Design an air spring that carries a load on the resistance of trapped gas to being compressed. Adjust the effective area, gauge pressure and air volume to see the spring rate, natural frequency and static-deflection equivalent update in real time, and explore a soft spring that isolates vibration.
Parameters
Effective area A
cm²
Effective area over which the air lifts the load
Gauge pressure P
kPa
Chamber pressure relative to the atmosphere
Air volume V
L
Total volume of body plus auxiliary tank
Polytropic index n
1.0 = isothermal, 1.4 = adiabatic (vibration)
Supported mass m
kg
Mass carried by one air spring
Results
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Absolute pressure (kPa)
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Supporting force (N)
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Spring rate k (kN/m)
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Natural frequency (Hz)
—
Static-deflection equiv. (mm)
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Isolation rating
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Air-spring cross-section — bounce animation
A bellows-type flexible air chamber bounces the mass on top at its natural frequency. The trapped air compresses and rebounds as the mass oscillates.
Spring rate k of the air spring and the natural frequency fn of the supported mass m. n: polytropic index, P_abs: absolute pressure, A: effective area, V: air-chamber volume. The spring arises from the trapped gas resisting compression.
$$F=P_{g}\,A,\qquad x_{st}=\frac{m\,g}{k}$$
Supporting force F (gauge pressure P_g acting on the effective area A) and the static-deflection equivalent x_st a steel spring of the same rate would have under m·g. A larger trapped air volume V gives a softer spring and a lower natural frequency.
What is an Air Spring?
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An "air spring" uses air in place of a spring? I always pictured a spring as that coiled-up piece of metal.
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Right, and that is the interesting part. A coil spring twists metal, a leaf spring bends a plate — they store energy by deforming a solid. An air spring instead puts the load on a trapped pocket of gas and supports it purely on the gas's reluctance to be compressed. You see them in tour-bus and luxury-car suspensions, and in the isolation mounts under precision machinery.
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If it supports the load with air, what is the advantage? A metal spring seems fine to me.
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Three big ones. First, the stiffness is adjustable: pump air in to make it stiffer, bleed some out to soften it — all without changing a single part. Second, the ride height can be held constant: a levelling valve adds air when the vehicle is loaded and releases it when unloaded, so a laden truck sits at the same height as an empty one. And third — the most important one for vibration isolation — an air spring can be made extremely soft while still carrying a very heavy load.
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Soft while carrying a heavy load — what does that mean? A soft spring would surely bottom out under something heavy.
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That is exactly the limit of a steel spring. Make a steel spring soft enough and it sags enormously under a heavy load, so it becomes impractical. But with an air spring, raising the pressure raises the supporting force, while the volume sets the stiffness separately. So you can both carry a heavy load and stay soft. Soft means a low natural frequency, and a low natural frequency means it isolates vibration and shock well.
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I see. So when I want it even softer, what do I change?
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Look at the spring rate k = n·P_abs·A²/V. It rises with the polytropic index n and the pressure, and falls as the air volume V increases. So increasing V is the standard trick: connect an auxiliary air reservoir to the air spring with a pipe and the effective volume goes up, making it much softer. Move V on the "Spring rate vs air volume" chart below — you'll see that falling curve, k dropping as the volume grows. This auxiliary-reservoir method is standard on rail vehicles and isolation tables.
Frequently Asked Questions
With the effective area A assumed constant, the spring rate of an air spring is k = n·P_abs·A² / V, where n is the polytropic index, P_abs is the internal absolute pressure and V is the air-chamber volume. The spring rate is proportional to pressure and to the index n, and inversely proportional to the air volume V. So the larger the auxiliary tank you connect to raise V, the softer the air spring becomes.
The lower the natural frequency fn, the better the air spring isolates vibration and shock at higher frequencies. In vibration isolation, the transmissibility drops below 1 once the excitation frequency exceeds √2 times the natural frequency, entering the isolation region. An air spring can easily be brought down to a 1-2 Hz natural frequency, isolating road roughness or machine vibration effectively. A steel spring soft enough to do the same would deflect impractically far.
The index n depends on how fast the air is compressed. For a slow, isothermal process where heat escapes, n = 1.0; for the fast, adiabatic process of vibration where heat cannot escape, n equals the specific-heat ratio of air, n ≈ 1.4. A real air spring is close to adiabatic in the vibration range, so n = 1.3-1.4 is generally used for natural-frequency calculations. The default of 1.30 in this tool is a practical mid-range value.
The most practical way to lower the spring rate k = n·P_abs·A²/V is to increase the air-chamber volume V. Connecting an auxiliary air reservoir to the air spring with a pipe increases the effective V and lowers the natural frequency. This is the standard arrangement for rail-vehicle suspensions and precision-machine isolation tables. Reducing the effective area A also lowers k, but to carry the same load you must raise the pressure, increasing P_abs and cancelling much of the gain.
Real-World Applications
Heavy-vehicle and bus suspensions: Heavy trucks, tour buses and trailers very often run air springs. The main reason is that the ride height stays constant even as the payload changes a great deal. A levelling valve adds or releases air with the load, so the step height stays the same fully loaded or empty. And because the natural frequency stays nearly constant regardless of load, ride comfort and cargo-bed stability go hand in hand.
Rail vehicles: Most rail vehicles, including high-speed trains, place air springs between the bogie and the car body. An auxiliary air chamber (supplementary reservoir) is fitted alongside the body, and air is exchanged through an orifice to obtain both a low natural frequency and a useful amount of damping. The pressure difference across air springs is also used for body-tilt control through curves.
Isolation of precision machinery and optical tables: Electron microscopes, semiconductor lithography tools and optical benches all lose resolution directly to micro-vibration from the floor. Air-spring isolators are used in their legs, lowering the natural frequency to around 1-3 Hz to block higher-frequency floor vibration. High-performance active isolation tables combine large reservoir tanks with servo control.
Machine mounting and vibration mounts: Air springs are also used in the mounting feet of vibration-producing machines — fans, compressors, generators, presses. Because they reach a lower natural frequency than steel springs at a small deflection, they transmit less machine vibration into the building and also pass less external shock into the machine.
Common Misconceptions and Pitfalls
A common misconception is treating the effective area A as a fixed value set by the geometry. In a real rolling-lobe or bellows air spring, the shape changes as the spring extends and contracts, so the effective area changes with deflection. This tool uses a first-order approximation with A held constant, which is enough for sizing a design, but strictly speaking this area-change term adds to the stiffness. Including the area-change effect, an air spring can be tuned to be "progressive" (stiffer as it sinks) or to hold a constant rate, depending on the design.
Next, assuming the polytropic index n is always 1.4. The index n depends on the speed of compression. For fast vibration, such as at the natural frequency, the process is close to adiabatic and n ≈ 1.4; for slow changes, such as ride-height adjustment, heat escapes and the process approaches isothermal, n → 1.0. When the body and an auxiliary tank are linked by a narrow orifice, the heat and flow losses at the orifice complicate matters further — and that is also a source of damping. Using one n implicitly for the natural-frequency calculation and a different one for the static deflection is a classic source of confusion.
Finally, assuming "an air spring does everything, including damping". An air spring on its own is essentially a spring element and provides almost no damping. Excited near its natural frequency, an undamped spring resonates strongly. Real installations supply damping through an orifice into an auxiliary chamber, or through a separate shock absorber. Focusing only on lowering the natural frequency and forgetting damping — so resonance actually amplifies the vibration — is one of the most common failures in vibration-isolation design.
How to Use
Enter piston area (cm²) using the slider or numeric field—typical air springs range 10–50 cm² depending on load capacity.
Set gauge pressure (bar)—industrial applications use 4–10 bar for suspension systems, 2–6 bar for isolation mounts.
Input air volume (liters) trapped in the spring cavity; smaller volumes (0.5–2 L) yield stiffer springs for precision machinery, larger volumes (3–8 L) for vehicle suspensions.
Adjust polytropic exponent (1.0–1.4)—use 1.0 for isothermal conditions, 1.4 for adiabatic compression in rapid cycling.
Read absolute pressure, supporting force, spring rate k, natural frequency, static deflection, and isolation rating in real-time.
Worked Example
Design an air spring for a pneumatic isolation table. Set piston area = 25 cm², gauge pressure = 5 bar (absolute = 6.013 bar), air volume = 1.2 liters, polytropic n = 1.25. Results: supporting force ≈ 1503 N (handles 150 kg load), spring rate k ≈ 42 kN/m, natural frequency ≈ 4.2 Hz, static deflection ≈ 3.6 mm. This configuration provides adequate isolation for sensitive optical instruments (target: 5 Hz isolation threshold).
Practical Notes
Increase piston area or reduce air volume to raise spring stiffness and natural frequency—critical when supporting heavier loads on compact machinery.
For automotive suspension tuning, maintain natural frequency 1.0–2.5 Hz; lower frequencies improve ride comfort but increase body roll.
Monitor absolute pressure: check that gauge pressure + 1.013 bar (atmospheric) never exceeds material limits (typically 16 bar for industrial bellows).