## What is terminal velocity?

#### What is terminal velocity? — EW, Fisher, Australia

After falling for a long time, an object will descend at a steady speed known as its “terminal velocity.” This terminal velocity exists because an object moving through air experiences drag forces (air resistance). These drag forces become stronger with speed so that as a falling object picks up speed, the upward air resistance it experiences gradually becomes stronger. Eventually the object reaches a speed at which the upward drag forces exactly balance its downward weight and the object stops accelerating. It is then at “terminal velocity” and descends at a steady pace.

The terminal velocity of an object depends on the object’s size, shape, and density. A fluffy object (a feather, a parachute, or a sheet of paper) has a small terminal velocity while a compact, large, heavy object (a cannonball, a rock, or a bowling ball) has a large terminal velocity. An aerodynamic object such as an arrow also has a very large terminal velocity. A person has a terminal velocity of about 200 mph when balled up and about 125 mph with arms and feet fully extended to catch the wind.

## If you use a heavier racket, will you be able to hit a badminton birdie farther?…

#### If you use a heavier racket, will you be able to hit a badminton birdie farther? — J, California

Any time you hit an object with a racket or bat, there’s a question about how heavy the racket or bat should be for maximum distance. Actually, it isn’t weight that’s most important in a racket or bat, it’s mass—the measure of the racket or bat’s inertia. The more massive a racket or bat is, the more inertia it has and the less it slows down when it collides with something else. A more massive racket will slow less when it hits a birdie. From that observation, you might think that larger mass is always better. But a more massive racket or bat is also harder to swing because of its increased inertia.

So there are trade offs in racket or bat mass. For badminton, the birdie has so little mass that it barely slows the racket when the two collide. Increasing the racket’s mass would allow it to hit the birdie slightly farther, but only if you continued to swing the racket as fast as before. Since increasing the racket mass will make it harder to swing, it’s probably not worthwhile. In all likelihood, people have experimented with racket masses and have determined that the standard mass is just about optimal for the game.

## Why does a badminton birdie have such a large tip? Does making it bigger protect…

#### Why does a badminton birdie have such a large tip? Does making it bigger protect the racket? — J, California

The large, rounded head of a badminton birdie serves at least two purposes: it makes sure that the birdie bounces predictably off the racket’s string mesh and it protects the strings and birdie from damage. If the birdie’s head were smaller, it would strike at most a small area on one of the racket strings. If it hit that string squarely, the birdie might bounce predictably. But if it hit at a glancing angle, the birdie would bounce off at a sharp angle. By spreading out the contact between the birdie and the string mesh, the large head makes the birdie bounce as though it had hit a solid surface rather than one with holes.

Spreading out the contact also prevents damage to the racket and birdie. If they collided over only a tiny area, the forces they exerted on one another would be concentrated over that area and produce enormous local pressures. These pressures could cut the birdie or break a string. But with the birdie’s large head, the pressures involved are mild and nothing breaks.

## How does air pressure affect the distance a soccer ball can be kicked?

#### How does air pressure affect the distance a soccer ball can be kicked? — SR, Pittsburgh, PA

In general, the greater the air pressure, the greater the air resistance. As the soccer ball moves through the air, the air in front of it experiences a rise in air pressure and pushes the ball in the direction opposite its motion. While there are various other changes in air pressure around the ball’s surface, this rising pressure in front of the ball remains largely unbalanced and it slows the ball down. The higher the air pressure was to start with, the greater its rise in front of the ball and the stronger the backward push of air resistance. Thus if you were to play soccer in the Rocky Mountains, where the air pressure is much less, you’d be able to kick the ball significantly farther.

## How do fletchings stabilize an arrow in flight after it is shot from a bow?

#### How do fletchings stabilize an arrow in flight after it is shot from a bow? — SH, Newton, TX

Like all isolated objects, the arrow naturally pivots about its own center of mass, a point located near its geometric center. If the arrow had no fletchings (or fins) it would tend to rotate wildly in flight. But the fletchings experience substantial aerodynamic forces whenever the arrow isn’t flying point first and these aerodynamic forces twist the arrow back toward its proper orientation. Thus whenever the arrow begins to rotate so that its point isn’t first, the air pushes hard on the fletchings and returns the arrow to its point-first orientation. The same effect keeps airplanes and birds flying nose (or beak) forward.

## How does the trajectory of a ball change when you give it a spin?

#### How does the trajectory of a ball change when you give it a spin? — BHL, Stavanger, Norway

As spinning ball tends to curve in flight. That’s because the ball deflects the airflow around it in one direction and accelerates in the opposite direction. There are two ways in which the spinning ball deflects the air. First, the spinning ball pulls the air it encounters around with it in one direction and produces an imbalance in the airspeeds on its two sides. The air flowing around the side of the ball that is turning back toward the thrower travels faster than the air flowing around the other side of the ball. Since the faster moving air has converted more of its total energy into kinetic energy, the energy of motion, it has less of its energy in the form of pressure. Thus the air pressure on the side of the ball turning toward the thrower is lower than the air pressure on the other side of the ball. The ball accelerates and curves toward the side turning toward the thrower. This effect is called the Magnus effect.

Second, a ball moving at any reasonable speed leaves behind it a turbulent wake and experiences a type of air resistance we call “pressure drag.” When the ball is spinning, this wake forms asymmetrically behind the ball and the pressure drag is not even balanced. The ball pushes the air in the wake to one side and the air pushes back. As a result, the ball accelerates sideways—to the same side as occurs with the Magnus force. In both cases, the ball curves toward the side turning toward the thrower. This second effect is called the wake deflection effect.

The direction in which a thrown ball curves depends on its direction of spin. If the left side of the ball turns back toward you after you have thrown it, the ball will curve toward your left. If the right side turns back toward you, it will curve toward your right. If the bottom turns back toward you, the ball will arc downward faster than it would with gravity alone (for example, topspin in tennis). If the top turns back toward you, the ball will arc upward or will at least not arc downward as much as it would with gravity alone (for example, backspin in golf and hanging fastballs in baseball).

## Why are there dimples on golf balls? – DM

#### Why are there dimples on golf balls? – DM

If there were no turbulence around a golf ball as it moved through the air, there would be regions of slow-moving high-pressure air in front of it and behind it, and regions of fast-moving low-pressure air around its sides. Because of their symmetry, these pressures wouldn’t exert any overall force on the golf ball and it would fly through the air without experiencing any air resistance. But there is turbulence behind a moving golf ball and this turbulence spoils the high-pressure region behind the ball. Since there is less high-pressure behind the golf ball to push it forward, the ball experiences a backward force—the slowing force of pressure drag. The size of this pressure drag force is roughly proportional to the size of the turbulent wake.

The size of the turbulent wake depends on the airflow behind the ball. On a smooth ball, air flowing into the rising pressure behind the ball experiences friction with the ball’s surface and loses energy. This surface air soon reverses its direction of flow, triggering a large turbulent wake. A golf ball’s dimples complicate the airflow very near the ball’s surface so that new, rapidly moving air is able to flow in close to the ball’s rear surface, where it can delay the onset of the flow reversal. The turbulent wake that eventually forms is relatively small, so that the golf ball experiences less pressure drag than a smooth ball. That’s why a golf ball can travel so far before slowing down.

## How does a Frisbee fly?

#### How does a Frisbee fly?

As you begin to move a Frisbee forward, the air in front of the Frisbee splits to flow either over the Frisbee or under it. Because of the Frisbee’s shape and the angle at which it’s held, the air that flows over the Frisbee has a longer distance to travel and arrives late at the back of the Frisbee. The air flowing under the Frisbee reaches the back first and initially flows upward, around the rear surface of the Frisbee. But once the Frisbee is moving fairly rapidly, this funny upward-flowing tail of air blows away from the back of the Frisbee. As it leaves, it draws the air flowing over the Frisbee with it and speeds that air up. As a result, the air over the Frisbee travels faster than the air under the Frisbee. But the airs above and below the Frisbee have the same amounts of total energy per gram. Since the faster moving air above the Frisbee has more kinetic energy than the slower moving air below the Frisbee, the air above the Frisbee must have less of some other form of energy than the air below the Frisbee. In fact, the air above the Frisbee has less pressure potential energy than the air below it—the air pressure above the Frisbee is less than that below the Frisbee. And since the pressure pushing on the bottom surface of the Frisbee is greater than the pressure pushing on the top surface of the Frisbee, there is a net upward pressure force on the Frisbee. This upward pressure force balances the downward weight of the Frisbee and keeps the Frisbee from falling.

## How does fuzz on a tennis ball make it fly faster? It seems counterintuitive to …

#### How does fuzz on a tennis ball make it fly faster? It seems counterintuitive to me.

Yes, it is counterintuitive. The reason for the fuzz is that a swirling layer of air close to the ball makes a good buffer between the ball and the main airstream. As a result, the main airstream flows most of the way around the ball before it breaks away as a turbulent wake. Without the swirling layer of air on the ball’s surface, the main airstream encounters backward-flowing air near the ball’s surface and breaks away from the ball early, leaving a larger turbulent wake.

## I am a little confused on how air pressure can drop as air flows through a small…

#### I am a little confused on how air pressure can drop as air flows through a small hole. I understand that speed and pressure are inversely proportional but aren’t volume and pressure inversely proportional as well?

If you squeeze air into a small space, its pressure will rise (yes, pressure and volume of stationary air are inversely proportional). But flowing air is a different story. When an airstream passes through a narrow channel, it must speed up and when it does, its pressure drops. That’s aerodynamics, not statics.