Parachutist's descent. How long does a skydive last? Drag coefficient of various bodies

Critical speed of falling body. It is known that when a body falls in the air, it is affected by the force of gravity, which in all cases is directed vertically downward, and the force of air resistance, which is directed at each moment in the direction opposite to the direction of the speed of fall, which in turn varies both in magnitude and and in direction.

Air resistance acting in the direction opposite to the movement of the body is called drag. According to experimental data, the force of drag depends on the density of the air, the speed of the body, its shape and size.

The resultant force acting on a body imparts acceleration to it a, calculated by the formula a = G – Q , (1)

Where G- gravity; Q– air drag force;

m- body mass.

From equality (1) follows that

If G –Q > 0, then the acceleration is positive and the speed of the body increases;

If G –Q < 0, then the acceleration is negative and the speed of the body decreases;

If G –Q = 0, then the acceleration is zero and the body falls at a constant speed (Fig. 2).

The set rate of fall of the parachute. The forces that determine the trajectory of a parachutist’s movement are determined by the same parameters as when any body falls in the air.

Drag coefficients for various positions of the parachutist's body when falling relative to the oncoming air flow are calculated by knowing the transverse dimensions, air density, air flow speed and measuring the amount of drag. To make calculations, a value such as mid-section is required.

Midsection (midship section)– the largest cross-section by area of ​​an elongated body with smooth curved contours. To determine the parachutist's midsection, you need to know his height and the width of his outstretched arms (or legs). In practice, calculations take the width of the arms equal to the height, thus the midsection of the parachutist is equal to l 2 . The midsection changes when the position of the body in space changes. For the convenience of calculations, the midsection value is assumed to be constant, and its actual change is taken into account by the corresponding drag coefficient. Drag coefficients for various positions of bodies relative to the oncoming air flow are given in the table.

Table 1

Drag coefficient of various bodies

The steady-state speed of a body's fall is determined by the mass density of the air, which varies with height, the force of gravity, which changes in proportion to the mass of the body, the midsection and the drag coefficient of the parachutist.

Lowering the cargo-parachute system. Dropping a load with a parachute canopy filled with air is a special case of an arbitrary body falling in the air.

As with an isolated body, the landing speed of the system depends on the lateral load. Changing the area of ​​the parachute canopy F n, we change the lateral load, and therefore the landing speed. Therefore, the required landing speed of the system is provided by the area of ​​the parachute canopy, calculated from the operating limitations of the system.

Parachutist's descent and landing. The steady speed of the parachutist's fall, equal to the critical speed of filling the canopy, is extinguished when the parachute opens. A sharp decrease in the falling speed is perceived as a dynamic shock, the strength of which depends mainly on the speed of the parachutist’s fall at the moment the parachute canopy opens and on the time of parachute opening.

The required deployment time of the parachute, as well as the uniform distribution of the overload, is ensured by its design. In landing and special-purpose parachutes, this function is in most cases performed by a camera (cover) placed on the canopy.

Sometimes, when opening a parachute, a parachutist experiences a six to eightfold overload within 1–2 seconds. The tight fit of the parachute suspension system, as well as the correct grouping of the body, helps reduce the impact of the dynamic impact force on the paratrooper.

When descending, the parachutist moves, in addition to the vertical, in the horizontal direction. Horizontal movement depends on the direction and strength of the wind, the design of the parachute and the symmetry of the canopy during descent. On a parachute with a round dome, in the absence of wind, the parachutist descends strictly vertically, since the pressure of the air flow is distributed evenly over the entire inner surface of the canopy. An uneven distribution of air pressure over the surface of the dome occurs when its symmetry is affected, which is carried out by tightening certain slings or free ends of the suspension system. Changing the symmetry of the dome affects the uniformity of air flow around it. The air coming out from the side of the raised part creates a reactive force, as a result of which the parachute moves (slides) at a speed of 1.5 - 2 m/s.

Thus, in a calm situation, in order to move a parachute with a round canopy horizontally in any direction, it is necessary to create glide by pulling and holding in this position the lines or free ends of the harness located in the direction of the desired movement.

Among special-purpose paratroopers, parachutes with a round dome with slots or a wing-shaped dome provide horizontal movement at a sufficiently high speed, which allows the paratrooper, by turning the canopy, to achieve greater accuracy and safety of landing.

On a parachute with a square canopy, horizontal movement in the air occurs due to the so-called large keel on the canopy. The air coming out from under the canopy from the side of the large keel creates a reaction force and causes the parachute to move horizontally at a speed of 2 m/s. The skydiver, having turned the parachute in the desired direction, can use this property of the square canopy for a more accurate landing, to turn into the wind, or to reduce the landing speed.

In the presence of wind, the landing speed is equal to the geometric sum of the vertical component of the descent speed and the horizontal component of the wind speed and is determined by the formula

V pr = V 2 dc + V 2 3, (2)

Where V 3 – wind speed near the ground.

It must be remembered that vertical air flows significantly change the speed of descent, while downward air flows increase the landing speed by 2 - 4 m/s. Rising currents, on the contrary, reduce it.

Example: The paratrooper's descent speed is 5 m/s, the wind speed at the ground is 8 m/s. Determine the landing speed in m/s.

Solution: V pr = 5 2 +8 2 = 89 ≈ 9.4

The final and most difficult stage of a parachute jump is landing. At the moment of landing, the parachutist experiences an impact on the ground, the strength of which depends on the speed of descent and on the speed of loss of this speed. Almost slowing down the loss of speed is achieved by special grouping of the body. When landing, the paratrooper groups himself so as to first touch the ground with his feet. The legs, bending, soften the force of the blow, and the load is distributed evenly over the body.

Increasing the parachutist's landing speed due to the horizontal component of wind speed increases the force of impact on the ground (R3). The force of the impact on the ground is found from the equality of the kinetic energy possessed by the descending parachutist and the work produced by this force:

m P v 2 = R h l c.t. , (3)

R h = m P v 2 = m P (v 2 sn + v 2 h ) , (4)

2 l c.t. 2l c.t.

Where l c.t. – the distance from the parachutist’s center of gravity to the ground.

Depending on the landing conditions and the degree of training of the parachutist, the magnitude of the impact force can vary within wide limits.

Example. Determine the impact force in N of a parachutist weighing 80 kg, if the descent speed is 5 m/s, the wind speed at the ground is 6 m/s, and the distance from the center of gravity of the parachutist to the ground is 1 m.

Solution: R z = 80 (5 2 + 6 2) = 2440 .

2 . 1

The impact force during landing can be perceived and felt by a skydiver in different ways. This depends largely on the condition of the surface on which it lands and on how it is prepared to meet the ground. Thus, when landing on deep snow or soft ground, the impact is significantly softened compared to landing on hard ground. If a paratrooper sways, the force of the impact upon landing increases, since it is difficult for him to take the correct body position to take the blow. The rocking must be extinguished before approaching the ground.

When landing correctly, the loads experienced by the paratrooper are small. To evenly distribute the load when landing on both legs, it is recommended to keep them together, bent so much that under the influence of the load they can, springing, bend further. The tension in the legs and body must be maintained evenly, and the higher the landing speed, the greater the tension.

The speed at which a skydiver falls depends on the time of fall, air density, area of ​​the falling body and drag coefficient. The weight of the falling body has little effect on the speed of falling.

A body falling in the air is acted upon by two forces: the force of gravity, always directed downward, and the force of air resistance, directed against the force of gravity. The speed of the fall will increase until the force of gravity and the force of air resistance are balanced. At the beginning of the body's movement in the air, the speed increases, then it becomes slower, and finally, at 11-12 seconds, the speed becomes almost constant. This condition is called steady decline, and the corresponding speed is maximum speed.

In addition to the duration of the fall, the speed of the body is greatly influenced by the height of the jump, weight, size and position of the body.

Since the density of air changes with height, the speed of fall will also change. The farther from the ground, the greater the speed of fall, because... air density decreases. The speed of your fall will not exceed 35 m/sec. After separation from the plane, you will descend under the stabilizing canopy.

Loads arising when the parachute opens.

The fit of the harness system is of great importance in relation to the load taken during parachute deployment. The more evenly and densely the straps lie, the more evenly it is distributed over the body. To bear loads, the condition of the body is essential - whether it is tense or relaxed. In anticipation of the breakthrough, the skydiver must group and tense his muscles. In this case, the “blow” will be endured much easier. The head should not be turned to the side or tilted, because straps may cause bruises.

Control of a parachute in the air and its physical essence.

Parachute control means the ability to change its position in space by maneuvering in direction and speed. Horizontal movement can also be achieved on a round dome.

To create horizontal forward movement needs tightening front straps, creating a sliding dome, and holding it in this position for the time necessary to move. In this case, the horizontal speed will be approximately = 1.5 - 2 m/s.

In order to obtain horizontal movement back, left, right, it is necessary to pull the rear, left or right straps accordingly.

When the lines are pulled up, the edge lowers, a canopy skew is created, while the main part of the air begins to exit from the opposite side, a reactive force is created and the parachutist begins to move.

Paratrooper descent on one and two canopies.

The parachutist's speed relative to the ground when landing depends on: rate of descent; wind speed; parachute control; presence of rocking.

The vertical speed of the parachute system depends on: the weight of a person with a parachute; parachute canopy drag coefficient, which depends on the area, shape of the canopy and air permeability of the material; air density.

It is approximately believed that if body weight is increased by 10%, then this causes an increase in the rate of decline by 5%.

For example: the weight of a parachutist with a D-6 parachute is 100 kg - descent speed = 5.0 m/s, and with a weight of 110 kg vertical speed = 5.25 m/s.

Depending on the altitude of the area above sea level, the rate of decline is measured something like this: with an increase of 200m, the rate increases by 1%. In winter, in frosty weather, when the air density increases slightly, the rate of decline can be considered 5% less than in summer in hot weather.

The parachutist's descent on two canopies is reduced slightly compared to the rate of descent on one canopy. The reason for the slight decrease in vertical speed is the collapse of the two domes during descent, which entails a decrease in the area of ​​the domes operating relative to the ground.

Reply for Guest.

Belly to ground position, top speed about 200 km/h. Upside down 240-290 km/h. Further minimization of 480 km/h.

Records:
Christian Labhart SUI World Cup 2010-Finland-Utti-4/6 June 2010 526.93 Km/h
Clare Murphy GBR World Cup 2007-Finland-Utti-15/17 June 2007 442.73 Km/h

The maximum speed of falling in air is the limiting value. And this limit is reached over a very short distance - about 500 meters. This means that a person who fell from the top of the Ostankino TV tower, and a person who fell out of an airplane at an altitude of 10 km, will not accelerate more than 240 km/h. But this speed depends on different inputs. For example, from a person’s clothing, the position of his body. For skydivers, for example, the maximum speed ranges from 190 km/h at maximum air resistance, when they fall flat with their arms outstretched, to 240 km/h when diving like a fish or a soldier.

The chances of surviving a fall from an airplane do not seem remote. American amateur historian Jim Hamilton collects statistics on such cases.

Here are some of them:

In 1972, Serbian flight attendant Vesna Vulović fell from a DC-9 plane that exploded over Czechoslovakia. The girl flew 10 kilometers, sandwiched between her seat, a buffet cart and the body of another crew member. She landed on a snowy mountain slope and slid along it for a long time. As a result, she received serious injuries, but remained alive...

In 1943, American pilot Alan Magee flew a combat mission over France. He was thrown from a B-17. After flying 6 kilometers, it broke through the glass roof of the railway station. Almost immediately he was captured by the Germans, who were shocked to see him alive.

Already in our time, one skydiver with a parachute that did not open fell onto a high-voltage transmission line. The wires springed and threw him up, in the end he survived.

In 1944, British pilot Nicholas Alkemade fell from a height of six kilometers. He landed in a snowy thicket and escaped with only minor injuries. Convinced of the latter, Nicholas stood up from the snowdrift and lit a cigarette.

In 1971, a Lockheed L-188A Electra was caught in a storm over the Amazon. Of the 92 people, 91 died. But 17-year-old German girl Juliana Knopke survived, falling from a height of about 3 kilometers. She came to her senses the next morning. There was a jungle, debris and piles of Christmas presents that had fallen from the plane. Juliana was strapped to the chair. Her collarbone was broken. Her mother died along with the rest of the passengers. Taking a bag of sweets with her and trying not to think about her mother, Juliana hit the road. For ten days she wandered through the jungle, along streams and rivers, following the advice of her biologist father, “if you get lost in the jungle, you will come out to people by following the flow of water.”

She walked around the crocodiles and pounded the shallow water with a stick to scare away the stingrays. I tripped somewhere and lost my shoe. In the end, all she had left was a torn miniskirt. On the tenth day she saw a canoe. It took her several hours to climb the coastal slope to the hut, where she was discovered the next day by a team of lumberjacks.

According to statistics from the ACRO service, which records all aircraft accidents, from 1940 to 2008, 118,934 people died as a result of crashes. Only 157 survived.

Of these lucky ones, 42 survived after falling from a height of more than 3 kilometers.

In 1959-1962, several stratospheric balloons were built, designed to test space and aviation spacesuits and parachute systems for landing from high altitudes. Such stratospheric balloons were, as a rule, equipped with open gondolas; spacesuits protected the stratonauts from the rarefied atmosphere. These tests turned out to be extremely dangerous. Of the six stratonauts, three died and one lost consciousness during free fall.

The American Excelsior project included three high-altitude jumps from stratospheric balloons with a volume of 85,000 m³ with an open gondola, which were performed by Joseph Kittinger in 1959-1960. He tested a compensating pressure suit with a helmet and a two-stage parachute of the Beaupre system, consisting of a stabilization parachute with a diameter of 2 m, which should protect the parachutist from rotation when flying in the stratosphere and a main parachute with a diameter of 8.5 m for landing. In the first jump from a height of 23,300 m, due to the early deployment of the stabilization parachute, the pilot’s body began to rotate at a frequency of about 120 rpm and he lost consciousness. Only thanks to the automatic deployment system of the main parachute did Kittinger manage to escape. The second and third flights were more successful, despite the fact that in the third the right glove depressurized and the pilot’s hand became very swollen. In the third flight, which took place on August 16, 1960, Kittinger set several records at once - flight altitude on a stratospheric balloon, free fall altitude and speed developed by a person without the use of transport. The fall lasted 4 minutes 36 seconds, during which the pilot flew 25816 m and in some areas reached a speed of about 1000 km/h, very close to the speed of sound.

The StratoLab project included four substratospheric flights and five stratospheric ones, four of them with a sealed gondola and one (StratoLab V) with an open one. The flight of StratoLab V "Lee Lewis" took place on May 4, 1961. The stratostat with a volume of over 283,000 m³ was launched from the aircraft carrier Antietam in the Gulf of Mexico and 2 hours 11 minutes after launch reached a record altitude of 34,668 m. Stratonauts Malcolm Ross and Victor Preter were dressed in space suits spacesuits. After a successful splashdown, Preter died, unable to stay on the ramp while climbing onto the helicopter and choking. He depressurized the suit ahead of time, as he was sure that the danger had passed.

In the USSR, for such tests, the SS-Volga stratospheric balloon was used, created by OKB-424 (now the State Unitary Enterprise Dolgoprudny Automation Design Bureau) under the leadership of M. I. Gudkov, the sealed nacelle of which imitated the descent module of a spacecraft, and was equipped with a device for bleeding air and a downward ejection device (the first unmanned flight in 1959). On November 1, 1962, a manned record flight with parachute jumps took place. The stratospheric balloon with testers Evgeny Andreev and Pyotr Dolgov reached a height of 25458 m, after which the gondola was depressurized and Andreev ejected. He flew in free fall for about 24,500 m and landed safely. He holds the registered free fall altitude record (Kittinger's record was set using a stabilization parachute). Dolgov jumped from a height of 28,640 m, but accidentally depressurized his helmet during ejection due to an impact with a protruding element of the cockpit and died. The Stratonauts were awarded the title of Hero of the Soviet Union (Dolgov posthumously).
The SS-Volga stratostat was actively used not only for record-breaking parachute jumps, but also for quite ordinary test flights to test rescue systems, life support and other components and systems, and to study the state of the body during flight. Various test pilots (for example, the future pilot-cosmonaut of the USSR, Major V.G. Lazarev) each logged dozens of hours on it.

In 1965-1966, American skydiver Nicholas Piantanida made three attempts to break the records set by Andreev and Kittinger, initiating the StratoJump project. On October 22, 1965, the first attempt took place, lasting about 30 minutes. At an altitude of about 7 km, the balloon was damaged and the pilot escaped by parachute. During its second flight on February 2, 1966, the stratospheric balloon rose to a height of 37,600 m, setting a record that has not yet been broken. But Piantanida was unable to disconnect from the oxygen cylinder installed in the gondola and switch to the autonomous system of the suit, so the jump had to be cancelled. Following a command from the ground, the gondola separated from the stratospheric balloon and successfully descended by parachute. On May 1, 1966, the third flight took place, which ended in tragedy - during the ascent at an altitude of 17,500 m, the pressure suit depressurized and the parachutist died.

On September 3, 2003, an attempt was made to set a new stratospheric balloon flight altitude record. The QinetiQ-1 cylinder, 381 m high and with a volume of about 1,250,000 m³, manufactured by the British company QinetiQ, was supposed to lift an open gondola with two pilots dressed in space suits to an altitude of 40 km. The attempt ended in failure - some time after the balloon began to be filled with helium, damage was discovered in the shell and the flight was cancelled.

Let's assume that a parachutist makes a long jump (Fig. 3.28). Let the mass of the parachutist be the coefficient of air resistance when the parachutist moves with an unopened parachute and with an open

The parachutist's movement before the parachute opens will be uneven. During movement, two forces act on it (Fig. 3.29): the force of gravity and the force of air resistance. We will consider the downward direction positive. Let us write the equation for Newton’s second law for this case:

There are two unknowns in this equation: . The necessary additional equation will be the equation relating the force of air resistance to speed:

Substituting the value from this equation into the equation of Newton's second law, we get:

Let's use this equation and monitor the change in acceleration. According to the condition, at the initial moment the speed, therefore, and the force of air resistance are equal to zero. Therefore acceleration. In the first moments of movement, the speed quickly increases. Along with it, the force of air resistance increases, the difference in forces decreases and the acceleration begins to decrease. A graph of acceleration over time is shown in Fig. 3.30, a.

Since the acceleration a becomes less and less, then in subsequent periods of time the increase in speed and the change in the resistance force slow down more and more.

As can be seen from the equation, it is possible to indicate the maximum control speed at which the force of air resistance becomes equal to the force of gravity and the acceleration becomes zero. The value of this speed is determined from the equation

Using the graph (Fig. 3.30, b), you can track the change in speed. At first the speed increases quickly. Then its growth slows down, and it gradually approaches the value of control equal to the speed of steady-state uniform motion.

To summarize, we can say that at first the parachutist’s movement was accelerated, and then uniform. At the same time, its acceleration decreased from value to zero, and its speed increased from zero to a value corresponding to the steady motion.

No matter from what sufficiently high altitude the parachutist began to fall, he, with an unopened parachute, would approach the Earth at a constant speed equal to approximately

Thus, the action of air resistance forces completely changes the whole picture of the free fall of bodies: when falling in the air, all bodies move accelerated only in the initial, not very long period of time, and then their movement becomes uniform. Such a picture of the emergence of stationary uniform motion can be seen by observing the fall of a ball in a vessel with some viscous liquid (Fig. 3.31).

Now let's look at what happens when the parachute opens.

During the deployment of the parachute, the force of air resistance increases sharply, and the drag coefficient becomes equal to The resistance force becomes greater than the force of gravity (Fig. 3.32). Upward accelerations occur. The movement becomes slower, starting from the moment the parachute is fully deployed.