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# Root Mean Square Slope (Rδq, Pδq, Wδq) | Surface Roughness Parameters

## Surface roughness parameters in JIS B 0601

• Peaks and valleys in the height direction
• Average amplitude in the height direction
• Average characteristics in the height direction
• Horizontal direction
• Hybrid
• Areal material ratio curve and probability density function

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## Root mean square slope (RΔq, PΔq, WΔq)

Root mean square slope indicates the root mean square of the local tilt dZ/dX along the sampling length.

The local tilt refers to the derivative of Z(x). Derivatives generally use the seven-point formula shown below (because the first three points on either end lack sufficient data, three- or five-point formulae are used).

## Surface Roughness Parameters

This section explains the main parameters of ISO 4287:1997. Each parameter is classified according to primary profile (P), roughness profile (R), and waviness profile (W) in order to evaluate different aspects of the profile. (When the wavelengths of the waviness and primary profile components are compared, the surface roughness component is the asperity component of that which has the comparatively shorter wavelength.)

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Peaks and valleys in the height direction Arithmetical mean height (Ra, Pa, Wa) Maximum height of profile (Rz, Pz, Wz) Maximum profile peak height (Rp, Pp, Wp) Maximum profile valley depth (Rv, Pv, Wv) Mean height of profile elements (Rc, Pc, Wc) Total height of profile (Rt, Pt, Wt) Root mean square deviation (Rq, Pq, Wq) Skewness (Rsk, Psk, Wsk) Kurtosis (Rku, Pku, Wku) Mean width of the profile elements (RSm, PSm, WSm) Root mean square slope (RΔq, PΔq, WΔq) Load length ratio (Rmr (c), Pmr (c), Wmr (c)) Profile cut level difference (Rδc, Pδc, Wδc) Relative load length ratio (Rmr, Pmr, Wmr) Material ratio curve (BAC) Probability density function (ADF)