fools so many experts because “it’s obvious.” This is also in part because most people’s experience with expanding ring-shaped objects are donuts. Donuts are not made of metal!

What happens when you heat a metal toroid (metal donut)? Thought experiment:

• Take a round metal bar
• Imagine it heated up
• It expands outward.
The bar gets thicker and longer. The diameter of the cross section (a circle) is bigger.

Let’s modify the bar to get our toroid:

• Take the now cool bar
• Bend it into a circle…and measure the diameter of the inner circle
• Heat bar up so it expands outward in every direction
As the DIAMETER of the cross section increases, the inside of the toroid closes up.
Side note: the compression force from expanding length of the bar, now that the ends are welded together, will be transferred to the expanding cross-section diameter.

You can actually do this as a real world experiment.

• Take a hanger
• Bend it into a circle
• Measure the inner circle (donut hole) diameter

Now to simulate expansion

• Wrap a good amount of duct tape around it to simulate heat expansion
• Measure the inner circle (donut hole) diameter

Look at that, it’s smaller! So I was wrong! And the video was wrong! And the physicists, mechanical engineers are wrong! And the mechanics who heat bearings to slip them onto shafts are, in fact, performing witchcraft and should be burned at the stake!

No. The thought experiment is wrong. Wrapping tape around a wire does not correctly simulate heating a metal ring. Neither does frying a gooey donut or cooking a bagle.

Watch the video again. The centerline of the ring expands outward faster than the inner-diameter opening can contract. Inner hole gets bigger.

## The Exceptions

This is the internet, so you have to cover the outlier cases or someone will say, “Ah-ha! This different example doesn’t work like you said, so your example is wrong.” Proof by exception is a valid method, when the exception is valid.

First exception: Donuts in oil, bagels in oven.
I hope it’s self-obvious. Bread products with expanding gasses inside them are soft, edible, and delicious. Metal rings are not soft, edible, delicious, or filled with expanding gasses when cooked. This exception does not apply.

Second exception: Very large rings (toroids) that can’t be heated uniformly.
If you have a small tube (1 foot diameter) drilled through a large block of metal (20 foot diameter or cube 20 foot on a side) then:

• Heating the very large ring/block evenly would make the hole diameter bigger, just as above, in the video, etc. You just need a bigger oven.
• But heating the large metal block by applying heat inside the tube/circle would make the inner diameter shrink. This is because inner-half of the ring would be trying to expand, but the cold outside of the ring would be maintaining it’s shape. The path of least resistance is to push inward, closing up the hole.

Again, this is a different case of a very large metal block, and non-uniform heating. It does not apply to uniformly heating a smaller toroid/ring.

## Conclusion

Physicists in the lab making videos, mechanics in the garage, mechanical engineers, all agree that heating a ring uniformly makes the inner diameter larger. Donuts, wrapping tape around a hanger, and uneven heating do not disprove this.

(*) Tom and Ray Jones, my mechanics. I did not mean to imply Tom and Ray Magliozzi were expert mechanics (joke).

OK, here’s a better experiment. Take a round 2" disk, scribe a cirle 1" in diameter concentric with the outer diameter. If you heat the disk until it’s, say, 2.1" in overall diameter, do you think the scribed circle will be SMALLER?? No, it will also be proportionally larger. This scribed circle is IDENTICAL to a 2" washer with a 1" hole in the center.

You’ve been given dozens of examples - pardon my CAPS, but you really need to carefully consider what you’ve been given.

“This scribed circle is IDENTICAL to a 2” washer with a 1" hole in the center."

Not true. A disk is not identical to a ring.

Dozens of examples? Rilly? Pile on much?

This made no sense to me - why would you want to make the bearings bigger? - until it occurred to me that you’re heating the races that the bearings sit in so you can slip the shaft in. Did I get it?

Wow, that was a long way to go.

"Thought experiment:

• Take a round metal bar

• Imagine it heated up

• It expands outward.
The bar gets thicker. The diameter of the cross section (a circle) is bigger."

&nbsp:&nbsp:&nbsp:The bar also gets longer. Remember that when you get to your toroid.

"Let’s modify the bar to get our toroid:

• Take the now cool bar
• Bend it into a circle…and measure the diameter of the inner circle
• Heat bar up so it expands outward in every direction…
As the DIAMETER of the cross section increases, the inside of the toroid closes up."

Well, no, it doesn’t. I respectfully disagree. I’m not going to copy and paste your whole post, but it seems like you are trying to take both positions at the same time. If it’s not clear it needs editing. You totally lost me with the heat sink. A heat sink take heat away, so you’re not really heating the tube, so why even bring it up?

The key to this is something Wayne left out - the straight bar also gets longer when heated - and it gets longer dependent on its starting length, which is much more than the growth in cross section.

A ring would also growth in circumference (and diameter) and since the circumference is much more than the cross section dimensions, the diameter grows faster than the cross section. Ergo, the inner diameter grows when it is heated.

This is why it is common to heat bearing races to get then to fit over slightly larger shafts. It’s called and interference fit.

My apologies, I was trying to be thorough and didn’t mean to confuse.

What my post shows:

• The common though experiment people use, which is incorrect (incorrect means believing the hole gets smaller)
• The correct answer: Hole gets larger. Includes video demonstration, and reason why (centerline expands faster) http://www.youtube.com/watch?v=V0ETKRz2UCA
• I then tried to cover the exception, where you don’t have a small toroid (donut), but a hole in a very large block that can’t easily be heated uniformly.

If that’s confusing and you still disagree, then I recommend:

• Watch the video, or the many others like it, where high school teachers and college professors heat a ring and measure the inner diameter. Every time the inner diameter circle gets bigger
• Try it yourself; school supply stores in most large towns have the metal ball and ring.

That’s correct, I was ignoring the compression effects. You can’t just bend a bar into a small circle; there is point of deformation on the inner diameter, much like your car has spider gears so the tired don’t chirp when you turn the corner. I was trying to keep examples simple (wire and tape).

CapriRacer had a good link to Interference Fit on Wikipedia, which mentions besides forcing rings onto shafts, you can heat them. This heating-to-expand-rings process is called Induction Shrink Fitting, http://en.wikipedia.org/wiki/Induction_shrink_fitting
This is what B.L.E. refereed to above…although he said he slips ball bearings onto a shaft, I think he means ball bearings in a circular cage (picture): http://en.wikipedia.org/wiki/Ball_bearing

Video demonstrations, multiple technical articles, testimonials from mechanics who heat rings on a regular basis…that should pretty much prove it short of heating a ring yourself. If you do, please video it and upload to youtube.

Thanks for the feedback. I will edit my post to put the correct answer first (hole gets bigger), then explain why it confuses people second.

It came to me in a dream. I awoke this morning understanding it better. The metal expands along the circunference of the ring pushing it out in all directions along its circumference. This is greater that the inward expansion of the metal to the center of the ring. The net result is the ring will get bigger. Ok, Tom and Ray, you prevail. My thanks to all. My favorite car: A 1900 De Dion Bouton.

It came to me in a dream. I awoke this morning understanding it better. The metal expands along the circunference of the ring pushing it out in all directions along its circumference. This is greater that the inward expansion of the metal to the center of the ring. The net result is the ring will get bigger. Ok, Tom and Ray, you prevail. My thanks to all. My favorite car: A 1900 De Dion Bouton.