Tag: balls birdies and frisbees

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? — 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 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? — 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? — 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? — 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

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.

Does the decreased density of the air in Denver make it easier to achieve turbulent flow at the boundary layer of a baseball and therefore make the ball fly farther?

Whew, this is a toughie. The air in Denver is less dense, so it tends to respond better to viscous forces. On that account, it would tend to be less turbulent. But it is also “thinner” and less viscous, so it would tend to be more turbulent. I think that those two effects essentially cancel, so that the ball experiences the same degree of turbulence at any altitude. However, the air in Denver has less pressure, so it exerts smaller forces on the ball than air at sea level. Thus, although the flow properties aren’t affected by the increased altitude, the pressures involved are. The ball should certainly carry farther in Denver than at sea level. Imagine playing on the moon, where there’s no air at all. The ball wouldn’t experience any drag at all!

Does the design of balls (pentagons on soccer balls, lines on basketballs, panels on volleyballs, etc.) have a purpose or are they merely there for design?

In most cases they are simply design. However, they do affect the flow of air over the ball and will change its motion. The classic examples of balls with designs that matter are golf balls and baseballs. A golf ball has dimples because they dramatically change the airflow over the ball and allow it to travel much farther. A baseball’s stitching also affects its flight from the pitcher to the mound and is very important to pitches like the knuckle ball and the spitball.

How does a boomerang work?

The correct way to throw a boomerang is overhand and, unlike a Frisbee, in a nearly vertical plane. (Usually the ideal angle is about 15° from vertical.) The boomerang is essentially a rotating airplane wing, and its shape produces lift using the Bernoulli effect in the same way an airplane wing does. But when it is thrown, notice that the top blade of the boomerang is moving faster through the air than the bottom blade, because of the rotation. This results in there being more lift on the top blade than on the bottom. From a right-handed thrower’s perspective, there is a lift up and to the left, more so at the top than at the bottom. The upward lift is what keeps the boomerang in the air. You might think the leftward twist flips the boomerang over, but wait! The boomerang is also a flying gyroscope. Leaning the gyroscopic boomerang over results in its turning to the left, much the same way that leaning a moving bicycle leftward toward the horizontal causes the front wheel to turn and not fall over. (This is also why spinning tops start to slowly turn their axis of rotation when they lean, a process called “precession”.) The boomerang doesn’t flip over, but instead turns its axis of rotation around in a large horizontal circle, and it comes back to you.

After a moment’s thought, you might wonder whether helicopters suffer the same effect. (How would a boomerang fly if thrown in a horizontal plane?) In fact, they do, and there is a tendency to pitch the helicopter upward (tip the nose up) precisely from this same effect, which the pilot instinctively corrects for.

(Thanks to Prof. Paul Draper, from the Physics Department of the University of Texas at Arlington, for writing this explanation.)