Measuring height with a measuring fork. The height of a tree can be measured with a measuring fork. To do this, it must be adjusted accordingly.

1. Drill a small hole in the fixed leg at a distance of 5 ... 8 cm from its end.

2. On the movable leg, exactly against the hole, mark the line and take it as a zero division. To the right and left of zero, apply oblique centimeter divisions, and to the left of zero, the dashes are applied with an inclination to the left, and on the right side, to the right.

3. Equip the measuring fork with a plumb line.

Measure the height as follows. The measurer measures a distance from the tree approximately equal to the height of the tree, and chooses a place so that the top and base of the tree are clearly visible, for example, at a distance of 24 m. Moves the movable leg a number of centimeters equal to the number of meters from the tree to the observer (in our example 24 cm) and secures in this position with a stopper. On the inner edge of the fixed leg

sights at the top of the tree. In this case, the thread with a plumb line will take a vertical position and cross a certain number of divisions on the movable leg, which corresponds to the height of the tree from the level of the observer's eye to the top (2.3).

In flat terrain, in order to measure the entire height of a tree, it is necessary to add the measurer's height to the resulting count. In a mountainous area, if the base of the trunk is located below the observer, first sight at the top of the tree and make a count, then sight at the base. The sum of the readings on the top and on the base of the trunk will be the height of the entire trunk. If, on the contrary, the base of the stem is located above the observer, then the height of the stem a will be equal to the difference between the readings to the top and to the base. The error of measuring the height of a tree with a measuring fork is ±5 ... 8%

pendulum altimeter. The pendulum altimeter, proposed by the taxpayer N. I. Makarov, is a flat steel plate measuring 8X10 cm in the form of a sector. A pendulum is fixed on the front side of the sector and two height scales are applied: the upper one for measuring height with a basis of 10 m and the lower one for measuring height with a basis of 20 m. The division scales are marked on both sides of the zero division. A sighting tube is soldered to the sector plate of the altimeter.

diopter, which is expanded in the form of a funnel (2.4). On the reverse side of the sector along the axis of the pendulum there is a latch in the form of a button. When pachiy presses the button, the pendulum moves and takes a vertical position; when you remove your finger from the button, the spring presses the pendulum against the plate and it stops.

To measure the height of a tree with a pendulum altimeter, proceed as follows:

1. Measure from the tree a basis of 10 m or 20 m in a horizontal distance, and if the height of the tree is up to 15 m, measure 10 m, if more than 15 m, measure 20 m.

2. Take the altimeter in the right hand so that the thumb is pressed against the recess under the scale, and the index finger against the sighting tube.

3. Through the eye diopter of the sighting tube, they sight at the top of the tree and at the same time press the button with the index finger of the left hand.

When the pendulum stops, and the top of the tree is in the center of the circle, carefully remove the finger of the left hand from the button and make a reading on the appropriate scale: with a basis of 10 m on a 10-meter scale, and with a basis of 20 m on a 20-meter scale (2.5) This the count is the height of the tree from the level of the observer's eye to the top. To obtain the entire height, you must add to it the height to the level of the observer's eyes.

If the base of the tree is below the observer's eye, then the height of the tree is equal to the sum of the counts to the top and base of the tree. If the base of the tree is above the observer, then the height of the tree is equal to the difference between the readings to the top and to the base.

The pendulum altimeter has proven itself to be a device that is easy to use and has a simple design. Tree height measurement error = n5%, To obtain more accurate results, it is necessary to calculate the arithmetic mean of two or three measurements.

Forest altimeter VUL-1. An altimeter-goniometer is designed to measure the height of growing trees, measure the distance (baseline) and determine the angle of inclination on the ground. It consists of a body, inside of which a drum with a balancer is suspended on an axis, ensuring a constant position of the scales in relation to the horizon (2.6K

Scales are applied to the drum for measuring the height of trees from a base distance of 15 and 20 m. Divisions in meters (on the right side) are applied on each scale for measuring height and divisions in degrees (on the left side) for measuring the angle of inclination. The basic distance is determined by a rangefinder using a special tape made of rubber-fabric oilcloth.

On the housing cover there is a scale for determining the basic distance in meters, taking into account the vertical angle (correction scale) and a braking device.

The procedure for determining the height of a tree on flat terrain:

choose a place from which its base and top are clearly visible;

fix the base tape on the tree trunk so that its first stroke is at eye level;

sighting on the base tape, through the rangefinder, ensure that the first stroke of the tape is aligned with the stroke of 15 m or 20 m; one division of the tape corresponds to 1 m distance to the tree;

sight through the eyepiece of the altimeter at the top of the tree and at the same time press the button of the braking device;

when the drum stops and the altimeter's hairline is aligned with the top of the tree, remove your finger from the button and take a count that corresponds to the height of the tree from the observer's eye to the top of the tree.

To obtain the entire height of the tree, it is necessary to add the distance to the level of the observer's eye to the obtained reading.

When determining the height of a tree on sloping terrain, you must:

fix the base tape on the tree trunk; using a range finder, determine the distance to the tree (15 or 20 m);

determine the angle of inclination in degrees, for which it is necessary to sight on the top stroke of the tape;

determine the exact distance from which the tree height will be measured on the scale located on the altimeter body, taking into account the vertical angle;

sight from this distance to the top of the tree and make a count, then sight to the base of the tree.

Altimeter-kronomer VK-1. The altimeter is designed to measure the height of a tree, distances, the angle of inclination on the ground and the radius of the crowns of growing trees. It is mounted in a metal case and consists of two blocks and a logarithmic calculator. In one block, in a hermetically sealed chamber, a disk suspended on an axis is installed, on which scales are applied: goniometric and altimeter. The camera has a reflective prism with a reference index and a magnifying glass, which are part of the sighting system. In the second block, a pentoprism is installed, with the help of which the altimeter-kronomer switches to vertical sighting (2.7).

Below the sighting system, a rangefinder is installed, consisting of a bioprism, an objective and an eyepiece. The edges of the bioprism shift the observed image of the scale (basic tape) in mutually opposite directions (up and down), forming a double image.

logarithmic calculator consists of two scales: movable and fixed. On the movable scale, there is an additional scale of corrections for the slope of the terrain, digitized in degrees. On the surface of the housing there is a handwheel that serves to switch the prism when measuring the height or crown of a tree. When measuring the height, the point on the handwheel head should be opposite the letter H on the body, when measuring the crown - against the letter R.

Measuring the height of a tree with an altimeter-kronomer is performed as follows:

1. Choose a place from which the base and top of the tree are clearly visible.

2. Hang the base tape on the tree trunk so that its middle is at the height of the observer's eye.

3. Sighting through the range finder on the base tape, the distance is read by the magnitude of the mutual displacement of its image.

4. Aiming at the middle of the base tape, determine the slope

5. After that, sighting at the top and at the base of the tree, readings are made on the altimeter scale.

6. On the fixed scale of the calculator, a division corresponding to the basis is found, and the beginning of the movable scale (number 10) is combined with it, or, if there is a slope, its value (digitized in degrees).

Then, on the movable scale, a division is found corresponding to the sum of readings on the altimeter scale, and against it, on the fixed scale, the value of the height of the tree is taken. The root-mean-square measurement error is no more than, %: tree heights ±3; distances ±1; tree crowns ±4; terrain slopes ±30".

Altimeter Blume - Leissa. It has a body in the form of a sector of a circle (2.8) and diopters: eye and object, located at the ends of the upper face of the altimeter body. Below the object diopter is a trigger, which fixes the altimeter pendulum in the desired position. A plate is attached to the back of the case for making adjustments depending on the steepness of the slope. The height of the trees is determined by four arcuate scales with different values ​​of the basis (15, 20, 30, 40 m).

The difference between the Blume-Leiss altimeter and the Makarov altimeter lies in the fact that to measure the distance to a tree, a basic folding tape with divisions 0, 15, 20, 30 and 40 is used, which plays the role of a rangefinder rod. The observer moves away from the measured tree at such a distance that the top and bottom of the tree can be clearly seen, and, moving back or forward several steps, looks for one of the four numbers (15, 20, 30 or 40) located on the base tape in the optical meter at the same level as zero division. If, for example, division zero is on the same level as division 30, this means that there are 30 meters from the observer to the tree.

After that, it is necessary to press the button located on the reverse side of the altimeter and release the pendulum. First, they sight at the top of the tree and, as soon as the pendulum stops swinging, they press the trigger with their finger, and the pendulum will stop at that division of the scale that will correspond to the height of the tree from eye level.

It's hard to believe, but the height of the tree was determined using a very long measuring tape; however, there are much simpler methods for determining the height of trees. Although these methods do not always measure height to the nearest centimeter (or inch), they are quite reliable and can be used to measure any tall object such as telegraph poles, buildings, and even a magical bean seed tree: it can be measured. any object as long as its vertex is visible.

Steps

Using a sheet of paper

This method allows you to find the height of a tree without resorting to mathematical calculations. All you need is a sheet of paper and a measuring tape. No calculations required; however, if you want to know how this method works, you will need a little familiarity with the basics of trigonometry.

• The "Using a clinometer or theodolite" section provides all the math and explanations, but they are not required to find the height of a tree with this method.

1. Fold a piece of paper diagonally to form a triangle. If the sheet is not square, but rectangular, it is necessary to make a square out of it. Bend a sheet of paper at the corner, aligning two adjacent edges and thus obtaining a triangle, then cut off the excess edge protruding from under it. As a result, you will get the necessary triangle.

   • The triangle will have one right (90 degree) angle and two acute 45 degree angles.

2. Bring the triangle to one eye. Hold the sheet vertically so that the right angle (90º) is placed down and away from you. One of the short sides (leg) should be horizontal (parallel to the ground), the other vertical (bottom to top). Place the triangle so that, with your eyes up, you can look along its long side.

   • The long side of a right triangle that your gaze is directed along is called the hypotenuse.

3. Move away from the tree until you see that its top coincides with the top of the triangle (its upper sharp corner). Close one eye while looking with the other along the long side of the triangle until the top of the tree appears above it. Make sure that your gaze, directed along the long side of the triangle, falls on the very top of the tree.

   Mark an appropriate spot on the ground and measure the distance from it to the base of the tree. This will be almost the full height of the tree. Your height should be added to the value obtained, since you did not look at the tree from the ground itself, but from the height of your eyes. Now you have found the relatively accurate height of the tree!

   • The principle on which this method is based is detailed below in the "Using a clinometer or theodolite" section. This method does not require any calculations, since it uses the simple fact that the tangent of an angle of 45º degrees (exactly such acute angles in our paper triangle) is equal to 1. Thus, we can write the following equality: (tree height) / ( distance from the tree) = 1. Multiplying both sides of the equation by (distance from the tree), we get: height of the tree = distance from the tree.

Shadow comparison

1. This method is suitable if you have a measuring tape or ruler. You will be able to estimate the height of the tree fairly accurately and you won't need any other tools. Calculations will be reduced to multiplication and division, without the use of other mathematical operations.

   • If you do not want to make any calculations yourself, you can use the online tree height calculatorby entering the measured values ​​\u200b\u200binto it.

2. Measure your height. Stand up straight and use a tape measure or meter ruler to determine your height. You must wear the same shoes that you will use to measure the height of the tree. For this method, you will need a piece of paper - write down the measured height on it so as not to forget the exact value.

   • Record height in a single unit of measure, such as centimeters, rather than a combination of meters and centimeters (feet and inches). If you are not sure how to correctly convert everything into one unit of measurement, use the length of a tape measure or meter ruler (1 meter or 3 feet) as such a unit. In this case, you will operate on the height of the ruler and the length of the shadow it casts on the ground.
   • If you are in a wheelchair or cannot stand up straight for any other reason, measure your height in whatever position you are comfortable with when you determine the height of the tree.

3. Stand on a flat, sunny patch of ground next to a tree. For accuracy of measurements, try to find a place where your shadow will fall on a flat surface of the earth. It is best to use this method on a sunny, clear day. On cloudy days, it will be difficult to measure the exact length of the shadows.

   Determine the length of your shadow. Using a tape measure or meter ruler, measure the distance from your heels to the top of the shadow you cast. If you don't have a helper, you can mark the end of the shadow by standing still and throwing a pebble at it. Even better, put a pebble on the ground and move away from it so that the end of your shadow coincides with it, then measure the distance from this place to the pebble.

   • Record all measurements. In order not to confuse the numbers, accompany each of them with a brief explanation.

4. Measure the length of the shadow cast by the tree. Using a tape measure, determine the distance from the base of the tree to the top of its shadow. It is best if the tree grows on a flat area; the results will be less accurate if the tree is located on a hillside. Measure the tree's shadow as soon as you determine the length of your own shadow, as the length of shadows changes over time due to the position of the Sun.

   • If the shadow of a tree falls on a sloping piece of land, you may be able to choose a different time of day when the shadow is shorter or its direction changes.

5. Add 1/2 of the tree's width to the length of the tree's shadow. Most trees grow vertically, in which case the top of the tree is in the middle of its trunk. Therefore, when determining the total length of the shadow, 1/2 of the diameter of the tree trunk should be added to the measured distance. This is due to the fact that the shadow from the very top of the trunk is blurred and practically invisible on the ground.

   • Measure the width of the tree trunk with a long ruler or tape measure, then divide it by 2 to get 1/2 of the width. If you are having difficulty measuring the width of the trunk, draw a tight square around the base of the trunk and measure the side of that square.

6. Based on your measurements, calculate the height of the tree. Previously, you measured three things: your own height, the length of your shadow, and the length of the shadow cast by the tree (including 1/2 the width of the trunk). The length of an object's shadow is proportional to its height. In other words, (the length of your shadow) divided by (your height) equals (the length of the tree's shadow) divided by (the height of the tree). Using this equation, you can find the height of the tree:

   • Multiply the length of the tree's shadow by your height. Suppose you are 1.5 meters (5 feet) tall and the tree casts a shadow 30.48 meters (100 feet) long. Multiplying these values, we get: 1.5 x 30.48 = 45.72 meters (or 5 x 100 = 500 feet).
   • Divide the resulting value by the length of your own shadow. In the example above, if your shadow is 2.4 meters (8 feet), we get: 45.72 / 2.4 = 19.05 meters (or 500 / 8 = 62.5 feet).
   • If you are having difficulty with calculations, use the online tree height calculator.

Using a pencil (assistant needed)

1. This method can be used as an alternative to the previous one (shadow comparison). Although the present method is less accurate, it can be used when it is not possible to find the height of a tree by comparing shadow lengths, such as on an overcast day. In addition, if you have a measuring tape, you can do without mathematical calculations. Otherwise, if you don't find a roulette, some simple calculations will be required.

   Stand far enough away from the tree so that you can see the whole tree, from the base to the top, without tilting or raising your head. To be more accurate, your feet should be level with the base of the tree, not above or below it. Stand so that nothing blocks or blocks the tree from you.

   Take a pencil in your hand and hold it out in front of you. Instead of a pencil, you can use another small, straight object, such as a stick or ruler. Taking the pencil in your hand, straighten it so that the pencil is directly in front of you (between you and the tree).

   Close one eye and wiggle the pencil until the top is aligned with the top of the tree. In this case, it is better to keep the pencil sharpened end up. It is necessary that the top edge of the pencil obscure the top of the tree from you while you look at the tree “through” the pencil.

   Run your thumb along the pencil until the tip of your finger is aligned with the base of the tree. Holding the pencil so that its top end is aligned with the top of the tree (see step 3), move your thumb along the pencil to where you can see the base of the tree coming out of the ground (as before, while looking through the pencil with one eye). on a tree). Now the pencil "covers" the full height of the tree, from its base to its top.

   Rotate your hand so that the pencil is horizontal (along the ground). As you do so, keep your arm outstretched in front of you and make sure your thumb is still pointing towards the base of the tree.

   Ask your assistant to stand so that you can see him or her "on" the tip of the pencil. That is, your friend should stand in such a way that his feet "coincided" with the top of the pencil. In this case, the assistant should be located at the same distance from you as the tree, no closer and no further. You and your assistant will be some distance apart (depending on the height of the tree), so you can communicate with him through gestures (using the second hand, which does not have a pencil), showing where to go (further or closer, right or left ).

   If you have a tape measure with you, measure the distance between your assistant and the tree. Ask a friend to stay where they are, or mark the spot with a branch or pebble. Then measure the distance from this place to the base of the tree with a tape measure. This distance will be equal to the height of the tree.

   If you don't have a tape measure handy, mark the height of your helper and the height of the tree on a pencil. Put a scratch or other mark on the pencil where your thumb was, thereby fixing the height of the tree from your vantage point. Then, just as before with the tree, move the pencil so that it partially obscures your helper, aligning the top of the pencil with the helper's head, and the thumb resting on the pencil with his feet. Again mark the position of the thumb on the pencil.

   Calculate the height of the tree by finding the measuring tape. To do this, you will need to measure the distance between the tip of the pencil and the marks made on it, as well as the height of your assistant; this can be done at home without returning to the tree. Scale the lines on the pencil according to your helper's height. For example, if your friend's height mark is 5 centimeters (2 inches) from the tip of the pencil, and the tree's height mark is 17.5 centimeters (7 inches), then the tree is 3.5 times taller than your helper, since 17.5 cm / 5 cm = 3.5 (7 inches / 2 inches = 3.5). Let's say your friend is 180 centimeters (6 feet), then the height of the tree is 180 cm x 3.5 = 630 cm (6 x 3.5 = 21 feet).

   • Note: If you have a measuring tape with you when you are near a tree, there is no need to do any calculations. Read carefully the "if you have a tape measure" step above.

Using a clinometer or theodolite

1. This method allows you to get more accurate results. Although the above methods are fairly reliable, with a little more extensive calculations and special tools, you can get more accurate results. This is not as difficult as it seems at first glance: all you need is a calculator with a tangent function, as well as a simple plastic protractor, a straw and a thread with which you can make a clinometer yourself. The clinometer, or inclinometer, allows you to measure the slope of objects, and in our case, the angle between you and the top of the tree. For this purpose, a more complex and precise instrument, called a theodolite, is used, the design of which includes a telescope or a laser.

   • In the “Using a sheet of paper” method, a paper triangle acts as a clinometer. This method, in addition to greater accuracy, allows you to determine the height of a tree from any distance, instead of approaching or moving away from the tree, achieving alignment of the sheet of paper with the tree.

2. Measure the distance to the observation point. Stand with your back to the tree and move away from it to a place that is flush with its base, from where the top of the tree is clearly visible. At the same time, walk along a straight line, measuring the distance from the tree with a tape measure. The distance from the tree can be arbitrary, but for this method it is best if it is 1-1.5 times the height of the tree.

   Determine the angle between the ground and an imaginary line connecting you to the top of the tree. Looking at the top of the tree, use a clinometer or theodolite to measure the "angle of elevation" between the tree and the ground. The angle of elevation is the angle between the horizontal plane of the earth and the line of your gaze directed at some tall object (in our case, the top of a tree), while you are at the top of this angle.

   Find the tangent of the angle of elevation. You can do this with a calculator or a table of trigonometric functions. How the tangent is calculated depends on the particular calculator; in most calculators, this is done using the “tg” (or “tan”) key - press it, then enter the angle value and press the “equals” (=) key. Let's say the elevation angle is 60 degrees: press the “tg” (“tan”) key, then enter “60” and press the equal sign.

3. Multiply the distance from you to the tree by the tangent of the angle of elevation. Recall that you measured the distance between you and the tree at the very beginning of this method. Multiply this distance by the calculated tangent. Since the top of the angle of elevation was at your eye level, the result will be how far the tree rises above that level.

   • From the section above, which gives the definition of tangent, you will understand the principle of this method. As noted, tangent = (height of the tree) / (distance to the tree). Multiplying both sides of this equation by (distance to the tree), we get (tangent) x (distance to the tree) = (height of the tree)!

Instruction

Set the altimeter to start mode. The first thing you should do is set the barometric pressure. The initial reading from the pressure that can be with a probability of 99% at the time in which the measurement is taken. As (depending on weather conditions), this value ranges from 950 to 1050 millibars.

Calibrate the sensor before taking a measurement. To do this, you should pay attention to the button with the arrow pointing up. This will help you accurately determine the data that you need. Using prompts when you turn on the main menu of the device will help you make all measurements and calculations accurately and quickly.

Measure the initial parameters to determine the height. When you hold down the Set button, which is in all modern altimeters, you will automatically enter the settings mode. The altimeter will show you the air temperature and the current pressure calculated at altitude. In this case, you have to reduce it to normal above sea level. To do this, use the arrow button and Set, which will be able to adjust the value you need. After that, there are two options for calculating the height above sea level. The first is incremental change, which is performed manually by pressing buttons or in automatic mode.

Go to main menu. After saving the settings made, go to the main menu mode. The display will show the following data - altitude and current atmospheric pressure. The accuracy of modern altimeters is more than 1 meter.

note

Be careful when calibrating the sensor. It should be carried out as many times as you will take altitude measurements above sea level. Such a need for constant regulation is due to the fact that pressure deviations per day can reach 5 millibars, and such an error can cause a difference in results up to several tens of meters.

Helpful advice

When using an altimeter, you can choose the unit of altitude that works best for you. It can be feet, meters, etc. (depending on the instrument model). Use the arrow button to select the unit of measure. If you need to save the data obtained after measurements, use the save mode - press the arrow button and Set. The altimeter can work in automatic mode and record data changes with an interval of 10 seconds.

When going to the mountains, take an altimeter (altimeter) with you, which will allow you to be always informed about the height of your location. It is important to know this not only for orientation, but for controlling your physical condition.

You will need

• - mechanical or electronic altimeter.

Instruction

Use an altimeter to determine the surrounding mountains. The mechanical instrument is based on the simple principle of atmospheric pressure as a function of altitude. The pressure drops with increasing height, the spring in the device unwinds and the arrow rises to an accuracy of 1 m, depending on the number of divisions on the dial. Now there are electronic altimeters.

Produce heights with a mechanical instrument. Set the arrow to 0 before the start of the ascent, the instrument will tell you the height in meters that you climbed. Please note that weather conditions greatly affect the readings of the device. If during for the atmospheric pressure changes sharply, it is necessary to reconfigure.

"A barometer is an instrument used to measure the height of towers in the late 20th century."
(World Encyclopedia, 2495)
Sir Ernest Rutherford, President of the Royal Academy and Nobel Laureate in Physics, told the following story, which is a great example of the fact that it is not always easy to give the only correct answer to a question.
Some time ago, a colleague contacted me for help. He was about to give the lowest grade in physics to one of his students, while this student claimed that he deserved the highest grade. Both instructor and student agreed to rely on the judgment of a third party, an uninterested arbitrator; the choice fell on me.
The exam question was: "Explain how you can measure the height of a building using a barometer." The student's answer was: "You need to climb with a barometer to the roof of a building, lower the barometer down on a long rope, and then pull it back and measure the length of the rope, which will show the exact height of the building."
The case was indeed difficult, as the answer was absolutely complete and correct! On the other hand, the exam was in physics, and the answer had little to do with the application of knowledge in this area.
I suggested that the student try to answer again. After giving him six minutes to prepare, I warned him that the answer must demonstrate knowledge of physical laws. After five minutes, he still hadn't written anything on the examination sheet. I asked him if he gave up, but he stated that he had several solutions to the problem, and he simply chooses the best.
Intrigued, I asked the young man to start answering without waiting for the allotted time to expire. The new answer to the question was: “Climb with a barometer on the roof and throw it down, measuring the time of the fall. Then, using the formula L = (a*t^2)/2, calculate the height of the building.”
Here I asked my colleague, the teacher, if he was satisfied with this answer. He finally gave in, recognizing the answer as satisfactory. However, the student mentioned that he knew several answers, and I asked him to reveal them to us.
“There are several ways to measure the height of a building with a barometer,” the student began. “For example, you can go outside on a sunny day and measure the height of a barometer and its shadow, and measure the length of a building's shadow. Then, solving a simple proportion, determine the height of the building itself.
"Not bad," I said. "Are there other ways?"
"Yes. There is a very simple way, which I am sure you will like. You pick up the barometer and go up the stairs, placing the barometer against the wall and making marks. By counting the number of these marks and multiplying it by the size of the barometer, you get the height of the building. Quite an obvious method.
“If you want a more complicated way,” he continued, “then tie a string to the barometer and, swinging it like a pendulum, determine the amount of gravity at the base of the building and on its roof. From the difference between these values, in principle, you can calculate the height of the building. In the same case, by tying a string to the barometer, you can climb with your pendulum to the roof and, swinging it, calculate the height of the building from the precession period.
“Finally,” he concluded, “among the many other ways to solve the problem, perhaps the best is this: take the barometer with you, find the building manager and tell him: “Mr. manager, I have a wonderful barometer. It's yours if you tell me the height of this building."
Then I asked the student - did he really not know the generally accepted solution to this problem. He admitted that he knew, but said that he was fed up with school and college, where teachers impose their way of thinking on students.
This student was Niels Bohr (1885–1962), a Danish physicist who won the Nobel Prize in 1922.
Here are the possible solutions to this problem proposed by him:
1. Measure the time the barometer falls from the top of the tower. The height of the tower is uniquely calculated in terms of time and free fall acceleration. This solution is the most traditional and therefore the least interesting.
2. With the help of a barometer, which is on the same level with the base of the tower, let a sunbeam into the eye of an observer located at its top. The height of the tower is calculated based on the angle of elevation of the sun above the horizon, the angle of the barometer and the distance from the barometer to the tower.
3. Measure the floating time of the barometer from the bottom of the water-filled tower. Measure the rate of ascent of the barometer in the nearest pool or bucket. If the barometer is heavier than water, tie a balloon to it.
4. Put the barometer on the tower. Measure the amount of compression deformation of the tower. The height of the tower is found through Hooke's law.
5. Pour a bunch of barometers the same height as the tower. The height of the tower is calculated from the diameter of the base of the pile and the coefficient of shedding of barometers, which can be calculated, for example, using a smaller pile.
6. Attach the barometer to the top of the tower. Send someone upstairs to take a reading from the barometer. The height of the tower is calculated based on the speed of movement of the sent person and the time of his absence.
7. Rub the wool on the top and at the base of the tower with a barometer. Measure the force of mutual repulsion of the top and bottom. It will be inversely proportional to the height of the tower.
8. Bring the tower and barometer into outer space. Install them motionless relative to each other at a fixed distance. Measure the time the barometer falls on the tower. The height of the tower is found in terms of the mass of the barometer, the fall time, the diameter and the density of the tower.
9. Put the tower on the ground. Roll the barometer from top to bottom, counting the number of revolutions. (A method that has become popular in Russia under the code name "named after 38 parrots").
10. Bury the tower in the ground. Take out the tower. Fill the resulting hole with barometers. Knowing the diameter of the tower and the number of barometers per unit volume, calculate the height of the tower.
11. Measure the weight of the barometer on the surface and at the bottom of the pit obtained in the previous experiment. The difference in values ​​will uniquely determine the height of the tower.
12. Tilt the tower. Tie a long rope to the barometer and lower it to the ground. Calculate the height of the tower from the distance from where the barometer touches the ground to the tower and the angle between the tower and the rope.
13. Put the tower on the barometer, measure the barometer deformation. To calculate the height of the tower, you must also know its mass and diameter.
14. Take one atom of the barometer. Put it on top of the tower. Measure the probability of finding the electrons of a given atom at the foot of the tower. It will unambiguously determine the height of the tower.
15. Sell the barometer on the market. With the proceeds, buy a bottle of whiskey, with which you can find out the height of the tower from the architect.
16. Heat the air in the tower to a certain temperature, having previously sealed it. Make a hole in the tower, near which to fix the barometer on the spring. Draw a graph of spring tension versus time. Integrate the graph and, knowing the diameter of the hole, find the amount of air released from the tower due to thermal expansion. This value will be directly proportional to the volume of the tower. Knowing the volume and diameter of the tower, we simply find its height.
17. Use a barometer to measure the height of half of the tower. Calculate the height of the tower by multiplying the resulting value by 2.
18. Tie a tower-length rope to the barometer. Use the resulting design instead of the pendulum. The period of oscillation of this pendulum will uniquely determine the height of the tower.
19. Pump air out of the tower. Upload it there again in a strictly fixed amount. Measure the pressure (!) inside the tower with a barometer. It will be inversely proportional to the volume of the tower. And we have already found the height by volume.
20. Connect the tower and the barometer into an electrical circuit, first in series and then in parallel. Knowing the voltage, the resistance of the barometer, the resistivity of the tower, and having measured the current in both cases, calculate the height of the tower.
21. Put the tower on two supports. Hang a barometer in the middle. The height (or in this case, the length) of the tower is determined by the amount of bending caused by the weight of the barometer.
22. Balance the tower and the barometer on the lever. Knowing the density and diameter of the tower, the arms of the lever and the mass of the barometer, calculate the height of the tower.
23. Measure the difference between the potential energies of the barometer at the top and at the base of the tower. It will be directly proportional to the height of the tower.
24. Plant a tree inside the tower. Remove unnecessary parts from the barometer body and use the resulting vessel to water the tree. When the tree grows to the top of the tower, cut it down and burn it. Determine the height of the tower by the amount of energy released.
25. Place the barometer at an arbitrary point in space. Measure the distance between the barometer and the top and between the barometer and the base of the tower, as well as the angle between the direction from the barometer to the top and bottom. Calculate the height of the tower using the law of cosines.
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Bohr, Niels Henrik David. Quotes (from Wikiquote)
* Your theory is crazy, but not crazy enough to be true.
(Said to Wolfgang Pauli regarding the electron spin.)
* If quantum theory hasn't shocked you, you haven't understood it yet.
* Every sentence uttered by me should be considered not as a statement, but as a question.
* How wonderful that we are faced with a paradox. Now we have hope for promotion!
* Never express yourself more clearly than you can think.
* Nothing exists until it is measured.
* No, but I've been told that it works even if you don't believe it.
(When asked if he really believes that a horseshoe over his door brings good luck.)
* The inverse of a true statement is a false statement. However, the opposite of a great truth may be another great truth.
* It is very difficult to make an accurate forecast, especially about the future.
* Truth is complemented by clarity.
* Stop telling God what to do.
(An answer to Einstein's famous saying: "God does not play dice." When quoting, it is sometimes added: "... with his bones")
* An expert is a person who has made all possible mistakes in some narrow field.
* Our language reminds me of this dishwashing. We have dirty water and dirty towels, and yet we want our plates and glasses to be clean. It's the same with language. We work with obscure concepts, we operate with logic, the limits of which are unknown, and for all that, we still want to bring some clarity to our understanding of nature.

Altimeter(in the first half of the 20th century - altimeter, from lat. altus - "high", in modern English also altimeter) - a device indicating the flight altitude. At present, the most commonly used definition altimeter. In aviation, they are used for barometric and radio engineering(otherwise radio altimeter) ways to determine the height.

Modern radio altimeters use frequency (low-altitude radio altimeters) and pulse (high-altitude radio altimeters) methods of measuring altitude. They show the true flight altitude, which is their advantage over barometric altimeters, since the barometric altitude, as a rule, differs from the true one.

A barometric altimeter is an ordinary barometer with an altitude scale instead of a pressure scale. Such an altimeter determines the aircraft's flight altitude indirectly by measuring atmospheric pressure, which changes with altitude according to a certain law. The barometric method of measuring height is associated with a number of errors, which, if not taken into account, lead to significant errors in determining the height. Despite this, barometric altimeters are widely used in aviation due to their simplicity and ease of use. Barometric altimeters have instrumental, aerodynamic and methodological errors.

• Instrumental altimeter errors occur due to imperfections in the manufacture of the instrument and inaccuracies in its adjustment. The causes of instrumental errors are imperfection in the manufacture of altimeter mechanisms, inaccuracy and inconstancy of adjustments, wear of parts, changes in the elastic properties of the aneroid box, backlash, etc. Each altimeter has its own instrumental errors. They are determined by checking the altimeter at the control installation, entered into a special table and taken into account in flight.
• Aerodynamic errors result from inaccurate altimeter measurements of atmospheric pressure at flight altitude due to distortion of the air flow around the aircraft, especially when flying at high speeds. The magnitude of these errors depends on the speed and altitude of the flight, the type of receiver that senses atmospheric pressure, and its location. For example, at an altitude of 5000 m, an error in measuring pressure of 1 mm Hg. Art. gives an altitude error of 20 m, and at an altitude of 11,000 m the same pressure measurement error causes an altitude measurement error of about 40 m. Aerodynamic errors are determined during aircraft flight tests and entered in the correction table. To simplify the accounting for instrumental and aerodynamic corrections, a table of altimeter readings is compiled, taking into account the total corrections, which is placed in the aircraft cockpit.
• Methodological errors arise due to the discrepancy between the actual state of the atmosphere and the calculated data that form the basis for calculating the altimeter scale. The altimeter scale is calculated for the conditions of the standard atmosphere (ISA) at sea level: air pressure P0 = 760 mm Hg. Art., temperature t0 = + 15° С, temperature vertical gradient trp = 6.5° per 1000 m altitude. The use of a standard atmosphere assumes that a given altitude corresponds to a well-defined pressure. But since in each flight the actual atmospheric conditions do not coincide with the calculated ones, the altimeter shows the height with errors. The barometric altimeter is also subject to errors due to the fact that it does not take into account changes in the topographic relief of the terrain over which the aircraft flies. Methodological errors of the barometric altimeter are divided into three groups:
  • Errors from changes in atmospheric pressure near the ground. In flight, the barometric altimeter measures altitude relative to the pressure level set on the altimeter's pressure scale. It does not take into account pressure changes along the route. Typically, atmospheric pressure at different points on the earth's surface at the same moment is not the same. Before departure, the altimeter needles are set to zero, and the altimeter pressure scale will be set to the pressure of the departure aerodrome. If a pilot on a route over flat terrain maintains a given indicated altitude, then the true altitude will vary depending on the distribution of atmospheric pressure near the ground. With a drop in atmospheric pressure along the route, the true altitude will decrease, with an increase in pressure, it will increase. The change in true altitude is due to the change in ground pressure over the area being flown relative to the pressure set on the altimeter. The change in atmospheric pressure with height is characterized by a barometric step - the height corresponding to a change in pressure by 1 mm Hg. Art. The barometric step is different at different altitudes. As altitude increases, the barometric step increases. In practice, the barometric step for low altitudes is taken equal to 11m. Therefore, for every millimeter of pressure change near the ground, there is a corresponding height of 11.1 m.
  • Errors from changes in air temperature. It occurs due to the deviation of the temperature near the earth from the temperature of the standard atmosphere. When the temperature near the ground drops below 15°C, the altimeter will show an underestimated value of the altitude and vice versa. The temperature error can reach a value equal to 8-12% of the measured height. The temperature error is taken into account