Does Ball Size Effect Accuracy or Speed When Throwing a Baseball or Softball?

My daughter, Natalie, did the following project entitled "The Physics of Baseball" for a science fair in 2012. 

Problem:

A baseball and a softball are different sizes, and may be thrown at different speeds. Using Newton’s laws, we know that the more mass a ball has, more force must be produced to throw the ball a given speed, as force is equal to mass x acceleration (F=MA). We also know that if both balls have the same mass, and are thrown the same speed, that they will produce the same amount of force.

Using Newton’s Law of Acceleration, Newton’s 2nd Law of Motion (The relationship between an object's mass m, its acceleration a, and the applied force F is F = ma) we know that throwing balls with different masses will affect velocity (speed).The mass of the ball does affect its velocity. Ball diameter may have an affect on speed. If both balls weigh the same, the diameter of the ball may affect speed and accuracy. Pitching may be more accurate with one ball than with another.

Hypotheses

The diameter (size) of a ball will affect throwing accuracy.

The diameter (size) of a ball will affect throwing speed.

Methods:

Materials

• Baseballs- size 23.5 cm; 5.25 oz
• Softballs- size 30.5 cm; 5.25 oz 
• Texas A&M University Corpus Christi Biomechanics Laboratory Batting Cage
• ATEC Radar Gun

Subjects

35 total (22 males and 13 females)

Mean age

20.5 years

Speed Test:

Each subject threw 10 throws with the softball, and 10 with the baseball. The ATEC radar gun measured ball speed.

Accuracy Test:

Each subject threw 5 throws with the baseball and five with the softball toward a standard target. Points were awarded according to zone they hit.

Results:

Throwing a ball with a smaller diameter will increase speed of the throw.

Throwing a ball with a smaller diameter will increase accuracy of the throw.

Table 1: Accuracy Results

Accuracy Test*	Baseball	Softball
Males	3.5	3.0
Females	2.75	1.5
Total	3.125	2.25

*Results based on softball accuracy test, with five being the highest accuracy, and zero being the lowest.

Table 2: Speed Results

Speed Test	Baseball	Softball
Males	55.2 mph	40.1 mph
Females	39.3 mph	27.4 mph
Total	47.25 mph	33.75 mph

Discussion:

With the softball (larger diameter), less of the ball is covered by the hand, and less energy is transferred. 

Larger diameter of ball= more air resistance. 

• When an object moves through air, it moves the air molecules out of the way. This creates a resistance force, or drag, on the moving object.
• A fast-moving object encounters more drag than a slow-moving object. The fast-moving object has to push harder to get the air molecules out of the way, and for the object to move through them.
• An object with a large cross-sectional area or diameter encounters more drag than an object with a small cross-sectional area. The air molecules have to travel farther to get out of the way of a large object. Newton’s 1st Law of Motion (Every object in motion tends to remain in motion unless an external force is applied to it) also explains the differences. 

Fingers and wrist cannot flex or grip the larger ball as much, so less muscle is used to throw ball. Using Newton’s 3rd Law of Motion (For every action there is an equal and opposite reaction) we know than since less energy is generated by the muscle, that less is transferred. The Law of conservation of energy (energy can neither be created nor destroyed by itself. It can only be transformed) tells us that the energy from the muscle is transferred to the ball. Since less is generated in the muscle due to the inability to recruit as much muscle, less energy is transferred to the ball during the throw, and the speed is less. 

Natalie Friery