The Effect of Temperature and Relative Humidity on MLB Baseballs’ COR Performance When Keeping Their

Weights Constant

Christopher Toribio

1

Abstract

In recent years, the production of homeruns in MLB games were increasing and NCAA baseball

games were finishing with very high scores. The MLB commission decided to provide funding to the

University of Massachusetts-Lowell to establish a Baseball Research Center. Baseball researchers have

focused on regulating the design and production for baseball bats, but not for baseballs. This study

investigates the effect of temperature on COR performance when the relative humidity is adjusted so the

weight of each baseball remains the same. The results demonstrate that in order to keep the weight of

each baseball constant, there must be an inverse relationship between temperature and relative humidity.

The results also demonstrate that as the temperature rises, the COR values for each baseball increases.

However, the mean COR value for Ball 1 decreased when the temperature increased from 90°F to 120°F

and the mean COR value remained the same for Ball 3 when the temperature increased from 70°F to

90°F. Establishing a RH for every temperature to keep the weight of the ball the same could be a key

factor to the game of baseball because it can increase the safety for infielders and prevent an increase in

homerun production.

2

Introduction

For over 150 years, baseball has been America’s most popular past time. It is arguably the first

sport Americans found a true passion for. In recent years, the production of homeruns in Major League

Baseball (MLB) games were increasing at a fast rate and National Collegiate Athletic Association

(NCAA) baseball games were finishing with very high scores. After the 1998 NCAA College World

Series ended with a score of 21-141, the MLB commission decided to provide funding to the University of

Massachusetts-Lowell to establish a Baseball Research Center that would help regulate the design and

production of baseball bats for MLB and NCAA baseball games2.

Over the past 15 years, NCAA testing protocols have measured the bat-ball collision to limit the

performance of baseball bats3. Ball Exit Speed Ratio (BESR) and Bat-Ball Coefficient of Restitution

(BBCOR) are two examples of these NCAA testing protocols3. Both of these protocols utilize the

LVSports (LVS) Machine4. The LVS Machine, as shown in Figure 1, consists of a large compressed air

tank at the bottom of the machine, which connects to the cannon barrel where the baseball is launched

towards the bat. The tube that connects the air tank and the cannon transfers the air released from the tank

and into the cannon, which determines how fast the baseball is launched. The baseball bat is mounted on

a horizontal pivot table at the end of the machine. The bat is free to swing following the impact and the

baseballs must be fired at a very high velocity throughout the testing process. By firing the baseball at a

high velocity, the players’ pitch and swing speed are held accountable. In between the cannon and the

baseball bat is the speed sensor box. Six speed sensors, three on each side, are attached to a Plexiglas box

which measures the inbound velocity of the baseball, the velocity before impact with the bat, and the

outbound velocity of the baseball, the velocity after impact with the bat. Six shots must be fired between

the 4-in. location of the bat from the barrel to the 8-in. location of the bat from the barrel 4. Each bat has a

certain numerical limit that it cannot exceed during the tests. If the bat exceeds its limit, it is considered

high performing and the prototype of the bat goes down as a bat failure4. If a baseball bat goes down as a

bat failure, the company that makes the bat is not allowed to sell that bat design in retail stores 4. The

difference between the BBCOR and BESR protocols is that BBCOR takes the specific weight and

performance level of each baseball individually into consideration, while BESR assumes that all baseballs

are uniform in weight and performance level within one shipment of baseballs4.

3

Figure 1

Before performing the BBCOR test, the performance level of each baseball must be measured.

Each baseball must be weighed, in grams, and they must be impacted with an inbound speed between

135-137 mph at the 6-in. location from the barrel of the American Society for Testing and Materials

(ASTM) standard bat4. Another test that is very similar to the preparation of the baseballs in the BBCOR

test is the Coefficient of Restitution (COR) test, which is also a test that measures the performance level

of baseballs5. In other words, it measures how “bouncy” the ball is6. The COR test is different from the

preparation of the baseballs in the BBCOR test because the COR test is done on a flat metal plate 5. The

preparations of the baseball for COR, are impacted with an inbound speed between 59.3-60.7 mph5. COR

performance of a baseball is calculated using the inbound velocity (V inbound) and the rebound velocity

(Vrebound). Equation 1 represents the formula used to find the numerical value of the COR for each

impact6.

COR= -V rebound (1) Vinbound

Dew-point temperature, relative humidity (RH), temperature, and the structure of a baseball are

factors that affect the performance of a baseball and are not taken into consideration when determining

the COR. Dew-point temperature is the temperature at which air must be cooled at constant pressure in

order for it to become saturated with the atmosphere7. The dew-point temperature can equal the

temperature of the atmosphere only if the RH of the atmosphere is 100% 7. A high temperature and RH

causes moisture to condense because of its high dew-point temperature7. When moisture begins to

condense, the ball’s weight may be affected because of the way it is constructed. The structure of a

baseball consists of three wool windings compressed by cowhide leather and the center of the ball, known

as the pill, is a cork surrounded by rubber6. This moisture accumulates inside the ball. The pill is not

affected because it is surrounded by rubber8. A low temperature and a low RH create a harder texture on

the surface of the baseball because the cowhide leather surrounding the ball is affected8.

4

This study investigates the effect of temperature on COR performance when the RH is adjusted

so the weight of each baseball remains the same. It is noteworthy to mention that there was only one other

experiment that was conducted similarly to this study in the review of literature. However, the previous

study did not control the RH, when adjusting the temperature6. The authors stated this over simplification

of the experimental procedure may have resulted in the different weight of the baseballs, and therefore,

affect the COR performance6. In order to control temperature and RH, my study utilized an environmental

chamber. To maintain the weight of each baseball under the different temperatures, the RH had to be

changed relative to each test temperature. This required a battery of tests before the COR performance

could be calculated. It was hypothesized that as the temperature rises, the COR performance level of the

baseballs will increase.

Materials & Methods

Before the objective of this study could be carried out, the relationship between temperature, RH

and keeping each baseball at the same weight needed to be determined.

Effect of Temperature on Baseballs When Dew-point Temperature is Constant

A hole was drilled through a NCAA baseball and an Extech thermocouple was used to measure

the core temperature of the ball. A thermocouple is a thermoelectric device for measuring temperature 9. It

consists of two wires of different metals connected at two points9. Inserting a thermocouple contributes to

very little change in the ball’s weight and its small size helps the baseballs readily adapt to different

temperatures9. If a meat thermometer were to be used, as was done in the previous study, a larger hole

would need to be drilled through the ball. Under lab conditions, the core temperature of the ball was

recorded at approximately 70°F; the same temperature the lab must be held at 6. The ball was then placed

inside an Associated Environmental-environmental chamber, shown in Figure 2, and the time it took for

the core temperature of the ball to adapt to the temperature inside the chamber was recorded. Since the

environmental chamber calculates the temperature in Celsius, the data was recorded in Celsius.

Figure 2

5

This experiment had to be completed in a limited amount of time and an experimental protocol

had to be developed. The amount of time it took for the core temperature of the baseball to adapt to the

temperature inside the chamber was specifically recorded to figure out an appropriate time schedule to

conduct the actual experiment. The primary goal of this procedure was to establish conditions that would

keep the dew-point temperature constant throughout the experiment. 50°F was used as the standard dew-

point temperature for this procedure because it is the dew-point temperature inside the lab. To figure out

how long it takes for the ball to adapt to cool temperatures, the chamber was set at 50°F, 20° less than the

temperature of the lab (70°F). The RH was set at 99% which allowed for a dew-point temperature of

50°F. However, the environmental chamber could not sustain these parameters. As a result, the

temperature inside the environmental chamber was raised to 53°F (12°C) and the RH was lowered to

87%. After about an hour and 30 minutes, the core temperature of the baseball dropped to 53°F, as seen in

Graph 1A. The ball was then taken out of the chamber and placed under lab conditions and the time it

took for the core temperature of the ball to adapt from cool conditions to lab conditions was recorded.

After about three hours, the core temperature of the ball reached the temperature inside the lab, as seen in

Graph 1B.

Graph 1A

0 10 20 30 40 50 60 70 80 90 1000

5

10

15

20

25Core Temp. of Baseball at 12°C

Time (relative,min)

Tem

per

atu

re (

°C)

6

Graph 1B

0 20 40 60 80 100 1200

5

10

15

20

25Core Temp. of Baseball at Room Temp.

Time (relative,min)

Tem

p. (

°C)

It was then placed back inside the chamber at 120°F (49°C) and 10% RH. The ball took longer

than three hours to reach this temperature and as a result, it was kept inside the chamber for two days.

After two days, the ball was taken out and the core temperature was approximately 118°F, as seen in

Graph 2A. It was placed under lab conditions once again and it took about four hours for the core

temperature of the ball to reach the temperature of the lab, as seen in Graph 2B.

Graph 2A

0 20 40 60 80 100 120 140 1600

5

10

15

20

25

30

35

40

45Core Temp. of Baseball 49°C

Time (relative,min)

Tem

p. (

°C)

Graph 2B

7

0 50 100 150 200 250 3000

10

20

30

40

50

60 Core Temp. of Baseball at Room Temp.

Time (relative,min)

Tem

p. (

°C)

A MLB baseball was then taken through the same process as the NCAA ball, except it was placed in the

chamber at 87°F (31°C) and 29% RH. This was to see if the ball takes the same amount of time heating

up 17° as to cooling down 17°. After about eight hours, the core temperature of the ball reached

approximately 85°F, as seen in Graph 3A. The ball was kept in the chamber overnight and in the morning,

the core temperature of the ball was found at approximately 87°F. The ball was then placed under lab

conditions and after about four hours the core temperature reached the temperature of the lab, as seen in

Graph 3B.

Graph 3A

0 50 100 150 200 250 300 350 400 450 5000

5

10

15

20

25

30

35 Core Temp. of Baseball at 31°C

Time (relative,min)

Tem

per

atu

re (

°C)

Graph 3B

8

0 50 100 150 200 250 300 350 400 450 5000

5

10

15

20

25

30

35 Core Temp. of Baseball at Room Temp.

TIme (relative,min)

Tem

per

atu

re (

°C)

These tests concluded that the chamber was not capable of maintaining a dew-point temperature of 50°F

and as a result, a relationship between temperature and RH had to be determined in order to keep each

baseball at the same weight. It was also found that the core temperature for both baseballs took about

three to six hours for them to be set at the desired temperature.

Effect of Temperature and RH on Weight of Wool

A strand of wool, from the third winding of a baseball, was then taken and placed inside the

chamber as a quick method for determining how a ball’s weight changes as it goes through different

temperatures. The goal of this procedure was to find the RH that can keep the wool weight the same

throughout the four different temperatures. Using a baseball might have taken days to find out how

temperature affects the weight. By using a loose strand of wool, this affect can be determined within

hours because the leather cover of the ball was not compressing the wool. The initial weight of the wool

under lab conditions was recorded at 42.2g, which became the target weight of this procedure. The wool

was then placed inside the chamber at 120°F and 50% RH and was left there overnight. The following

morning, the weight of the wool was recorded at 41.6g. The strand of wool weighed 0.6g less than its

initial weight. The wool was then placed back inside the chamber and every 30 minutes, the weight of the

wool was measured until the wool reached and maintained its weight at 42.2g. After about five hours, it

was found that the RH to keep the wool weight the same for 120°F was 66%. After placing the wool in

the chamber at 90°F, it was found that the RH to keep the weight the same was 50%, the same as the RH

inside the lab. The wool was then placed inside the chamber to see at what RH the weight would remain

9

the same under cool conditions. 50°F was the first cool temperature it was placed under, but after the

chamber failed to adapt to 45% RH, the temperature was increased various times until the wool reached

the target weight. 66°F was established as the cool temperature and the RH that kept the wool weight the

same under that temperature was 40%. This procedure was done many times with pieces of wool having

different weights. The data from these experiments were not consistent. Graphs 4-6 illustrate show no

linear trend between temperature and RH, while wool weight remains constant, while Graphs 7 and 8

illustrate a linear trend.

Graph 4

60 80 100 120 1400

10203040506070

Environmental Conditions that Maintain Weight of Wool at 42.2g

Temperature

Rel

ativ

e H

um

idit

y

Graph 5

10

40 50 60 70 80 90 100 110 120 1300

20

40

60

80

100

Environmental Conditions that Maintain Weight of Wool at 44.0g

Temperature

Rel

ativ

e H

um

idit

y

Graph 6

0 20 40 60 80 100 120 1400

10

20

30

40

50

60

Environmental Conditions that Maintain Weight of Wool at 41.8g

Temperature

Rel

ativ

e H

um

idit

y

Graph 7

11

60 80 100 120 1400

10

20

30

40

50

60

Environmental Conditions that Maintain Weight of Wool at

41.6g

Temperature

Rel

ativ

e H

um

idit

y

Graph 8

60 80 100 120 1400

10

20

30

40

50

60

70

Environmental Conditions that Maintain Weight of Wool at 42.4

Temperature

Rel

ativ

e H

um

idit

y

Effect of Temperature and RH on weight of the Leather Cover and the Complete Baseball

It was then decided to see if a linear trend between temperature and RH existed while the weight

of the leather cover of a baseball remained constant. As a result, a MLB baseball, a piece of the leather

cover from a MLB baseball, and wool from a third winding were placed inside the chamber. Throughout

the process, there was very little change in the leather’s weight, but the baseball’s weight was constantly

changing. It was concluded that the wool contributes to the weight change of the baseball when subjected

12

to various temperatures and RH’s. The goal then became to establish four temperatures with their

associated RH that would keep each Practice MLB baseball at a constant weight, so the COR could be

measured. Practice MLB baseballs are used for testing how well the COR machine is working in the lab

(See Fig. 3).

Figure 3

Establishing the Four Test Temperatures and RH

The temperature in the chamber was set at 40°F and 5% RH. The chamber could not adapt to

such a low RH so after one day, the chamber was found at 40°F and 77% RH and the ball weighed

145.3g. Based on the data from the relationship between temperature and RH, while maintaining the

weight of the wool (Graphs 4-8), a RH was estimated and established for the other three temperatures.

The ball was left in the chamber for a certain amount of time and its weight was constantly measured to

see if it changed or remained the same. The other three test temperatures and RH were established at 70°F

73% RH, 90°F 70% RH, and 120°F 67% RH. It was determined that there was an inverse relationship

between the temperate and the RH: As the temperature goes up, the RH goes down and vice versa.

Although the RH decreases as the temperature increases, the change in RH appeared not to be significant.

The test temperatures that were used represent the different weather conditions throughout the United

States. 40°F is the temperature that represents the weather conditions in the northern region of the country

in early April and late October. 70°F is the standard temperature for COR testing and it is the temperature

inside the lab. 90°F is the temperature that represented the weather conditions from about June to August.

120°F represented the temperature for extremely hot conditions. A practice COR test was done on the ball

after it was taken out of each condition and after comparing the average COR values, it was found that as

13

the temperature was increased, the average COR value increased except for when it was increased to

120°F.

Conducting the Actual Experiment

The effect of temperature on baseball COR performance was investigated by using three MLB

Rawlings baseballs, shown in Figure 4. Three baseballs were used in order to have a variety of data

within the four test temperatures and RH. Using more than three baseballs was not necessary because the

COR test requires for every baseball to have an inbound velocity between 59.3-60.7 mph 5. This means

that if the three balls are placed under the same condition, it is very unlikely for them to have a significant

difference in the COR values.

Figure 4

The three MLB baseballs were taken and placed in the chamber at the four test temperatures and RH. The

three balls spent at least 24 hours under each condition and then they were taken out for a COR test. Each

ball was taken out of the chamber individually and they spent no more than three minutes out under lab

conditions. After three minutes, the balls were placed back inside the chamber, regardless of the six valid

shots being taken. This allowed for the ball’s weight and core temperature to remain the same throughout

the testing. After each ball is fired and impacted the metal plate, the COR machine measured the inbound

and outbound velocity. The COR was calculated using the COR equation6.

COR= -V rebound Vinbound

After the COR value for each baseball under each test temperature and RH was calculated, the mean COR

value, and the standard deviation was determined for each baseball.

Results

The mean COR values and their standard deviations for each ball, under each temperature, are

shown in Table 1. The mean COR value was calculated for each baseball after each ball went through six

shots at each temperature. Other than ball 1, the trend in Graph 9 demonstrates that there is an increase in

COR performance as the temperature rises. The COR values for ball 1 increase as the temperature

increases except for when the temperature goes from 90°F to 120°F. The standard deviation was

14

calculated to see how much variation there are from the average COR values. A low standard deviation

indicates that the data points tend to be very close to the mean, whereas a high standard deviation

indicates that the data are spread out over a large range of values10. The low standard deviations for each

baseball demonstrated that the average rates were consistent. The data also demonstrates that the change

in the COR is smaller at the higher temperatures than at the lower temperatures. When one looks at each

baseball, the difference in the COR between 120°F and 90°F is -0.005 for Ball 1, 0.001 for Ball 2, and

0.003 for Ball 3. The difference in the COR between 90°F and 70°F is 0.008 for Ball 1, 0.003 for Ball 2,

and 0.000 for Ball 3. The difference between the COR at 70°F and 40°F is 0.017 for Ball 1 and 2 and

0.018 for Ball 3 (see Table 1 and Graph 9).

Table 1

Temp. (°F) Ball 1 Ball 2 Ball 3

40°F 0.531 ± 0.005 0.533 ± 0.005 0.532 ± 0.005

70°F 0.548 ± 0.005 0.550 ± 0.003 0.550 ± 0.003

90°F 0.556 ± 0.001 0.553 ± 0.005 0.550 ± 0.004

120°F 0.551 ± 0.004 0.554 ± 0.002 0.553 ± 0.001Mean COR values and standard deviations for each baseball under each temperature

Graph 9

30 40 50 60 70 80 90 100 110 1200.51

0.52

0.53

0.54

0.55

0.56

Mean COR Values

Ball 1Ball 2Ball 3

Temperatures

COR

Val

ues

Discussion

15

This paper investigates the effect of temperature on COR performance when the RH is adjusted

so the weight of each baseball remains the same. Developing the experimental protocol was crucial

because no other study in the scientific literature measured COR while varying temperature and RH while

keeping the weight of the baseball constant. Temperature and RH were under controlled conditions

because this study used an environmental chamber. It was hypothesized that as the temperature and RH

rises, the COR performance of each baseball increases. It is important to re-iterate that the COR

determines the “bounciness” of a baseball and therefore, is a parameter that can determine a baseball’s

performance6. The data from this study appears to partially support the hypothesis. Graph 9 and Table 1

illustrate that as the temperature increases, the COR value increases. The COR values for balls 1, 2, and 3

increased as the temperature increased from 40°F to 120°F. Ball 1’s COR value was 0.531 at 40°F and it

increased to 0.551 at 120°F. Ball 2’s COR value was 0.533 at 40°F and it increased to 0.554 at 120°F.

Ball 3’s COR value was 0.532 at 40°F and it increased to 0.553 at 120°F. Some of the data did not

support the hypothesis. Ball 1’s COR value decreased as the temperature rose from 90°F to 120°F and

Ball 3’s COR value remained the same as the temperature rose from 70°F to 90°F. It is not understood

why these COR values did not increase and further studies need to be done in order determine the

reproducibility of the data. A novel finding in the data shows that the difference in COR measurements

between 40°F and 70°F is much greater than the difference between the measurement of the COR

between 70°F and 120°F (see Table 1 and Graph 9). For the temperatures between 40°F and 70°F, the

difference in the COR value of Balls 1 and 2 is 0.017 and for Ball 3 it is 0.018. The difference in the COR

between 70°F and 90°F is 0.008 for Ball 1, 0.003 for Ball 2, and 0.000 for Ball 3. The difference in the

COR values between 90°F and 120°F is -0.005 for Ball 1, 0.001 for Ball 2, and 0.003 for Ball 3. The

standard deviation was found to see how much variation there are from the average COR values (see

Table 1). A low standard deviation indicates that the data points tend to be very close to the mean,

whereas a high standard deviation indicates that the data are spread out over a large range of values10. The

low standard deviations for each baseball demonstrated that the average rates were consistent10.

The only other study done in 2004 showed the effect of temperature on COR performance6.

Household appliances such as a toaster, an oven, and a refrigerator were used to change the temperature

of the baseballs6. Although these appliances changed the temperature of the baseballs, they were unable to

keep the weight of the baseball constant through the experimentation because RH was not taken into

consideration6. The mean COR values in the previous study showed an increase in COR value as the

temperature rose6. In addition, the data in that study was also similar to this experiment. At 120°F the

COR values were approximately 0.550 and at 40°F the COR values were between 0.530-0.540. 25°F was

used as a subfreezing temperature in the previous experiment6. Although I considered testing baseballs at

25°F, I could not because the environmental chamber’s lowest temperature could only be set at 32 °F

16

(0°C). While the COR tests were being done on the balls used for that study, the weight of each baseball

was unable to be kept constant because RH, which changes as a result of the change in temperature, was

not taken into consideration6. As a result, the standard deviations of the COR measurements varied much

more than those calculated in my study6. The environmental chamber’s ability to regulate the temperature

and RH inside the chamber kept each baseball’s weight constant throughout my experiment.

An experimental flaw in this study was the inability to completely establish a linear relationship

between temperature and RH while maintaining the weight of the various pieces of wool. The linear

relationship appeared to occur for pieces of wool that had a weight of 41.6 g and 42.4 g (see Graphs 7 and

8). The linear relationship did not exist for pieces of wool that had a weight of 42.2 g, 44.0 g, and 41.8 g

(see Graphs 4-6). Since the wool seemed to have been the component of the baseball that determined the

variation of the change in weight of the balls when varying the temperature and RH, a standardized

mathematical relationship could not be determined. Mathematically establishing the relationship between

RH and temperature should be an equation that would have to include the inverse relationship between

temperature and RH found in this study. Future experimentation will be needed to be carried out to

establish this relationship, which would allow the weight of each baseball, which is tested, to remain the

same when measuring the COR as the temperature is varied. Once completed, a standardization process

for testing baseball performance may be established, which would also help regulate how baseballs are

manufactured. In the literature, many baseball researchers have only focused on limiting the performance

of baseball bats but never considered limiting the performance of baseballs. If there is a certain RH that is

established for every temperature to keep the weight of the ball the same, this process could be used for

the preparations of the balls for the BBCOR test as well. Making a standard for the baseballs might cause

a possible change in the structure. There has already been a consideration for replacing the wool of a

baseball with rubber. By surrounding the inner structure of the baseball with rubber, this may eliminate

the factor of the baseball absorbing the moisture from the air. As long as the rubber does not affect the

initial weight of the ball, using this material would be easier to establish a RH for each temperature

because the weight of the ball may have very little change. It was found that the weight of the leather

cover of the ball is not as affected in the change in temperature and RH as the wool is. If the leather cover

is the only absorbing factor on the ball, the change in weight of the ball would not vary as much because

the affect of temperature and RH on wool would no longer be considered.

The research in this paper is significant to the game of baseball because not every part of the

country plays under the same weather conditions. Baseballs being played in Arizona can have a different

effect on the game of baseball than baseballs being played with in Boston. Temperatures around Arizona

are consistently warm which may give the ball a high COR performance throughout the entire year.

Temperatures around Boston vary throughout the year, which may give the baseballs an inconsistent COR

17

performance. Establishing a RH for every temperature to keep the weight of the ball the same could be a

key factor to the game of baseball because it might help regulate the homerun production. In addition, it

can also increase the safety for infielders such as third basemen and first basemen because the speed at

which the balls come at these position players may be reduced. Studies to finding out how to standardize

the performance level of the baseball will continue to be conducted.

Reference

18

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http://en.wikipedia.org/wiki/1998_College_World_Series.

2. University of Massachusetts-Lowell Baseball Research Center Homepage

(http://m-5.eng.uml.edu/umlbrc/index.htm)

3. Drane, P.J., Sherwood, J.A. (2010). Baseball studies: baseball bat testing protocol development.

Procedia Engineering, 1-6. Retrieved January 9, 2011, from

http://m-5.eng.uml.edu/umlbrc/Publications/ISEA2010-Drane.pdf

4. NCAA Standard for Testing Baseball Bat Performance (2009). Bat-Ball Coefficient of Restitution.

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http://bzwxw.com/soft/UploadSoft/new4/ASTM--F1887-2002.PDF

6. Drane, P.J., Sherwood, J.A. (2004). Characterization of the Effect of Temperature on Baseball COR

performance. Proceedings of the 5th International Conference on the Engineering of Sport, 1-7.

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http://m-5.eng.uml.edu/umlbrc/Publications/Drane_Sherwood_ISEA2004.pdf

7. Wallace and Hobbs. What Exactly Is The Dew Point? Atmospheric Science: An Introductory Survey.

Retrieved July 10, 2011, from http://weathersavvy.com/Q-Science_Dewpoint.html

8. Drane, P.J. (2003). Characterization of the Effects of Use and Moisture Content on Baseball Bat

Performance using Experimental. Appendix A in Thesis. Retrieved September 20, 2011, from http://m-

5.eng.uml.edu/umlbrc/publications/Thesis_Patrick%20J%20Drane.pdf

9. Duff, Matthew, Towey, Joseph (2010). Two Ways to Measure Temperature Using Thermocouples

Feature Simplicity, Accuracy, and Flexibility. Analog Dialogue, 44, 1-6. Retrieved July 17, 2011, from

http://www.analog.com/library/analogDialogue/archives/44-10/thermocouple.pdf

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10. Wikipedia (2001, March 7). Standard Deviation. Retrieved March 11, 2011, from

http://en.wikipedia.org/wiki/Standard_deviation

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