Downloaded from SAE International by Sylvia Hall-Ellis, Friday, December 22, 2017
`
`SAE TECHNICALPAPER SERIES950601The Geometry of Automotive RearviewMirrors - Why Blind Zones Existand Strategies to Overcome ThemGeorge Platzer ConsultantReprinted from: Human Factors in Vehicle Design:Lighting, Seating and Advanced Electronics(SP-1088)The Engineering SocietyFor Advancing MobilityLand Sea Air and SpaceINTERNATIONALInternational Congress and ExpositionDetroit, MichiganFebruary 27 - March 2, 1995(cid:226)400 Commonwealth Drive, Warrendale, PA 15096-0001 U.S.A. Tel: (412)776-4841Fax:(412)776-5760
`
`

`

`Downloaded from SAE International by Sylvia Hall-Ellis, Friday, December 22, 2017
`
`The appearance of the ISSN code at the bottom of this page indicates SAE’s consent that copies of the paper may be made for personal or internal use of specific clients. This consent is given on the condition, however, that the copier pay a $5.00 per article copy fee through the Copyright Clearance Center, Inc. Operations Center, 222 Rosewood Drive, Danvers, MA 01923 for copying beyond that permitted by Sections 107 or 108 of the U.S. Copyright Law. This consent does not extend to other kinds of copying such as copying for general distribution, for advertising or promotional purposes, for creating new collective works, or for resale. SAE routinely stocks printed papers for a period of three years following date of publication. Direct your orders to SAE Customer Sales and SatisfactionDepartment. Quantity reprint rates can be obtained from the Customer Sales and Satisfaction Department. To request permission to reprint a technical paper or permission to use copyrighted SAE publications in other works, contact the SAE Publications Group.All SAE papers, standards, and selectedbooks are abstracted and indexed in theGlobal Mobility Database.No part of this publication may by reproduced in any form, in an electronic retrieval system or otherwise, without the prior written permission of the publisher.ISSN 0148-7191Copyright 1995 Society of Automotive Engineers, Inc. Positions and opinions advanced in this paper are those of the author(s) an d notnecessarily those of SAE. The author is solely responsible for the content of the paper. A process is available by which discussions will be printed with the p aper ifit is published in SAE transactions. For permission to publish this paper in full or inpart, contact the SAE Publications Gro up.Persons wishing to submit papers to be considered for presentation or pub licationthrough SAE should send the manuscript or a 300 word abstract of a pro posedmanuscript to: Secretary, Engineering Activity Board, SAE.Printed in USA 90-1203D/PGGLOBAL MOBILITY DATABASE
`
`

`

`Downloaded from SAE International by Sylvia Hall-Ellis, Friday, December 22, 2017
`
` The Geometry of Automotive Rearview Mirrors - WhyBlind Zones Exist and Strategies to Overcome ThemGeorge PlatzerConsultantABSTRACT Equations are derived which describe and relate themagnification, viewing angle and reflected illuminance ofconvex mirrors as used in automotive applications. Thederived equations are compared to those for plane mirrors.Using these equations, the viewing angles of automotiverearview mirrors are calculated and depicted. The blind zonesare defined in terms of the viewing angles, obstructions tovision, perceptibility limitations, and the lateral separation ofvehicles. Various strategies for overcoming the blind zonesare discussed.INTRODUCTION The blind zones produced by automotive rearviewmirrors have long been of concern. A variety of ways ofcoping with them are in use, and new ways are beingproposed. Blind zones are an important factor in accidentscaused by lane changing maneuvers. The NationalHighway Traffic Safety Administration (NHTSA) CrashAvoidance Research Program has targeted LaneChange/Merge (LCM) crashes as one of five categories ofcrashes potentially suitable for high technology IntelligentVehicle Highway System (IVHS) crash avoidancecountermeasures (Knipling, 1993). Wang and Knipling (1994)estimate that LCM crashes account for 4.0% of passenger carcrashes, 225 fatalities and 630,000 crashes annually. About50% of these occur on urban divided highways, and about75% occur during daylight hours. Involvement by directionof lane change is about equally split between right to left andleft to right changes. An analysis of LCM crashes by Najmet. al., 1994 shows that in 61.2% of crashes, the driver did notsee the other vehicle. In 29.9% of crashes, the drivermisjudged the position and /or speed of the other vehicle. Mirror blind zones are not responsible for all of the LCMtype crashes. However, they are extremely important in that they are not well understood by the average driver, and yetthey are an integral part of the data acquisition system used by drivers in LCM maneuvers. Understanding the blind zones is important, and key elements in understanding them are theviewing angles of the mirrors and where the views aredirected. Equations will be derived which quantify the viewingangles in terms of the relevant parameters. Much of thederivations are by way of review, but some new relationshipsare shown. Graphical methods can be used to show viewingangles, but analytical methods bring out insights notobtainable graphically. Hence the analytical approach. The derived equations are next used to calculate theviewing angles of the mirrors on a vehicle using theirdimensions and their positions relative to the driver. Then theblind zones are defined and depicted. Several factors inaddition to the viewing angles determine the extent of theblind zones, including obstructions to vision due to thevehicle, the driver’s ability to perceive objects in both themirror and his or her peripheral vision, and the lateralseparation of the vehicles on the roadway. Once the blind zones have been established, variousstrategies which have been developed to overcome the blindzones will be reviewed.GEOMETRY OF REARVIEW MIRRORS On US passenger cars, the inside mirror and left outsidemirror are plane, and the right outside mirror is convex.Europe and Japan allow the use of convex mirrors on thedriver’s side. Since a plane mirror is a special case of aconvex mirror with an infinite radius, the convex mirrorequations will be derived first. The spherical convex mirror presents an image at amagnification less than unity. Most introductory physicsbooks give the equations relating the mirror radius, the objectdistance, the image distance and the magnification. For thespherical convex mirror of Figure 1, it is easily shown that; 1 + 1 = 2 = lp q r f EQ(l)143 .950601
`
`

`

`Downloaded from SAE International by Sylvia Hall-Ellis, Friday, December 22, 2017
`
` , qm = EQ(2)Pwhere, p = distance of the object from the mirrorq = distance of the image from the mirrorr = radius of the mirrorf = focal length of the mirrorm = magnification. Figure 1In Figure 1, distances to the right of the mirror arepositive and distances to the left are negative. The imagedistance and the radius will be negative for the convexmirror. The image of the convex mirror is erect and virtual, i.e., an object in the mirror appears standing right side up,and the image cannot be focused on a screen. Concavemirrors have inverted real images which may be focused on ascreen. Since we want to know what an image in the mirrorlooks like to the driver, lets begin by calculating the imagedistance and height of an object from EQ(1). The imagedistance is; q = rp2 p – rThe image height is; h i = mh o = q hP o EQ(3)where h o is the height of the object. Substituting EQ(3) intoEQ(4), shows that; h i = r h o .2p – r Note that r has negative values for the convex mirror and thath i does not go to infinity when p = r / 2 . The magnificationis: h i rm= =h o 2p– r . EQ(6)The magnification is seen to be a function of the objectdistance. As a numerical example, choose r = - 0.5 ft. and p =5.0 ft. Then m = - 0.5 . How does this compare to a planemirror? For a plane mirror r = ¥ , and m is always -1.Now we know that the convex mirror produces a virtualimage smaller than that of a plane mirror and that the imagesize is a function of the object distance from the mirror. Theeye forms an image on it’s retina of the mirror’s virtualimage. We could calculate the overall magnification from theobject height to the retinal image height if we assumed a“standard” eye with an associated “standard” focal lengthlens and lens to retina distance. However, as drivers or mirrorengineers, we really only want to know how the eye sees theconvex mirror image compared to a plane mirror image, i.e.,how much smaller is the image from a convex mirror thanthe image from a plane mirror. To do this, we only need tocompare the angles subtended from the eye to the mirrorvirtual images. This is because the retinal image height isproportional to the subtended angle. Figure 2 shows the subtended angle, j , for a convexmirror. For simplicity, the eye and the object being viewedare on the axis of the mirror. The eye is shown at a distance sfrom the mirror. The construction lines show the image of theobject and the angle subtended at the eye by the image. Figure 2From Figure 2 it is seen that the subtended angle j is; j = tan -1 h i = ta n -1 rh os – q (s – q)(2p – r)j = tan -1 h o2 sp – (s+p) EQ(7)144and , . EQ(4)EQ(5), r .
`
`

`

`Downloaded from SAE International by Sylvia Hall-Ellis, Friday, December 22, 2017
`
`~
`
`~
`
`~
`
`EQ(7) is the subtended angle for a convex mirror, andletting r go to infinity in EQ(7) gives the subtended anglefor a corresponding plane mirror. The relative magnificationof the convex mirror compared to the plane mirror will bedenoted by m R , and it is: Next, an expression for the viewing angle of a convexmirror will be derived. Figure 4 shows a convex mirror ofradius, r, and width, w, in a horizontal plane to depict thehorizontal viewing angle. An observer is shown at a distances from the mirror. The incoming ray shown defines thewidest angle that can be seen for the mirror width and eyetan -1 h o . position depicted. The total viewing angle of the mirror willm R = 2 sp – (s + p)h o EQ(8)tan -1 (s + p)While precise, EQ(8) is difficult to interpret at a glance. Thiscan be helped by recalling that ; EQ(9)For an automotive mirror, r = - 5 ft, s = 4 ft, and h o is atmost 1/3 of p. In this case, the higher order terms areextremely small and they may be ignored. Then; 1m R = 1– 2spr (s+ p ) EQ( 10) Figure 4be twice the angle that the incoming ray makes with the axisline. This angle is obviously:Finally, we have a simple understandable equation thatcompares what we would see in a convex mirror with what we would see in a like plane mirror. Figure 3 is a graph of m R vs p for r = - 5 ft and s = 4 ft.It is seen that m goes to unity at p = 0 and to .38 atp = ¥ . As a car approaches, it appears to increase in size at afaster rate than would a car in a plane mirror. Noting that,Figure 3 and,then, = 2(2 EQ(l1)a = tan w2 rb = tan -1 w , EQ(l2)EQ(13)w + tan -1 w2r 2 s EQ(14)It is of interest to compare this angle with the viewingangle of a plane mirror of the same width at the sameposition. The ratio of the convex mirror viewing angle to theplane mirror viewing angle will be denoted by q R , and it is;145r –c c c ctan -1 3 53 5 = – + - ...
`
`.R q 2 2 tan -1= .2 s-1 ,q a b+ )
`
`

`

`Downloaded from SAE International by Sylvia Hall-Ellis, Friday, December 22, 2017
`
`.
`
`.
`
`R p = ~
`
`.
`
`2 s–1 r
`
`EQ(16)EQ(17)
`
`l 12 tan -1 = ss ,tllt t lo EQ(21)[ ] [ ]q
`q R = 2 2 tan -1 w + tan -1 w2 tan -1 w= 1+2 tan -1 wtan -1 EQ(15)For automotive mirrors, w, s and r have values such that;In EQ(l0), when the object distance goes to infinity therelative magnification becomes: 1m = ¥ 1m p EQ(18)EQ( 17) is evaluated with negative values for r, since r was defined as being negative in Figure 1. Hence, we can write ;Then; 1 EQ(l9)That is, the viewing angle of a convex mirror is greater thanthe plane mirror viewing angle by a factor equal to thereciprocal of the relative magnification evaluated at p = .Figure 4 shows the eye on the axis of the mirror, and ofcourse, this is not the way the mirror is used. Figure 5 showsthe eye off the mirror axis as it would be for a right sideconvex mirror. The mirror is at an angle l to the line fromthe eye to the center of the mirror. To the eye, the mirrorappears to be reduced in width by a factor of cas . Then Figure 5EQ(14) becomes; + tan wc o s2r 2s . EQ(20)It is easily shown that,where s is the distance along a longitudinal axis of a vehicle from the driver’s eye to a transverse axis through the center of the mirror, ands is the distance along a transverse axis of a vehicle from the driver’s eye to a longitudinal axisthrough the center of the mirror.Figure 5 also shows that l is the angle of incidence to themirror of the ray from the rear which is reflected to the eye. Using values of r = 60 in., s = 50 in., s = 20 in. andw = 6 in., q is calculated by EQ(20) and EQ(21) to be 16.73 o .CADAM shows q to be 16.75 . Hence, EQ(20) is a goodapproximation for automotive mirrors.1462r 2 s2 sq R 2r ,w2 sq R =~ 1 + 2 sr
`m R p = ¥ ¥l = ~ 2 2 tan -1 w -1 l
`
`2 s1 r+q R =~
`
`R = ¥ =~
`
`.
`
`.
`
`

`

`Downloaded from SAE International by Sylvia Hall-Ellis, Friday, December 22, 2017
`
`,
`
`One other characteristic of the convex mirror is ofinterest here, and that is the intensity of light reflected from it. Figure 6 shows a point source of light at a distance pfrom a convex mirror, forming a virtual image of the sourceat distance q behind the mirror. An eye looks at the mirrorfrom a distance s . Distances r, p and q are defined as inEQ(l). Figure 6The point source of light has a luminous intensity of I p . Then [the illuminance at the mirror surface due to I P will be;E 1 = I pp 2 EQ(22)The eye sees a point source of light at a distance q behind ]]the mirror having a luminous intensity of I q . If I q were a realilluminant, the illuminance at the mirror due to I q would be;If the reflectance of the mirror is r , = rE
`and,Then, EQ(23)EQ(24)EQ(25)EQ(26)and substituting EQ(3) into EQ(26), EQ(27)The illuminance seen by the eye is, I qE 3 = (s – q) EQ(28)If the convex mirror were a plane mirror, the illuminance at the eye due to I p would be, E 4 = rI p(s + p) 2 . EQ(29)The ratio of E 3 to E 4 is the relative illuminance from aconvex mirror compared to a plane mirror, and it will bedenoted by E R .Substituting EQ(27) into EQ(30), EQ(30)= , EQ(31)and substituting EQ(3) into EQ(3l), = l – 2r(s + p) EQ(32)E R is a measure of the glare potential of a convex mirror. Ifthe mirror has a 55% chromium coating and r = - 5 ft, s = 4 ft. and p = 100 ft, the mirror has as effective reflectivity of8.5%. Table 1 summarizes the results of EQ(l) throughEQ(32), giving a concise statement of the characteristics ofboth the convex and plane mirror.147.E = I .2 qq 2E 2I qq 2 = I pp 2 .rI q = r I p q 2p 2
`I q = r I p ( )2p – rr 2 . 2 .E R = I qrI p ( )s + ps q– 2
`E R (s + p)( )s q- (2 ) -p r 2E R r[ ( )s – p r2 –p r (2 )–p r(s + p) r 2 ’E R = [ l sp ] = m R2 .
`
`,
`
`,
`
`1
`

`

`Downloaded from SAE International by Sylvia Hall-Ellis, Friday, December 22, 2017
`
`Summary of Mirror Characteristics
`
`Convex Mirror
`
`Plane Mirror
`
`Relative Magnification
`
`11 – 2 sp = Rpr(s+p)
`(monocular, on axis) m
`(monocular, on axis) tan - 1 w + tan - 1 2 r tan - 1
`
`Viewing Angle
`
`Relative Viewing Angle
`
`Reflected Illuminance
`
`Relative Reflected Illuminance
`
`[ ]
`
`Table 1 148 12 2 2 w 2 s w 2 s1 1Rm = ¥r I p2 s pr – (s+p)[ ] 2Rm 2 1r I p(s+p) 2
`
`

`

`Downloaded from SAE International by Sylvia Hall-Ellis, Friday, December 22, 2017
`
`The equations of Table 1 alone are not enough to definethe viewing angles on a car. Most of us see with two eyes.and our eyes are off the axis of the mirror. Figure 7 shows the viewing angles in a horizontal planegenerated by two eyes spaced equidistantly about the axis of when the left eye looks at the right edge of the mirror and theright eye looks at the left edge of the mirror. We would like to know what angle the incoming ray makes with the mirror axis. If we displace a line parallel to the axis and goingthrough the point where the incoming ray hits the mirror, wecan easily calculate the angle which the incoming ray makeswith this displaced axis. This angle is equal to the angle the incoming ray makes with the original axis. Twice this angleis obviously the viewing angle of the mirror. In Figure 8. EQ(33)and the total viewing angle will be, EQ(34)Figure 7the mirror. The left and right eye viewing angles aredesignated by q LT and respectively. The total viewingangle generated by both eyes separately is designated B .SAE Recommended Practice Jl050a calls this total view theambinocular view. The view where and overlap ismarked , and it is designated by J1050a as the binocularview. It will be stereoscopic. The total viewing angle is easily derived from Figure 8(half of Figure 7), noting that the widest angle is obtained Again, for off axis viewing, q A 2 2tan -1 w + tan - 1 wcos 2s . EQ(35)@where l is the angle between a line perpendicular to thecenter of the mirror and a line from the center of the mirror to a point midway between the eyes. A similar analysis for the binocular viewing angle showsthat. EQ(36)Figure 8 149 This is the same as EQ(35) except for the sign of D. Table 2summarizes the viewing angle equations, q qLT q R T A q q [ ]q A 2 2tan -1 w + tan - 1 w 2s ’[ ]b = 2 2tan -1 w = tan - 1 w+D 2s ’l2rq B 2 2tan -1 w + tan - 1 wcos l _2s .@ [ ]2rs+ D D+ D + D D= r2R T
`
`

`

`Downloaded from SAE International by Sylvia Hall-Ellis, Friday, December 22, 2017
`
`Mirror Viewing Angles
`
`Convex Mirror
`
`Plane Mirror
`
`wcosl2 2tan - 1 w +tan - ]2r 2 + D
`
`22
`
`Monocular
`
`Ambinocular
`
`Forward
`Center
`Back
`
`Forward
`Center
`Back
`
`Inside Error Left Outside Error31.9 18.328.9 16.625.7 15.1 Right Outside Error 19.119.018.9Table 4 150 [ s1wcos l2 2 tan - 1 w + tan -2r 2 s1 wcos l2 2 tan - 1 w + tan -2r 2 s1 wcos ltan - 2 s1 + Dwcos ltan - 2 s1 – Dwcos ltan - 2 s1Seat Position
`MirrorS 1 w = 5.75 in., r = 60 in.¥[[ ]]
`Binocular – D 2Table 2Table 3Seat Position
`
`Representative Eye to Mirror Distance - Inches
`
`Inside Left Outside Right Outsidew = 8.0 in., r = ¥S 1 S t S t S l S t48484891317 141414 162024 181818 162024w = 5.75 in., r =
`
`Ambinocular Viewing Angle - Degrees
`
`

`

`Downloaded from SAE International by Sylvia Hall-Ellis, Friday, December 22, 2017
`
`WHY BLIND ZONES EXIST Using the equations of Table 2, the viewing angles ofautomotive rearview mirrors are easily calculated, and withthe angles so determined we can make scale drawings toaccurately show the blind zones. First, we must select valuesof the independent variables in the Table 2 equations whichwill provide the viewing angles of most interest. This wasdone by taking a mid-size passenger car and measuring themirror widths, the radius of curvature of the convex mirror,and the eye to mirror longitudinal and transverse distances.The measurements were made for three conditions; driver’sseat full forward, centered, and full back. This particularvehicle had a manual seat and the measurements were madewith the recliner full forward. Table 3 shows themeasurements taken, with distances rounded to the nearestinch. lane. The outside mirrors are adjusted to just see theside of the car. The shaded regions are blind zones which arebounded by the outer vision limits of the outside mirrors andthe lines where the driver’s peripheral vision begins. Let’s examine the driver’s side blind zone more closely,beginning with the peripheral vision line. Figure 10 shows aTable 4 shows the viewing angles obtained by using themeasurements of Table 3. Note that short drivers have aconsiderably better rearview than tall drivers. The viewingangles of the Table 4 center position will be used to depictthe viewing angles attained by an average height driver.These viewing angles are shown in Figure 9, which is a scaledrawing of a mid-size passenger car in a standard 12 ft. wide Figure 10Figure 9 driver with head turned slightly and eyes directed at theoutside rearview mirror. If driver’s had 180 o of forwardvision, the peripheral vision line would be perpendicular to aline from the driver’s left eye to the mirror. However, asshown by Burg (1968), driver’s do not have 180 o of vision.The horizontal peripheral vision angle measured from theaxis of the eye to the widest angle at which a target isperceived was found by Burg to be a function of age. Burgmeasured this angle with an apparatus which momentarilyintroduced a white illuminated object into the subject’s fieldof view. The object was contrasted against a blackbackground, and it would suddenly appear at discrete angularintervals. Thus conditions for detecting the object wheregood. Burg found that the peripheral vision angle peaked atabout 88 o at age 20 and diminished to about 75 o at age 70.Ball et al (1988) show that the useful field of view,which involves detection and identification of targets, varieswith factors such as the conspicuity of the target, the centraltask being performed, any distracting influences and age.Significant error rates in target identification were observedat relatively low eccentricities from the fixation point of theeye, as low as 30 o .151
`
`

`

`Downloaded from SAE International by Sylvia Hall-Ellis, Friday, December 22, 2017
`
` distance and closing velocity of a following vehicle, thedriver’s foveal vision is fixed on that mirror. Objects outsidethe foveal region may or may not be detected for any of thereasons set out by Ball. Another restriction on the driver’s peripheral vision maybe the vehicle itself. A tall driver with the seat all the wayback, and perhaps partially reclined, may well find that theleft B pillar restricts peripheral vision to the left. On the rightside, the right seat back, right B pillar and a right sidepassenger can all restrict the right peripheral vision. As far as the peripheral vision line is concerned then, itcan vary from a couple of degrees less than perpendicular tothe eye to mirror line, to many degrees less thanperpendicular, depending on conditions. Thus, the peripheralvision line is not at a specific location. Only its maximumextent of about 88 o is known.So, we find that the forward edge of the blind zone isvariable. How about the rear edge? It might appear that therear edge of the blind zone is defined by the outer boundaryof the viewing angle of the outside mirror and how the mirroris positioned. Geometrically, this is true. If a car is forwardof the rear edge of the blind zone, that car will not be seen inthe outside mirror. But, if a vehicle is in the blind zone, doesit have to be totally forward of the rear edge not to beperceived? Depending on factors such as relative speed,color, contrast and scene content, the probability ofperceiving a vehicle only partially within the blind zone canbe expected to vary with the amount of the vehicle which isexposed. Data to quantify this has not been found. One other factor effects the ability to hide a vehicle inthe blind zone, and that is the lateral separation of thevehicles. The farther apart the vehicles are laterally, thelonger the available space is in which a vehicle can behidden. Observing cars traveling on multi-lane dividedhighways, it is observed that vehicles in close proximity tendto separate laterally. Typically, cars separate an additional 2to 4 feet beyond what the separation would be if they werecentered in their lanes. Summarizing, we can define a geometric blind zonedetermined by the outer edge of the outside mirror’s viewingangle and a line from the driver’s eyes which is a couple ofdegrees less than perpendicular to a line from the eyes to theoutside mirror. The actual blind zone is larger than thegeometric blind zone because of environmental and humanfactors and cannot be precisely defined. This is true for boththe left and right outside mirrors. Now let’s apply what we know about the blind zones toactual driving conditions. Figure 11 is a scale drawingshowing three mid-sized cars on standard 12 ft. wide lanes.The two outer cars are hidden in the center car’s blind zones.The hidden vehicles are displaced three feet laterally. Theleft mirror peripheral vision line is shown at 85 o to the eye tomirror line, corresponding to a 50 year old driver in Burg’sdata. The mirror viewing angles are as shown in Figure 9. Noother environmental or human factors have been included toreduce the peripheral vision line below 85 o . The reality ofcourse, is that it can be far less than the 85 o shown, whichwould result in a larger blind zone. From Figure 11 three facts are apparent. 1. The blind zones can be large enough to easilyconceal a vehicle. 2. The outside mirrors add little additional visibilitybeyond that provided by the inside mirror. The addition isonly a strip about four feet wide. 3. The inside mirror provides by far the best viewand the most information. It allows the driver to accuratelyjudge the distance and speed of vehicles approaching fromthe rear. Figure 11If the inside mirror is so superior, why have outsidemirrors? Well, outside mirrors can be useful, especially if theview from the inside mirror is blocked by cargo or by a carimmediately to the rear in stopped traffic. The left outsidemirror is large enough and close enough to be of value,except it can’t be large enough or close enough to eliminatethe blind zone without causing other problems. Given that theleft mirror is worth putting on a passenger car, despite theblind zone, then we seem to require a right mirror to makethe car symmetrical. But putting the same size plane mirroron the right side would produce a nearly useless viewingangle. In fact, the viewing angle for a right side plane mirror152When the left rearview mirror is used to observe the
`
`

`

`Downloaded from SAE International by Sylvia Hall-Ellis, Friday, December 22, 2017
`
`6 inches wide would be only about 5.5 o . So instead of a planemirror, a convex mirror with about a 20 o viewing angle isused. The only problem is that the driver can’t accuratelyjudge either the distance or approach speed of vehicles seenin it, and it still has a blind zone. However, the stylists arecontent because the car is symmetrical, and the mirror peopleappear satisfied because they have more than a 5.5 o viewingangle. STRATEGIES TO OVERCOME THE BLIND ZONES Given then that we have inside and outside mirrors, howdo we overcome the blind zones produced by them? Themost common procedure on passenger cars is to set theoutside mirrors to just see the side of the car. When changinglanes, the driver first looks in the outside mirror to determinethe position and approach speed of vehicles to the rear andthen turns to look for vehicles in the blind zone. There areproblems that exist with this procedure. First, the driver mustremember to turn and look before changing lanes. Failing todo so can prove disastrous. Second, turning to look into theblind zone results in a loss of forward vision for times in theorder of a second. At highway speeds this translates intoabout 100 feet of travel with the driver’s eyes off the road.Third, turning one’s head can get tiresome. Fourth, somedrivers, especially older ones, have difficulty turning theirheads. One alternative to turning to look into the blind zoneswould be to increase the horizontal viewing angles of theoutside mirrors to about 35 o . At such an angle, it isimpossible to hide a car in the remaining blind zone. On theright side, a plane mirror with a 35 o viewing angle would be36 inches wide, so that’s out. A right side convex mirror 6.5inches wide would require a radius of curvature of 28 inches,and that is less than the 35 inch minimum required byFMVSS 111. So, we can’t get 35 o with a reasonably sizedright side mirror. On the left side, a plane mirror with a 35 o viewing anglewould be 16 inches wide, also unacceptable. A left sideconvex mirror 6.5 inches wide would require a radius ofcurvature of 44 inches, but any convex mirror on the driver’sside is prohibited by FMVSS 111. Volvo has developed an interesting solution to the blindzone problem which was first sold in Sweden in 1979(Pilhall,1981). They use a mirror 6.7 inches wide with aradius of curvature of 82.7 inches on the inner 2/3’s of themirror and then a decreasing radius in the outer l/3, goingdown to about a 10 inch radius. The magnification of theinner 2/3’s is about 0.7 and the viewing angle is about 20°.The remaining l/3 captures any vehicle in the blind zone. Another approach car owners can use to address theblind zone problem is to add stick on high curvature mirrorsto their existing mirrors, since owners are not restricted byFMVSS 111. Stick ons have the disadvantages of reducingthe viewing angle of a plane mirror by effectively reducingits width, and of marring the styling of the mirrors. However,a large number of people are sufficiently dissatisfied withtheir mirrors to resort to stick ons. Olson and Winkler (1985) found in a study of 620 vehicles that 6.6% had stick onmirrors on the driver’s side mirror. A simple and logical strategy to overcome the blindzones is suggested by further contemplation of Figure 11. Aspreviously stated, the inside mirror provides by far the bestview to the rear. Again, as seen in Figure 11, the outsidemirrors actually provide very little additional viewingcapability. This being the case, the blind zones can beeffectively eliminated simply by rotating the outside mirrorsto look into the Figure 11 blind zones as shown in Figure 12.The visible area now increases dramatically, and theremaining blind zones are incapable of hiding a car. Figure 12Driving with the mirrors positioned as in Figure 12 callsfor a different lane change strategy. With this setting, thedriver first looks in the inside mirror to check the positionand approach speed of vehicles to the rear.
`
`Then, the driverglances at the outside mirror to see if a car is in what used tobe the blind zone.153
`
`

`

`Downloaded from SAE International by Sylvia Hall-Ellis, Friday, December 22, 2017
`
`There are many advantages to the Figure 12 setting.1. It is no longer necessary to turn to look into theformer blind zones since they are now visible in the outsidemirrors. 2. The forward driving scene is always within thedriver’s peripheral vision when glancing at the outsidemirrors, as opposed to the loss of this forward vision whenturning to look into the blind zones. 3. Less time is required for a glance to the outsidemirror as compared to turning to look into the blind zone. 4. Older or physically restricted drivers no longer havethe difficulty of turning to look into the blind zones. 5. It is now possible to include the former blind zones ina scan of the driving scene by a quick glance to the outsidemirrors. Good drivers continually scan. By being able toinclude the former blind zones in their scanning, drivers willbe less likely to forget the blind zones when contemplating alane change. 6. Glare from the left outside mirror is effectivelyeliminated. This is because the only headlamps that can beseen it that mirror will be from a single vehicle close by inthe left lane. In that position, the intense portion of theheadlamp’s beam is displaced far enough sideways of themirror so that it does not produce blinding glare. Only thelower intensity peripheral portion of the beam is seen. Acknowledging that Figure 12 presents the most logicalway to set the mirrors, how then can a driver properlyachieve this setting. The viewing areas should be positionedto balance the shaded areas in Figure 12. This requiresmoving the mirror outward from the Figure 11 position byabout 7 o to 8 o , which in turn moves the viewing area outwardby double that amount. One way to do this with the leftmirror is to put the side of your head against the window, andthen adjust the mirror so that you just see the side of yourcar. To make sure that this setting is correct, observe avehicle passing in the left lane while seated in the normaldriving position. Make sure that the passing car appears inthe outside mirror before it leaves the inside mirror, and thatit appears in your peripheral vision before leaving the outsidemirror. This assures you that the blind zone has beeneliminated. The same procedure can be used with the rightside mirror, except, place your head at the center line of thecar and then set the right mirror to just see the car’s rightside. This procedure is cumbersome, and furthermore it isannoying to shift your head back and forth every time youwant to see if the setting is corre