How to descend from the sky scientifically?

When I was a kid, I watched "Kung Fu" and thought the Tathagata Palm was so cool. I fantasized that one day I would be able to descend from the sky like this.

Later, after I studied physics, especially after learning about free fall, I realized that this fantasy would never come true. Then I also doubted the scientific nature of the "falling from the sky" scenes in movies, TV shows and literary works. Hey, who made me study physics╮（╯＿╰）╭.

Falling from the sky with an umbrella

Curtain parachute

And the clothes and pants parachute below.

It turned out that Ouyang Feng was trapped on the top of Tumu Peak. Although he was a martial artist, he could not slide down from the peak. After several days of freezing and starvation, he suddenly came up with an idea. He took off his pants and tied both legs tightly. Fearing that his pants would not be tight, he took off his clothes and tied them to his pants. He held the waistband with both hands, gritted his teeth and jumped down from the mountain. This method was originally very risky, but it was just a way to survive. There was no other way. Sure enough, one of his pants was filled with air, which greatly reduced his downward momentum.

——The Legend of the Condor Heroes Chapter 37: Falling from the Sky

If you want to know how to drop from the sky scientifically, you first need to know what happens in the air when you drop from the sky.

Terminal velocity

We learned about free fall in high school, but this did not take into account the effect of air resistance. When an object falls from a high altitude, if it is in free fall, its speed will continue to increase. But in fact, due to the existence of air resistance, the speed of an object falling from a high altitude will not increase indefinitely, but has a limit, which is called terminal velocity.

If we ignore the buoyancy of air, we get the following formula:

Fd is the air resistance;

ρ is the density of the air in which the object is falling;

v is the velocity of the falling object;

cd is the drag coefficient of the object, which is related to factors such as the shape of the object;

A is the projected area of ​​the object.

When the falling speed of an object is high enough, the air resistance and gravity are equal in magnitude and opposite in direction , so the falling speed no longer increases and reaches the terminal velocity. The terminal velocity of the falling object can be calculated as follows:

If a skydiver takes a prone position and does not open his parachute, his terminal velocity is about 55m/s (~195km/h) , which is about the same speed as the D-type EMU trains in China. If a skydiver folds his limbs and points his head downward, performing a similar movement as when Iron Man flies, his terminal velocity will increase to 90m/s (~320km/h), which is almost as fast as the speed of a peregrine falcon when it is chasing its prey downwards [1].

On August 16, 1960, US Air Force Captain Joseph Kittinger set a record when he jumped from a helium balloon basket floating at an altitude of 31,330 meters. During the descent, his maximum speed reached 274 meters per second , which is about 9/10 of the speed of sound [2]. This record was not broken until 2012, when Felix Baumgartner flew to an altitude of 39,045 meters on a high-altitude helium balloon and jumped down, reaching a maximum speed of 373 meters per second , breaking the speed of sound. Of course, this maximum speed was achieved at high altitudes because the atmosphere there is thin.

Joseph Kittinger | Source: Wikipedia

After saying so much, what I actually want to express is: if you want to fall from the sky scientifically, the way is to increase the air resistance . When you want to increase the air resistance when falling, you may first think of a parachute. The parachute mainly increases the air resistance through a huge projected area.

A parachute can reduce terminal velocity by more than 90% , so a person wearing a parachute can hit the ground at a relatively low speed of 3-4 m/s (~12 km/h) [3].

There are two main types of common parachutes, one is a round parachute and the other is a wing parachute .

Round umbrella | Source: explainthatstuff.com

Parafoil | Source: explainthatstuff.com

As the name suggests, a round parachute is a round parachute that looks like a jellyfish. A parachute consists of a main parachute and a reserve parachute . The reserve parachute is used when the main parachute cannot be opened.

A circular parachute structure (1 is the guide parachute, 3 is the top hole of the parachute, 4 is the main parachute, and 9 is the control stick) | Source: explainthatstuff.com

There are generally two ways to open the main parachute: one is to pull the parachute bag open with the rope, and the pilot parachute in the parachute bag pops out first, generating enough tension to pull the main parachute open . The other is to pull the stabilizing parachute open with the rope , and at the same time the unlocking device starts timing. After a few seconds, the restriction on the stabilizing parachute is released, so that the main parachute is pulled out and opened [4]. The 1 in the above figure is the pilot parachute.

The small parachute in the picture is a stabilizer parachute | Source: "Our Sky" WeChat official account

The tension increases rapidly after the main parachute is released, as you can see from this diagram.

Schematic diagram of the force changes on a skydiver after parachuting | Source: hypertextbook.com

If you pay close attention, you will find that there always seem to be several "holes" on the dome. These are actually exhaust holes , not "holes", and they are intentional. The top hole is called the top hole , which allows air to escape slowly from the top of the dome instead of escaping from the "skirt" of the dome, which helps reduce the shaking of the parachute . In addition, you can use the joystick to control the opening and closing of the front and rear exhaust holes, thereby controlling the landing speed, changing the direction of movement, and reducing the impact of the stratus wind and shaking.

The "skirt" of the parachute has front and rear exhaust holes | Source: "Our Sky" WeChat official account

What will happen if you use an umbrella as a parachute? If your umbrella is not strong enough, it will either be blown over or the umbrella and ribs will be blown apart; if the umbrella is strong enough, don't be too happy, because the umbrella will be blown sideways. So, forget about using an umbrella as a parachute.

Source: Guokr.com[5]

In addition to the round parachute, another common type is the wing parachute, which is the abbreviation of the wing-shaped parachute, also called the wing-shaped gliding parachute or the gliding parachute . As the name suggests, it can glide in the air. Most wing parachutes are rectangular and designed as stamping.

Ramfoil parafoil | Source: hypertextbook.com

The so-called ram type is like the picture above. The upper and lower wing surfaces of the parafoil are made of airtight fabric. The upper and lower wing surfaces are connected by ribs and divided into many small air chambers. There are ventilation holes on each rib to facilitate air circulation between the air chambers, so that the parachute can be quickly inflated when descending.

Source: China Military TV

The leading edge of the parafoil is open and the trailing edge is closed. When gliding, air rushes in from the leading edge opening, filling each small air chamber to form a wing shape , which has good maneuverability.

Source: China Military TV

Both circular parachutes and wing parachutes are used in the military, but their usage scenarios are different. The main reason is that the descent ratio and maneuverability of the two parachutes are different.

The glide ratio is the ratio of the speed in the horizontal direction to the speed in the vertical direction after the speed is decomposed into two directions: vertical and horizontal. The glide ratio of a round parachute is generally about 1:1 , while a wing parachute has better gliding ability because of its wing shape. The glide ratio is generally 3:1 . At the same altitude, the air time of a round parachute will be shorter than that of a wing parachute, which is convenient for rapid landing. In addition, a wing parachute is more maneuverable than a round parachute, making it easier to land accurately.

Precise landing, hitting the bull's eye | Source: "Our Sky" WeChat official account

The circular parachute is very suitable for quickly deploying a large number of troops in a relatively small area and at a relatively low altitude . However, because it is difficult for parachutists to control the landing point of the circular parachute, they need to fly the aircraft over the target area before they can parachute and land. This requires facing enemy artillery fire, which is dangerous and lacks surprise. Therefore, the enemy's air defense system must be destroyed before landing, otherwise the airborne troops may suffer heavy losses before landing. [6]

The circular parachute can deliver troops in a dense manner | Source: Wikipedia

A parafoil can glide horizontally 3 meters for every meter it descends, so it can glide long distances in the air. If a parachutist jumps at an altitude of 5,000 meters, he or she can glide to a landing 15 kilometers away. Well-trained paratroopers can parachute at a considerable distance from the target area, then control the parafoil to avoid obstacles and dangerous areas, glide to the target area and land, greatly improving the concealment and suddenness of the operation.[6]

However, it is difficult and dangerous to control parafoils in the air, and it requires high parachuting skills of paratroopers. Therefore, parafoils are mainly used for early penetration raids in airborne operations, to meet subsequent large airborne troops, or to perform certain special operations tasks.

There is a scene in Operation Red Sea where parafoils appear. In the yellow cake snatching scene at the end of the movie, in order to launch a surprise attack quietly, the team members started gliding in wing suits when they were still two kilometers away from the target location, and then opened the parafoil to land, achieving a surprise effect.

Wingsuits and parafoils in the movie "Operation Red Sea"

To become a qualified skydiver, you need to go through a lot of training, for example, some may need to practice high-altitude free fall in a wind tunnel. There is a huge fan below that can blow people up to simulate the scene of skydiving.

Wind Tunnel Training

Skydivers train in a wind tunnel | Source: ForGIFs.com

Finally, let's answer the question mentioned at the beginning of the article. Umbrellas cannot safely drop from the sky, so can curtains? Let's do some calculations. Reference [7] is a rocket parachute size calculator . By inputting the mass of the rocket, the required parachute diameter can be calculated. Although humans and rockets are different, it is not a bad idea to treat humans as rockets and do the calculations. Assuming the mass is 60kg, if the speed is 4m/s, the diameter of the parachute needs to be about 10m. So the question is, where can we find such a large curtain?

So, forget about the curtain parachute or the clothes parachute. Let’s descend from the sky scientifically using the crystallization of science - the parachute.

Alas, after studying physics, life not only lacks miracles, but also lacks fantasy. Life after studying physics is so plain, boring and dull.