INTERNATIONAL STANDARD ISO 7176-8 Second edition 2014-12-15 Wheelchairs — Part 8: Requirements and test methods for static, impact and fatigue strengths Fauteuils roulants — Partie 8: Prescriptions et méthodes d’essai pour la résistance statique, la résistance aux chocs et la résistance la fatigue Reference number ISO 7176-8:2014(E) © ISO 2014 ISO 7176-8:2014(E) COPYRIGHT PROTECTED DOCUMENT © ISO 2014 All rights reserved Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior written permission Permission can be requested from either ISO at the address below or ISO’s member body in the country of the requester ISO copyright office Case postale 56 • CH-1211 Geneva 20 Tel + 41 22 749 01 11 Fax + 41 22 749 09 47 E-mail copyright@iso.org Web www.iso.org Published in Switzerland ii © ISO 2014 – All rights reserved ISO 7176-8:2014(E) Contents Page Foreword v Introduction vii 1 Scope Normative references Terms and definitions 4 Requirements 4.1 Strength requirements 4.2 Disclosure requirements 10 11 12 Test apparatus Preparation of the test wheelchair 13 6.1 Setup and adjustment of the wheelchair 13 6.2 Test dummies 14 6.3 Preparation of wheelchair 14 6.4 Records 14 6.5 Safety during testing 14 Sequence of tests 14 Test methods for static strength 15 8.1 Principle 15 8.2 Wheelchair preparation 15 8.3 Selection of loading pad 15 8.4 Arm supports: Resistance to downward forces 15 8.5 Foot supports: Resistance to downward forces 16 8.6 Tipping levers 19 8.7 Handgrips 21 8.8 Arm supports: Resistance to upward forces 22 8.9 Foot supports: Resistance to upward forces 24 8.10 Push handles: Resistance to upward load 27 8.11 Scooter steering handles: Resistance to forward forces 29 8.12 Scooter steering handles: Resistance to rearward forces 30 8.13 Scooter steering handles: Resistance to downward forces 31 8.14 Scooter steering handles: Resistance to upward forces 32 Test methods for impact strength 33 9.1 Principle 33 9.2 Wheelchair preparation 33 9.3 Back support: Resistance to impact 33 9.4 Handrim: Resistance to impact 35 9.5 Castors: Resistance to impact 36 9.6 Foot supports: Resistance to impact 38 9.7 Impacts on anti-tip devices 40 Fatigue tests 43 10.1 Principle 43 10.2 Preparation of test wheelchair for fatigue tests 43 10.3 Multi-drum test 44 10.4 Drop test 46 10.5 Fatigue test of manually operated parking brakes 48 Evaluation of test results 49 11.1 Evaluation and records of individual tests 49 11.2 Evaluation at end of testing 49 Test report 49 © ISO 2014 – All rights reserved iii ISO 7176-8:2014(E) Annex A (informative) Principles applied to derive static test loads .51 Annex B (informative) Design considerations 61 Annex C (informative) Derivation of pendulum swing angle for castor and foot support impact tests 62 Annex D (informative) Calculation of pendulum centre of percussion 65 Bibliography 67 iv © ISO 2014 – All rights reserved ISO 7176-8:2014(E) Foreword ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO member bodies) The work of preparing International Standards is normally carried out through ISO technical committees Each member body interested in a subject for which a technical committee has been established has the right to be represented on that committee International organizations, governmental and non-governmental, in liaison with ISO, also take part in the work ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization The procedures used to develop this document and those intended for its further maintenance are described in the ISO/IEC Directives, Part In particular the different approval criteria needed for the different types of ISO documents should be noted This document was drafted in accordance with the editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives) Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights ISO shall not be held responsible for identifying any or all such patent rights. Details of any patent rights identified during the development of the document will be in the Introduction and/or on the ISO list of patent declarations received (see www.iso.org/patents) Any trade name used in this document is information given for the convenience of users and does not constitute an endorsement For an explanation on the meaning of ISO specific terms and expressions related to conformity assessment, as well as information about ISO’s adherence to the WTO principles in the Technical Barriers to Trade (TBT), see the following URL: Foreword — Supplementary information The committee responsible for this document is ISO/TC 173, Assistive products for persons with a disability, Subcommittee SC 1, Wheelchairs This second edition cancels and replaces the first edition (ISO 7176-8:1998), which has been technically revised ISO 7176 consists of the following parts, under the general title Wheelchairs: — Part 1: Determination of static stability — Part 2: Determination of dynamic stability of electric wheelchairs — Part 3: Determination of the effectiveness of brakes — Part 4: Energy consumption of electric wheelchairs and scooters for determination of theoretical distance range — Part 5: Determination of dimensions, mass and manoeuvring space — Part 6: Determination of maximum speed, acceleration and deceleration of electric wheelchairs — Part 7: Measurement of seating and wheel dimensions — Part 8: Requirements and test methods for static, impact and fatigue strengths — Part 9: Climatic tests for electric wheelchairs — Part 10: Determination of obstacle-climbing ability of electrically powered wheelchairs — Part 11: Test dummies — Part 13: Determination of coefficient of friction of test surfaces — Part 14: Power and control systems for electrically powered wheelchairs and scooters – Requirements and test methods © ISO 2014 – All rights reserved v ISO 7176-8:2014(E) — Part 15: Requirements for information disclosure, documentation and labelling — Part 16: Resistance to ignition of postural support devices — Part 19: Wheeled mobility devices for use as seats in motor vehicles — Part 21: Requirements and test methods for electromagnetic compatibility of electrically powered wheelchairs and scooters, and battery chargers — Part 22: Set-up procedures — Part 25: Batteries and chargers for powered wheelchairs — Part 26: Vocabulary — Part 28: Requirements and test methods for stair-climbing devices A technical report (ISO/TR 13570-1) is also available giving a simplified explanation of these parts of ISO 7176 vi © ISO 2014 – All rights reserved ISO 7176-8:2014(E) Introduction This part of ISO 7176 has been an important part of the strength testing of wheelchairs since its publication in 1998 It contains test methods and sets minimum requirements for static, impact, and fatigue strength of both the overall wheelchair and individually stressed components Several parts of this International Standard have been reviewed In particular: — the fatigue testing elements, including the speed and size of slat of the two-drum test machine, and the number of test cycles for both two drum and drop tests have been reviewed through empirical testing and confirmed; — the failure criteria have been clarified, and permissible adjustments and repairs more clearly defined to minimize variation between laboratories; — a more precisely defined setup procedure for the reference configuration of adjustable wheelchairs as given in ISO 7176-22; — static, impact, and repeated load test procedures for Postural Support Devices (PSDs) have been revised and are contained in ISO 16840-3 It is anticipated that all parts of this International Standard will continue to be developed and future revisions may include the results of ongoing work in the following areas: — consideration of whether the fatigue test requirements should be revised for wheelchairs intended for use in less resourced settings; — review of the test methods and apparatus to facilitate testing in less resourced settings; — further development of the test dummies to improve the way in which they load the backs of test wheelchairs and, in particular, to improve their suitability for use with wheelchairs with low back supports © ISO 2014 – All rights reserved vii INTERNATIONAL STANDARD ISO 7176-8:2014(E) Wheelchairs — Part 8: Requirements and test methods for static, impact and fatigue strengths 1 Scope This part of ISO 7176 specifies requirements for static, impact, and fatigue strength of wheelchairs including scooters It specifies the test methods for determining whether the requirements have been met It also specifies requirements for disclosure of the test results The test methods can also be used to verify the manufacturers’ claims that a product exceeds the minimum requirements of this part of ISO 7176 This International Standard applies to occupant- and attendant-propelled manual wheelchairs and electrically powered wheelchairs intended to provide indoor and outdoor mobility for people with disabilities NOTE For the purposes of this part of ISO 7176, “wheelchair(s)” is used as an abbreviation for manual wheelchair(s) or electrically powered wheelchair(s), including scooter(s), to which the requirements and test methods are applied NOTE Clauses of this part of ISO 7176 will be used as a basis for developing requirements and test methods for wheelchairs not covered by this part of ISO 7176 Normative references The following documents, in whole or in part, are normatively referenced in this document and are indispensable for its application For dated references, only the edition cited applies For undated references, the latest edition of the referenced document (including any amendments) applies ISO 7176-6, Wheelchairs — Part 6: Determination of maximum speed, acceleration and deceleration of electric wheelchairs ISO 7176-7, Wheelchairs — Part 7: Measurement of seating and wheel dimensions ISO 7176-11, Wheelchairs — Part 11: Test dummies ISO 7176-15, Wheelchairs — Part 15: Requirements for information disclosure, documentation and labelling ISO 7176-22, Wheelchairs — Part 22: Set-up procedures ISO 7176-26, Wheelchairs — Part 26: Vocabulary Terms and definitions For the purposes of this document, the terms and definitions given in ISO 7176-7, ISO 7176-11, ISO 7176-26, and the following apply 3.1 fracture unintentional separation (of a component) into two or more pieces © ISO 2014 – All rights reserved ISO 7176-8:2014(E) 3.2 operator adjustable intended to be adjusted, moved, or set up by the operator without the help of tools or with the help of tools if those tools are supplied with the wheelchair 3.3 visible crack break, without complete separation into parts, visible to the naked eye and which has occurred during a test 4 Requirements 4.1 Strength requirements When tested in accordance with Clauses 8, 9, and 10, a single wheelchair shall meet all the following requirements at the conclusion of the tests a) No component shall show evidence of visible cracks, be fractured, or have become detached, with the following exceptions 1) Readjustment of postural supports is allowed after each of the tests in Clauses 8 and 2) Re-tightening, readjusting, or refitting of components that are identified in the operator’s manual as operator-adjustable components is allowed at 25 % intervals during each of the multi drum, drop, and manual brake fatigue testing procedures (Clause 10) Operator adjustable components, as identified in the operator’s manual, may not be adjusted using tools unless the tools are supplied with the wheelchair If there are operator adjustable components, fatigue test equipment may be stopped at 25 % plus or minus 5 % intervals, to determine if re-tightening, readjusting, or refitting of operator-adjustable components is required Re-tightening, readjusting, or refitting shall then be performed, following the procedures outlined in the operator’s manual Restart the test equipment after re-tightening, readjusting, or refitting has been performed 3) Re-tightening, readjusting, or refitting of any other component is not allowed 4) During the fatigue testing (Clause 10), the following wear items, if they are identified in the operator’s manual, may be replaced no more than twice per item: tyres (including solid tyres), inner tubes, drive belts, castor wheel rubber In the case of castor wheels that are a single integral part, replacement is only permitted because of wear or failure of the running surface, but not for failure of the wheel structure or other elements (e.g bearings) No other wear items may be replaced 5) Cracks in surface finishes, such as paint, that not extend into the structural material not constitute a failure b) No externally visible electrical cable shall be cut, abraded, or crushed No externally visible electrical connector shall be crushed or disconnected c) All parts intended to move, rotate or be removable, folding or adjustable shall operate as described by the manufacturer d) All power-operated systems shall operate as described by the manufacturer e) Handgrips shall not be displaced f) No component or assembly of parts shall exhibit visible plastic deformation, free play, or loss of adjustment that adversely affects the function of the wheelchair g) The brake mechanism shall not have moved from the pre-set positions 2 © ISO 2014 – All rights reserved ISO 7176-8:2014(E) Dimensions in millimetres Key tipping lever downward vertical force (F3) Figure A.1 — Load on tipping levers A.4.1.1 For manual wheelchairs Up to a limit of 1000N For a 100 kg dummy: F3 = 13 (100 + 20) = 560 N; use maximum value = 1 000 N For a 50 kg dummy: F3 = 13 (50 + 20) = 910 N A.4.1.2 For electrically powered wheelchairs F3 = 13 (Md + Mw) up to a limit of 000 N 54 © ISO 2014 – All rights reserved ISO 7176-8:2014(E) A.5 Handgrip loads A.5.1 Principle The level of handgrip adhesion becomes a safety issue when the wheelchair and occupant are being lifted up or down a curb The test load is derived from the assumption that the wheelchair and occupant are restrained from rolling down the curb by a person holding one handgrip It is assumed that the weight of the wheelchair and occupant are compensated for by the curb as shown in Figure A.2 NOTE The safety issues are compounded if the chair is being lifted up or down stairs As this is not recommended practice, this focus of these tests is the clearance of curbs, a more common form of assistance From the loads in Figure A.2, it may be shown that the pulling force H is 52 % of the combined mass of wheelchair and occupant Dimensions in millimetres Key G 1 000 N r 30 cm a 20 cm b 15 cm c 90 cm e 16 cm α arc cos[(r − h)/r] β arc tan[(a + b)/(c-r-(a/tan α)] γ 180 – α - β F g sin α/sin γ H F sin β V F cos β Figure A.2 — Wheelchair loads on curbs © ISO 2014 – All rights reserved 55 ISO 7176-8:2014(E) A safety factor, S, of 1,5 is introduced because of the safety issue and to accommodate the larger forces that can occur with different wheel sizes Tests have shown that humans are not generally capable of holding a handgrip at forces in excess of 750 N and so the applied load is limited to this level A.5.2 Calculations From Figure A.2, it can be seen that F4 = S × 0,52 (Md + Mw) g A.5.2.1 For manual wheelchairs Up to a limit of 750 N For a 100 kg dummy: F4 = 1,5 × 0,52 × (100 + 20) × 9,807 = 918 N; use maximum value of 750 N For a 75 kg dummy: F4 = 1,5 × 0,52 × (75 + 20) × 9,807 = 726 N A.5.2.2 For electrically powered wheelchairs F4 = 1,5 × 0,52 × (Md + Mw) × 9,807 Most electrically powered wheelchairs weigh more than 75 kg, even for children (occupant mass 25 kg), thus F4 = 1,5 × 0,52 × (25 + 75) × 9,807 = 765 N Use 750 N for all electrically powered wheelchairs A.6 Arm supports upward load A.6.1 Principle Helpers will often lift a wheelchair by the arm supports when assisting in the negotiation of curbs, steps, etc Experiments have shown that humans are generally unable to exert a force greater than 1 000 N on arm supports and so this force is specified as an upper limit Arm supports should either detach (or swing up) at very low loads, indicating they are not suitable for lifting, or bear as much load as is needed and expressed in this Clause A.6.2 Calculations A safety factor, S, of 1,5 is introduced because of the safety issue A.6.2.1 Manual wheelchairs The assumption is that two people can lift the whole mass of the wheelchair and occupant by the arm supports The direction of the lifting force is angled outwards The maximum value of F5 shall be set at 1 000 N 56 © ISO 2014 – All rights reserved ISO 7176-8:2014(E) For a 100 kg or more dummy: F5 = 1, (100 + 20) × 9, 807 cos 10 For a 75 kg dummy: F5 = 1, (75 + 20) × 9, 807 cos 10 For a 50 kg dummy: F5 = 1, (50 + 20) × 9, 807 cos 10 For a 25 kg dummy: F5 = NOTE 1, ( 25 + 20) × 9, 807 cos 10 = 896, N, which is rounded to 896 N = 709, N, which is rounded to 710 N = 522, N, which is rounded to 523 N = 336, N, which is rounded to 336 N For dummy mass more than 100 kg, 100 kg shall be used to calculate force A.6.2.2 Electrically powered wheelchairs Since most electrically powered wheelchairs are heavy, it is assumed that no more than one-third of the combined mass of wheelchair and occupant will be lifted from the arm supports and that a third person will lift from, say, the foot supports Hence F5 = S (Md + M w ) cos 10 = 4, 98 ( M d + M w ) Use (Md + Mw) = 7, 47 ( M d + 20) Use 7,5 (Md + 20) However, where this assumption leads to a lower load than that for the equivalent manual wheelchair, the loading for the manual wheelchair is applied F5 = S ( M d + 20) g cos 10 Whichever is greater, the applied force shall not exceed 1 000 N A.7 Foot support upward load A.7.1 Principle Helpers will often lift a wheelchair by the foot supports when assisting in the negotiation of steps, etc In addition, foot supports can be forced to carry significant upward load when a chair backs down over a high kerb Failure while negotiating stairs would almost certainly lead to injury and so a factor of safety is applied Foot supports should either detach at very low loads, indicating they are not suitable for lifting, or bear as much load as is needed and expressed in this Clause A.7.2 Calculation It is assumed that each of the foot supports will carry one quarter of the combined mass of the wheelchair and occupant © ISO 2014 – All rights reserved 57 ISO 7176-8:2014(E) Hence, F6 = S (Md + M w ) g = 3, 68 ( M d + M w ) This is rounded to F6 = 3,7 (Md + Mw) For manual wheelchairs: Up to a limit of 1 000 N For a 100 kg or more dummy: F6 = 3,7 × (100 + 20) = 444,0 N For a 75 kg dummy: F6 = 3,7 × (75 + 20) = 351,5 N, which is rounded to 352 N For a 50 kg dummy: F6 = 3,7 × (50 + 20) = 259,0 N For a 25 kg dummy: F6 = 3,7 × (25 + 20) = 166,5, which is rounded to 166 N For wheelchairs with a one-piece foot support, it is assumed that loads of both foot supports are affected to the centre of the foot support Hence F6 = 1,5/2 (Md + Mw) g, which is rounded to F6 = 7,4 (Md + Mw) NOTE For dummy mass more than 100 kg, 100 kg shall be used to calculate force A.8 Push handle upward load A.8.1 Principle Helpers will often lift a wheelchair by the push handles when assisting with the negotiation of steps, etc Failure of a push handle while negotiating stairs would almost certainly lead to injury and so a safety factor is applied For manual wheelchairs, it is assumed that the combined mass of wheelchair and occupant can be lifted by the push handles, each carries half the load, and handles comprising a horizontal bar will need to carry the full load at the centre A.8.2 Calculations NOTE Experiments have shown that humans are generally incapable of exerting a double-handed upward pull force greater than 880 N,[1] so this force is specified as an upper limit for each single push handle, and twice that level if two assistants can grab a one-piece cross bar handle 58 © ISO 2014 – All rights reserved ISO 7176-8:2014(E) A.8.2.1 For manual wheelchairs Hence, for manual wheelchairs with two push handles F7 = S (Md + M w ) g which is rounded to F7 = 7,35 (Md + Mw), up to a limit of 880 N For manual wheelchairs with bar-type handles: F8 = S (Md + Mw) g which is rounded to F8 = 14,7 (Md + Mw), up to a limit of 1 760 N For a 100 kg dummy: F7 = 7,35 × (100 + 20) = 882,0 N for each of two handles and F8 = 764 N for bar-type handles For a 75 kg dummy: F7 = 7,35 × (75 + 20) = 698,25 N, which is rounded to 698 N for each of two handles and F8 = 1 396 N for bar-type handles For a 50 kg dummy: F7 = 7,35 × (50 + 20) = 514,5 N, which is rounded to 515 N for each of two handles and F8 = 1 028 N for bar-type handles For a 25 kg dummy: F7 = 7,35 × (25 + 20) = 330,75 N, which is rounded to 330 N for each of two handles and F8 = 660 N for bar-type handles A.8.2.2 For electrically powered wheelchairs For electrically powered wheelchairs, it is assumed that three people will lift the wheelchair and that the third of the combined mass of the wheelchair and occupant can be carried by each push handle Hence, F7 = 1, ( M d + M w ) g This is rounded to F7 = (Md + Mw) or 000 N whichever is smaller For electrically powered wheelchairs with bar-type handles: F8 = × 1, ( M d + M w ) g This is rounded to F8 = 10 (Md + Mw) or 000 N whichever is smaller The forces calculated under A.8.2.2 shall not be less than that of a manual wheelchair for an occupant of the same mass © ISO 2014 – All rights reserved 59 ISO 7176-8:2014(E) A.9 Steering Handles: Resistance to forward forces A.9.1 Principle During acceleration, the maximum occupant mass (half to each handle simultaneously) can be applied to the steering handles with deceleration equal to the maximum requirement (4 m/s2) No allowance is given to binding the occupant to the seat A.9.2 Calculations Failure of component(s) from forces applied to the steering handles can be dangerous and so a safety factor is introduced Tests have shown that humans are generally not capable of holding a handgrip at forces in excess of 750 N and so the applied load is limited to this level F9 is equal to the force on each steering handle, with both handles to be stressed simultaneously with equivalent force F9 = where a ( M daS ) up to a maximum of 750 N is the maximum deceleration = 4 m/s2 Table A.1 — Forces on steering handle Test dummy mass Force Use 150 kg F9 = (150 × 4 × 1,5)/2 = 450 N 450 N 100 kg F9 = (100 × 4 × 1,5)/2 = 300 N 300 N 25 kg F9 = (25 × 4 × 1,5)/2 = 75 N 75 N 75 kg 50 kg F9 = (75 × 4 × 1,5)/2 = 225 N F9 = (50 × 4 × 1,5)/2 = 150 N A.10 Steering handles: Resistance to rearward forces 225 N 150 N See A.9 with all forces and accelerations reversed A.11 Steering handles: Resistance to downward forces See A.2 A.12 Steering handles: Resistance to upward forces See A.8 60 © ISO 2014 – All rights reserved ISO 7176-8:2014(E) Annex B (informative) Design considerations B.1 General The aspects of wheelchair design in this Annex are of considerable importance; nevertheless, it has not been found possible to identify satisfactory, repeatable test methods suitable for all designs at the time of publication of this part of ISO 7176 Designers should make every effort to conform to the recommendations given B.2 Removable arm supports and foot supports Those trying to help a person in a wheelchair to ascend or descend stairs are likely to try to lift the wheelchair using arm supports or foot supports Hence, removable arm supports should be designed so that any retaining devices are strong enough to permit the wheelchair to be lifted (see 8.8) or that they pull off the wheelchair easily, preventing the wheelchair from being lifted Designs that “jam” so that the wheelchair can be lifted and then free when shaken or jolted are particularly dangerous and should be avoided B.3 Resistance to being dropped Wheelchairs are often lifted into motor vehicles and there are other similar situations where there is a likelihood of their being dropped Designers should seek to minimize the risk of damage to wheelchairs if they are dropped during unoccupied transport (e.g back of car, off baggage handling belt) This might also need to be combined with low temperature testing Precautions should be taken to minimise any risk of damage to key parts B.4 Resistance to impact of seating systems Many occupants fall heavily on to the wheelchair seat when sitting down The resulting impact might not be central on the seat Designers should ensure that seats can withstand such impacts © ISO 2014 – All rights reserved 61 ISO 7176-8:2014(E) Annex C (informative) Derivation of pendulum swing angle for castor and foot support impact tests C.1 Philosophy Before impact, the wheelchair has a specific amount of momentum This momentum is a vector quantity and has a component normal to the barrier, V1, and a component parallel to the barrier, Vp In theory, the component of momentum normal to the barrier is lost due to the impact, but the component parallel to the barrier should be conserved since no forces act in that direction Thus, the total velocity of the wheelchair is reduced due to the impact causing a reduction of kinetic energy This loss in kinetic energy is the amount of energy the wheelchair absorbs during the impact with the barrier, ignoring small loses from heat and sound production C.2 Calculations The change in kinetic energy before and after impact is represented by the following formulae: Eimp = E1 - E2 (C.1) E1 = E2 = where ( M d + M w )Vp2 (C.2) (C.3) Eimp is the kinetic energy lost due to impact, expressed in joules; E2 is the kinetic energy before impact, expressed in joules; Md is the kinetic energy after impact, expressed in joules; is the mass of the test dummy, expressed in kilograms; E1 Mw V1 Vp 62 ( M d + M w )V12 is the mass of the wheelchair, expressed in kilograms; is the velocity of the wheelchair before impact, expressed in metres per second; is the component of the wheelchair velocity parallel to the barrier, expressed in metres per second © ISO 2014 – All rights reserved ISO 7176-8:2014(E) Hence, for an impact from a wheelchair velocity of 1 m/s at an angle of incidence of 45°: E imp = (Md + M w ) (1 − cos ) 45 = ( M d + M w ) (C.4) The kinetic energy of a pendulum Ep is: Ep = mp gh (C.5) h = d (1 – cos Ө) (C.6) where mp is the pendulum mass equal to 10 kg; g h d is the gravitational constant equal to 9,807 m/s2; is the change in height of the pendulum centre of gravity, expressed in metres; is the distance from the pendulum pivot point to the centre of percussion, expressed in metres Ep = 94,18 (1 - cos Ө) (C.7) Hence, if the pendulum is to deliver the same amount of energy to the wheelchair as an impact at 1 m/s, Formula (C.4) shall equal Formula (C.7) 94, 18 (1 − cosθ ) = Therefore cosθ = − (Md + M w ) (Md + M w ) 376, 72 See Figure C.1 for a graphical representation of this relationship © ISO 2014 – All rights reserved 63 ISO 7176-8:2014(E) Figure C.1 — Pendulum swing angle (0) for castor/foot support test 64 © ISO 2014 – All rights reserved ISO 7176-8:2014(E) Annex D (informative) Calculation of pendulum centre of percussion D.1 Principle An impact pendulum should be specified to yield consistent results from one laboratory to another The mass, geometry, and point of impact affects the momentum imparted from the pendulum to the wheelchair The pendulum should make contact with the wheelchair with the line of action passing through the pendulum’s centre of percussion to ensure consistent transfer of momentum The following calculations apply to a pendulum that consists of two major components: a block that comprises the majority of the pendulum’s mass and a rod that connects the block to the pendulum’s pivot D.2 Nomenclature d M R I is the distance from the pendulum pivot point to the centre of percussion; is the mass of the pendulum; is the distance from the pendulum pivot point to the centre of mass of the pendulum; is the moment of inertia of the pendulum about its pivot point; Mr is the mass of the rod; Mb is the mass of the block; w h is the width of the block; is the height of the block; Lr is the length of the rod; Rr is the distance from pendulum pivot point to the centre of mass of the rod; Rb is the distance from pendulum pivot point to the centre of mass of the block; Ir is the moment of inertia of the rod about the pendulum pivot point; T is the period of oscillation; Ib g is the moment of inertia of the block about the pendulum pivot point; is the gravitational constant D.3 Calculations The distance from the pendulum pivot point to the centre of percussion is d = I/MR (D.1) where d and R are expressed in meters, I is expressed in kilogram meters squared, and M is expressed in kilograms © ISO 2014 – All rights reserved 65 ISO 7176-8:2014(E) This distance can be expressed in terms of the two main components of the pendulum as d = (Ir + Ib)/(MrRr + MbRb) (D.2) where the rod can be treated as a slender rod Ir = (1/3)MrLr2 (D.3) and a block such as in Figure 3 can be treated as a rectangular block, ignoring the chamfers Ib = (1/12)Mb(w2 + h2) + MbRb2 (D.4) where Rr = Lr/2 (D.5) Rb= Lr + h/2 (D.6) and the masses can be calculated from volume and density or measured by weighing The period of oscillation of the pendulum is T = 2π(d/g)0,5 (D.7) where T is expressed in seconds and g is expressed in meters per second squared For a pendulum of length d = 1,000 m, the period is 2,006 s Thus, d can be verified with an uncertainty of approximately 5 mm by measuring the time for 200 periods rounded to the nearest s 66 © ISO 2014 – All rights reserved ISO 7176-8:2014(E) Bibliography [1] Gordon C.C., Churchill T., Clauser C.E., Bradtmiller B., McConville J.T., Tebbetts I (1989) 1988 Antropometric survey of US Army personnel: Summary statistics Interim Report Technical Report NATICK/TR-89-028 (Natick, MA: US Army Natick Research, Development & Engineering Centre) [2] ISO 7176-4, Wheelchairs — Part 4: Energy consumption of electric wheelchairs and scooters for determination of theoretical distance range [4] ISO 2439, Flexible cellular polymeric materials — Determination of hardness (indentation technique) [3] ISO 845, Cellular plastics and rubbers — Determination of apparent density © ISO 2014 – All rights reserved 67 ISO 7176-8:2014(E) ICS 11.180.10 Price based on 67 pages © ISO 2014 – All rights reserved