A corrugated-side pressure tube has a lower inlet and an index hand connected at its upper end. Pressure moves the corrugated side and turns the hand. Enter a pressure calibration and end rise to explore the pointer motion through a short cap arm and a longer index hand.
Corrugated-side Tube Gauge · Deflection and Pointer Travel
Explore a corrugated-side tube and a constrained index-hand lever. Enter a calibration span and end rise; the model calculates finite-angle hand motion. Autoplay sweeps pressure from zero to the selected value and back.
Equation Used
- The lower inlet and upper reference pivot are fixed.
- Corrugated-side end rise is proportional to pressure within the entered calibration.
- A selected 5 mm cap arm and long hand rotate together.
- Pointer-tip travel is an arc, not straight-line travel.
- Wall shape and pressure sweep timing are illustrative.
The illustration uses a 5 mm cap arm and an entered calibration. Use measured instrument calibration for real measurements; the drawing does not provide manufacturing dimensions.
A corrugated side drives a long hand
The inlet and lower tube support are fixed. The corrugated wall runs up one side; the opposite reference side carries the upper pivot. In the illustrated model, a short cap arm and the long index hand form one rigid lever about that pivot. As the corrugated-side end rises, the cap rotates and carries the hand across its arc scale.
The upper connection is enlarged separately so the pivot and moving tip can be inspected. The main tube outline flexes schematically. The cap arm keeps its length and its moving end follows a circular path; it does not stretch to meet an independently animated pointer.
The model uses a 5 mm short arm, an adjustable long arm and an assumed linear relationship between pressure and tube-end rise. These dimensions illustrate the motion; they do not specify how to manufacture or calibrate a gauge.
Use measured calibration values
Choose a full-scale pressure and an assumed or measured end rise at that pressure. Applied pressure is entered as a percentage of that span, from zero to 120%. The calculator reports the corresponding pressure, end rise, hand rotation and arc travel.
Changing the long-to-short arm ratio changes the hand length and its tip travel. It does not change the rotation of the common rigid lever. The scale is laid out using the same geometry, so its percentage ticks are not artificially forced to have equal angular spacing.
Autoplay ramps from zero pressure to the selected value, holds it briefly, and returns. This is an explanatory sweep, not a simulation of gauge response time or hysteresis.
Calibration followed by exact lever geometry
Let s be the entered percentage divided by 100, Pfs the chosen full-scale pressure, and xfs the selected full-scale end rise. The applied pressure is P=sPfs and the assumed end rise is x=sxfs.
The short arm is a=5 mm. Its end rises by x along a circle, so hand rotation is θ=asin(x/a). The moving end has coordinates(a cosθ,−a sinθ) relative to the fixed upper pivot, with downward screen coordinates positive.
Long-arm length is L=Ra, where R is the entered arm ratio. Pointer-tip arc travel is y=Lθ with θ in radians. The reference pointer angle is 135° in the drawing and becomes 135°−θ. The approximation y=Rx applies at small angles. The calculator uses y=Lθ to obtain the arc travel at finite angles.
The control limits keep x/a at or below 0.72, so this selected assembly remains geometrically reachable. Overrange is max(0,100s−100) percent of the chosen span. That is a calibration-span warning, not a structural overload rating.
Example: 1 in WC span and 2 mm end rise
At 100% of a 1 in WC span, the assumed end rise is 2 mm. A 5 mm short arm rotates by asin(2/5), about 23.58°. With a 10:1 arm ratio, the hand is 50 mm long and its tip travels about 20.58 mm along the scale.
At 50% pressure, end rise is 1 mm, rotation is about 11.54°, and arc travel is about 10.07 mm. At 120%, the model extrapolates to 2.4 mm rise, about 28.69° rotation and 25.03 mm arc travel. It also reports 20% overrange.
Doubling full-scale pressure while retaining the same percentage and calibration travel doubles the indicated pressure but leaves the lever pose unchanged. Doubling long-arm ratio doubles tip arc travel without changing angular rotation.
Calibration and operating limits
A single corrugated-side tube moves the index hand through its upper connection. The pressure-to-rise calibration is entered separately from the lever geometry.
The calculator does not determine material stiffness, elastic limit, fatigue life, pressure rating, accuracy, temperature sensitivity or hysteresis. It uses an entered calibration and a selected lever geometry. Real instruments require measured calibration and manufacturer data.
Above 100% of the chosen span, the displayed values extrapolate the stated linear calibration. They do not establish that a real sensing tube remains linear or undamaged.
Corrugated-tube gauge questions
What moves the index hand?
Pressure moves the corrugated side of the tube. Its upper end turns the short cap arm and the attached index hand.
Why does arm ratio change tip travel but not angle?
The cap and hand rotate as one rigid lever in this model. A longer hand covers a greater arc at the same angle.
Why are the scale marks not equally spaced?
The selected lever obeys θ=asin(x/a), while end rise is assumed proportional to pressure. The scale follows that finite-angle relationship.
Does the animation predict the actual tube shape?
No. The wall is a schematic flexible outline. The calibrated end rise and rigid lever closure are the quantified parts of this model.
Primary reference
Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances, device 151, printed page 50: corrugated tube side, inlet and linked index hand. The illustration uses assumed dimensions and an entered calibration.
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