angle between them. Hour and minute hands online. Angle between them Tasks that occur on the exam

The time calculator is designed to perform various time calculations and has several functions:

indication of the user's current time,
calculation of the time interval between two given points,
conversion of time from one unit to another (seconds, minutes, hours, days, HH:MM:SS).

Time calculator will help you determine the remaining time to a given moment. For example, by setting the end time of the working day, you can find out exactly how much you still have to work today. Or, for example, how much time is left for sleep. To do this, just enter the time for which you set your alarm and the current time.

But, in addition to the comic ways of using the time calculator, it can also be used really for business. Officials responsible for calculating the time worked by employees of the organization, to determine the processing, can also resort to a time calculator. To do this, it is enough to enter the time of arrival and exit of the employee from work according to the electronic pass system, and the calculator itself will calculate the number of hours worked.

In addition, the time calculator can be useful for determining the recording time on the video media. If several recordings are made on the video media, then by setting the start and end times of the recording, you can determine its duration.

In addition to the indicated ways of using the time interval calculation function, many more examples can be given, but we can say with confidence that everyone can find it to be used both for personal, maybe entertainment purposes, and for serious work issues.

Time calculator

Hours: Minutes: Seconds

Time #1	:	:
Time #2	:	:

Difference:

The function of the time calculator for converting from one unit of time to another makes it easy to convert days to hours, minutes and even seconds, to hours-minutes-seconds, and vice versa.

For example, you are going to the cinema to watch some of the latest news, and when you go to a site with a description of films, you find out that the duration of the film is 164 minutes, which, you see, is not very clear. But, with the help of the time calculator, you can easily determine that the duration of the film is 2 hours and 44 minutes, which is already much more understandable for planning your time.

Let us turn again to school tasks and tasks for intelligence. One of these tasks is to find out what angle the minute and hour hands form between themselves on a mechanical watch at 16 hours 38 minutes, or one of the variations - how much time will be after the beginning of the first day when the hour and minute hands will form an angle of 70 degrees.

The simplest question that many people manage to give the wrong answer. What is the angle between the hour and minute hands on a clock at 15:15?

The answer zero degrees is not the correct answer :)

Let's figure it out.

The minute hand makes a complete revolution on the dial in 60 minutes, that is, it makes a 360-degree revolution. During the same time (60 minutes), the hour hand will travel only one twelfth of the circle, that is, it will move 360/12 = 30 degrees

As for the minute, everything is very simple. We make a proportion minutes are related to the angle traveled as a complete revolution (60 minutes) to 360 degrees.

Thus, the angle passed by the minute hand will be minutes / 60 * 360 = minutes * 6

As a result, the output Each minute that passes moves the minute hand 6 degrees.

Excellent! Now what about the clock. And the principle is the same, only the time (hours and minutes) must be reduced to fractions of an hour.

For example, 2 hours 30 minutes is 2.5 hours (2 hours and its half), 8 hours and 15 minutes is 8.25 (8 hours and one quarter of an hour), 11 hours 45 minutes is 11 hours and three quarters of an hour, that is, 8.75)

Thus, the angle passed by the hour hand will be hours (in fractions of an hour) * 360.12 \u003d hours * 30

And as a consequence, the conclusion Every hour that passes moves the hour hand 30 degrees.

angle between hands = (hour+(minutes/60))*30 -minutes*6

where hour+(minutes /60) is the position of the hour hand

Thus, the answer to the problem: what angle will the arrows make when the clock is 15 hours 15 minutes, will be as follows:

15 hours 15 minutes is equivalent to the position of the hands at 3 hours and 15 minutes and thus the angle will be (3+15/60)*30-15*6=7.5 degrees

Determine the time by the angle between the hands

This task is more difficult, since we will solve it in a general way, that is, determine all pairs (hour and minute) when they will form a given angle.

So, let's recall. If time is expressed as HH:MM (hour:minute) then the angle between the hands is expressed by the formula

Now, if we denote the angle by the letter U and translate everything into an alternative form, we get the following formula

Or, getting rid of the denominator, we get the basic formula relating the angle between two hands, and the positions of these hands on the dial.

Note that the angle can be negative as well. o there, within an hour, we can meet the same angle twice, for example, an angle of 7.5 degrees can be at 15:15 and 15:00 and 17.72727272 minutes

If we, as in the first problem, were given an angle, then we get an equation with two variables. In principle, it is not solved, unless we accept the condition that the hour and minute can only be integers.

Under this condition, we obtain the classical Diophantine equation. The solution of which is very simple. We will not consider them yet, but we will immediately give the final formulas

where k is an arbitrary integer.

Naturally, we take the result of hours modulo 24, and the result of minutes modulo 60

Let's count all the options when the hour and minute hands coincide? That is, when the angle between them is 0 degrees.

At least we know two such points 0 hours and 0 minutes and 12 noon 0 minutes. And the rest??

Let's create a table, the positions of the arrows when the angle between them is zero degrees

Oops! on the third line, we have an error at 10 o'clock, the hands do not match in any way. This can be seen by looking at the dial. What's the matter?? It seems like everyone got it right.

And the thing is that in the interval between 10 and 11 o'clock, in order for the minute and hour hands to coincide, the minute hand must be somewhere in the fractional part of a minute.

This is easy to check by the formula by substituting the number zero instead of the angle, and the number 10 instead of hours

we get that the minute hand will be between (!!) divisions 54 and 55 (quite exactly at the position of 54.545454 minutes).

That's why our last formulas didn't work, since we assumed that the hours and minutes of the number are integers (!).

Tasks that meet on the exam

We will consider problems that have solutions on the Internet, but we will go the other way. Perhaps this will make it easier for that part of schoolchildren who are looking for a simple and easy way to solve problems.

After all, the more different options for solving problems, the better.

So, we know only one formula and we will use only it.

The clock with hands shows 1 hour 35 minutes. In how many minutes will the minute hand align with the hour hand for the tenth time?

The arguments of the "solvers" on other Internet resources made me a little tired and confused. For those "tired" like me, we solve this problem differently.

Let's determine when in the first (1) hour the minute and hour hands coincide (angle 0 degrees)? We substitute the known numbers into the equation and get

that is, at 1 hour and almost 5.5 minutes. is it earlier than 1 hour 35 minutes? Yes! Great, so we do not take this hour into account in further calculations.

We need to find the 10th coincidence of the minute and hour hands, we begin to analyze:

for the first time, the hour hand will be at 2 o'clock and how many minutes,

the second time at 3 o'clock and how many minutes

for the eighth time at 9 o'clock and how many minutes

for the ninth time at 10 o'clock and how many minutes

for the ninth time at 11 o'clock and how many minutes

Now it remains to find where the minute hand will be located at 11 o'clock, so that the hands would coincide

And now multiplies 10 times the turnover (and this is every hour) by 60 (turning into minutes) we get 600 minutes. and calculate the difference between 60 minutes and 35 minutes (which were given)

The final answer was 625 minutes.

Q.E.D. There is no need for any equations, proportions, nor which of the arrows with what speed moved. All this is tinsel. It is enough to know one formula.

A more interesting and difficult task sounds like this. At 8 pm, the angle between the hour and minute hands is 31 degrees. How long will the hands show the time after the minute and hour hands form a right angle 5 times?

So in our formula, again, two of the three parameters 8 and 31 degrees are known. We determine the minute hand according to the formula, we get 38 minutes.

When is the nearest time when the arrows will form a right (90 degree) angle?

That is, at 8 o'clock 27.27272727 minutes it is the first right angle in this hour and at 8 o'clock and 60 minutes it is the second angle in this hour.

The first right angle has already passed relative to the given time, so we do not consider it.

The first 90 degrees at 8 hours 60 minutes (you can say that exactly at 9-00) - times

at 9 o'clock and how many minutes is two

at 10 o'clock and how many minutes is three

again at 10 and how many minutes is 4, so there are two coincidences at 10 o'clock

and at 11 o'clock and how many minutes is five.

Even easier if we use a bot. Enter 90 degrees and get the following table

Time on the dial when there is a given angle

Hour	Minute
0	16.363636363636363
0	16.363636363636363
1	10.909090909090908
1	21.818181818181816
2	5.454545454545454
2	27.272727272727273
3	0
3	32.72727272727273
4	5.454545454545454
4	38.18181818181818
5	10.909090909090908
5	43.63636363636363
6	16.363636363636363
6	49.09090909090909
7	21.818181818181816
7	54.54545454545455
8	27.272727272727273
9	0
9	32.72727272727273
10	5.454545454545453
10	38.18181818181818
11	10.909090909090906
11	43.63636363636363
12	16.36363636363636

that is, at 11:10:90 there will be just the fifth time when a right angle forms again between the hour and minute hands.

We hope this analysis will help you both formulate tasks for students and easily solve similar intelligence tests in the exam.

Good luck with your calculations!

Hour. 3 hours 15 minutes

"The East was on fire."

Infantry soldier,

Bug River… City of Brest

Gerd Habedank, a war correspondent, was advancing along with elements of the 45th Infantry Division. The goal is the fortress of the city of Brest.

“Under the scorching sun, along the roads of Eastern Poland, dusty and clogged with vehicles and troops, we moved to the Bug, bypassing forest clearings along the way, clinging to tree branches with our body, past artillery batteries and mobile command posts hidden under the crowns of pines.

Silently, without making a sound, we crawled to the very bank of the Bug. All access roads to the river were strewn with a thick layer of sand - on it the steps of our forged boots were deaf. Assault groups were already concentrating along the roadsides. Against the background of the dawn-colored sky, the outlines of inflatable rubber boats loomed.

Having reached the dugout, which housed the headquarters of the battalion, Khabedank glanced at the opposite bank of the Bug and at the Russians, who were some hundred meters away in a similar shelter. I wonder what they are thinking now. “Voices were clearly audible from the other side,” he recalled, “and somewhere in the fortress itself a loudspeaker sounded.”

Rudolf Gshöpf, division chaplain, celebrated mass at 20:00. After that, he met with an officer of the medical service, and meanwhile, doctors of a lower rank were digging communications between the dressing station of the 3rd battalion of the 135th regiment. Soon everyone gathered in a small building and exchanged a few words - the tension was becoming unbearable. At 2 o'clock in the morning, they watched in surprise as a freight train proceeded across the bridge. "Surely with the goods provided for by the economic part of the German-Soviet treaty of 1939." A steam locomotive wrapped in puffs of steam dragged wagons to Germany. This completely peaceful picture did not fit in with the preparations that reigned around for the upcoming assault on the citadel on the other side.

“On the opposite side inside the citadel, everyone seemed to be sleeping peacefully. Two steps below, the waves of the Bug lapped peacefully, and the darkness of the night enveloped the buildings, which were about to turn into ruins.

The 2nd tank group of General Guderian was tasked with crossing the Bug on both sides of the Brest Fortress. Since the demarcation line between the Soviet Union and the part of Poland occupied by the Wehrmacht passed through the river, the Germans occupied the western forts of the fortress, and the Red Army occupied the eastern forts.

Even before the invasion of Russia, Guderian knew that "the high command, despite the experience of the Western campaign, did not have a unified view on the use of tank formations." The generals, who had nothing to do with the tank forces, were of the opinion that the first blow should be delivered by infantry divisions, having previously carried out strong artillery preparation, and the tanks should be brought into battle only after the penetration had reached a certain depth and there was a possibility of a breakthrough. On the contrary, the tank generals attached great importance to the use of tanks from the very beginning in the first echelon, because it was in this type of troops that they saw the striking force of the offensive. They believed that tanks could quickly penetrate deep and then immediately build on the initial success using their speed. The generals themselves saw the results of the use of tanks in the second echelon in France. At the moment of success, the roads were blocked by endless, slow-moving horse-drawn columns of infantry divisions, which impeded the movement of tanks. The tank generals resolved the issue as follows: in the breakthrough areas, use tanks in the first echelon, ahead of the infantry, and where other tasks were solved, for example, the capture of the [Brest] fortress, use infantry divisions. The fortifications of the Brest Fortress could probably be considered obsolete, however, “the fortress of Brest-Litovsk (now the city of Brest, Belarus. - Note. transl.) with its old fortifications, separated from us by the Western Bug and Mukhavets rivers, as well as numerous ditches filled with water, only infantry could take possession. Therefore, the 12th Infantry Corps was transferred under the command of Guderian, one of whose divisions, the 45th, was to storm Brest. Guderian concluded that:

"Tanks could take it only with a sudden blow, which we tried to do in 1939. But in 1941 there were no conditions for this."

Brest Fortress was built in 1842. It was located on four islands of partly natural, partly artificial origin, located at the confluence of the Bug and Mukhavets. There were three others around the Central Island: Western (Border), Southern (Hospital) and Northern (Kobrin). The central, most fortified, part of the citadel was surrounded by a two-story brick building, 500 casemates and underground bunkers served as storehouses for supplies and shelters for personnel, and also provided powerful defense. Underground bunkers were connected by underground communication passages. Numerous buildings and structures were located outside the outer walls, including the officers' house, 74 and the church. The thick outer walls were impenetrable to artillery shells of any caliber. The Western, Northern and Southern islands formed a belt of external defense with ramparts 10 meters high. The ramparts and bastions of the three bridgeheads - forts - covered the citadel, preventing the enemy from direct fire. Each such fort was an independent fortress in miniature.

However, this heavy-duty fortification had one weak point. It was built to provide all-round defense. But after the end of the Polish campaign, the fortress was divided by a demarcation line. The most important center of defense, the western one, went to the Germans. In addition, only three gates provided access to the six-kilometer ring of defensive structures, which allowed the citadel to be used according to its original defensive concept. This increased the time for bringing the personnel to combat readiness and for them to occupy positions for defense. Major General Sandalov, chief of staff of the 4th Army, estimated this time at 3 hours - it was at this time that the defenders of the fortress would suffer significant losses in the event of a sudden attack on it. Only 2 km of defensive walls went to the west, that is, to the main direction from which a threat could arise. And they could accommodate only one infantry battalion and half a battalion of border guards. Judging by some information, on the night of June 21-22, 1941, 7 battalions of the 6th and 42nd rifle divisions of the Red Army, as well as several training units and several artillery regiments, were in Brest.

On the opposite bank of the Bug, 9 Wehrmacht infantry battalions prepared for the attack, and 18 more concentrated on the flanks. The 12th Army Corps of the 4th Army was given the task of encircling the fortress and ensuring the passage of the advanced formations of the 2nd Tank Group - the 24th and 47th Tank Corps. The 45th Infantry Division was to attack the city directly. The 31st and 34th divisions were to bypass the city and secure the inner flanks of the advancing tank corps.

The 45th Infantry Division included 3 regiments (130th, 133rd and 135th) of 3 battalions each. They were tasked with capturing the Brest Fortress, a four-track railway bridge across the Bug, and five other bridges across Mukhavets south of the city. This opened up the possibility of creating a "corridor" for the tanks of the 2nd tank group, heading further to Kobrin.

The division's offensive plan provided for a strike in two directions - north of the citadel and south. On the left flank, the Germans intended, having landed on the Western Island, to strike at the citadel, taking advantage of the surprise factor, seizing it and reaching the eastern outskirts of Brest. To carry out this task, two battalions of the 135th Infantry Regiment were allocated, supported by two training tank platoons. On the right flank, the 130th Infantry Regiment was to cross the Mukhavets and occupy the South Island. The task of capturing the bridges across the Mukhavets was assigned to nine specially trained groups of sappers. One battalion remained in the division commander's reserve, while 3 battalions of the 133rd Infantry Regiment formed the corps' reserve. Nine light and three heavy batteries of divisional artillery, supported by long-range large-caliber guns and three divisions of mortars, were to carry out a five-minute artillery preparation, and then fire at predetermined targets. It was assumed that the other two divisions of the 12th Corps, the 34th and 31st, would also take part in the assault on the city. A special unit, the 4th Regiment of Chemical Protection, a secret unit until June 22, 1941, supported the operation with an attack by a new type of weapon - multi-barreled rocket launchers. “There will be no living place left,” the artillerymen assured the personnel of the shock groups.

Wehrmacht soldiers unshakably believed in victory. Lieutenant Michael Wechtler of the reserve regiment had no doubt that the operation would be "easy", despite the fact that on the first day the regiment had to reach a line 5 km east of Brest. If you look at the citadel from afar, it "looked more like an ordinary barracks, but not a fortress at all." This optimism found expression in the fact that only 2 out of 9 battalions were allocated for the first strike of 76. Three battalions were in the second echelon, and another 4 remained in reserve.

The 45th Infantry Division had experience of participating in the French campaign, where the loss of the dead amounted to 462 soldiers and officers. As in most infantry divisions concentrated near the border with the USSR, the personnel of the division were full of energy and in a combat mood. Being in quarters in Warsaw before the start of the Russian campaign, the soldiers had the opportunity to inspect the defeated Polish capital. Many, going around the city center in cabs, were photographed as a keepsake. Combat training was successful. Basically, the skills of forcing water barriers with high, steep banks and methods of attacking fortifications were worked out. In general, an idyll and nothing more. During the hot hours off duty, the soldiers walked around in shorts. Those who had to cross the Bug in boats often held "sea battles" and playful regattas. And they preferred not to think about what exactly they were trained for.

Sending to the 180-kilometer march from Warsaw took place to the music of the military band of the 133rd regiment. Suddenly a downpour poured down, and everyone was soaked to the skin, but the hot summer sun peeking out right there from behind the clouds lifted the fallen mood. The march was not an easy one, but it was prudently divided into 40-kilometer stages, places for halts were chosen near water bodies, so that the dust of the roads of Eastern Poland could be washed off. The march ended 27 kilometers from the border with Russia. We stopped for a stay in a Polish village, in cozy and clean houses. There they drank the last bottles of trophy French champagne and, finally, wrote home. Searchlight units were divided into platoons of those who wished to shave their heads bald before the campaign. Searchlight crews were photographed for the last time at a carefully camouflaged halt. Everyone was well aware that it was unlikely that there would be an opportunity to gather again in the same composition. And at dawn on June 22, parts of the division began to advance to their starting lines.

Dawn June 22, 1941. The headquarters of the 2nd Panzer Group of General Guderian a few minutes before the start of the invasion

Shortly before 3 o'clock in the morning, chaplain Rudolf Gschöpf left the small building, where he was waiting for the attack to begin. “As the hour “H” approached,” he recalled, “the minutes dragged on unbearably, it seemed that the hours had passed.” Dawn broke. It was quiet, except for the usual night sounds. Glancing at the ribbon of the river below, he remarked:

“At the Bug, there was not a single sign of the presence of assault groups. Disguised as it should be. It is not difficult to imagine the nervous tension in which there were those who, a few minutes later, were to face an unknown enemy!

Gerd Khabedanka, who was in the car, was brought out of his thoughts by the metallic chime of the alarm clock. “A great day is coming,” he wrote in his diary. Silvery light flickered in the east as he made his way to the dugout on the banks of the Bug, where the battalion's command post was located. It was full of people there.

« The hustle and bustle, everyone in helmets, with weapons, this constant ringing of field phones. But then the calm voice of the Hauptmann sounded, and everyone calmed down in an instant. "Gentlemen, it's already 3 hours and 14 minutes, exactly one minute remains."

Khabedank looked again through the viewing slot of the bunker. Everything was still. Gerd's ears again heard the phrase of the battalion commander, which he said yesterday: "It will be like nothing else."

"Air attack ... with the first rays of the sun"

The pilot of the Xe-111 bomber, which was gaining altitude, pulled the steering wheel even more strongly. He glanced at the altimeter - the fluttering needle, frozen for a moment, moved clockwise again. 4500 meters ... 5000 meters ... The crew was ordered to put on oxygen masks. Exactly at 3 o'clock in the morning, the plane, strainingly buzzing, passed the Soviet border at maximum height. Below was a deserted area - entirely forests and swampy lowlands.

The 53rd bomber squadron took to the air while it was still dark from one of the airfields near Warsaw. Having reached almost the height ceiling, the planes headed for enemy airfields concentrated on the territory of Belarus, between Bialystok and Minsk. Do-217Z from the 2nd bomber squadron invaded the airspace of the USSR to the north, between Grodno and Vilnius. The 3rd bomber squadron, taking off from under Deblin, continued to climb between Brest and Kobrin. Pilots carefully studied the ground under the wing in search of landmarks. The crews of the machines were completed by experienced pilots who had flown more than a dozen hours. These 20-30 vehicles formed the advanced group of forces that participated in the first air strike. The crews were faced with the task of secretly bypassing the Soviet border and attacking the Soviet Air Force bases on the central sector of the future front. Three bombers were allocated to attack each Soviet airfield.

And here they are, buzzing motors, headed for the intended targets. Below, in a shroud of morning mist, lay the territory of the enemy. Rare lights indicated that it was still inhabited. Ahead, at the eastern edge of the horizon, a barely noticeable bright stripe appeared. Cloudiness was practically non-existent. There were no more than 15 minutes left until the hour "H".

The rear airfields, located on the territory of Poland occupied by the Wehrmacht, became like disturbed beehives. The loading of bombs was in full swing, the pre-flight briefing continued. Engines sneezed, frightened birds soared from the branches of the trees that surrounded the heavily camouflaged airstrips and makeshift hangars.

Lieutenant Heinz Knoke, a Me-109 fighter pilot from a squadron stationed at the Suwalki airfield near the Russian border, watched the silhouettes of Ju-87 dive bombers and Messerschmitts from his unit begin to emerge in the predawn twilight. Rumors about an upcoming attack on Russia have been circulating for a long time. "I'm all for," he wrote in his diary, "Bolshevism is enemy No. 1 for European culture and Western civilization." The previous evening, an order was received to shoot down a passenger plane making regular flights on the Berlin-Moscow line. This caused a stir. The immediate superior of Heinz Knoke, as part of the headquarters squadron, tried to carry out this order, but could not find the Douglas.

Knoke on the last evening, sitting in the company of colleagues, discussed with them the expected development of events. “The order to shoot down the passenger Douglas of the Russians,” he wrote, “convinced me that a serious war was planned against Bolshevism.” Everyone was waiting impatiently for the alarm.

“No one thought to sleep,” recalled Arnold Döring, navigator of the 53rd bomber squadron of the Condor Legion, “unless you fall asleep before the first attack.” The crews got up at half past one in the night to conduct a briefing and set a combat mission. The Belsk-Pilichi airfield was to be attacked. According to available data, significant forces of Russian aviation were stationed at this airfield. Running, "as if insane", heading for the aircraft, the pilots "saw dawn in the east - a sign of the coming day." And although the Doering unit did not participate in the first strike, having risen into the air, the pilots, not without difficulty, lined up in battle formation - the lack of experience in night flights affected. “I had such a confusion in my head,” Döring recalled. - How to take off in the dark, and even on a car loaded to the eyeballs with bombs? We didn’t have time to study this airfield properly over the past few days! ”

The Luftwaffe pilots were not the first to experience such operations, however, as always before the attack, many were nervous.

Hans Vowinkel, a 35-year-old bomber pilot, wrote to his wife:

“I have not yet described everything that I felt then, but I would like to. There just isn't time to paint everything. And you will soon understand why. So much will remain unsaid. But I have no doubt that you will understand everything correctly!

It was assumed that as a result of this massive air raid on Soviet airfields, the Luftwaffe would gain air supremacy, which would allow it to provide effective support to ground forces. The operation itself was developed in Gatow near Berlin at the Luftwaffe Academy, starting on February 20, 1941. The command of all Luftwaffe forces involved in the implementation of the Barbarossa plan was entrusted to Field Marshal Albert Kesselring, commander of the 2nd Air Fleet. Hitler, convinced of the "inferiority" of the Russians, as it soon became clear, was "amazed" by the information about the power of the Red Air Force contained in the first combat reports. Luftwaffe intelligence reported 10,500 combat aircraft, 7,500 of which were deployed in the European part of the USSR, and 3,000 in its Asian part. Of these, only 50% were considered modern. This number did not include transport aircraft, the number of which, according to various sources, was 5700 units. It was assumed that about 1360 bombers and 1490 fighters could take part in the fighting. During the second half of 1941, the Red Army Air Force was to receive 700 new vehicles. According to the plans of the Soviet military leadership, it was supposed to replace 50% of the bomber fleet, but a general increase in numbers was not envisaged. The Soviet Air Force had 15,000 trained pilots, 150,000 ground personnel and 10,000 training aircraft.

As for the Luftwaffe, on June 21, 1941, it had 757 combat-ready bombers out of a total of 952 vehicles, 362 out of 564 dive bombers, 64 Me-110 type fighters (twin-engine) and 735 out of 965 conventional fighters, in addition, it had some reconnaissance, transport and seaplanes. Despite the Soviet numerical superiority - three or even fourfold - the Luftwaffe was distinguished by a high level of combat training and combat experience. Due to the length of operational areas and skepticism about the level of combat, technical and operational training of the Russians, it was believed that the Soviet Air Force would not be able to provide effective support to their ground forces. Luftwaffe General Konrad provided Halder, Chief of Staff of the OKW, with a selective report on the capabilities of the Soviet Air Force. According to this document, Soviet fighters were clearly inferior to German ones. Soviet bombers also received a low rating from Konrad. The level of combat training, command and tactical training of personnel were also rated extremely low.

It was this obviously subjective point of view that prevailed in planning and assessing the forces of the Soviets as a potential enemy. On June 22, 1941, according to the Luftwaffe, the Soviet Air Force had only 1,300 combat-ready bombers and 1,500 fighters in the European part of the USSR (out of a total of 5,800 vehicles). Moreover, according to radio intercept data, the number of aircraft concentrated in the western part of Russia has grown to 13,000-15,000 units. General Jeschonnek, Chief of Staff of the Luftwaffe, had previously reported to Halder that "the Luftwaffe expects massive air raids on our forward units, but believes that they will be repulsed thanks to our superior technology and combat experience." Everything was based on an unshakable belief in the effectiveness of a surprise strike, for which the Soviet Air Force was clearly not ready and, as a result, extremely vulnerable, and therefore doomed to be destroyed on the ground. "The ground structures of the Russians ... are clumsy and difficult to restore," Eshonnek argued.

Kesselring's mission was very clear:

“The orders I received from the Commander-in-Chief of the Luftwaffe were mainly to achieve superiority and, if possible, air supremacy and to support the ground forces, especially tank groups, in their combat operations against the Russians. Setting any other tasks in addition to those mentioned would lead to a very unproductive dispersion of forces, so they should have been postponed until later.

Contrary to the original plan, the details of which were agreed with the Luftwaffe command, the time "H", that is, the start time of the operation, was shifted by 3 hours and 15 minutes on June 22. This decision was not easy and caused fierce disputes between representatives of the general staffs of both the ground forces and the Luftwaffe.

“The start of the operation was scheduled for the pre-dawn time. This was done despite objections from the Luftwaffe, based on the very specific tactical consideration that single-engine fighters and dive bombers would not be able to maintain a clear formation at the indicated time. This moment represented a serious difficulty for us, but we managed to overcome it.”

To achieve maximum surprise, the ground troops needed just the dark time of the day, but already with the first rays of the sun, they might need air support like air. Field Marshal von Bock, commander of Army Group Center, said: “The enemy will immediately catch on when they hear the roar of engines of aircraft crossing the border. And the element of surprise will be lost.” In the end, the command made a compromise decision to strike the first blow with specially trained crews. This, it was believed, would be quite enough until the main aviation forces took to the air.

On the night of June 22, 60% of the combat power of the Luftwaffe was concentrated along the borders with the USSR: 1400 out of 1945 units of operational aviation, 1280 of which were considered combat-ready. The mentioned forces were distributed over four air fleets. The 1st Air Fleet carried out support for the North Army Group, half of the 2nd Air Fleet struck together with the Center Army Group, the 4th Air Fleet operated on the operational sector of the South Army Group, and the 5th Air Fleet was supposed to operate in the north from Norwegian airfields. It is believed that the Luftwaffe concentrated 650 fighters, 831 bombers, 324 dive bombers, 140 reconnaissance and 200 transport aircraft to participate in Operation Barbarossa. The air forces of Romania (230 aircraft), Hungary, Slovakia operated in the southern strategic direction, 299 Finnish aircraft were to take part in the hostilities a little later.

However, these forces did not go to any comparison with the forces of the Russians. The Germans underestimated the strength of the Soviet Air Force by at least half. In general, only 30% of all aircraft available to the Russians were deployed on the European part. There were twice as many fighters as the Germans expected, and two-thirds more bombers. And yet the command and personnel of the Luftwaffe were convinced of their victory, they had skill plus the element of surprise on their side.

Arnold Döring took to the air as part of the 53rd bomber squadron. The pilots, despite all the difficulties, managed to line up the cars in battle order. They headed for the Siedlce airfield, where escort fighters were to join them. “Only our defenders weren’t visible,” said Döring, upset. The pilots eagerly peered into the sky, and in the end they had no choice but to change course and continue the task without cover. “Slightly off course, we headed towards our targets,” Döring recalls.

On June 21, Berlin was suffocatingly hot. Joseph Goebbels, Reich Minister of Propaganda, overwhelmed with premonitions of a great day, could not concentrate on the daily routine. And yet he did not speak.

“The situation in Russia is becoming more dramatic every hour,” he wrote in his diary. “We are simply ignoring the protests of Russians about violations of Soviet airspace.” Molotov sought permission to leave for Berlin, but he was bombarded with false promises. “It is naive to believe otherwise,” says Goebbels. He should have thought about this six months ago. There is no unity in the ranks of our opponents.”

At noon, the Minister of Propaganda received the Italian delegation. The meeting took place at his house in Schwanenwerder. The attention of the guests was offered a recently released American film - "Gone with the Wind". He made an impression on those present. However, despite the congestion, by his own admission, Goebbels could not get rid of the excitement that plagued him. His closest subordinates in the Ministry of Propaganda also knew about the upcoming operation, and he decided to invite them to his place so that "in case of emergency, they were at hand."

Late in the evening there was a telephone call from the Imperial Chancellery. The Fuhrer urgently wished to meet with his chief propagandist. Judging by the brightly lit windows of the army headquarters, there were feverish preparations for an invasion of Russia. The code word "Dortmund", brought to the attention of those in charge, meant that the time "H" would come at 3 hours 30 minutes. In case of unforeseen delays, another code word was provided - "Altona". But no one seriously believed that they would have to use it.

Hitler informed Goebbels of the final preparations. The Soviet ambassador in Berlin made yet another protest against the violations of Soviet airspace by German planes in order to take aerial photographs of Soviet territory, but once again he was given an evasive answer. After conferring, they decided to set the time for the broadcast of the official announcement of the beginning of the war with the USSR on the radio - 5 hours 30 minutes in the morning on June 22, 1941. Foreign correspondents were invited to 4 o'clock in the morning. “By that time,” Goebbels continues to write, “the enemy will have figured out what’s what, and the nation will be ready to find out the truth.” In the meantime, both Berliners and Muscovites slept peacefully at home in blissful ignorance of impending catastrophic events.

Goebbels left Hitler at half past two in the morning. “The Führer is solemnly serious and calm. He wanted to lie down for a couple of hours. It's probably the best thing for him right now." Goebbels went to the building of his ministry, noting that "there is not a soul around on Wilhelmplatz, both Berlin and the Reich are fast asleep." When he began his morning meeting with colleagues, it was barely dawn. “General amazement on their faces, but surely many guessed what was happening, although not all.” Employees immediately sat down to prepare morning reports, calling for help from newsreel operators, newspaper correspondents and radio reporters. Goebbels glanced at his watch every minute. "Half past three. Here are the guns. God bless our fighting power!”

The units of the bombers of the 2nd, 3rd and 53rd bomber squadrons reached the Soviet airfields unnoticed. It was still dark, only in the east the dawn of the coming day lit up. Air units operating separately began to descend and reach the target. By 03:15 they were already moving at low altitudes. Hundreds of two-kilogram SD2 fragmentation bombs, invisible against the night sky, rained down from open bomb hatches. They fell on the rows of Soviet aircraft lined up wing to wing near the runways of airfields, and on personnel tents located nearby. There was serenity below. Soviet planes were not even camouflaged. The alarm signal given after the attack could not change anything. And in a few seconds, the explosions of low-yield bombs turned the planes into flaming torches. The radius of destruction of each such bomb was 12 meters. Exploding, it hit everything around with 50-250 tiny fragments. A direct hit was equivalent to a medium-power anti-aircraft projectile. From the gasoline that gushed out of the punched containers, which immediately ignited, huge clouds of thick black smoke shot up into the sky. On earth reigned total hell, chaos. There was no way to localize and extinguish the multiplying fires. Troop control was completely lost due to a breakdown in communication with higher headquarters. Desperate attempts were made to get on the air from small portable radio stations.

Only four hours later did the first reports with information about the situation arrive. From the headquarters of the 3rd Soviet Army located in Grodno, northeast of Bialystok, a message flew to the headquarters of the Western Special Military District:

“Starting from 4 o’clock in the morning, the Germans carried out air raids with forces from 3 to 5 aircraft. Air attacks were made every 20–30 minutes. Objects in Grodno, Kropotkin, and especially army headquarters were bombed. At 7:15 am, 16 enemy planes raided Grodno, attacking the city from a height of 1,000 meters. Dombrovo and Novy Drogun are engulfed in fires. From 4 am to 7 am, a total of four air raids were carried out on the Novy Dvor airfield in groups of 13-15 enemy aircraft. Our losses: 2 aircraft burned, 6 disabled. 2 personnel were seriously injured and 6 lightly. At 6 o'clock in the morning, the airfield in Sokulka was subjected to bombing and shelling from the air. Two killed and 8 wounded."

Meanwhile, the Ju-87 dive bombers and the Me-109 fighter-bombers, which had taken off in the predawn twilight from the main airfield in Suwalki, did their best to carry out the combat mission. Lieutenant Hans Knoke recalls that the general alarm signal for all air squadrons sounded at 4 o'clock in the morning. “The airfield came to life, all units were involved,” Knoke testifies. Gradually, the scale of the operation that had begun began to reach everyone. “All night,” says Knoke, “I heard the hum of tank engines in the distance. We were only a few kilometers from the border.” Within an hour, the air squadron in full force took to the air. Four bombers of Knoke's squadron, including his car, were equipped with automatic bombers. Behind were many hours of training. “And now, under the belly of my dear Emil, small fragmentation bombs hung on a suspension,” he recalls. - And with great pleasure I brought them down on the stupid heads of the Ivanovs.

One of the targets of the bombing was the headquarters and command post of the Russians in the forests west of Druskininkai. They were to be attacked from a strafing flight. Before reaching the target, “we noticed long columns of our troops stretching to the east. Immediately, almost wing to wing, we noticed dive bombers flying in our direction. They now had to strike the main blow.

Kesselring's air fleets took to the air in full force and lined up in battle formations with the first rays of the sun. After the first air raids of small groups of bombers had taken place, they now had to strike the main blow. For this, the Luftwaffe command allocated 637 bombers and 231 fighters. Their goals are 31 airfields of the Soviet Air Force.

The plane of navigator Arnold Döring (53rd bomber squadron of the Luftwaffe) crossed the border at 04:15. The crew members acted in strict accordance with the instructions received.

“I made course corrections as usual. Then, looking out the window, he noticed that the ground was shrouded in fog, but the targets were still distinguishable. Most of all, I was struck by the inaction of enemy air defense systems.

The unit began bombing. Everywhere along the Eastern Front from the North Cape to the Black Sea, the planes of Kesselring's four air armies rolled over the borders of the USSR in waves to unleash hundreds of tons of bombs on the unsuspecting enemy. Dive bombers with a terrible howl attacked easily distinguishable targets, and medium bombers continued to head for pre-determined objects. Fighter-bombers bombarded and bombed Soviet airfields. “We just couldn’t believe our eyes,” said Hans von Hahn, commander of the 1st Squadron of the 3rd Fighter Squadron, operating in the sector south of Lvov. “Wave after wave of reconnaissance aircraft, bombers and fighters swept by - just like in an air parade.”

Having completed the bombing, Döring's Xe-111 again gained altitude. The steward recalls:

“Puffs of smoke, fire, rising dust. Our bombers ignored the underground ammunition depots located to the right of the runway. But several cars passed over the runway and, dropping bombs, disabled it. We noticed two huge sinkholes. Not a single enemy vehicle will take to the air again!”

Soon another group of aircraft appeared over the airfield. Döring, turning around as the planes climbed, remarked: “About a dozen fighters standing at the runway were engulfed in flames. The barracks of the personnel were also on fire. Having completed the first combat mission, Xe-111 headed back to the base. "The sortie was so successful that there was even no need for a second planned attack on this airfield."

But even these seemingly easy victories in the first hours of the war were not without losses. Siegfried Lauerwasser, a war newsreel cameraman, filmed bombers returning to their airfield in Poland. “That's how it all started,” he commented on excerpts from a documentary made for television after the war. It immediately became clear that not everyone had returned from the mission. It turned out to be “a big surprise,” Lauerwasser continues, “when we were informed that, they say, such and such a car did not return. We kept waiting." But the crew never showed up. “It came as a shock to us. How so? How could this happen? We knew them, we were friends, they were our comrades all these long months.

The most powerful first strike in the short history of aviation thus gave impetus to the further development of events.

"The shortest night of the year ... H time"

Lieutenant Heinrich Haape, medical officer of the 3rd Battalion, 18th Infantry Regiment, stood with the battalion commander, Major Neuhof, and the battalion commander's aide-de-camp, Hillemans, on the top of a hillock in the southeastern section of the border in East Prussia. The officers peered into the darkness, trying in vain to see the Lithuanian plain that stretched out in the distance. There were still 5 minutes left before the time "H".

“I glanced at the luminous watch face. It was exactly 3 o'clock. I realized that perhaps at that moment millions of German soldiers were also looking at the arrows. All watches in the Wehrmacht were checked that night.

Haape even sweated from the excitement that gripped him. In the last minutes it seemed that "it is impossible to withstand this terrible tension of the last fateful minutes."

He's writing:

“Someone is smoking. Immediately, a jerky command is heard, and the red light is trampled. Everyone is silent, occasionally the clatter of hooves and barely audible snoring is heard - the horses are also restless. Here, in the eastern part of the sky above the horizon, a barely distinguishable light strip appears. Dawn is coming. Grey. God, well, do these seconds never end! I look at the clock again. Two more minutes."

The shortest night of the year was coming to an end. And although the night darkness still reigned around, the sky brightened noticeably, became bluish.

Erich Mende, Oberleutnant of the 8th Silesian Infantry Division, recalls a conversation he had with his superior during those last moments of peace. “My commander was twice my age,” he says, “and he had already had to fight the Russians near Narva in 1917, when he was in the rank of lieutenant.”

“Here, in these endless expanses, we will find our death, like Napoleon,” he did not hide his pessimism. By 11 pm on June 21, we were informed that the time "H" remained unchanged, so the operation would begin at 3 hours 15 minutes. “Mende,” he turned to me, “remember this hour, it marks the end of the former Germany. Finis Germany!

But Mende was not touched by the prophetic revelations of the commander. He attributed his condition to the unbridled optimism so characteristic of young soldiers and officers, and the confidence that the war, in fact, was over, and ended victoriously for Germany. “So we didn’t really listen to the grumblings of these old people, which we considered our commander.”

The scale of the forthcoming campaign, its broadest front, was also determined by the different times of "H" in different areas. In the sector of Army Group North, dawn came at 3 hours and 5 minutes. On the sector of the Army Group "Center" - at 3 hours and 15 minutes, and on the sector of the Army Group "South" - at 3 hours and 25 minutes. And the eyes of all the soldiers along the gigantic front line were intently following the pace of the minute hands on the clock. The last, decisive moments are forever imprinted in the memory of those who were destined to die or remain crippled in the coming meat grinder.

Hauptmann Alexander Shtalberg of the 12th Panzer Division recalls:

“We were sitting in pitch darkness in tanks. Many simply lay down on the forest ground. Nobody could sleep.

At about 3 o'clock in the morning, the non-commissioned officer, bypassing everyone in turn, woke us up. The drivers started their engines, and the column began to slowly crawl out of the forest. In the field, our newly formed 12th Panzer Division made an impressive impression - it's no joke to say, 14,000 personnel plus equipment.

Walter Stoll, a radio operator from an infantry unit who was in the immediate vicinity of the Bug, recalls the hectic preparations of the last minutes.

“And so we were ordered to move forward. Personnel with assault boats and other watercraft received dry rations and ammunition. We were then even given chocolate, cognac and beer. Everyone fed each other."

As we moved towards the border, more and more troops appeared on the roads, especially artillery units, moving into position. "There was no end to these mortars." They moved along the soft velvet dust of country roads, along sandy forest paths to their starting lines. In one village, where it was impossible to step a step from self-propelled artillery installations, we left everything that had nothing to do with the upcoming attack, taking only the most necessary. The vehicles were left behind. Infantrymen began to form into assault groups.

Corporal Erich Kubi, sitting in one of the "ferrets" at the edge of the forest, observed: "It was a fine morning, cool, clear, there was fog in the lowlands." After the turmoil of recent days, "everything was perceived as the calm before the storm." The vehicles were frozen in anticipation of the order. And the order came, already when it was almost completely dawn. Kubi recalls: “The sky brightened, trees and tanks lined up in a long column loomed in dark silhouettes.” This scene of serenity contrasted sharply with what was to be experienced a few moments later.

Senior officers gathered at observation posts to evaluate the results of the upcoming artillery preparation. General Guderian, commander of the 2nd Panzer Group, went to the command post, located on an observation tower south of Bohukal, 15 kilometers north of Brest. “It was still dark when we arrived there at 3:10,” we read in his diary.

General Günther Blumentritt, Chief of Staff of the 4th Army, was also nearby, in the sector of the 31st Infantry Division. “We saw,” he recalls, “how German fighters take off and head east. Their navigation lights were clearly visible. The H-hour was approaching, “the sky was brightening, acquiring a unique yellowish tint. Everything around me breathed silence.

In the area of the 30th Panzer Division at Suwalki, on the northern flank of Army Group Center, "the usual pre-offensive tension also reigned. The endless rows of tanks froze in immobility and seemed like outlandish ships sailing through the sea from the fog. From time to time, on one of the machines, the commander, having opened the hatch, got out and, putting binoculars to his eyes, tried to make out something in the false light of the coming morning. Around three in the morning, the drone of dive bombers was heard, then they were followed by squadrons of medium bombers heading for their targets.

Two minutes before one o'clock, Lieutenant Haape of the 18th Regiment - and not just him - suddenly remembered his wife.

“My thoughts returned to Martha. She is also sleeping, as all our wives, girlfriends and mothers were sleeping now, like millions of ordinary people on both sides of this boundless front!

Corporal Erich Kubi from Army Group South, who was waiting for the signal to attack, in the last minutes wrote a letter to his wife. He foresaw what a blow the coming events would be for both her and their child.

“Now you are talking about everything [about the attack on the Soviet Union. - Approx. auth.] you know and you understand everything no worse than me. But now, when I write these lines, you are still sleeping, suspecting nothing. At 7 o'clock on the radio will broadcast a message about the war with the Russians. Frau Schultz will surely wake you up and you will be shocked. Then take our Thomas out into the garden and tell him that his dad will be back soon.”

The inevitability of future events occupied the minds of everyone without exception. Heinrich Haape consoled himself with the fact that at least his wife was given one more serene night. “And we have to throw to the east,” Haape admitted. And in a minute they will all perform. “Tomorrow, where the sun rises today, war will blaze.”

Hidden near the waters of the Bug, Heinrich Eikmeier saw how the first shell almost silently entered the breech of his 88-mm anti-aircraft gun. All the officers around were constantly looking at the stopwatches. Eikmeier froze with the release cord in his hands. Is it really up to him to become the one who fires the first shot on the Eastern Front?

Ludwig Thalmeier, from the heavy gun battery attached to the 63rd Infantry Regiment, was struggling to sleep in the back of a truck parked in the woods. But sleep did not come. He later wrote in his diary:

“Dawn here began earlier than in Germany. Birds chirped, somewhere in the distance a cuckoo called. And now - it was exactly at 3 hours and 15 minutes - the German artillery suddenly roared. The air shuddered ... "Gerhard Frei, an artilleryman, recalls:" Exactly at 3 hours and 15 minutes, the first team broke the silence, and then hell began! I have never heard such a roar before. Everything around was on fire, the volleys of countless guns merged into one endless roar. And then flashes of breaks flashed on the opposite bank of the Bug. Yes, it was hard for those who fell into this meat grinder without thinking and without guessing!

Ober-lieutenant of artillery Siegfried Knappe at night, by the light of the moon, studied his first target properly - the village of Sasnya, which lay directly in front of the battle formations of his battery. Now there was something unimaginable going on.

“From the observation post, I saw shell explosions, yellow and black clubs rising up. A disgusting powder burn hit the nose, the guns hit without a break. A quarter of an hour later, we stopped firing, in the distance, on the enemy side, the last bursts sounded with weak pops, and then the infantry rushed to the attack.

The sudden silence after the roar of artillery fire seemed unbearable. Artillery Private Werner Adamczyk of the 20th Artillery Regiment describes what befell those who served the 150 mm guns:

“You stand next to the gun, a shot is heard, and every time it seems that you are about to be crushed to the ground. The blast and roar from the shot is so strong that you have to open your mouth to reduce the load on the eardrums.

The infantry and part of the armored vehicles began to move forward. The soldiers went forward with mixed feelings. Goetz Reger of the Armored Car Division later vividly described his impressions of the beginning of the Barbarossa plan:

“Of course you are terrified. You are ordered to go ahead, and, naturally, your stomach grumbles with fear. But nothing can be done - you have to go, this is the order, and orders must be followed ... "

Three powerful groupings of the German armies were concentrated on the Russian border from Memel in the Baltic to Romania on the Black Sea. That dawn of the longest day of the year is captured on dozens of frames of the military newsreel "Deutsche Wochenschau". And these impressive shots were shown in all cinemas in Germany a week after the start of the war. On the screens, the predawn sky illuminated by flashes of guns. Traces of tracer bullets over a single-span railway bridge, flashes of explosions, silhouettes of confidently advancing infantrymen snatching out of the darkness. On the Russian side, Russian observation towers are burning like candles. Puffs of smoke majestically rising to the sky stretched to the horizon, eclipsing the rising sun. The outlines of columns of infantrymen, in full gear, confidently advancing towards intact bridges across the border river.

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