Re: Could you please explain the physics of bowling?

The physics of bowling becomes extremely complicated when one considers anything but the most simple cases. For example, bowling balls are spheres but the internal weight distribution is not uniform. So all the attempts to model the path of a rolling/sliding bowling ball using a uniform sphere may be a bit misleading. A previous question/response on the inner core of bowling balls discusses the some of the advantages of an offset weight distribution. Qualitatively the physics can be discussed so that basic effects and events can be analyzed, knowing full well that the real world is going to be more complicated.

I would break the physics of bowling into 3 distinct components to be pieced together:

Actually bowling can be fairly decent physical exercise if one is careful not to place one's back, shoulder, or wrists at risk. An anatomy question/response How many muscles are used in bowling? states that many muscles are used in bowling. The bowler starts with the ball about waist level and approaches the foul line while raising the ball upwards and behind herself. The ball is usually released a few inches off the ground, so the ball has the potential energy of height from the shoulders to the ground imparted to it as kinetic energy. The arm of the bowler mainly serves to redirect this energy toward the pins. The walking to almost sprinting approach of the bowler serves the purpose of steadying the bowler as well as imparting some speed to the released ball (although I have seen may a recreational bowler come to a complete stop at delivery).

Your average bowler probably lifts the ball about elbow level and releases the ball about 4 inches off the ground. An approximate difference in height of 3 to 4 feet (depending on the bowler's height). From conservation of energy the speed can be found to be:From conservation of energy the speed can be found to be:

speed = SQRT[2*acceleration of gravity*height difference]

If we just consider this rise of about 3 feet the ball will be released with about a speed (SQRT [2 * 32 ft/s^s * 3 ft]) of 13.9 ft/s (or 9.5 mile/hour).

However, Most power bowlers actually lift the 14 to 16 pound ball just above their shoulder with a mostly straight arm. Which will result in a speed of around 17.9 ft/s (or 12.2 mph).

Of course many bowlers will throw the ball harder by adding energy to the release. The head pin is 60 feet away from the foul line and typically the ball gets there in 3 to 6 seconds, which means the ball is travelling at a speed in the range of 20 ft/s to 10 ft/s, which is consistent with much of the speed coming from the lift and decent of the ball around the shoulder. Even "extreme power bowlers" (20+ ft/s by my definition) get about half the power from the lift of the ball.

I refer the reader to The Physics of Sports edited Angelo Arementi, Jr. The reprint entitled of "Bowling frames: Paths of a bowling ball" American Journal of Physics 45, 263-266 (1977) is about the level of college calculus based general physics.

The ball and oily alley interaction is extremely difficult to model completely, yet many experienced bowlers can figure the lane to lane variation in about 5 minutes and make the adjustments to their game to be successful. The ball slides on the lane until the frictional force causes it to roll without slipping. The direction of the frictional force is constant. This produces a parabolic trajectory if the ball has any side spin.

When the ball rolls, the side spin takes over and the ball can hook back toward the middle of the lane in a straight line. The combination of sliding in a parabolic path and then rolling in a straught line looks like a big hook when some bowlers throw the ball. The alley is 3.5 feet wide and it 63 to the end of the alley (60 feet to the headpin). But it can look like the ball covers a huge arc because it is thrown out toward the gutter and bites and comes back into the pins.

The pins are arranged across the 3.5 feet of the alley and 3 feet deep

( 7)    ( 8)    ( 9)    (10)
    ( 4)    ( 5)    ( 6)
        ( 2)    ( 3)
            ( 1)

The collision of the ball with the pins is a chaotic system. Small variations in the velocity (speed and direction) of the ball when it hits the pin, as well as collision location can lead to widely different results. For example, a very straight throw that hits the head pin head on, can lead to a 7-10 split which is nearly impossible to make. In fact, making the 7-10 is a shot that requires a huge amount of good luck. The "pocket" is defined as between 1-3 for righthanded bowlers and 1-2 for lefthanders. Hitting the pocket does not guarantee a strike but it is where experience dictates a strike is more likely. In fact, most strikes happen as a result of "good pin carry." Good pin carry is when the pins knock each one another over after the first one is hit by the ball. It is actually possible to have bad pin carry in which pins miss each other and remain (this happens most often when a bowler leaves a 5, 1-5, 2-8, 3-9, or 4-7-10, and many other combinations. The ball weights anywhere from about 10 pounds to 16 pounds and the pins weigh in at 4 pounds. So the ball can change course significantly after contact, while the pins fly off in all directions.

There is no reasonable way to predict the collision results. Bowlers who bowl a perfect 300 game often speak of being in the groove, which may refer to having a reproducible approach and release, but almost any 300 game has a least one "lucky" throw in it.

I found a site that has an PC compatible video (I haven't viewed it myself).
http://www.algor.com/videos/pow.htm

Sincerely,

Tom "Turkey Tex" Cull