Some Bourdon tube experiments:
Here are some videos of a home made bourdon tube under heat to demonstrate the
principle
of a self powered thermostatic boiler control.
One video is high speed to make the movement more obvious.
I'll post more detail as I record it.
Video link-
Video link-
With no load, the deflection at 600
degrees is very close to 1/2 inch.  The
force of pull is about 30 pounds.  
The tube is a quarter inch iron pipe
(1/2 inch diameter)
hammered flat and
curved.  It took on some work
hardening and that has been left in it
.
As you can see, it is very rough.
The steam driven bourdon tube as a boiler control is appealing because;

-the entire system is fully sealed without piston seals, diaphragms, bellows, or any other wearing
or leaking part.

-it is essentially a boiler within a boiler so it is self powered providing several pounds of force and
a relatively long deflection.

-Bourdon tubes are known for their linear and repeatable operation (thus their use in gauges)
-the sensing and the actuator elements would be connected with a length of sturdy tubing
isolating them from motion, vibration, and thermal expansio
n... unlike mechanical linkages.
I got carried away with the direct heat
and the tip deflected about an inch,
which was beyond yield for whatever
semi steel alloy is used in black pipe.
I'm encouraged enough by these
results to order some 17-4 stainless
and make a few heat treated tubes.
This video shows a test with the tube
under load.  A spring scale is used to
load the tube to 22 lbs and the dial
indicator is zero'ed for the start temp of
79.
Y
ou can see where the tube
overcomes the preload and then
extends
.300 at about 440 F, at which
point the scale reads 24lbs.
Link to video