Steel Grating Slip Resistance and Ramp Slope Calculation: PTV, DIN R-Ratings and the 13 mm Clear-Opening Rule

2026-10-29 · Technical Calculation · ASPER 阿斯珀尔

On procurement sheets for industrial platforms and maintenance walkways, "serrated grating" is treated as synonymous with "slip resistant". From a calculation standpoint that claim is missing three parameters: slip resistant under which contaminant, on what slope, and for which user. This article turns all three into recalculable arithmetic, worked through on two of the most common specifications, G303/30/100 and G325/30/100.

Scope of judgement (basis statement)
Included: pendulum (BS 7976 / BS EN 13036-4) PTV to COF conversion; DIN 51130 ramp R-grade slope equivalents; friction-cone demand on ramps; the contact-area question under classical friction law; the GB 55019-2021 mandatory limit on grating opening width along accessible routes.
Not included: individual footwear material and tread variation (no test data); long-term PTV decay from wear (no usable primary data, so a re-test criterion is given rather than a decay model); icing and condensation dynamics; the effect of hot-dip zinc spangle roughness on PTV, where the direction and magnitude of the effect are still disputed.
The "equivalent safety margin" criterion (Section 4) is a model assumption introduced by this article for slope conversion, not a direct quotation of any GB or EN clause. It has been cross-checked against the ΔPTV = 100 × tanα rule stated in the official BS 7976 pendulum test report: across six gradients the largest divergence is 0.07 of a PTV unit (under 0.15%), erring toward the higher, safer PTV.

1. Why "serrated" is not the same as "slip resistant"

Serration is a geometric feature; slip resistance is a system performance. The same serrated bar can show friction coefficients differing by a factor of several between dry, water-wet, oil-contaminated and iced conditions. Treating a geometric feature as a performance conclusion means substituting "has teeth" for "is adequate", which cannot be evidenced at handover.

The deeper problem is that the industry runs at least three parallel slip criteria that measure different things and whose numbers are not interchangeable. Mixing them is the most common source of error on site.

2. Three criteria, three different things: PTV, DIN R-grades, static friction angle

The first is the pendulum, to BS 7976-2 and BS EN 13036-4, read as a Pendulum Test Value (PTV; called BPN in the US and SRV in earlier UK usage). A spring-loaded rubber slider simulates a heel strike and the energy loss of the swinging arm is converted to dynamic friction. Two sliders exist: No. 96 (4S) for shod pedestrians and No. 55 (TRL) for barefoot.

The second is the ramp, to German standard DIN 51130. Operators wear cleated safety boots and walk a motor-oil-coated panel whose inclination is increased until they slip; the maximum non-slip angle is averaged and mapped onto grades R9 to R13.

The third is the static friction angle, the purely geometric μ = tanθ check familiar from structural self-locking calculations.

The decisive practical difference: the pendulum works in situ on installed floors, the ramp method is laboratory-only. A supplier R-grade certificate describes a laboratory panel. It cannot capture weld distortion, zinc spangle, installation misalignment or wear. The pendulum can.

Cross-check: the UK Health and Safety Executive states in technical guidance GEIS2 that grade R10 covers a coefficient of friction range from 0.18 to 0.34. tan10° and tan19° are 0.1763 and 0.3443. The match confirms that the R-scale is essentially a tanθ banding, so the conversion is sound.

HSE nonetheless records reservations about the standard: motor oil is not representative of typical workplace contaminants, and the bands are wide. Within a single R10 band the COF may vary from 0.18 to 0.34, nearly a factor of two, so two products both sold as R10 can perform very differently. Both HSE and the UK Slip Resistance Group therefore rank the pendulum as the preferred method.

3. Exact PTV to COF conversion: two formulas that are actually one

The most widely circulated shortcut divides PTV by 100 to get the coefficient of friction. That approximation is accurate only near PTV 30 and degrades with distance. Two exact forms exist:

μ = 3 × PTV ÷ (330 − PTV)

μ = (110 ÷ PTV − 1/3)⁻¹

The first appears in the Chinese standard for sports surface slip resistance testing; the second comes from a White Rose open-access paper on standardised shoe-surface friction testing and is reused across rail and road friction literature. The two are mathematically identical: inverting the first gives 1/μ = (330 − PTV) ÷ (3 × PTV) = 110 ÷ PTV − 1/3, which is exactly the bracketed term of the second.

Step by step at 36 PTV:

330 − 36 = 294

3 × 36 = 108

108 ÷ 294 = 0.3673

That 0.3673 matches the UKSRG table entry "36 PTV corresponds to COF 0.367" exactly, and is consistent with the HSE surface-roughness criterion of Rz not less than 20 μm for low risk.

Inverting the relation is more useful at design stage, when the required friction is known and the required PTV is not:

PTV = 330 × μ ÷ (3 + μ)

Back-substitution check with μ = 0.3673:

3 + 0.3673 = 3.3673

330 × 0.3673 = 121.21

121.21 ÷ 3.3673 = 35.99

Returns to 36. Closed.

The important information in this table is the direction of the error, not the numbers. The approximation overstates friction below PTV 30 and understates it above, with error growing with distance; at 65 PTV it understates by 11.67%. In the low-risk range the shortcut understates how good the material is; in the high-risk range it overstates it, and that is the dangerous direction of error. Use the exact form at handover.

That standards do not compare across methods is settled professional consensus. A US safety flooring technical note on PTV to DCOF conversion makes the point directly: one and the same floor can return coefficients of 0.4, 0.5, 0.6 or 0.7 depending purely on the test method used. That country's occupational safety regulator long prescribed a minimum COF of 0.50 without naming a test method, which made the figure meaningless at the time. Every conversion given here therefore carries its source standard and slider condition.

The UKSRG and HSE thresholds are: PTV of 36 and above is low slip potential, 25 to 35 moderate, 0 to 24 high. Critically, 36 is calibrated for straight-line walking on a level surface, derived from the Harper et al. force-plate work of 1961 and cited in BS 8300. Once a slope appears, the threshold is no longer 36.

4. How slope eats the margin: from static self-locking to the friction cone

Structural checks on ramps usually use static self-locking: if the coefficient of friction is at least the tangent of the slope angle, a standing person will not slide.

μ ≥ tanθ

At 1:4, tanθ = 0.2500, so it looks as though μ = 0.25 suffices. But that is a standing criterion, not a walking one. During gait the foot delivers horizontal shear at contact, so the demanded friction is far above the static balance value, and it is that dynamic margin which the PTV 36 threshold carries.

Tilt the ground by θ and the body still pushes relative to gravity, but the ground frame rotates. With RCOF₀ the level-surface demand:

RCOF_θ = (RCOF₀ + tanθ) ÷ (1 − RCOF₀ × tanθ)

The denominator is below unity, which further amplifies demand. Taking the level low-risk reference RCOF₀ = 0.3673 (the value at 36 PTV) and converting each result back through the inverse relation of Section 3:

The last column is the one to remember. Across the slopes used most in practice, 1:20 to 1:8, the static check understates demand by a factor of 4 to 8.5. A 1:12 ramp needs only 0.0833 to prevent a standing person sliding, but on the equivalent-margin basis it actually needs 0.4649, equivalent to PTV 44, eight PTV units above the level threshold.

Set this beside the accessibility code. GB 55019-2021 clause 2.3.1 limits wheelchair ramp longitudinal gradient to 1:12, or 1:10 where constrained and the rise over a single flight does not exceed 150 mm, and caps crossfall at 1:50. Clause 2.3.4 requires handrails both sides where the ramp height exceeds 300 mm and the gradient exceeds 1:20. The slip background to those limits is precisely the 44 PTV at 1:12 and 46 PTV at 1:10 in the table above.

4b. International cross-check on the slope addition: ΔPTV = 100 × tanα

There is an independent international figure against which the friction-cone demand above can be checked. The official BS 7976 pendulum test report text states that where a sloping surface has to be negotiated, the required PTV must be increased by one hundred times the tangent of the slope angle.

ΔPTV = 100 × tanα

At 1:20, tanα is 0.0500, so the addition is 5 units and the required PTV becomes 41. The friction-cone model of Section 4 arrives independently at 40.96, a difference of 0.04 of a PTV unit.

Across six gradients the largest divergence between the two routes is 0.07 of a PTV unit, a relative difference not exceeding 0.15%. That agreement is not coincidence. Expand the friction cone expression as a first-order series about tanα = 0 and it reduces exactly to the linear addition; this model retains the second-order term. Over the gradients normally used it therefore sits 0.04 to 0.07 of a unit above the linear rule, and since the more demanding figure is the higher PTV, it errs safe.

This also answers the main objection to Section 4. The equivalent-margin assumption is not an isolated conservative superposition; it agrees numerically with the rule in current UK pendulum practice. For routine judgement, ΔPTV = 100 × tanα is adequate and quick. Where more precision is needed, return to the friction cone form.

A supporting detail: a UK manufacturer publishes the same rule rounded to whole PTV units, giving 42 for a 3° slope (the exact value 41.25 rounded up). The 1:20 case here is 2.86° and requires 41, continuous with that table under the same convention.

4c. A trap worth naming: gradient ratio or slope angle

A European grating manufacturer publishes an R-grade to PTV comparison giving two columns, one for level surfaces and one for a 5% ramp, which provides a direct test of the conversion above.

Setting that table against Section 4 exposes a discrepancy that needs clearing up. Its two columns differ by 9 PTV units. Under ΔPTV = 100 × tanα, if "5%" means a gradient ratio then tanα is 0.0500 and the addition should be 5 units; if "5%" is read as a slope of 5 degrees then tan5° is 0.0875 and the addition is 8.75 units, matching the table.

100 × 0.0500 = 5.00

100 × 0.0875 = 8.75

This is not an arithmetic error on either side. It is that the word "slope" is written two different ways in slip literature: as a gradient ratio (1:20, 5%) or as an angle in degrees (2.86°, 5°). The two tangents differ by nearly a factor of two, which lands as 5 against 8.75 in PTV terms. Before quoting any ramp slip table, establish whether its "%" means ratio or angle. This article uses the gradient ratio convention throughout.

The same table offers one useful cross-check: it places level PTV 36 near the start of the R11 band, the same territory as the UKSRG and HSE "36 and above is low risk" threshold. The two systems agree on where "acceptable" begins; they differ only in how they express it.

One more caution, this time on Chinese-language sources. A trade technical site gives the critical slip angles of DIN 51130 grades R11 to R13 as 12° to 19°. The HSE publication of the DIN 51130 classification gives R11 as 19° to 27°, R12 as 27° to 35° and R13 as above 35°. The gap is large, so the grade boundaries must be taken from the standard itself.

5. Open area is not slipperiness: contact area under classical friction

A widespread claim holds that a large open area means less contact underfoot and therefore more slip. Under classical friction law that is false: friction force equals μ × N and is independent of apparent contact area. Open area still has to be calculated, though, because it drives two other things: local contact pressure and drainage.

Open area is computed per direction: across the bearing bars it is (centre spacing − bar thickness) ÷ centre spacing; along the cross bars it is (cross bar pitch − cross bar size) ÷ cross bar pitch. The product is the areal open area.

For G303/30/100 (30 mm deep × 3 mm thick bearing bars at 30 mm centres; 6 mm twisted square cross bars at 100 mm pitch):

30 − 3 = 27

27 ÷ 30 = 0.9000

100 − 6 = 94

94 ÷ 100 = 0.9400

0.9000 × 0.9400 = 0.8460

Open area 84.60%, effective contact 15.40%.

The pressure factor is the reciprocal of the contact fraction. On G303/30/100 local pressure under the sole is 6.49 times that on a solid plate of the same material. That amplification works in opposite directions depending on the sole:

• Viscoelastic soles such as rubber: higher local pressure increases real contact area, so friction may rise, which is one reason grating is no worse than checkered plate when dry;
• Rigid soles such as leather or hard plastic: they cannot fill the voids, contact occurs only on a few narrow bar tops, and the heel edge may drop into an opening, creating trip and entrapment risk.

The real slip advantage of grating is drainage, not contact area. Water falls straight through, no continuous film forms, and the hydroplaning regime never arises. That is why grating often outperforms checkered plate on outdoor stairs in rain. With high-viscosity contaminants such as oil the advantage disappears immediately, because the oil does not drain away. That is exactly why DIN 51130 specifies motor oil as the contaminant.

6. 25 mm clear openings against the GB 55019 13 mm mandatory limit

This is the point most easily missed and with the most direct consequence. Clause 2.2.4 of GB 55019-2021, a mandatory provision of the Chinese accessibility code, states: where manhole covers or gratings occur on an accessible route, the width or diameter of the openings shall not exceed 13 mm, and linear openings shall run perpendicular to the direction of travel.

Every clause of that code has been mandatory since 1 April 2022. It tightened the 15 mm figure in GB 50763-2012, the intent being to prevent wheelchair castors, canes and crutch tips from catching.

The width of a steel grating linear opening is simply the clear gap between bearing bars:

clear = bar centre spacing − bar thickness

The conclusion is blunt: the three gratings used most on industrial platforms all have clear openings above 25 mm, between 1.9 and 2.7 times the accessible route limit, and cannot be used directly as drainage gratings on an accessible route.

One boundary has to be stated clearly or this will be misread. Clause 2.2.4 governs covers and gratings on accessible routes. Industrial maintenance platforms, plant walkways and pipe-rack gangways are not accessible routes and are not bound by it; they may continue to follow YB/T 4001.1-2019 (maximum clear spacing between bearing bars below 35 mm, maximum clear cross bar spacing not above 150 mm for walkway platforms). Municipal footways, park paths, plazas and intercepting channels at building entrances are accessible routes and must meet 13 mm.

A directional requirement is also frequently overlooked: linear openings shall run perpendicular to travel. On steel grating the linear openings run along the bearing bars, and the bearing bar direction is fixed by structure, since the bars must span between supports. Where the support layout puts the bars parallel to the main travel direction, the openings are also parallel to travel, and the directional requirement fails even if the opening width passes. That is a genuine conflict between structural layout and accessibility, and it has to be resolved at scheme stage rather than at completion.

Where grating is unavoidable on an accessible route, densification is the only direct compliance path, and its cost must be priced. Changing G325/30/100 to G325/15/100:

Nearly doubling the weight raises supporting steel, fixings and installation cost in step, while losing 15.66 points of open area weakens drainage and ventilation, which is the whole reason for choosing grating over plate. Once densification pushes open area down to 62.67%, it is worth re-asking whether grating is still the right answer, or whether a slotted or perforated cover plate is better.

7. Serration thresholds and heel geometry

YB/T 4001.1 requires serrated bearing bar to carry not fewer than 5 teeth per 100 mm, tooth width not below 0.55 mm, tooth depth between 1.5 mm and 2.5 mm, and tooth pitch not above 25 mm. These are geometric thresholds, not performance figures: meeting them does not imply any particular R-grade or PTV.

Match tooth pitch against heel geometry, taking 60 mm as a typical adult heel contact length:

60 ÷ 30 = 2.00

A heel spans 2.00 teeth at 30 mm bar centres. At the 25 mm upper limit on tooth pitch:

60 ÷ 25 = 2.40

It spans 2.40 teeth. This is the minimum geometric condition for serration to work. Fewer than two teeth under the heel and the foot meets a single ridge rather than a serration; the mechanism degrades from multi-tooth interlock to single-point contact and performance drops markedly.

The transverse direction needs checking too. At 100 mm cross bar pitch:

60 ÷ 100 = 0.60

The heel spans less than one cross bar, so there is a real chance it lands entirely between two, with transverse support coming only from the bearing bars. That is why codes suggest 50 mm cross bar pitch for stairs, ramps and anywhere foot comfort matters:

60 ÷ 50 = 1.20

At least one cross bar is always engaged.

8. Serration direction, the rail effect and installation orientation

Teeth are cut across the width of the bearing bar, so the tooth ridges run perpendicular to the bar length. That creates an orientation issue:

• Walking across the bars (travel perpendicular to the bars), the ridges are perpendicular to travel. Every bar crossed gives a fresh ridge to bear against, and slip resistance is at its best.
• Walking along the bars (travel parallel to the bars), the ridges are parallel to travel and form continuous rail-like channels. Longitudinal friction is still acceptable but lateral resistance drops sharply, and the foot can slide along the channel when turning or under sideways load.

On ramps, therefore, the main travel direction should run perpendicular to the bearing bars wherever the structure allows. Where it does not, use a denser 50 mm cross bar pitch with serrated bar over the ramp length, or switch to a checkered plate surface.

9. Failure boundaries in three states: wet, oily, iced

Water-wet is where grating performs best. Water passes straight through, no continuous film forms and hydroplaning cannot occur, which is why grating generally beats checkered plate on outdoor stairs.

Oily is the weak case. Motor oil at 40 ℃ has a kinematic viscosity around 100 mm²/s, two orders of magnitude above water at about 1 mm²/s. It clings, does not drain, and builds a stable film on the bar tops. Serration then works by punching through that film with the tooth tips to restore direct sole-to-metal contact, a boundary lubrication mechanism. The 1.5 mm minimum tooth depth exists for exactly this: shallower teeth cannot break the film.

Iced is the most dangerous state, and here grating has a reversed disadvantage. Air circulates freely above and below, drawing heat away, so the grating surface runs colder than a solid plate in the same environment and condensation and icing start earlier. Once snow is compacted into the openings by traffic it forms a flush ice layer that fills the serration completely and disables it. On outdoor ramps in northern climates, where snow cannot be cleared promptly, serrated grating degrades toward the performance of plain bar, and heated covers or a non-perforated ramp surface should be considered instead.

10. Measuring it properly on site: pendulum operating discipline

A recurring handover problem is substituting a laboratory panel certificate for site testing. The pendulum is valuable precisely because it works in situ, but only if the operating discipline is right:

• Record condition and slider together. A PTV without the dry/wet condition and the 96 or 55 slider designation is meaningless. Almost any dry floor exceeds 36 PTV, so using dry data to demonstrate safety proves nothing.
• Contact length must be 127 mm. The conversion in Section 3 is calibrated for a 127 mm slider contact length; a different length invalidates it.
• Apply temperature correction. Slider rubber hardness varies with temperature and the test method supplies a correction table, zero at 19-22 ℃ and stepped either side. The corrected value, PTV_Corr, is what feeds the conversion.
• Lay out the test points. Each test position takes three points no more than 400 mm apart, five swings per point, and the position PTV is the mean of three determinations.
• Record direction. For directional surfaces such as serrations or ribs, record the angle between test direction and travel direction and repeat along the least favourable direction.

Put the measured PTV through the exact conversion of Section 3 to get μ, then compare against the slope demand table in Section 4. That closes the loop from measurement to judgement without relying on any manufacturer performance claim.

11. Recalculation checklist

Every key figure on this page, step by step, so it can be checked with a calculator.

Frequently asked questions

Does serrated grating automatically achieve R11?

No, performance cannot be derived from geometry. Serration has to meet the YB/T 4001.1 geometric thresholds (5 teeth per 100 mm minimum, tooth width not below 0.55 mm, depth 1.5 to 2.5 mm, pitch not above 25 mm), but R-grades and PTV are measured performance depending on serration, surface condition, contaminant and footwear. Procurement should require a test report to DIN 51130 or BS 7976 rather than accepting the word "serrated". Note too that a laboratory report describes the panel; the pendulum should still be run on site.

On a 1:12 ramp, is accepting 36 PTV enough?

No. 36 is calibrated by UKSRG and HSE for straight-line walking on a level surface. On a 1:12 ramp the equivalent margin basis used here raises the demand to 0.4649, equivalent to PTV 44. The conversion follows the friction cone RCOF_θ = (RCOF₀ + tanθ) ÷ (1 − RCOF₀ × tanθ) with tanθ = 0.0833. Accepting 36 treats the ramp as level and gives away roughly 8 PTV of margin on the most common accessibility gradient.

Must grating on industrial platforms meet the 13 mm opening limit?

It depends on location. Clause 2.2.4 of GB 55019-2021 governs covers and gratings on accessible routes. Industrial maintenance platforms, plant walkways and pipe-rack gangways are not accessible routes and may follow YB/T 4001.1-2019 instead (clear spacing between bearing bars below 35 mm for walkway platforms). Municipal footways, park paths, plazas and intercepting channels at building entrances are accessible routes and must meet 13 mm. Common specs G303/30/100 and G325/30/100 give clear openings of 27 mm and 25 mm, 2.08 and 1.92 times the limit. Compliance means moving to a dense spec such as G325/15/100, which raises self weight from 44.69 to 86.56 kg/m² (+93.7%) and cuts open area from 78.33% to 62.67%, so supports and drainage need rechecking.