Ever wondered why parachutists eventually reach full speed when they fall, when the force of gravity in a vacuum causes objects to accelerate uniformly? A falling object will reach a constant velocity when there is a drag force, such as the drag of air. The force exerted by gravity near a large body is usually constant, but forces, such as air resistance, increase more rapidly as the object falls. If allowed to fall freely for a sufficiently long time, the falling object will reach a speed at which the frictional force becomes equal to the gravitational force, and the two will cancel each other out, causing the object to fall at the same speed until it hits the ground. This speed is called the terminal velocity.
Step
Method 1 of 3: Finding Terminal Speed
Step 1. Use the terminal velocity formula, v = square root of ((2*m*g)/(ρ*A*C))
Plug the following values into the formula to find v, the terminal velocity.
- m = mass of falling object
- g = acceleration due to gravity. On Earth, this acceleration is about 9.8 meters per second per second.
- = density of the fluid through which the falling object passes.
- A = area of object projection. This means the area of the object if you project it onto a plane that is perpendicular to the direction in which the object is moving.
- C = Coefficient of drag. This number depends on the shape of the object. The more aerodynamic the object, the smaller the coefficient. You can find some approximate drag coefficients here.
Method 2 of 3: Find the Force of Gravity
Step 1. Find the mass of the falling object
This mass is preferably measured in grams or kilograms, in the metric system.
If you use the imperial system, remember that the pound is not really a unit of mass, but of force. The unit of mass in the imperial system is the pound-mass (lbm), which under the influence of the gravitational force of the earth's surface, will feel a force of 32 pounds-force (lbf). For example, if a person weighs 160 pounds on earth, that person actually feels 160 lbf, but the mass is 5 lbm
Step 2. Know the acceleration due to Earth's gravity
Close enough to the earth to overcome air resistance, this acceleration is 9.8 meters per second squared, or 32 feet per second squared.
Step 3. Calculate the downward gravitational pull
The force that pulls an object down is equal to the mass of the object times the acceleration due to gravity, or F = Ma. This number, multiplied by two, is the top half of the terminal velocity formula.
In the imperial system, this force is the lbf of the object, a number usually called the weight. More precisely, the mass in lbm times 32 feet per second squared. In the metric system, force is mass in grams times 9.8 meters per second squared
Method 3 of 3: Determine the Resistance
Step 1. Find the density of the medium
For an object falling in Earth's atmosphere, its density will change with altitude and air temperature. This makes calculating the terminal velocity of a falling object very difficult, because the density of the air will change as the object loses altitude. However, you can look up air density estimates in package books and other references.
As a rough guide, the density of air at sea level at 15 °C is 1,225 kg/m3
Step 2. Estimate the object's coefficient of resistance
This number is based on how aerodynamic an object is. Unfortunately, this is very complicated to calculate, and involves making certain scientific estimates. Don't try to calculate drag coefficient on your own without the help of wind tunnels and complicated aerodynamic math. However, seek estimates based on objects that are nearly identical in shape.
Step 3. Calculate the projected area of the object
The last variable you need to know is the area of the object that hits the medium. Imagine the silhouette of a falling object that is visible when viewed directly from below the object. The shape, which is projected on a plane, is the area of the projection. Again, this is a difficult value to calculate for any object, except for simple geometric objects.
Step 4. Find the drag force against the downward gravitational pull
If you know an object's velocity, but don't know its drag, you can use this formula to calculate the drag force. The formula is (C*ρ*A*(v^2))/2.
Tips
- The actual terminal speed will change slightly during freefall. Gravity increases slightly as the object gets closer to the center of the earth, but its magnitude is negligible. The density of the medium will increase as the object gets deeper into the medium. This effect will be more visible. A parachutist will actually slow down during the fall because the atmosphere becomes thicker as the altitude decreases.
- Without an open parachute, a parachutist would hit the ground at 130 miles/h (210 km/h).
