Initial tension in extension springs

Every extension spring wound with its coils touching stores a force before it is ever stretched. Grab one of these springs and pull gently: for the first moment nothing happens — the coils stay pressed against each other. Only after a certain effort do they separate and the spring begins to lengthen. That starting force has a name — initial tension — and it is one of the most misunderstood features in spring design.

Initial tension (written F0) exists only in extension springs and is fixed at the moment of manufacture. Ignoring it leads to gross sizing errors, because the force an extension spring delivers never starts from zero. This guide explains what initial tension is, where it comes from, how to measure it, what its practical limits are, and how to use it correctly when calculating a spring.

What initial tension is, and why only tension springs have it

Initial tension is the force already stored in a close-wound extension spring while it sits at rest, at its free length. It is the load that must be overcome before the coils start to open. As long as the applied force stays below the initial tension, the spring simply does not move — it behaves like a rigid body.

This does not happen in compression springs. A compression spring is wound with space between the coils (open pitch) and reacts to the smallest load. An extension spring, by contrast, is usually wound with the coils touching, and it is precisely that tight contact that traps the preload. That is why initial tension is a characteristic property, unique to close-wound extension springs.

The physics: closed coils and a trapped preload

During coiling the wire is forced into the helical shape with a small residual twist. Because the coils are laid down touching one another, they cannot fully relax: each coil pushes on its neighbour, and the whole stack sits under an internal axial compression. That coil-to-coil compression is the initial tension. It holds the spring closed as if an invisible clamp were keeping every turn pressed together.

To separate the coils you must apply an external force that cancels this internal compression. The instant the applied force equals the initial tension, the coils begin to part — the end coils first, then the central ones — and the spring enters its normal elastic regime, stretching in proportion to any additional load.

The force–deflection relationship

Once the initial tension is overcome, an extension spring obeys a linear law just like any helical spring, but with an offset origin. The total force is the sum of the preload and the elastic part proportional to deflection:

Reading the force–deflection line

In the equation, F is the applied force (N), F0 is the initial tension (N), k is the spring rate (N/mm) and x is the deflection from the free length (mm). The key point is the intercept: when x = 0, the force is not zero but F0. Plotted, the force–deflection line does not pass through the origin — it crosses the force axis at the level of the initial tension.

Below F0 the spring does not move. Strictly, there is a small non-linear region right at the start, while the first coils unseat; the ideal straight line described by the equation only holds once every coil is already open.

How initial tension is created — and its limits

Initial tension is set during coiling, by the angle at which the wire is laid down (the pitch or wind angle). Winding the wire more tightly raises the preload; winding it looser lowers it. It is a process adjustment, controlled by the tooling and the coiling speed.

A point that confuses many people: initial tension cannot be added afterwards, by heat treatment or heat setting. It is a geometric property of the winding. Stress-relief heat treatment may even slightly reduce the initial tension, but it can never create it. If a spring was wound with open coils, there is no way to turn it into a preloaded spring later.

The amount of initial tension you can wind in a stable way is not free: it must fall inside a preferred band of shear stress, and that band depends on the spring index, C = D/d. The shear stress associated with the preload, τ0, is estimated by:

• Low-index springs (small C, tightly wound) can hold high initial tension — the close winding traps a large, stable preload.
• High-index springs (large C, coils open relative to the wire) sustain only low initial tension — forcing too much preload keeps the coils from staying closed.
• Above the upper band the process becomes uncontrolled and the coils may distort; below the lower band the coils tend to gap at rest.
• As a design rule, keep the initial tension inside the preferred band for the chosen index; if you need more preload, lower the index (thicker wire or smaller diameter).

How to measure initial tension

Initial tension cannot be read directly, because the start of the test is non-linear: the first coils release gradually and the curve rounds off near the origin. The correct way to determine F0 is by extrapolation.

The procedure is: mount the spring in a tensile tester, apply increasing load and record force against deflection. In the clearly linear region (with all coils already open), fit the straight line that best represents the points and extend it back to x = 0. The force where the line crosses the axis is the initial tension. This method removes the effect of the initial non-linear zone and gives the ideal F0, consistent with F = F0 + k·x.

Measuring two well-separated points in the linear region and solving the system also works: with (x1, F1) and (x2, F2), first find the rate and then the initial tension:

The effect of too much or too little

Initial tension must be specified with the same care as the spring rate, because errors in either direction have consequences. Too much initial tension makes the spring hard to start: a high force is needed just to begin the motion, which may not fit the mechanism. A very high preload also means high wire stress at rest, raising the risk of permanent deformation (coil-set) and of relaxation over time — and the hook, in particular, becomes overloaded.

Too little initial tension wastes a useful feature and, at the limit, leaves the coils gapping even at rest — the spring rattles and loses a defined starting point. In positioning applications this hurts repeatability.

• Do: specify F0 together with k and the working range — the three define the spring.
• Do: check the hook stress whenever the preload is high.
• Don't: rely on adding preload later by heat treatment — it does not work.
• Don't: run the spring so that useful loads fall below F0 — in that range there is no movement.

Hook stress: the most critical point

In almost every extension spring the point of highest stress is not the body of the spring but the hook. The transition from the last coil into the hook has a small bend radius, and that is where bending and torsional stress concentrate. A spring whose body is perfectly sized can still fail at the hook if this detail is ignored.

When the initial tension is high, the hook is already loaded at rest, and any extension adds to that load. For this reason, designs with high F0 call for hooks with a generous bend radius — standard machine hooks, half hooks, extended hooks — chosen to lower the stress concentration. Always check the stress at the inner radius of the hook, not just in the spring body.

A worked example

Consider a stainless-steel extension spring with initial tension F0 = 12 N and spring rate k = 2 N/mm. We want the force required to stretch it 20 mm beyond its free length. Applying the equation:

Interpreting the example

The result is 52 N. The essential detail is what happens at the start: the first 12 N produce no movement at all — they are spent only to overcome the initial tension and begin to open the coils. Only from there does each additional newton produce displacement, at a rate of 1 mm for every 2 N. Anyone who forgets F0 and computes only k·x = 2 × 20 = 40 N underestimates the real force by 12 N, that is by almost 25%.

Note also that the force at rest is not zero: even with no stretch, the spring is internally holding 12 N. That is the value shown at the graph intercept and the one that must be overcome in any application.

On molas.app.br, when you build an extension spring you do not have to guess this value: from the geometry (wire diameter, outer diameter, number of coils and material) the tool suggests a realistic initial tension, inside the preferred stress band for your spring's index, and recalculates force and deflection automatically as you adjust the dimensions.