OAKES, Chief Judge:
This appeal is by the losing plaintiffs in an action against the United States for $3.5 million in damages resulting from a grounding of their barge on Diamond Reef in the Hudson River, New York. Judge Charles H. Tenney of the United States District Court for the Southern District of New York held that the cause of the grounding was not due to any misrepresentation or omission in navigational publications, to the scale of the charts involved, or to the misloeation of the buoy marking the reef, but rather was due to the inexperience of the mate who was piloting the tug pushing the barge and his fear of running up on the western shore of the river in the shadow of the bluffs in that area. See McAllister Bros. v. United States, 709 F.Supp. 1237 (S.D.N.Y.1989).
On appeal it is argued that the mate relied — with disastrous consequences — on the buoy, its location, its markings, its propriety, and the presumed competence and good faith of the Coast Guard and the United States Government, and that the plan and actions of the Coast Guard and other governmental agencies charged with preserving the safety of navigation in the Hudson River were ill-conceived and “callously indifferent” to the dangers of navigation. Indeed, we are asked to “conduct a trial de novo and decree liability of the United States to plaintiffs” or, alternatively, to reverse and remand. We decline the invitation and affirm the judgment of Judge Tenney.
Judge Tenney made detailed findings of fact, familiarity with which as reported at 709 F.Supp. at 1238-45 will be assumed. For our purposes we need only recount that the Barge McAllister # 80 was being pushed by the tug Marjorie McAllister, which was secured snugly into a notch of the barge, making both vessels an integrated tug and barge unit 445 feet long. The barge was loaded with approximately 8,100 barrels of gasoline and drew twenty feet forward and aft; the tug drew twelve feet forward and fourteen feet aft. The mate of the tug in charge of the navigation of the flotilla at all material times was Anthony J. McAllister, III, who had received a license as third mate in 1981 and joined the Marjorie McAllister as mate in July 1982. Prior to the grounding on January 9, 1983, he had participated as mate in only one trip up the Hudson River to Albany. On that trip, he had not been on watch when the flotilla passed the Diamond Reef area, so that this was the first time he himself was navigating a tug-barge flotilla in the area of Diamond Reef.1
The mate had relieved the captain at 1750 hours when the flotilla was in the vicinity of the Tappan Zee bridge. The weather was clear. A seven-inch screen Decca radar with eight scale options at varying distances was operational and in use. After examining the charts for about twenty to thirty minutes, but without plotting courses or computing distances, the mate proceeded at nine knots through the water with a one-knot flood current,2 making good a speed over the ground of ten knots toward Diamond Reef. The Hudson River in the relevant area is about 620 yards wide. On Chart 12347 the Diamond Reef area is shown in the lowest left-hand panel about one mile north of the beginning or lower part of the chart on a scale of 1:40,000. Diamond Reef is a natural obstruction near the center of the river and is charted as being about 100 yards wide with a five-foot sounding inside a three-fathom or eighteen-foot curve. The words “Dia[584]*584mond Reef” are printed on the chart next to the blue tinted area denoting the reef, and the chart shows that between the westerly edge of the reef and the westerly shore of the river there is a channel for a distance of at least 300 yards and another channel approximately 200 yards wide on the easterly side of the reef. A survey of the reef shows that at a twenty-foot curve, it is 250 feet long east to west, with 930 feet in distance from that depth curve to the westerly shore.
The reef, like two others in a six-mile stretch of the river, is, or at the time of the grounding was, marked with a single floating aid to navigation, a buoy to its south. This buoy was attached to a concrete sinker with a chain, the length of which permitted the buoy’s ground tackle to withstand the pressures of the current, the wind, and wintertime ice. The Coast Guard Light List informed the mariner that during winter months the Diamond Reef buoy was replaced by an unlighted nun buoy. The Diamond Reef buoy was painted with red and black stripes, the uppermost being red, thereby designating the buoy as a bifurcation or obstruction buoy, signifying a danger to navigation or an obstruction in the channel, with the preferred channel to be passed in accordance with the upper stripe. Judge Tenney found that the buoy sinker was positioned approximately 100 feet to the south of and to the center of the shallower part near the twenty-foot depth curve of Diamond Reef, the sinker being five feet square and three feet thick, made of concrete, and weighing approximately 12,500 pounds. He also found that because the current in the river runs north and south, the buoy would move generally in a north-south direction with a minimal east-west movement of a few yards.
The Coast Pilot, a Coast Guard publication, describes Diamond Reef and states that the west side of the river should be favored. Judge Tenney found that all navigators who had been on the river and testified referred to the use of the westerly shore of the river as the guide for the safe passage between the reef and the shore, and that to build an ice-resistant warning structure on Diamond Reef would cost about $600,000.
Traffic statistics for the years 1971-74 that were before the Southern District in the case of Tug Ocean Prince v. United States, 436 F.Supp. 907, 915 (S.D.N.Y.1977), rev’d in part, aff'd in part, 584 F.2d 1151 (2d Cir.1978), cert. denied, 440 U.S. 959, 99 S.Ct. 1499, 59 L.Ed.2d 772 (1979), showed approximately 246,000 upbound and 250,000 downbound transits of the river during that four-year period. In the thirteen years prior to 1983 over 1.2 million vessels and tug/barge flotillas passed the Diamond Reef area during which time the only marking of the reef was with one buoy to the south of the reef as marked on January 9, 1983.
It must be pointed out, however, that before the date of this grounding the Coast Guard had considered marking Diamond Reef differently. On November 16, 1979, the commanding officer of the Coast Guard Marine Safety Office in Albany, New York, sent a communication to the commander of the Third Coast Guard district in which he referred to three recent vessel casualties in the vicinity of Diamond Reef. The communication stated that the incidents revealed “a disturbing pattern of navigation on the part of operators of uninspected towing vessels,” since in two of the three casualties the operators passed the buoy “within fifty feet.” He suggested that the marking of Diamond Reef be reevaluated. Only one of the three casualties, however, involved a northbound vessel leaving the Diamond Reef buoy to starboard — the case of the tugboat Katherine Tilton, which grounded on the reef, having passed the buoy within fifty feet of her starboard side. The second casualty involved a loss of steering, and the other involved a ship forced off course to the east of the buoy by another vessel.
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OAKES, Chief Judge:
This appeal is by the losing plaintiffs in an action against the United States for $3.5 million in damages resulting from a grounding of their barge on Diamond Reef in the Hudson River, New York. Judge Charles H. Tenney of the United States District Court for the Southern District of New York held that the cause of the grounding was not due to any misrepresentation or omission in navigational publications, to the scale of the charts involved, or to the misloeation of the buoy marking the reef, but rather was due to the inexperience of the mate who was piloting the tug pushing the barge and his fear of running up on the western shore of the river in the shadow of the bluffs in that area. See McAllister Bros. v. United States, 709 F.Supp. 1237 (S.D.N.Y.1989).
On appeal it is argued that the mate relied — with disastrous consequences — on the buoy, its location, its markings, its propriety, and the presumed competence and good faith of the Coast Guard and the United States Government, and that the plan and actions of the Coast Guard and other governmental agencies charged with preserving the safety of navigation in the Hudson River were ill-conceived and “callously indifferent” to the dangers of navigation. Indeed, we are asked to “conduct a trial de novo and decree liability of the United States to plaintiffs” or, alternatively, to reverse and remand. We decline the invitation and affirm the judgment of Judge Tenney.
Judge Tenney made detailed findings of fact, familiarity with which as reported at 709 F.Supp. at 1238-45 will be assumed. For our purposes we need only recount that the Barge McAllister # 80 was being pushed by the tug Marjorie McAllister, which was secured snugly into a notch of the barge, making both vessels an integrated tug and barge unit 445 feet long. The barge was loaded with approximately 8,100 barrels of gasoline and drew twenty feet forward and aft; the tug drew twelve feet forward and fourteen feet aft. The mate of the tug in charge of the navigation of the flotilla at all material times was Anthony J. McAllister, III, who had received a license as third mate in 1981 and joined the Marjorie McAllister as mate in July 1982. Prior to the grounding on January 9, 1983, he had participated as mate in only one trip up the Hudson River to Albany. On that trip, he had not been on watch when the flotilla passed the Diamond Reef area, so that this was the first time he himself was navigating a tug-barge flotilla in the area of Diamond Reef.1
The mate had relieved the captain at 1750 hours when the flotilla was in the vicinity of the Tappan Zee bridge. The weather was clear. A seven-inch screen Decca radar with eight scale options at varying distances was operational and in use. After examining the charts for about twenty to thirty minutes, but without plotting courses or computing distances, the mate proceeded at nine knots through the water with a one-knot flood current,2 making good a speed over the ground of ten knots toward Diamond Reef. The Hudson River in the relevant area is about 620 yards wide. On Chart 12347 the Diamond Reef area is shown in the lowest left-hand panel about one mile north of the beginning or lower part of the chart on a scale of 1:40,000. Diamond Reef is a natural obstruction near the center of the river and is charted as being about 100 yards wide with a five-foot sounding inside a three-fathom or eighteen-foot curve. The words “Dia[584]*584mond Reef” are printed on the chart next to the blue tinted area denoting the reef, and the chart shows that between the westerly edge of the reef and the westerly shore of the river there is a channel for a distance of at least 300 yards and another channel approximately 200 yards wide on the easterly side of the reef. A survey of the reef shows that at a twenty-foot curve, it is 250 feet long east to west, with 930 feet in distance from that depth curve to the westerly shore.
The reef, like two others in a six-mile stretch of the river, is, or at the time of the grounding was, marked with a single floating aid to navigation, a buoy to its south. This buoy was attached to a concrete sinker with a chain, the length of which permitted the buoy’s ground tackle to withstand the pressures of the current, the wind, and wintertime ice. The Coast Guard Light List informed the mariner that during winter months the Diamond Reef buoy was replaced by an unlighted nun buoy. The Diamond Reef buoy was painted with red and black stripes, the uppermost being red, thereby designating the buoy as a bifurcation or obstruction buoy, signifying a danger to navigation or an obstruction in the channel, with the preferred channel to be passed in accordance with the upper stripe. Judge Tenney found that the buoy sinker was positioned approximately 100 feet to the south of and to the center of the shallower part near the twenty-foot depth curve of Diamond Reef, the sinker being five feet square and three feet thick, made of concrete, and weighing approximately 12,500 pounds. He also found that because the current in the river runs north and south, the buoy would move generally in a north-south direction with a minimal east-west movement of a few yards.
The Coast Pilot, a Coast Guard publication, describes Diamond Reef and states that the west side of the river should be favored. Judge Tenney found that all navigators who had been on the river and testified referred to the use of the westerly shore of the river as the guide for the safe passage between the reef and the shore, and that to build an ice-resistant warning structure on Diamond Reef would cost about $600,000.
Traffic statistics for the years 1971-74 that were before the Southern District in the case of Tug Ocean Prince v. United States, 436 F.Supp. 907, 915 (S.D.N.Y.1977), rev’d in part, aff'd in part, 584 F.2d 1151 (2d Cir.1978), cert. denied, 440 U.S. 959, 99 S.Ct. 1499, 59 L.Ed.2d 772 (1979), showed approximately 246,000 upbound and 250,000 downbound transits of the river during that four-year period. In the thirteen years prior to 1983 over 1.2 million vessels and tug/barge flotillas passed the Diamond Reef area during which time the only marking of the reef was with one buoy to the south of the reef as marked on January 9, 1983.
It must be pointed out, however, that before the date of this grounding the Coast Guard had considered marking Diamond Reef differently. On November 16, 1979, the commanding officer of the Coast Guard Marine Safety Office in Albany, New York, sent a communication to the commander of the Third Coast Guard district in which he referred to three recent vessel casualties in the vicinity of Diamond Reef. The communication stated that the incidents revealed “a disturbing pattern of navigation on the part of operators of uninspected towing vessels,” since in two of the three casualties the operators passed the buoy “within fifty feet.” He suggested that the marking of Diamond Reef be reevaluated. Only one of the three casualties, however, involved a northbound vessel leaving the Diamond Reef buoy to starboard — the case of the tugboat Katherine Tilton, which grounded on the reef, having passed the buoy within fifty feet of her starboard side. The second casualty involved a loss of steering, and the other involved a ship forced off course to the east of the buoy by another vessel. In December 1979, the commander of the Third Coast Guard district wrote to the commanding officer of the Coast Guard cutter Red Beech to suggest the possibility of establishing another lighted buoy directly to the north of the present buoy on the opposite side of the reef to alert vessels approaching from the north, relocating the present buoy to a [585]*585point at the west end of the reef, changing the color of the present buoy to solid red with a flashing red light, and finally installing an orange-and-white horizontally banded, special purpose buoy at the location of the present buoy. Another suggestion involved stationing a red radar reflective nun buoy on the western extremity of the reef, a black radar reflective can buoy on the eastern extremity, and an unlighted junction buoy at the northern, upstream end. In February 1980, however, the commander of the Third Coast Guard District wrote the Coast Guard Marine Safety Office that he and his staff had reached agreement that “the present system is the most logical one” and that the addition of any other buoys in the area would tend to confuse mariners, confine traffic to one side or the other of the reef, and possibly set a precedent for other areas being similarly marked. From 1975 to 1982 the only reported grounding on Diamond Reef due to navigational error was that previously stated of the tugboat Katherine Tilton.
On January 9, 1983, Mate McAllister observed the Diamond Reef buoy by radar from a distance of one-and-one-half miles and saw it visually from a distance of one-half mile. The radar scope also showed both shorelines of the river from a distance of one-and-a-half miles, so he had ample opportunity to gauge the distance between the buoy and the shore. At the speed he was going through the water, he had six minutes to gauge the distance between the westerly shore and the buoy when he was one mile away. He had ascertained that there was no other traffic in the area. The mate testified that he had intended to pass the obstruction buoy by two or three times the width of the barge, i.e., by 140 to 210 feet. He also testified that the distance between the buoy and the western shore was approximately 400 yards and that he was trying to split the distance and stay 200 yards off the western shore. Unfortunately, he did not do so. He himself determined by radar after the grounding that he was 300 to 400 yards off the westerly shore. At the time of the grounding, he said, the buoy was about 150 feet off the starboard bow.
At the time of the accident, McAllister Brothers, Inc., had little doubt about who was to blame. The manager of seagoing personnel and loss prevention stated in a letter of admonition to the mate dated January 21, 1983, that the striking of the reef was due solely to the mate’s negligence. The mate was suspended from duty until March 1983. Indeed, at the Coast Guard license hearing the mate admitted a certain degree of culpability by saying that he had let down his peers, his fellow employees, and his family. Judge Tenney concluded that the striking of the reef was caused by the inexperience and negligence of the mate.
DISCUSSION
Appellants concede, as they must, that findings of fact made by the court after a bench trial may be disturbed only if they are “clearly erroneous,” i.e., “when ... ‘the reviewing court on the entire evidence is left with a definite and firm conviction that a mistake has been committed.’ ” McAllister v. United States, 348 U.S. 19, 20, 75 S.Ct. 6, 8, 99 L.Ed. 20 (1954) (quoting United States v. United States Gypsum Co., 333 U.S. 364, 395, 68 S.Ct. 525, 542, 92 L.Ed. 746 (1948)).
The rhetoric of the appellants’ brief (“[t]he grounding of the barge was proximately caused by such a concatenation of faults on the part of the Government ... as to inspire shock on the part of anyone who is willing to give fair effect to the evidence”) betrays the weakness of the appellants’ arguments. Here we note a few instances.
Appellants quote at length from the mate’s testimony, underscoring that “the buoy looked like the chart. The charts looked like what I saw on the radar, what I saw on the radar looked like the charts ... therefore everything seemed normal.” He thought he was a couple of hundred feet west of the buoy. Then appellants go on to say that “[t]he lower Court’s finding that the buoy neither engendered reliance nor was causally related to the happening of the casualty appears so stubbornly per[586]*586verse as to imply a parallel contamination of its other factual findings.” This, however, is a gross misinterpretation of the district court’s findings. The court never said that the buoy did not engender reliance. The court did find that the buoy was not causally related to the happening of the casualty, because what caused the casualty was the negligence of the mate.
Appellants also quote the Coast Guard Light List at page xiii to the effect that a mariner is “cautioned that he must not rely completely upon the position or operations of buoys to determine the position of his vessel” but must utilize bearings or angles from fixed aids to navigation and objects on shore when available as well as other sources of navigational information. They further quote the language that “a vessel attempting to pass close aboard risks collision with a yawing buoy or with the obstruction the buoy marks.” Then, ignoring the application of these warnings to this case, they seek to fault the Government for not having any objective standard of what “close aboard” means in its system of buoys.
Appellants refer to the testimony of their expert, Captain Stillwaggon, who told of a Swedish tanker running aground on Diamond Reef in the late 1940s and the Coast Guard making a “serious promise to blow up the reef,” but when the court said, “I will have to have a little better evidence of plans like that,” counsel replied simply, “You will, Your Honor.” We are referred to no such evidence.
Stillwaggon further opined that the scale of the chart was too small to render effective assistance to a navigator and that in view that the chart showed neither the actual dimensions nor the shape of the reef, and that the buoy marked only a general location of the reef, there was a real hazard for northbound traffic. But, as Judge Tenney found, Mate McAllister testified that he was aware of the scale of the charts and that he took account of its limitations. See 709 F.Supp. at 1247. McAllis-ter never testified that he was misled by the chart. See id.
Stillwaggon also hypothesized that if the buoy were placed completely on the west side of Diamond Reef, a vessel would immediately know that anything to the west of that buoy would be safe water, especially if the buoy were red.
As a preliminary matter, we note that Stillwaggon spoke with the voice of experience. He had a Hudson River pilot's license and had made a thousand passages up and down the river. He was eminently qualified to run the river. In stating that one could gauge the distance from shore using a searchlight and that there is enough room in the area between Diamond Reef and the westerly shore for two vessels to pass in the 300-yard space, he admitted that he capitalized on his knowledge of the river as a pilot and that he would in proceeding northbound stay 400 feet off the westerly shore, give or take fifty feet.
Mate McAllister lacked experience. Even a navigational instructor who had a master’s license and spent considerable time practicing and teaching the science and art of navigation testified that he would be reluctant to take a 400- to 450-foot flotilla by himself up the Hudson, as “that would be a pretty tough job.”
Appellants rely on Eklof Marine Corp. v. United States, 762 F.2d 200 (2d Cir. 1985), in which another vessel grounded on Diamond Reef after the grounding in this case had occurred. There, this court, in reviewing the district court’s ruling as a grant of summary judgment, found that although the Coast Guard had no duty to mark Diamond Reef, once it acts to mark an obstruction or maritime danger, a duty arises to do so in a way that does not create a new hazard. See id. at 202. The court took into account the Coast Guard’s awareness of the practice of buoy-hopping and held that it was “under a duty to place the buoy in such a position that mariners who follow normal practice would not be enticed to enter upon a danger that otherwise might have been avoided.” Id. at 203. The court went on to say, however, that whether the buoy was mispositioned or whether more buoys were necessary to mark the obstruction adequately “are ques[587]*587tions of fact for the trial court to decide.” Id. The question of law decided was simply that there was a duty to act with due care.
In this case, Judge Tenney found as a matter of fact that the buoy was not mispositioned and that more buoys were not necessary to mark the obstruction adequately. Having the same 1979 Coast Guard report before him as was referred to and relied on by this court in Eklof, Judge Tenney resolved the questions of fact in the Government’s favor. Although it had opinion evidence from Captain Stillwaggon that would have enabled it to find otherwise, the district court held that under all the circumstances and based on the information which the Coast Guard had, it was reasonable to mark Diamond Reef with a single buoy as indicated on the charts. 709 F.Supp. at 1254-55.
We cannot fault its findings. The buoy had been so positioned since 1947, and during the thirteen years prior to 1983 over 1.2 million vessels and tug/barge flotillas passed through the Diamond Reef area with only four reported groundings. The court was aware of the subsequent grounding of the tanker involved in the Eklof case and that subsequently there were changes made in the markings of the reef, but nevertheless made its findings on the basis of the circumstances and the knowledge of the Coast Guard as of January 9, 1983. Congress has granted the Coast Guard broad discretion in the marking of obstructions to navigation. 14 U.S.C. § 86 (1982).
The final point made by the appellants is that the buoy was to the east side of the reef, either because it had been mislocated or because its chain was so long in relation to the water depth that the current or wind or combination of the two could put it there. Appellants argue that the length of the chain for the buoy in question as of January 9, 1983, was 135 feet, although the depth of the water was about fifty feet, and that, using a Pythagorean theorem, this length would produce a “watch circle” radius3 of 125.39 feet, a range of movement of the buoy that was excessive. Adding the watch circle diameter to the targeted charted position diameter4 of 150 feet, appellants say there is over a 400-foot possible variance for the location of the buoy from its charted position. To confirm that this possibility actually occurred, appellants offer aerial photographs taken on the afternoon of the day following the grounding purporting to show the buoy to the east of disturbed waters (supposedly indicating the position of the shallow reef). The trial court said that the disturbed waters areas outlined on the photographs are no different from other areas in the photographs and are noticeable primarily because of the ink outline placed around them in the exhibits received in evidence.5 Moreover, because the depth of the water was in excess of ten feet over all but a small area, the trial court found that any surface disturbance was not likely due to the effect of the reef. Although appellants’ photographic evidence is somewhat persuasive, we decline to hold the trial court’s findings clearly erroneous.
Finally, as stated by Captain Sherwood Patrick, a licensed Hudson River pilot who had made 125 to 150 trips up and down the river, the buoy would either be going upstream or downstream because of the direction of the moving water and would be only a few yards out of a normal east-west position. The district court found this to be so, and it rings true to us as a matter of logic and common sense, and perhaps as a matter of physics. In short, we will not overturn the trial court’s findings that the buoy was not mispositioned. See 709 F.Supp. at 1250-51.
One would suppose that when a pilot sees a reef marked on the chart, and sees [588]*588an obstruction buoy marking it, it might be prudent to examine the chart to determine precisely how wide the reef is and to stay as clear of it as possible. Instead of relying on the charts or the buoy, however, Mate McAllister testified that he looked at the configuration of the shoreline. With a clear sky, the bluffs along the shore had a tendency
to cast very dark shadows so that most mariners with my experience would have a very difficult time ascertaining the shoreline.
So, therefore, I was relying on the radar to actually show me where the shoreline actually was, and as you can see when you approach Diamond Reef, that shoreline is encroaching on you more and more.
Therefore, visually, you are sensing that you are getting closer and closer to the shoreline, and it’s always been my experience if you get closer to the shoreline you are going to be in some sort of trouble.
709 F.Supp. at 1253 (emphasis omitted). In light of that testimony, the court found that
[wjorried by the poor visibility in the shadow of the bluffs he stayed further to the east than he intended and briefly scraped along the western edge of the reef.... It is clear, however, that he was not led astray by any buoy but that the shadow under the bluffs and his fear of the shoreline drove him farther to the east than he intended. When he looked at the radar after the grounding he found himself three or four hundred yards to the east of the western shoreline.
Id. One is reminded of the older pilot’s advice to the young apprentice Mark Twain:
“You see, this has got to be learned; there isn’t any getting around it. A clear starlit night throws such heavy shadows that if you didn’t know the shape of a shore perfectly you would claw away from every bunch of timber, because you would take the black shadow of it for a solid cape; and you see you would be getting scared to death every fifteen minutes by the watch. You would be fifty yards from shore all the time when you ought to be within fifty feet of it.”
M. Twain, Life On the Mississippi 55.
The district court summed it all up well by attributing the sole cause of the grounding to the inexperience of the pilot and his undue concern about the shadows along the western shoreline of the Hudson River. See 709 F.Supp. at 1255. Perhaps if he had had more experience, he would have had more information about Diamond Reef and the river at that point, including its shoreline, but, it will be recalled, he was not on watch at the time during his previous trip up the river when the vessel had passed Diamond Reef. Again, to quote Mark Twain, Life On the Mississippi 88:
First of all, there is one faculty which a pilot must incessantly cultivate until he has brought it to absolute perfection. Nothing short of perfection will do. That faculty is memory. He cannot stop with merely thinking a thing is so and so; he must know it; for this is eminently one of the “exact” sciences.
(Emphasis in text.)
Judgment affirmed.