Applied Geodesy. We measure the height with a pencil, mirror or balloon

Recommendation points

• Determining the height of an inaccessible object
• Statistical evaluation method
• Photo score
• Ball pen
• Shadow measurement
• Mirror method
• Balloon
• Piano in the bushes

Sizing of inaccessible objects is easiest to accomplish with specialized surveying equipment. Modern electronic total stations with reflectorless measurement mode, laser tape measures and altimeters greatly simplify the task, allowing you to measure the height of a tree or the width of a river.

Unfortunately, not everyone can afford to have equipment worth several thousand dollars in stock in the pantry, and sometimes you have to deal with such tasks at the household level. To solve these problems, knowledge drawn from the cycle “Applied Geodesy” comes to our aid: “History of the industry”, “Choosing an electronic total station”, “Independent measurements using a tape measure, pegs and ingenuity”, a school geometry course, well, a little ingenuity (where without her).

Determining the height of an inaccessible object

To determine the location of the future cottage or any other building, it is important to know the heights of nearby objects, such as poles or dry trees. This will exclude the possibility of destruction of your property from the fall of the object in the event of a natural disaster or for any other reason..

Another important point before the start of construction is determining the height of the sagging of the wires of the power lines passing in the area of ​​the site. The construction crane can touch the power line, which will lead to dire consequences. Do not forget about the breakdown voltage – there is a possibility of electric shock even a few meters from the high voltage wire in wet weather.

For the experiment, we will try to determine the height of the 10 kV power transmission line from the ground to the upper insulator by various methods and write the obtained values ​​into the table.

Statistical evaluation method

It is also popularly called the “by eye” method. Its essence lies in the visual comparison of a known height and an inaccessible one. For convenience, you place a stick with a known height vertically near the object to be measured. The “standard” for comparison should be as high as possible. Having moved away at a convenient distance, estimate the height, and write down the result in the table. As you can imagine, one person cannot make “measurements” accurately, therefore, to get a good result, ask your relatives or friends to perform similar actions. The more people participate in the “measurements” – the more accurate the result.

Then comes the processing time: discard the extreme values ​​(maximum and minimum), and from the rest of the results calculate the arithmetic mean. The resulting value will give an idea of ​​the height of the inaccessible object. The error of this method depends on the experience of people and the quality of their spatial orientation..

Photo score

The rapid development of technology has made it possible to integrate a camera into almost any modern gadget, so the selection of equipment for such an experiment will not be difficult. The essence is the same – an estimate of the height of an inaccessible object, but not by eye, but by calculating the proportion between the photographic image of the reference and its real height.

You place a stick with a known height near the object to be measured (we used a geodetic pole), move a distance when the top of the object is placed in the frame. Ideally, the height of the reference and the shooting level should be approximately the same, and the camera itself should be kept level. If possible, use a photographic tripod, the height of which should be adjusted according to the tape measure.

Dump the image onto your computer and brush up on the information from our article series in which we introduced the concept of scale. We got an image, the dimensions of which are proportional to the dimensions in nature, we just need to calculate the scale and recalculate the height of the inaccessible object. To do this, you can print a photo for measurements with a ruler or use any image processing program that allows you to measure distances in a photo in centimeters.

This method is more progressive, but requires a computer and a camera, and in the field this cannot always be achieved..

Ball pen

There is always a writing device in the desk, and it will help us in determining the height of an object using the perspective method. Instead of a pen, you can use a pencil, straight stick, or any other similar object. We also need an assistant and a tape measure..

We move away to such a distance when we will see the whole object of measurements. Clutching the pen in a fist, we extend a straight arm in front of us so that its tip coincides with the top of the object. Extend your thumb to the side, parallel to the ground, so that you end up with a right angle. Then we turn the brush with a ballpoint pen 90 degrees, as a result, our thumb looks at the ground parallel to the object being measured, and the tip of the pen indicates the place where the assistant needs to move.

We have projected the height of the object by parallel translation to the ground. Now it will not be difficult to measure the distance obtained with a tape measure from the assistant to the post, it will be equal to the determined height. The method is well suited for field conditions, quite accurate, but requires an assistant.

Shadow measurement

The method used by the ancient Egyptians and Greeks is easily reproduced in modern realities and requires a minimum of labor. To determine the height, we need to simultaneously measure the length of the shadow from an object with a known height and the length of the shadow from an inaccessible object.

Measurements should be made in the evening or morning, when the length of the shadow is maximum. This will eliminate errors, and the result is calculated by compiling the simplest proportion:

Pillar height = person’s height * pillar shadow length / person’s shadow length

Mirror method

The angle of incidence is known to be equal to the angle of reflection. We will use this postulate to calculate the inaccessible height. We put the mirror on the ground approximately as shown in the photo, move aside until the top of the measured object is reflected in the mirror.

We measure the required distances from a person to a mirror, from a mirror to a pillar, and get the required height after calculating the proportion.

Post height = person’s height * distance from mirror to post / distance from person to mirror

Balloon

You can take measurements according to the “Winnie the Pooh method” to please your own children. Despite some comic, he also has the right to life, tk. under favorable conditions it gives acceptable results.

For work we need a ball filled with inert gas, a rope and a tape measure. Gently release the ball on a string parallel to the object being measured, when it reaches the top, fix the height of the string, lower the ball and measure the required distance with a tape measure. To get a more accurate value, your assistant should move a significant distance to more accurately visualize the location when the height of the ball and the object is equal. We cite this method as one of the alternative, so we will not conduct laboratory tests using it..

Piano in the bushes

We have covered several basic methods for measuring the height of an inaccessible object. I would like to find out which one is the most accurate. This will help us “piano in the bushes” – an electronic tacheometer with special software that allows you to get the height value in the field.

For convenience, we will enter all the values ​​in the table, which will give us the necessary clarity. As can be seen from the table, all methods have a small error, but this is quite enough to estimate the height of an inaccessible object..

Method of measurement	Received value, m	Error,%
statistical evaluation	ten	4
the photo	nine	6
ball pen	9.2	4
shadow	10.25	7
mirror	8.90	7
electronic total station	9.57	0

The arithmetic mean of the obtained values ​​is 9.47 m, so to obtain an optimal result, the methods must be combined, and the obtained values ​​must be averaged. In case you need high accuracy, you can purchase a pendulum altimeter, which is used by foresters for taxation of green spaces.

Well, the most accurate result will be obtained when ordering a topographic survey. In the terms of reference, it is worth noting a special requirement – measuring the heights of trees and other inaccessible objects. As you can imagine, this will affect the estimated cost of the work, so we will devote the next article from our cycle to estimates. Incomprehensible terms may hide unnecessary work processes, and vice versa, some important points may fall out of sight due to ignorance. Armed with this knowledge, you will be able to communicate with specialists almost on an equal footing, which will ultimately save money.