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The two numbers that decide service life

Bend Radius & Live Length

Static and dynamic radius, the difference between live and overall length, and the formulas for sizing a moving installation.

Two numbers govern whether a moving hose reaches its design life: the radius it is allowed to bend to, and the flexible length available to do the bending. Get either wrong and the assembly fails at the fitting.

Live length is not overall length

Live length is what moves. Overall length is what you measure between faces.
Fig. 1 Live length is what moves. Overall length is what you measure between faces.

Overall length is measured face to face, including the fittings. Live length is the flexible portion between the fitting terminations — the part that actually moves. Every formula below uses live length. When you specify a length on an enquiry, tell us which one you mean, because the difference on a short assembly with heavy flanges is substantial.

Static and dynamic bend radius

Two different radii for two different duties.
Fig. 2 Two different radii for two different duties.

We publish both, because they answer different questions.

Static bend radiusFlexing bend radius (Type-1 / Type-2)
DefinitionA permanently formed installation bend, made onceThe radius to design to for repeated movement — two figures, ask us which duty applies
UseInstalled, clamped, left aloneRepeated movement, vibration, loops
RelationshipBaselineType-2 runs 2.9× the static figure at DN65, rising to 5.6× at DN6
Installing to the static radius and then flexing the hose is the most common avoidable cause of early failure we are asked to investigate. If it moves, use the dynamic figure.

Calculating the length you need

Most metal hose failures are length failures. Too short and it over-bends at the fittings. Forced to take axial movement and it destroys its own braid. Two rules cover nearly everything.

Rule 1 — movement in one plane only

A braided hose absorbs movement across its axis, not along it. Never apply axial compression, extension or torsion. If the line moves axially, use an expansion joint or install the hose as a loop.

Rule 2 — lateral offset, both ends fixed

Lateral offset geometry
Fig. 3 Lateral offset. T is the total travel across the hose axis.
Lv = √( 6 · R · T + T² )

Lv = live length, the flexible length between braid ferrules   R = bend radius — flexing column for repeated movement, static for a one-time offset   T = total lateral travel (mm)
Installed projected length: Lp = √( Lv² − T² )

Worked example. DN25 single-braid hose, repeated lateral movement of 25 mm. Flexing radius from the table is 325 mm.
Lv = √(6 × 325 × 25 + 25²) = √49,375 ≈ 222 mm.
Specify a live length of at least 225 mm, plus the fitting lengths.

Rule 3 — 90° change of direction

A 90° bend needs 1.57 × R of live length, plus a straight tangent at each fitting.
Fig. 4 A 90° bend needs 1.57 × R of live length, plus a straight tangent at each fitting.
Lv ≥ 1.57 × R   plus straight tangents at each fitting

DN50 as a static 90° bend: Lv ≥ 1.57 × 160 = 251 mm, so specify 255 mm live. The same bend as flexing duty uses R = 490 mm, giving Lv ≥ 770 mm. That is the difference the duty makes.

Rule 4 — vibration duty

Install the hose across the main vibration direction, use the flexing radius, and keep it slack at the operating position. Treat the vibration amplitude as T in Rule 2. Clamp the rigid pipework only — never the hose or the braid.

Rule 5 — keep fittings out of the bend

Leave a straight tangent of at least two times the hose outside diameter after each fitting before the bend starts. Never let a bend begin at the braid ferrule.

These give a minimum. Add allowance for installation tolerance, for thermal growth in the pipework around it, and for settlement. A hose slightly too long is a nuisance. One slightly too short is a failure. If you are unsure, send us the movement, the mounting orientation and the space you have — we will size it.
Lateral offset with both ends fixed, and the formula that sizes it.
Fig. 5 Lateral offset with both ends fixed, and the formula that sizes it.
Inside the radius the convolutions open evenly. Below it they bottom out.
Fig. 6 Inside the radius the convolutions open evenly. Below it they bottom out.

Rules that apply to every geometry

The stiffest point on the assembly is where flexible meets rigid.
Fig. 7 The stiffest point on the assembly is where flexible meets rigid.
Angular travel at one end, with the other end fixed.
Fig. 8 Angular travel at one end, with the other end fixed.
Horizontal travelling loop, where the hose lies flat and the travel is sideways.
Fig. 9 Horizontal travelling loop — the hose lies flat and the movement is taken as a change in loop geometry.
Vertical travelling loop, where the load is carried by the loop itself.
Fig. 10 Vertical travelling loop, where the load is carried by the loop itself.

Tell us about the job. We will work out what it needs.

Send the medium, pressure, temperature, movement and end connections — or just describe the problem. You get back a specified assembly and a drawing, and a price once the specification is settled.

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