Solid height of a spring: the physical limit of travel

Every compression spring has an absolute minimum length: the point at which all coils touch, metal to metal, and the spring simply stops deflecting. That length is the solid height (Ls), and it sets the physical limit of travel. No force, however large, compresses the spring beyond it — from there on the assembly behaves like a solid steel tube, and the rate shoots up to enormous values.

Understanding solid height is what separates a design that works with margin from one that bottoms out and fails. This guide shows how to calculate solid height for each end type, how to relate it to free length and available deflection, how much clearance to leave before the coils clash, and why any robust spring must survive being compressed solid without taking a permanent set. A full worked example ties every concept together at the end.

What solid height is

Solid height is the length of the spring when it is fully compressed and every coil touches its neighbor. In that state there are no gaps left between the turns: what remains is the stacked wire sections. Because of this, solid height depends essentially on two things — the wire diameter (d) and the total number of coils (Nt) — and almost nothing on the free length or the pitch.

One important consequence: two springs with the same wire diameter and the same total coils have the same solid height, even if one stands much taller than the other at rest. Free length sets how much travel the spring offers; solid height sets where that travel ends. Keep in mind that the real solid height carries a small tolerance, because the wire diameter, the seating of the ends, and the grinding vary from part to part.

Calculation by end type

The end coils do not stack the same way the active coils do, and that changes the arithmetic. When the ends are closed (squared), the last turn is brought against its neighbor to form a flat seat — which adds material at the top and the bottom. When the ends are ground, roughly half a coil at each end is dressed away, reducing the stacked height. The formulas below are the standard design approximations, with Nt being the total coils and d the wire diameter.

• Closed and ground (squared and ground): Ls ≈ d · Nt.
• Closed, unground (squared only): Ls ≈ d · (Nt + 1).
• Open ends (plain): Ls ≈ d · (Nt + 1).
• Open and ground (plain ground): Ls ≈ d · Nt.

Free length, solid height and available deflection

The quantity that truly matters to the designer is not solid height on its own, but the difference between the free length (FL) and the solid height. That difference is the available deflection: the total geometric travel the spring can cover before it bottoms out. It is the raw space into which all of the spring's work must fit.

The golden rule is simple: the maximum working deflection has to stay below the available deflection. If the mechanism demands a stroke larger than FL − Ls, the spring is geometrically impossible for that free length — adding force does not help, because there is nowhere left to compress. And, as we will see, not even all of the available deflection can be used: part of it must be held in reserve.

Clearance before clash (clash allowance)

Designing a spring to work exactly down to its solid height is a mistake. In practice, manufacturing tolerances, dynamic overshoot (when the load arrives quickly or vibrates), misalignment, and temperature swings make the spring compress a little further than planned. With no reserve, the spring hits the block, the rate explodes, the peak stress spikes, and the coils hammer each other every cycle — a direct road to fatigue and fracture.

For that reason a safety margin is left, known as the clearance or clash allowance. Common practice is to reserve 10 to 15% of the working deflection as margin between the maximum-load position and the solid height. An equivalent way to think about it is to guarantee a minimum gap per active coil at the point of greatest load, so that the sum of those gaps never falls below that margin. In dynamic and fatigue applications, many designers widen the reserve so as not to use more than about 80% of the available deflection.

Solid-stress check

Compressing the spring to solid produces the highest shear stress it will ever see in its entire life — it is the absolute worst case. There are two design philosophies for handling this, and a well-sized spring follows at least one of them. In the first, you guarantee that the mechanism never lets the spring reach the block: a hard stop, a limited stroke, or the clash allowance itself keeps it off the bottom. In the second, you design the spring so that, even fully compressed, the solid stress stays below the material limit, so that going solid causes no permanent set at all.

The second strategy is the safer one for products where the user could accidentally compress the spring all the way. To check it, you compute the solid load from the rate and the deflection to solid, then the corresponding stress, corrected by the Wahl factor. If the solid stress exceeds the material's elastic limit in shear, the spring takes a set: it permanently loses free length and never again delivers the original force. A spring that can be driven solid without taking a set is, in practice, abuse-proof.

Worked example

Let us apply all of this to a concrete spring. Take a wire of d = 3 mm, Nt = 8 total coils, closed and ground ends, and a free length FL = 60 mm. Because the ends are closed and ground, the solid height is Ls ≈ d · Nt = 3 × 8 = 24 mm. That is the absolute minimum length: the spring will never sit shorter than 24 mm.

The available deflection is FL − Ls = 60 − 24 = 36 mm. Those 36 mm are the raw geometric stroke. Now we apply the clash allowance: reserving 10 to 15% so as not to hit the block, the design working deflection should land around 30 to 32 mm. In other words, at maximum load the spring should measure roughly 60 − 31 = 29 mm, still with about 5 mm of reserve above the 24 mm solid height.

The next step, which must not be skipped, is to check the stress. With the spring rate k, the solid load would be F_solid = k · 36 mm; the corresponding stress, corrected by Wahl, has to stay below the material limit if we want the spring to survive being driven solid. If it does, the spring is abuse-tolerant; if it does not, you need more coils, thicker wire, or a hard stop that prevents reaching the bottom of travel.

Choosing free length and coil count

Designing backwards helps: start from the working deflection the application demands, add the clash allowance, and add the solid height — the result is the minimum free length that makes sense. From there, the coil count is a trade-off. More coils reduce the rate (the spring becomes softer and the travel per newton grows), but they raise the solid height, because there is more wire to stack. Fewer coils stiffen the spring and lower the solid height, freeing up travel, at the cost of more stress per millimeter.

• Always keep FL > Ls, with margin — never design right at the limit.
• Leave 10 to 15% of the working deflection as clearance before clash.
• More coils: softer spring, but higher solid height and less available travel.
• Fewer coils: stiffer spring and lower solid height, but higher stress per millimeter.
• Check the solid stress, not just the available geometric travel.

How Molas Online computes solid height

In the Molas Online 3D designer, solid height is computed automatically from the wire diameter, the total coils, and the chosen end type, and it is compared against the free length in real time. As soon as the geometry approaches the block — or when the working deflection eats into the clash allowance — the tool warns you before the coils touch, showing the available deflection and the reserve to solid as you adjust the dimensions.