THE DIFFERENCE BETWEEN COEFFICIENT-OF-FRICTION AND DRAG FACTOR

Transcription

1 THE DIERECE BETWEE COEICIET-O-RICTIO AD DRAG ACTOR Mark George, Am SAE-A Director, Accident Investigation Services Pty Ltd, Sydney, Australia. May 2005 The terms coeicient-o-riction (µ) and drag actor () are expressions oten used in crash investigation and are commonly associated ith various vehicle speed calculations based upon tyre mark geometry. Accordingly, the deinitions and application o the respective terms are accepted doctrine by the various international educational institutions associated ith crash investigation. Because the terms are closely related, their deinitions and application are oten conused by investigators and can result in misinterpretation, errors and conusion associated ith vehicle speed calculations. This paper briely discusses the speciic scientiic dierences and applications beteen the to terms. The coeicient-o-riction µ is deined as the ratio o the tangential orce (tan) (parallel to the surace) applied to an object sliding across a surace to the normal orce (perpendicular to the surace) o an object. 1 ormal orce µ (tan) (tan) cosθ (tan) / cosθ MOTIO µ (angle o repose) (tan) cos (tan) Tangential orce cos sin igure 1. Graphical deinition o µ. rom the above illustration, it can be seen that the relationship beteen (tan) and is proportional to that o the horizontal orce and eight. Thus, a simpler illustration is shon in igure 2 or a level surace. 1 RICKE L.B. (1990), The Traic Accident Investigation Manual, Vol 2 Traic Accident Reconstruction, orthestern University Traic Institute, 1 st Edition. Topic 862, Drag actor and Coeicient o riction in Traic Accident Reconstruction. -1-

2 µ MOTIO igure 2. Simpliied deinition o µ. Because opposing orces are equal in magnitude and opposite in direction (eton s 3 rd la o motion), the coeicient-o-riction beteen to suraces can be measured by pulling (or dragging) an object across a surace and resolving the orces. or convenience, igure 3 illustrates an object being pulled (ith orce ) across a level surace. µ MOTIO igure 3. Simple method o measuring µ This basic concept is used in crash investigation to measure the coeicient-o-riction beteen vehicle tyres and road pavements and can be achieved in various ays. The most basic orm o measurement is ith a drag sled, here a eighted portion o a vehicle tyre is dragged across the road pavement in a controlled manner hereupon µ is obtained by resolving the orces. I the surace is level, µ is obtained by dividing the horizontal orce required to drag the sled, by its eight. i.e. i 10 kg and 5 kg, then µ I the surace is not level there ill be tangential orces to consider (i.e. less orce is required to drag an object donhill and greater orce or uphill), hoever, as illustrated in igures 1 and 2, resolving these orces ill produce the same µ value as i the surace as level. This eectively means that µ beteen to suraces does not alter ith changes in gradient. -2-

3 DRAG ACTOR Drag actor () is a non-dimensional (no units) number used to represent the acceleration or deceleration o a vehicle. It is deined as the total orce (tot) required or a vehicle s acceleration (or deceleration) in the direction o acceleration, divided by the vehicle s eight. With reerence to igure 4, the equation or is expressed: (tot) (tot) igure angle o repose (tan) Vector diagram o orces associated ith drag actor and coeicient o riction. cos sin It can be seen rom igure 4 that the equation or is similar to the simpliied equation or µ, and hence the to deinitions are oten conused. Hoever there is a distinct dierence beteen the to. When measuring and µ on a level surace, (tot) and, hich produces identical values or and µ. As applicable to a vehicle speed rom skid analysis, this means that µ only hen a vehicle is skidding ith all heels locked on a level surace. It is common knoledge that it is easier to pull something don hill than uphill, and that dongrades make vehicle stopping distances longer than upgrades. Hence, or a skidding vehicle, ill reduce ith a dongrade and increase or an upgrade, but µ remains constant regardless o the grade. Consequently, investigating and µ or a sloped surace ill produce dierent values. It is important that investigators do not conuse these values and understand the dierences. A comparative investigation is illustrated belo. 30 kg 30 kg igure 5. (tot) (tot) 25 angle o repose (tan) cos sin Coeicient-o-riction Drag actor 25 angle o repose (tan) 27.2 ( tot) 14.5 µ (tan) cos sin -3-

4 It is sometimes necessary to reer to published charts or estimating a range o µ or a given surace, i.e. dry/et concrete, asphalt, gravel, sno, ice etc. I this inormation is to be applied to a sloped roaday, then a range or needs to be investigated. I the case in question involves a speed rom skid analysis, then can be provisionally solved i the grade is knon, but ill only be relevant i the vehicle is skidding ith all heels locked. I not all heels are locked, urther investigations are necessary to solve or the vehicle s resultant drag actor R. RESULTAT DRAG ACTOR - R During harsh braking, a car experiences orard load shit, increasing the load on its ront axle and reducing the load proportionally on its rear axle. I all heels are locked during the skid, as discussed earlier the vehicle s deceleration ill equal µ and i the surace is level, or just i on a sloped surace. I not all heels lock during the skid, particularly on an axle group, it cannot be assumed that the vehicle has decelerated ith a drag actor equal to locked heel conditions. Where a vehicle has unequal axle drag actors, the vehicle s resultant drag actor R is expressed: R x ( 1 z( r ) r ) here: R resultant vehicle drag actor drag actor on ront axle r drag actor on rear axle x horizontal distance o the centre o mass rom the ront axle as a decimal raction o heelbase z height o the centre o mass as a decimal raction o the heelbase. Analysis o unequal axle drag actors on a vehicle thereore requires a more detailed investigation o the subject vehicle s mass and careul consideration o the variables in question. COCLUSIO The coeicient-o-riction µ beteen to suraces does not alter ith changes in gradient. Drag actor changes proportionally to the gradient. As applicable to crash investigation, µ only hen a vehicle is skidding ith all heels locked on a level surace. -4-

5 REERECES 1. RICKE L.B. (1990), The Traic Accident Investigation Manual, Vol 2 Traic Accident Reconstruction, orthestern University Traic Institute, 1 st Edition. 2. Britannica Macropaedia Vol. 23, Edition 15, 1992 Mechanics. ACKOWLEDGEMETS George Bonnett JD, Reconstruction Technology, Rockledge, L USA or peer revie o the article. AUTHOR Mark H. George Am SAE-A Director/Principal Investigator Accident Investigation Services Pty Ltd P.O. Box 695, Kingsood SW Australia Tel: accidentinvestigation.com.au [email protected] -5-