DUNIWAY, J.
This is another of the many cases that have come before the appellate courts in which an unsuccessful plaintiff, injured in a collision of moving vehicles at an intersection, claims error in refusing to instruct the jury upon the doctrine of last clear chance. Counsel asserts “that the evidence in this case virtually cries out for the application of the last clear chance doctrine.” Our examination of the record,
in the light of the controlling authorities, persuades us that the evidence makes no such cry; the cry is merely that of counsel.
The doctrine was elaborately reviewed by the Supreme Court in
Brandelius
v.
City & County of San Francisco,
47 Cal.2d 729 [306 P.2d 432], which has become the leading case upon the subject. Its restatement of the applicable formula appears at page 743 of the opinion and we do not repeat it here. We note, however, that the opinion reiterates and emphasizes certain considerations that control this case. "[T]he time element is the all important factor.” (P. 738.) "[B]ut defendant is not liable under the doctrine unless after the time that he is chargeable with the required knowledge of the injured person’s inability to escape, he ‘has the last clear chance to avoid the accident by exercising ordinary care. ’ ” (P. 741.) This is but another way of saying that the defendant must have not only a
last
chance, but a
clear
chance to avoid the accident.
(Rodabaugh
v.
Tekus,
39 Cal.2d 290, 296, 297 [246 P.2d 663] ;
Doran
v.
City & County of San Francisco,
44 Cal.2d 477, 487 [283 P.2d 1].)
These rules are the basis for the oft-repeated statements of our courts that ordinarily the doctrine cannot be applied to an intersection ease involving a collision between two moving vehicles, and that the doctrine “never meant a splitting of seconds when emergencies arise”
(Bagwill
v.
Pacific Electric Ry. Co.,
90 Cal.App. 114, 121 [265 P. 517], quoted in our recent decision in
Kowalski
v.
Shell Chemical Corp.,
177 Cal.App.2d 528, 529, 537 [2 Cal.Rptr. 319]). The earlier eases are collected and discussed at length in
Johnson
v.
Sacramento Northern Ry.,
54 Cal.App.2d 528 [129 P.2d 503]. Other late eases restating and applying one or both of these principles are:
Hildebrand
v.
Los Angeles Junction Ry. Co.,
53 Cal.2d 826 [3 Cal.Rptr. 313, 350 P.2d 65] ;
Hall
v.
Atchison, T. & S. F. Ry. Co.,
152 Cal.App.2d 80 [312 P.2d 739] ;
Clarida
v.
Aguirre,
156 Cal.App.2d 112 [319 P.2d 20]
; Nemer
v.
Atchison, T. & S. F. Ry. Co.,
156 Cal.App.2d 445 [319 P.2d 770];
Barcelone
v.
Melani,
156 Cal.App.2d 631 [320 P.2d 203];
Holman v. Viko,
161 Cal.App.2d 87 [326 P.2d 551];
Hickambottom
v.
Cooper Transp. Co.,
163 Cal.App.2d 489 [329 P.2d 609];
Miller
v.
Atchison, T. & S. F. Ry. Co.,
166 Cal.App.2d 160 [332 P.2d 746].
We recognize that the doctrine is a “humanitarian” one
(Brandelius
v.
City & County of San Francisco, supra,
47 Cal.2d 729, 739), in that it relieves the plaintiff from the otherwise
adverse consequences of his own negligence. There is always a tendency to stretch such a doctrine so as to bring within it cases that would once have been excluded from its operation. But we think that to apply it here would stretch it to the breaking point and, as we said in Kowalski,
supra,
“would mean that there could be no intersection collisions to which the doctrine would not apply, and would completely do away with the defense of contributory negligence in such cases” (177 Cal.App.2d at p. 533).
Viewed most favorably to the contention that the doctrine is applicable
(Warren
v.
Ubungen,
177 Cal.App.2d 605, 608 [2 Cal.Rptr. 411]), the evidence discloses the following: As frequently happens, appellant suffered a retrograde amnesia at the time of trial, and had no memory of the events of the day of the accident, in exchange for which disability he is given the benefit of the presumption that he acted with due care. The result is that the only testimony of eyewitnesses comes from employees of the defendant.
The accident occurred on Madison Street, in Oakland, at its intersection with certain tracks of respondent Southern Pacific Company (“S.P.”). Appellant was driving a Ford truck north on Madison, which runs north and south. The time was 4:30 in the afternoon, and there is no claim that visibility was poor. As he approached the intersection, appellant had on his right an open field, across which he could see the S.P. tracks for a considerable distance. Also on his right, and about 150 feet before the first track crosses Madison, there is a round, highway type railroad crossing sign. The first two tracks ahead of appellant were Santa Fe tracks, not in use at the time. They occupy about 18 feet, and the northernmost rail of these tracks is about 40 feet south of the first S.P. rail. The first S.P. rail was thus about 208 feet north of the crossing sign. Also on the right, and about 20 feet south of the first S.P. rail is the usual white “crossbuck” type of railroad crossing sign.
The first S.P. track ahead of appellant was a “drill track,” 5 feet in width, used for temporary storage of box cars. On appellant's right, one box car was on this track. It was about 42 feet long, and its westerly end was about 10 feet east of the east line of Madison. On his left, a string of four similar cars was on the drill track, with the easterly end about 15 feet west of the west line of Madison. Appellant’s view to the left was fully obstructed by buildings and then partially obstructed by a storage yard until he reached a point about 95
feet south of the drill track, at which point he had a clear view of the S.P. tracks to his left, except as it was obstructed by the four box ears. The second S.P. track, 8% feet further north and 5 feet wide, was the main eastbound track of S.P. The next, 10% feet north of it, was the main westbound track. Still farther north was another drill track, not here involved.
As appellant proceeded, there was approaching from his right, on the' westbound track, a single diesel engine of the S.P. (referred to as “the engine”). It was 55 feet long and weighed 250,000 pounds. Its headlights were on, but its bell was not ringing and it did not sound its whistle. Its cab was at least 10 feet back from its front end, so that the engineer, who was on the right, could not see appellant, but the fireman, who was on the left, could and did. The throttle, the principal braking controls, and the whistle control were next to the engineer. At the same time, there was approaching from appellant’s left on the eastbound track a 66-car freight train (referred to as “the train”). It was sounding its bell and its headlights were on, but it did not whistle as it approached Madison Street.
Just as the cab of appellant’s truck became visible to the fireman of the engine, when the truck appeared from behind the end of the single freight ear on the drill track to appellant’s right, the fireman saw that appellant was looking toward his left, in the direction of the train, and not toward the engine. The front of the truck was then less than 30 feet from a point at which it would, in its forward progress, intersect the path of the oncoming engine. The fireman yelled “hold it” (which means to apply the emergency brake) and the engineer did so. The left front pilotboard of the engine struck the right front of the truck, near the motor, and knocked it back onto the eastbound track, where it was struck by the train and thrown still farther south, against the crossbuck. Fortunately, appellant was thrown out of the truck by the first collision and clear of the train, so that he was not personally involved in the second collision.
Appellant does not assert that all of the elements of the last clear chance doctrine were present before his truck appeared from behind the box car and the fireman saw that he was still proceeding and looking the other way. It was at that point, for the first time, that defendant “knew that plaintiff was in a position of danger and further knew, or in the exercise of ordinary care should have known, that plaintiff was unable to escape therefrom.”
(Brandelius
v.
City & County of San
Francisco, supra,
47 Cal.2d 729, 743.) Until then, the engine crew had a right to assume that appellant would stop and let both the train and the engine go by.
(Nemer
v.
Atchison, T. & S. F. Ry. Co.,
156 Cal.App.2d 445, 451, 452 [319 P.2d 770], and cases there cited;
Powell
v.
Pacific Electric Railway Co.,
35 Cal.2d 40, 46-47 [216 P.2d 448].)
Appellant asserts that after that time, the engine crew still had a last clear chance to avoid the accident, either by stopping the engine, or by slowing it and sounding a warning which would have alerted appellant so that he would have speeded up and passed ahead of the engine. It is apparent that if, instead of speeding up, appellant had tried to stop, he would almost certainly have been struck by the train. We think that it is sheer speculation that he would have done the former rather than the latter. The record contains no evidence from which a jury could infer that appellant could have stopped short of the eastbound track, which was only between 8 and 11 feet or so from the nose of his truck, not allowing for the “overhang” of the train beyond the rails. There is no evidence as to the length or weight of the truck or the condition of the truck’s brakes, as to the distance in which it could have been stopped at any given time, or as to appellant’s possible reaction time.
Basically, appellant’s contentions rest upon mathematical calculations which in turn rest upon certain assumptions that are contrary to some of the direct evidence in the case. Appellant says that these assumptions can be made because the direct testimony was given by S.P. employees, two of whom were defendants, and all of whom were called under Code of Civil Procedure, section 2055, and appellant is not bound by their testimony.
(Brandelius
v.
City & Comity of San Francisco, supra,
47 Cal.2d 729, 745.)
According to the testimony, appellant was going at a constant speed of about 20 miles per hour (the engine fireman, who watched the truck for some distance before it disappeared behind the box car), or 25 miles per hour (the train engineer), or 20 miles per hour (the train fireman). The speed of the engine was placed by its engineer at 15 miles per hour. The fireman agrees. According to the engineer, the engine was about 25 feet from the crossing when the fireman yelled. The fireman, at the trial, said the engine was 25 to 35 feet east of the intersection; in his deposition, he said 45 to 50 feet. The time elapsed between the time that the fireman saw appellant emerge from behind the box car and the impact was variously
estimated at “only a few seconds” (by the engineer of the engine), ‘1 about three seconds” (by its fireman),1 ‘ only a split second” (by the train fireman).
Simple mathematics demonstrates that, if the truck was doing 20 miles per hour, it would cover the distance to the point of impact (less than 30 feet) in less than one second.
(Johnson
v.
Sacramento Northern Ry.,
54 Cal.App.2d 528, 541 [129 P.2d 503].) If its speed was 25 miles per hour, the time would .be even less. Certainly this did not afford anyone a
last clear
chance to avoid the accident. The only evidence as to the stopping time and distance for the engine was that of a qualified expert who said that if the engine were doing 15 miles per hour, it could be stopped in 112 feet, on a dry track. It would go 44 feet before there would be any material reduction in speed, and the rate of reduction in speed thereafter would increase as the distance traveled increased. It would take longer to stop a 66-ear freight going at the same speed. In this testimony, no allowance is made for reaction time.
To escape from this dilemma, appellant resorts to assumptions and speculations. The argument runs as follows: The train fireman testified that when he first saw appellant’s truck, it was 1 ‘ alongside the Howard Supply Company storage yard,” which, says appellant, would be 250 feet from the point of impact. According to scale diagrams in evidence, the distance could be not over 225 feet and could be as little as 120 feet. Yet appellant says 250 feet. The train fireman also said that at the time that he first saw the engine approaching, he was between Alice and Jackson Streets, closer to Jackson. (Jackson is the first street parallel to Madison to the west; Alice is the next.) At that time, the engine was “down around the housing project.” (The housing project lies to the east of Oak Street, which is the first parallel street east of Madison, and a witness who lived there said that she lived approximately 100 feet east of Fallon Street, which is the second street to the east.) Thus, says appellant, the engine was “at least” 900 feet east of the point of impact at the approximate time the truck was 250 feet away from it. “It follows therefore,” says appellant, “that the truck’s speed, which was at a constant rate, was less than one-third that of the diesel,
i.e.,
approximately five miles per hour.” Since the truck had less than 30 feet to go when appellant’s position of danger first became apparent to the engine fireman, this would mean that there would be something less than four seconds of time in which the engine crew could exercise
their last clear chance. At 5 miles per hour, the truck would travel about 7.5 feet per second.
Appellant, by assuming that the engine was traveling more than three times as fast as the truck, places it 105 feet from the point of impact (three and one-half times appellant’s assumed distance of 30 feet) when the fireman first became aware of appellant’s position of danger. By a further set of assumptions, the engine’s distance from the point of impact at that time is stretched by appellant, in his reply brief, to 200 feet. This is based upon claimed testimony of the two engineers that each train was traveling at the same speed, and that they were at one point equidistant from the crossing. Of course, on this assumption, and accepting the further assumption that appellant was only going 5 miles per hour, the engine, in order to reach the point of impact when it did, would have to be traveling at least 50 feet per second, or over 33 miles per hour, if we also assume that its brakes were never applied and it continued at a constant speed. There is no evidence whatever as to the stopping time or distance for such an engine at such a speed. This will not do. Appellant’s conclusions are based upon estimates which are quite insufficient to support his calculations.
In the first place, the farther away we assume the engine to have been when appellant, sitting in the
cab
of the truck, an unknown number of feet behind its nose, became visible from behind the box car to the engine fireman, the closer the truck would have to be to the point of impact. There is nothing in the record from which one can calculate the difference in distance that would be involved.
In the second place, there is no evidence on which to base appellant’s assertion that the truck was 30 feet from the point of impact; what evidence there is, including the scale diagrams, and it is not precise, would indicate 25 feet or less.
In the third place, it is a pure guess to say that appellant was 250 feet from the point of impact when first seen by the train fireman. The frontage of the storage yard on Madison is about 105 feet, and the testimony is that appellant was “alongside” the yard. This could mean anywhere within that distance, and could reduce appellant’s claimed 250 feet to about 120 feet. The southern corner of the yard, on Madison, adjoins a building, which would cut off the train fireman’s view, and is not over 225 feet, not 250 feet, south of the south rail of the westbound track.
In the fourth place, the testimony is that when the train fireman first saw the engine it was “down around” the housing project. No evidence shows any such exact distance as 900 feet, or any exact distance, from the housing project to Madison Street. The testimony, by a witness looking down the track, from a moving train, at the moving engine, from a distance of 1,500 or more feet, does not support and does not purport to state any such exact assumption as to the location of the engine.
In the fifth place, the record does not support the assertion that the train fireman saw both the truck and the engine, at the assumed distances from the point of impact, at the same time, or even at “approximately” the same time. That is just not pinned down in the record.
In the sixth place, there is no evidence whatever in the record as to the time it would take the fireman to react and yell to the engineer, or the engineer to react and apply the brakes or sound a warning, or the appellant to react and either stop or step on the gas, or the truck to stop or to pick up speed enough to get across in front of the engine. Yet these are all elements material to a decision as to whether the fireman and engineer had the “vital” time within which to prevent or avoid the accident.
(Cf. Buck
v.
Hill,
121 Cal.App.2d 352 [263 P.2d 643] ;
Rodabaugh
v.
Tekus, supra,
39 Cal.2d 290, 295;
Jobe
v.
Harold Livestock Com. Co.,
113 Cal.App.2d 269, 272-273 247 P.2d 951];
Hickambottom
v.
Cooper Transp. Co., supra,
163 Cal.App.2d 489, 494;
Hall
v.
Atchison, T. & S. F. Ry. Co.,
152 Cal.App.2d 80, 84 [312 P.2d 739].) Nor is there evidence as to the dimensions of the truck, or its weight, or the condition of its brakes. The meager evidence of this type in the record does indicate that the nose of the truck would have to have been substantially less than 30 feet, perhaps as little as 23 feet, from the point of impact, when appellant himself first became visible to the engine fireman. And it was not until then that the second element of the doctrine, as laid down in
Brandelius,
would be met.
The case is one peculiarly appropriate for application of the principle that “ [m]ere doubt as to the credibility of defendant or the accuracy of his estimate of distance would not amount to affirmative evidence of any material fact.”
(Jobe
v.
Harold Livestock Com. Co., supra,
113 Cal.App.2d 269, 275, quoted in
Kowalski
v.
Shell Chemical Corp., supra,
177 Cal.App.2d 528, 535 [2 Cal.Rptr. 319].) Mathematical calculations, when based upon reasonably precise data, are
most helpful to a court or a jury, but when they are based upon the vague type of assumptions that appellant is compelled to make here, they are dangerously deceptive. To hold that in this case a jury could find that the defendants had a “last clear chance” to avoid the accident would be to read into those simple words a meaning that they do not have and were never intended to have.
Because the facts in a given accident case are always unique, we do not discuss the cases upon which appellant chiefly relies
(Sills
v.
Los Angeles Transit Lines,
40 Cal.2d 630 [255 P.2d 795] ;
Buck
v.
Hill, supra,
121 Cal.App.2d 352), except to state that in our opinion they are not controlling here. They apply, to different factual situations, the same principles that we are applying.
Appellant complains that the court’s instructions unnecessarily and repetitiously overemphasized the element of his contributory negligence. There was some repetition, but the court, at the outset, carefully instructed the jury to disregard any repetition that there might be. The principal instance was one in which the court obviously inadvertently reread certain instructions. It immediately realized what it had done and again cautioned the jury. The evidence that appellant was contributorily negligent is overwhelming, and his contention that the doctrine of last clear chance applies is based upon an assumption that he was.
(Hickambottom
v.
Cooper Transp. Co., supra,
163 Cal.App.2d 489, 495.) We cannot conceive that any prejudice resulted.
(Chambers
v.
Southern Pac. Co.,
148 Cal.App.2d 873, 878 [307 P.2d 662].)
Finally, it is urged that the court erred in instructing the jury that defendant S.P. would not be negligent in failing to have a flagman at the crossing, or to install an automatic signaling device or crossing gate, these not being required, “as a matter of law,” by the Public Utilities Commission, unless the jury found that the crossing was “particularly dangerous and hazardous” or “more than ordinarily hazardous.” A careful reading of the instruction persuades us that it correctly states the law, and that it does not say, or convey the impression, as appellant contends, that the safety requirements of the Public Utilities Commission are maximum rather than minimum standards of care for S.P.
(Cf. Martindale
v.
Atchison, T. & S. F. Ry. Co.,
89 Cal.App.2d 400, 417-418 [201 P.2d 48];
Green
v.
Southern Pac. Co.,
53 Cal.App. 194, 202 [199 P. 1059] ;
Ross
v.
Atchison, T. & S. F. Ry. Co.,
141 Cal.App.2d 178 [296 P.2d 372] ;
Peri
v.
Los Angeles Junction Ry.,
22 Cal.2d 111, 123 [137 P.2d 441] ;
Hinkle
v.
Southern Pacific Co.,
12 Cal.2d 691, 701 [87 P.2d 349]; and see 42 Cal.Jur.2d Railroads, § 109, p. 100; 74 C.J.S., Railroads, § 725, p. 1339;
Grand Trunk Railway Co.
v.
Ives,
144 U.S. 408 [12 S.Ct. 679, 36 L.Ed. 485], note, 5 A.L.R.2d 112, 123;
Flagg
v.
Chicago Great Western Ry. Co.,
143 F.2d 90.)
Moreover, we again cannot see how prejudice could have resulted if the instruction were erroneous. Appellant was thoroughly familiar with the crossing. He had worked for over five years at the place from which he was coming at the time of the accident and had driven across the tracks twice daily, and he knew that there was no flagman, gate or signaling device. It is hard to believe that the jury could find that the lack of any of these, if such lack indicated negligence of the S.P., was the proximate cause of the accident, as distinguished from appellant’s own negligence in proceeding across the tracks when he had a clear view of both tracks, with plenty of time to stop, for some distance before he got there. Although appellant has the benefit of the presumption of due care, which raises a conflict in the evidence, to be resolved by the jury, the evidence very nearly compels the conclusion that he was contributorily negligent, in that he was trying to get across ahead of the train, at which he was looking, and forgot about the engine, which, by reason of the open field on his right, was visible to him for some distance before he could see the train.
Affirmed.
Bray, P. J., and Tobriner, J., concurred.