{
  "url": "https://openlegislation.uk/eu-regulation-2015-68/annex-XI/appendix-2",
  "json_url": "https://openlegislation.uk/eu-regulation-2015-68/annex-XI/appendix-2.json",
  "legislation": "eur/2015/68",
  "legislation_title": "Commission Delegated Regulation (EU) 2015/68 of 15 October 2014 supplementing Regulation (EU) No 167/2013 of the European Parliament and of the Council with regard to vehicle braking requirements for the approval of agricultural and forestry vehicles (Text with EEA relevance)",
  "legislation_url": "https://openlegislation.uk/eu-regulation-2015-68",
  "path": "annex/XI/appendix/2",
  "kind": "appendix",
  "number": "2",
  "heading": null,
  "text": "Utilisation of adhesion\n1.\nMethod of measurement for tractors\n1.1.\nDetermination of the coefficient of adhesion (k)\n1.1.1.\nThe coefficient of adhesion (k) shall be determined as the quotient of the maximum braking forces without locking the wheels and the corresponding dynamic load on the axle being braked.\n1.1.2.\nThe brakes shall be applied only on one axle of the vehicle under test, at an initial speed of 50 km/h. The braking forces shall be distributed between the wheels of the axle to reach maximum performance. The anti-lock braking system shall be disconnected, or inoperative, between 40 km/h and 20 km/h.\n1.1.3.\nA number of tests at increments of line pressure shall be carried out to determine the maximum braking rate of the vehicle (zmax). During each test, a constant input force shall be maintained and the braking rate shall be determined by reference to the time (t) taken for the speed to reduce from 40 km/h to 20 km/h using the formula:\nz = 0,566 t zmax is the maximum value of z in m/s2,\nt is in seconds.\n1.1.3.1.\nWheel-lock may occur below 20 km/h.\n1.1.3.2.\nStarting from the minimum measured value of t, called tmin, then select three values of t comprised within tmin and 1,05 tmin and calculate their arithmetical mean value tm, then calculate\nz m = 0,566 t m If it is demonstrated that for practical reasons the three values determined above cannot be obtained, then the minimum time tmin may be utilised. However, the requirements of point 1.3 still apply.\n1.1.4.\nThe braking forces shall be calculated from the measured braking rate and the rolling resistance of the un-braked axle(s) which is equal to 0,015 and 0,010 of the static axle load for a driven axle and a non-driven axle, respectively.\n1.1.5.\nThe dynamic load on the axle shall be calculated from the braking rate, static axle load, wheelbase and centre of gravity height.\n1.1.6.\nThe value of k shall be rounded to three decimal places.\n1.1.7.\nThen, the test shall be repeated for the other axles(s) as defined in points 1.1.1 to 1.1.6 (for exemptions, see points 1.4 and 1.5).\n1.1.8.\nFor example, in the case of a two-axle rear-wheel drive vehicle, with the front axle being braked, the coefficient of adhesion (k) is given by:\nk f = z m × P × g − 0,015 F 2 F 1 + h E z m × P × g 1.1.9.\nOne coefficient shall be determined for the front axle kf and one for the rear axle kr.\n1.2.\nDetermination of the adhesion utilised (ε)\n1.2.1.\nThe adhesion utilised (ε) is defined as the quotient of the maximum braking rate with the anti-lock braking system operative (zAL) and the coefficient of adhesion kM, i.e.\nε = z AL k M 1.2.2.\nFrom an initial vehicle speed of 55 km/h, or vmax whichever is lower, the maximum value for the braking rate (zAL) shall be measured with full cycling of the anti-lock braking system. This value for zAL shall be based on the average value of three tests, as previously described in point 1.1.3, using the time taken for the speed to reduce from 45 km/h to 15 km/h, according to the following formula:\nz AL = 0,849 t m 1.2.3.\nThe coefficient of adhesion kM shall be determined by weighting with the dynamic axle loads:\nk M = k f × F fdyn + k r × F rdyn P × g Where:\nF fdyn = F f + h E × z AL × P × g F rdyn = F r − h E × z AL × P × g 1.2.4.\nThe value of ε shall be rounded to two decimal places.\n1.2.5.\nIn the case of a vehicle equipped with an anti-lock braking system of category 1 or 2, the value of zAL is based on the whole vehicle, with the anti-lock braking system in operation, and the adhesion utilised (ε) shall be given by the same formula quoted in point 1.2.1.\n1.2.6.\nIn the case of a vehicle equipped with an anti-lock braking system of category 3, the value of zAL shall be measured on each axle which has at least one directly controlled wheel.\nExample: for a two-axle vehicle with an anti-lock braking system acting only on the rear axle (2), the adhesion utilised (ε) is given by:\nε 2 = z AL × P × g − 0,010 × F 1 k 2 F 2 − h E z AL × P × g This calculation shall be made for each axle having at least one directly controlled wheel.\n1.3.\nIf ε > 1,00, the measurements of coefficients of adhesion shall be repeated. A tolerance of 10 % is acceptable.\n1.4.\nFor tractors equipped with three axles, any axles that are interconnected by either suspension components and thereby react to weight transfer under braking or driveline may be disregarded in establishing a k value for the vehicle.\nUntil a uniform test procedure is agreed, vehicles with more than three axles and special vehicles shall be subject to consultation with the technical service.\n1.5.\nFor tractors with a wheel base less than 3,80 m and with h/E > 0,25, the determination of the coefficient of adhesion for the rear axle shall be omitted\n1.5.1.\nIn that case, the adhesion utilised (ε) is defined as the quotient of the maximum braking rate with the anti-lock braking system operative (zAL) and the coefficient of adhesion (kf), i. e.\nε = z AL k f 2.\nMethod of measurement for towed vehicles\n2.1.\nGeneral\n2.1.1.\nThe coefficient of adhesion (k) shall be determined as the quotient of the maximum braking forces without locking the wheels and the corresponding dynamic load on the axle being braked.\n2.1.2.\nThe brakes shall be applied on only one axle of the towed vehicle under test, at an initial speed of 50 km/h. The braking forces shall be distributed between the wheels of the axle to reach maximum performance. The anti-lock braking system shall be disconnected or inoperative between 40 km/h and 20 km/h.\n2.1.3.\nA number of tests at increments of line pressure shall be carried out to determine the maximum braking rate of the vehicle combination (zCmax) with the towed vehicle only braked. During each test, a constant input force shall be maintained and the braking rate shall be determined by reference to the time taken (t) for the speed to reduce from 40 km/h to 20 km/h using the formula:\nz c = 0,566 t 2.1.3.1.\nWheel-lock may occur below 20 km/h.\n2.1.3.2.\nStarting from the minimum measured value of t, called tmin, then select three values of t comprised within tmin and 1,05 tmin and calculate their arithmetical mean value tm.\nthen calculate:\nz c max = 0,566 t m If it is demonstrated that for practical reasons the three values determined above cannot be obtained, then the minimum time tmin may be utilised.\n2.1.4.\nThe adhesion utilised (ε) shall be calculated by means of the formula:\nε = z AL k R The k value shall be determined according to point 2.2.3 for drawbar towed vehicles or point 2.3.1 for rigid drawbar towed vehicles and centre-axle towed vehicles, respectively.\n2.1.5.\nIf ε > 1,00 the measurements of coefficients of adhesion shall be repeated. A tolerance of 10 % is accepted.\n2.1.6.\nThe maximum braking rate (zRAL) shall be measured with full cycling of the anti-lock braking system and the tractor unbraked, based on the average value of three tests, as in point 2.1.3.\n2.2.\nDrawbar towed vehicles\n2.2.1.\nThe measurement of k (with the anti-lock braking system being disconnected, or inoperative, between 40 km/h and 20 km/h) shall be performed for the front and rear axles.\nFor one front axle i:\nF bRmaxi = z cmaxi F M + F R − 0,01 F Cnd − 0,015 F Cd F idyn = F i + z Cmax F M × h D + g × P × h R − F WM × h D E k r = F bRmaxi F idyn For one rear axle i:\nF bRmaxi = z cmaxi F M + F R − 0,01 F Cnd − 0,015 F Cd F idyn = F i − z Cmax F M × h D + g × P × h R − F WM × h D E k r = F bRmaxi F idyn 2.2.2.\nThe values of kf and kr shall be rounded to three decimal places.\n2.2.3.\nThe coefficient of adhesion kR shall be determined proportionally according to the dynamic axle loads.\nk R = k f × F fdyn + k r × F rdyn P × g 2.2.4.\nMeasurement of zRAL (with the anti-lock braking system operative)\nz RAL = z CAL × F M + F R − 0,01 F Cnd − 0,015 F Cd F R zRAL shall be determined on a surface with a high coefficient of adhesion and, for vehicles with a category A anti-lock braking system, also on a surface with a low coefficient of adhesion.\n2.3.\nRigid drawbar towed vehicles and centre-axle towed vehicles\n2.3.1.\nThe measurement of k (with the anti-lock braking system being disconnected, or inoperative, between 40 km/h and 20 km/h) shall be carried out with wheels fitted only on one axle, the wheels of the other axle(s) are removed.\nF bRmax = z Cmax F M + F R − F WM F Rdyn = F R − F bRmax × h k + z c × g × P × h R − h k E R k = F bRmax F rdyn 2.3.2.\nThe measurement of zRAL (with the anti-lock braking system operative) shall be carried out with all wheels fitted.\nF bRAL = z CAL × F M + F R − F WM F Rdyn = F R − F bRAL × h k + z c × g × P × h R − h k E R z RAL = F bRAL F Rdyn zRAL shall be determined on a surface with a high coefficient of adhesion and, for vehicles with a category A anti-lock braking system, also on a surface with a low coefficient of adhesion.",
  "extent": "E+W+S+N.I.",
  "status": null,
  "version": "current",
  "annotations": [],
  "outstanding_effects": [],
  "provenance": {
    "source": "legislation.gov.uk",
    "source_url": "https://www.legislation.gov.uk/eur/2015/68/annex/XI/appendix/2",
    "retrieved_at": "2026-11-01T14:46:56.586941+00:00"
  },
  "licence": "Open Government Licence v3.0",
  "licence_url": "https://www.nationalarchives.gov.uk/doc/open-government-licence/version/3/",
  "attribution": "Contains public sector information licensed under the Open Government Licence v3.0. Source: legislation.gov.uk, The National Archives."
}