Paper Breaking Length
Compute the breaking length (self-rupture) of paper, L = tensile index / 9.80665, in km — the length of a paper strip that, hung from one end, would break under its own weight. It is an intuitive, classic way to express tensile strength, independent of grammage. Common papers break around 3–8 km; high-strength papers, more. Enter the tensile index (N·m/g).
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Paper breaking length
Breaking length is a wonderfully intuitive way of expressing the strength of a paper: it is the length of a strip of paper that, hung vertically from one end, would break under its own weight. Surprisingly, that length does not depend on the grammage nor on the thickness of the strip — only on the intrinsic quality of the material — since both the resisting force and the weight grow in proportion to the cross-section. It follows straight from the tensile index: L (km) = tensile index / 9.80665 (gravity). Ordinary papers come in at 3 to 8 km — in other words, a strip of copy paper would have to be kilometres long to tear under its own hanging weight. High-strength grades (kraft sack paper, security papers) reach 10 km or more; weak grades (tissue, low-quality newsprint) fall short of the range. It is a classic concept in paper physics, matching the breaking length used for textile fibres and cables as well, and an elegant way of comparing materials by their strength-to-weight ratio. Enter the tensile index.
Related Tools
Paper Tensile Index
Compute the paper tensile index, index = tensile strength (N/m) / grammage (g/m²), in N·m/g, normalizing the strength by the grammage to allow comparing papers of different weights. It is one of the most important mechanical properties, linked to fiber strength, inter-fiber bonding and refining. Packaging and sack papers require a high tensile index. Enter the tensile strength and the grammage.
Paper Tear Index
Compute the paper tear index, index = tear force (mN) / grammage (g/m²), in mN·m²/g, normalizing the tear resistance by the grammage. Tearing depends greatly on fiber length (long fibers resist more) — which is why packaging papers use long softwood fibers. It is a property that often competes with tensile (more refining raises tensile but lowers tear). Enter the tear force and the grammage.
Percent Elongation
Calculate the percent elongation, A% = (L_f − L₀) ÷ L₀ × 100%, from the initial gauge length L₀ and the final length L_f measured after rupture in a tensile test (fitting the two halves of the specimen back together). The result, in %, is a direct measure of the material's ductility — how much it stretches before breaking. Ductile steels reach 20–40%; brittle materials, a few percent. Elongation depends on the gauge length used, so it is always quoted with it (e.g. A% over 50 mm). Enter the initial and final lengths.
Flexural Modulus of Rupture (Ceramic)
Compute the three-point flexural modulus of rupture (MOR) of a ceramic, MOR = 3·F·L/(2·b·d²), from the breaking load (F), the support span (L), the width (b) and the thickness (d) of the test bar. It is the main mechanical-strength measure of ceramics and tiles (ISO 10545): porcelain tiles exceed 35 MPa. The d² dependence shows why thicker pieces resist far more. Enter the load, the support span, the width and the thickness.
Geosynthetic Rupture Safety Factor
Calculate the safety factor against tensile rupture of a geosynthetic reinforcement layer, FS = T_adm ÷ T_req, from the allowable tensile strength T_adm (kN/m, the ultimate already reduced by creep, installation-damage and degradation factors) and the required tension T_req (kN/m, the force the soil demands at that layer). This is the final design check for a reinforcement layer: the available (allowable) strength must exceed the demand (required) with an adequate margin. Reinforced-soil codes require tensile-rupture safety factors typically around 1.3-1.5 (since many uncertainties — creep, damage, degradation — are already covered by the partial reduction factors embedded in T_adm). If FS is below the required, a stronger geosynthetic is chosen, the layer spacing reduced (lowering T_req per layer) or both. Besides tensile rupture (this calculation), reinforced-soil design also checks PULLOUT stability (sufficient anchorage), INTERNAL stability (failure surfaces cutting the reinforcements), EXTERNAL stability (sliding, overturning and bearing capacity of the whole mass) and deformations. This rupture FS is one of the fundamental checks. Enter the allowable strength and the required tension.
Train Movement Resistance (Davis)
Calculate a train's specific movement resistance by the Davis equation, R = A + B·V + C·V², from coefficient A (rolling resistance and mechanical friction, speed-independent), B (resistance proportional to speed, from flange friction and oscillations), C (aerodynamic resistance, proportional to speed squared) and the speed V (km/h). The Davis equation, from the 1920s and still standard in railway engineering, describes the total resistance to motion the locomotive must overcome on straight, level track, per unit weight (N/t or kgf/t). At low speed the constant and linear terms (friction) dominate; at high speed the quadratic aerodynamic term dominates, decisive for high-speed trains (hence their careful streamlining). Davis resistance, plus grade (gravity) and curve resistances, sets the required tractive effort, energy consumption and locomotive traction capacity. It is the basis of traction calculation and train performance. Enter coefficients A, B and C and the speed.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.