At impact, your string is not at the tension you strung it

Every conversation about string happens at stringing tension. It is the only figure a player knows, the only one written on the frame, the only one compared from one stringer to the next. And it is a figure the ball never meets.

What actually compresses during contact

The ball stays in the string bed for four to five milliseconds. Two things compress at once, and not in equal shares: the ball is the softer of the two springs. On a committed stroke it flattens by something like two centimetres, while the string bed itself sinks one to two and a half. It is that sinking we care about, and it is smaller than people imagine — smaller still when the string is stiff.

A main string that bows gets longer: both ends are locked at the grommets and it has nowhere to draw length from. A string you lengthen is a string whose tension rises. A small deflection prevents nothing: it is the stiffness of the string that decides what that lengthening costs in kilos, and a stiff string charges more for it.

The model fits in three lines

Take a central main of half-span a, strung at tension T₀, pushed in by x at its midpoint. On each side its length goes from a to √(a² + x²). The imposed strain is therefore:

ε(x) = ( √(a² + x²) − a ) ⁄ a

It is quadratic in x: doubling the deflection does not double the stretch, it quadruples it. Tension follows as soon as the string's stiffness is known:

T(x) = T₀ + EA · ε(x)

and EA is read straight off our bench. Our curves give the stretch in millimetres over a 180 mm gauge length. If a string stretches c millimetres per extra kilo, then EA = 180 ⁄ c, in kilograms-force. No borrowed constant, no fitted coefficient: the tensile modulus is a reading of a slope. Finally, what the bed opposes to the ball, for n mains and crosses effectively loaded:

F(x) = n · 2 · T(x) · x ⁄ √(a² + x²)

What it gives, in kilos

Over the 25–31 kg band, in 1.25, the bench gives 0.833 mm per kilo for N°4 and 0.333 for N°5: that is EA = 216 and EA = 541 kilograms-force. For a central main of 13 cm half-span, strung at 24 kg:

Deflection 1.0 cm → strain 0.30 % → N°4: 24.6 kg · N°5: 25.6 kg

Deflection 1.5 cm → strain 0.66 % → N°4: 25.4 kg · N°5: 27.6 kg

Deflection 2.0 cm → strain 1.18 % → N°4: 26.5 kg · N°5: 30.4 kg

Deflection 2.5 cm → strain 1.83 % → N°4: 28.0 kg · N°5: 33.9 kg

The result is counter-intuitive, and it is the heart of the matter. The stiffer string does not escape the tension rise: it takes more of it. At equal deflection, N°5 gains ten kilos where N°4 gains four. And since the transverse stiffness of a string bed at small deflections is governed by the stringing tension — the same for both — the deflections are close. The stiff string therefore travels a far higher stretch of its own curve, on every stroke.

A check we owed ourselves

A model that can be checked nowhere is not a model. This one checks out against the material. EA divided by the string's cross-section gives a Young's modulus: 1.7 GPa for N°4, 4.3 GPa for N°5, over a 1.23 mm² section. Oriented polyesters live between 2 and 4 GPa. N°4 comes out at the bottom, N°5 at the top — and the gap between them is a real difference in material stiffness, not an artefact of the bench.

N°4 and N°5 swap roles at twenty-six kilos

Read at stringing tension, the order is the expected one: between fifteen and twenty-five kilos, N°5 stretches 0.90 mm per extra kilo, N°4 stretches 0.65. N°5 is the softer of the two.

Above twenty-six kilos the order reverses and never comes back. Between thirty-one and thirty-nine kilos, N°4 gives 1.25 mm per kilo and N°5 gives 0.63. N°4 is the only string in the range whose compliance clearly increases under load: it nearly doubles from the bottom of the range to the top, while N°5's drops by about a third.

The model turns that into force. At two centimetres of deflection, a bed strung with N°5 opposes about 540 newtons, the same bed strung with N°4 about 475: fourteen per cent apart, at identical geometry and stringing tension. At equal stroke energy, N°4 sinks a little deeper, for a little longer, at lower tension. N°5 stops the ball earlier, higher, shorter.

That is what generosity under load means for N°4. And that is what predictability means for N°5: it returns the same thing whatever you commit — a string that deforms less notches less, and lasts longer.

Shape completes the picture. N°4 is octagonal, N°5 is round: on top of that generosity under load, N°4 adds a bite N°5 does not have. That combination is what makes it our starting point for the widest range of players.

What our bench does not tell you

Our curves are recorded in quasi-static tension: tension is raised step by step and the stretch is read. A stroke is dynamic and lasts a few milliseconds. A polymer does not respond in exactly the same way to a slow load and to a shock — under shock it is generally somewhat stiffer.

The model is deliberately simple: a taut string that stretches, with no grommet friction, no coupling from the crosses, no ball compression. Each of those simplifications pulls in a known direction. Grommet friction stops the main from drawing length from neighbouring segments, and therefore pushes tension higher than the calculation. Coupling from the crosses spreads the load, and therefore reduces the deflection of the central main. What the model establishes with certainty is the order and the relative magnitude between two strings; what it does not give is the absolute value, millisecond by millisecond.

We say so because it is true, and because a measurement whose scope is stated is worth more than one left to look as if it proved everything.

What to do with this when choosing

First, stop choosing a string on an adjective read at stringing tension. Soft and stiff describe a point on the curve, and that point is not where you play. The way the market sells string — one stretch figure, one adjective, one player profile — is read at rest. The ball always arrives somewhere else.

Second, if you hit hard, or take the ball early and high, you push the bed deeper and climb higher up the curve. A string that closes up under load will hand you a short ball at the exact moment you are asking for the most. That is often what a player describes as no longer being able to finish a shot, when nothing has left the stroke.

Third, if you play on the counter, against balls that arrive already loaded, your string spends more time at the top of the range than that of a player who builds the point. At identical technique, that is not the same number for you.

The range's curves are recorded under the same conditions, which is what lets them be compared — they are plotted on the Understand page. And if you would rather start from your game than from a curve, the configurator asks six questions and returns a number and a tension.