Pendulum Suspension Spring Scaling Calculator
Use a working pendulum and suspension as the reference, then scale its free length, thickness, and total active width for a new effective pendulum length. You can preserve geometric proportions or hold the same axial stress for a known target mass.
Target total blade width (mm)0.63
- Linear scale factor
- 0.25
- Target free blade length (mm)
- 6.25
- Target blade thickness (mm)
- 0.03
- Design target suspended mass (g)
- 62.5
- Width of each blade (mm)
- 0.63
- Axial stress ratio
- 100%
- Estimated full oscillation period (s)
- 1
- Estimated beats per minute
- 119.98
The blade-width result is total active width; divide it by the number of identical blades only after confirming the blades share load equally.
The period uses the simple-pendulum approximation at standard gravity and is a rate check, not a finished clock adjustment.
How to use this calculator
- Measure the reference and target effective lengths from the suspension point to each pendulum’s center of oscillation.
- Enter the reference spring’s free blade length, one-blade thickness, and total active width between its clamps.
- Enter the mass carried by the reference suspension, including the bob and all supported parts.
- Choose geometric scaling or enter the actual target suspended mass, then check the calculated stock against the mounting blocks.
How suspension-spring scaling works
This calculator starts with a suspension that is known to work and applies proportional scaling to it. Let s = Lₜ ÷ Lᵣ, where Lᵣ is the reference effective pendulum length and Lₜ is the target effective length. The flexible, unclamped blade length and the blade thickness both scale directly: lₜ = s × lᵣ and tₜ = s × tᵣ.
For a geometrically similar pendulum, mass scales as the cube of length and active width as the square: Mₜ = s³ × Mᵣ and wₜ = s² × wᵣ. The width is the combined active width of every blade carrying the load. A two-blade spring with two equal blades therefore uses half the displayed total width for each blade.
If the target bob does not have the geometrically scaled mass, the calculator instead preserves the reference axial mass-to-area ratio. It solves Mₜ ÷ (wₜ × tₜ) = Mᵣ ÷ (wᵣ × tᵣ), which gives wₜ = wᵣ × (Mₜ ÷ Mᵣ) ÷ s. The displayed stress ratio is that target mass-to-area ratio divided by the reference ratio. It should be 100% before stock rounding; a different result signals a measurement or calculation problem.
Measure the flexible part, not the assembly
Free blade length is only the steel that can bend between rigid clamps. It is not the overall length including blocks, pin spacing, holes, or terminal plates. Commercial listings commonly distinguish overall length, spring length, width, and thickness, so compare each dimension on its own. Enter the sum of active widths when the reference has more than one working blade; entering one blade’s width as a total makes the target too narrow.
The effective pendulum length is also different from rod length. It runs from the suspension point to the center of oscillation. A shift in bob position, rod mass, or suspension flexibility can change it even when the physical rod is unchanged. The target and reference must be measured on the same basis for the scale factor to mean anything.
Rate check and limits of this tool
As a sanity check, the calculator estimates the small-angle full period with T = 2π × √((Lₜ ÷ 1000) ÷ 9.80665), with length in millimeters and period in seconds. It then reports 120 ÷ T beats per minute because a full oscillation contains two beats. A seconds pendulum is close to a two-second full period and 60 beats per minute.
This is not a first-principles replacement-spring selector. It does not model steel alloy, heat treatment, elastic modulus, blade prestress, clamp compliance, pin geometry, fatigue, escapement geometry, amplitude, or the pendulum’s mass distribution. Confirm that available stock fits the blocks, then test the movement gently before final rate adjustment.
Worked example
Start with a 994 mm reference pendulum carrying 4,000 g on a suspension with 25 mm free blade length, 0.10 mm thickness, and 10 mm total active width. A 248.5 mm target has s = 248.5 ÷ 994 = 0.25. Geometric scaling gives a 6.25 mm free blade, 0.025 mm thickness, 0.625 mm total width, and a 62.5 g target suspended mass.
If the 248.5 mm target actually carries 500 g, use custom-mass mode. The width becomes 10 × (500 ÷ 4,000) ÷ 0.25 = 5 mm, while the thickness and free length stay 0.025 mm and 6.25 mm. The calculated stress ratio remains 100%. Its simple-pendulum period is about 1.000 seconds, or about 119.98 beats per minute.
Common questions
What is the free length of a pendulum suspension spring?
Free length is the flexible steel length between the parts that clamp it rigidly. Do not use the overall assembly length, the distance between fixing holes, or the length including brass blocks unless those boundaries are also the true clamp points.
How do I measure effective pendulum length?
Effective length runs from the suspension point to the pendulum’s center of oscillation. For a simple bob it is close to the bob’s center, but rod mass, bob shape, and suspension behavior can move it, so timing measurements are often more reliable than a ruler alone.
Why does a heavier target pendulum need more spring width?
For the same thickness, more width increases the spring’s load-carrying cross-sectional area. Custom-mass mode sizes total width to keep the reference mass-to-area ratio, while retaining the length-based thickness scaling.
Should multiple suspension blades be measured separately?
Measure the thickness of one blade, but enter the sum of the widths of all blades that share the load. The displayed result is also total active width; divide it among identical blades only when their clamping and load sharing are genuinely equal.
Can this identify a replacement spring from a movement model alone?
No. Movement models can have revisions, and the spring depends on dimensions, mass, block geometry, and the original design. This tool is most useful when you have a measured working reference to scale from.