Have you ever wondered why skydivers reach maximum speed the moment they fall, even though the force of gravity in a fluid causes an object to accelerate continuously? A falling object will reach a constant speed when there is a holding force, such as air resistance. The force exerted by gravity near a massive body is mostly constant, but forces such as air increase the resistance the faster the object falls. If it has been in free fall for long enough, a falling object will reach such a speed that the drag force will equal that of gravity, canceling each other out and causing the object to fall at a constant speed until it hits the ground. This is called terminal speed.
Steps
Method 1 of 3: Calculate the Terminal Speed
Step 1. Use the terminal velocity formula, v = square root of ((2 * m * g) / (ρ * A * C))
Insert the following values into the formula to find v, the terminal velocity.
- m = mass of the falling object
- g = acceleration due to gravity. On earth this is about 9.8 meters per second squared.
- ρ = the density of the fluid through which the object is falling.
- A = area of the section of the object orthogonal to the direction of motion.
- C = drag coefficient. This number depends on the shape of the object. The slimmer the shape, the lower the coefficient. Some approximate coefficients can be searched here.
Method 2 of 3: Find the Force of Gravity
Step 1. Find the mass of the falling object
This should be measured in grams or kilograms, in the metric system.
If you are using the imperial system, remember that the pound is not actually a unit of mass, but of strength. The unit of mass in the imperial system is the pound-mass (lbm), that is the mass that, under the action of the gravitational force on the surface of the earth, would undergo a force of 32 pound-force (lbf). For example, if a person weighs 160 pounds on earth, that person is actually feeling 160 pounds of force f, but its mass is 5 lb m.
Step 2. Learn about the acceleration of Earth's gravity
Close enough to the earth to meet air resistance, this acceleration is 9.8 meters per second squared, or 32 feet per second squared.
Step 3. Calculate the downward force of gravity
The force with which the object falls is equal to the mass of the object due to the acceleration due to gravity: F = m * g. This number, multiplied by two, goes to the top of the terminal velocity formula.
In the British imperial system, this is the pound-force of the object, the number commonly referred to as "weight". More properly it is the mass in lbm per 32 feet per second squared. In the metric system, force is mass in grams per 9.8 meters per second squared
Method 3 of 3: Determine the Drag Force
Step 1. Find the density of the medium
For an object falling through the Earth's atmosphere, the density varies based on the altitude and air temperature. This makes it particularly difficult to calculate the terminal velocity of a falling object, since the density of the air changes with the loss of altitude of the object. However, you can look up the approximate air density on textbooks and other references.
As a rough guide, know that the density of air at sea level when the temperature is 15 ° C is 1,225 kg / m3.
Step 2. Estimate the drag coefficient of the object
This number is based on how thin the object is. Unfortunately it is a very complex number to calculate and involves certain scientific assumptions. Do not attempt to calculate the drag coefficient by yourself, without the help of a wind tunnel. You will also need to know the mathematics that can describe and study aerodynamics. Instead, look for an approximation based on an object of similar shape.
Step 3. Calculate the orthogonal area of the object
The last variable you need to know is the sectional area that the object presents to the medium. Imagine the shape of the falling object seeing when you look at it directly from below. This shape, projected on an airplane, is the orthogonalized surface. Again, this is a difficult value to calculate with complex, far from simple, geometric objects.
Step 4. Imagine the resistance opposing the force of gravity, directed downwards
If you know the speed of the object, but not the drag force, you can use the formula to calculate the latter. It holds: C * ρ * A * (v ^ 2) / 2.
Advice
- Terminal velocity changes slightly during free fall. Gravity increases very little as the object approaches the center of the earth, but the amount is negligible. The density of the medium will increase proportionally to the descent of the object into the fluid. This is a much more obvious effect. A skydiver will actually slow down as the fall proceeds, because the atmosphere becomes thicker and thicker as the altitude decreases.
- Without an open parachute, a skydiver would have to fall to the ground at about 130 miles per hour.
