UNITS OF MEASURE Textbook Appendix A

The measuring units most commonly used in exercise physiology are those variables related with exercise, physiology, body size, and meteorology. Numerous variables are described with such measuring units as kilogram (kg), liter (L), meter (m), and kelvin (K) in accordance with the International System (SI) of nomenclature. Quite often in exercise physiology there will be a combination of units such as liters per minute or milliliters per kilogram per minute. SI is the universally accepted means of expressing measurement and is based on the decimal and metric systems which simplifies the conversion between units. Many units are derived from names of individuals who developed the measurement standard. These names include joule, newton, kelvin, and watt. When using these terms spelled out we do not capitalize them even though they are proper nouns. When expressing these names in combination with other units we do not hyphenate the combined unit such as newton meter. SI units are abbreviated only when they are associated with a number. Thus, the sentences below are proper presentations of the term kilogram:

The subject weighed 79 kg prior to the start of the session.

Kilograms is a unit of measurement for mass.

While we do not capitalize the names of these great scientists who gave the measurements their surnames, we do capitalize the abbreviation of newton (N), watt (W), kelvin (K). An abbreviation is never to be written in plural. For instance, 123 kg is acceptable while 123 kgs is not. SI units do not require a period to follow unless they are at the end of a sentence. Two component unit measurements such as newton meters are abbreviated with a centered dot between the abbreviations (12 n·m) rather than with a dash. We never mix abbreviations and unit names such as N·meter or numerals and names such as 250 newtons. Thus, 12 n·m is correct but twelve n·m is not. The proper presentation of the word ‘per’ SI is to use a centered dot preceding the unit with its negative exponent following. The term liters per minute is expressed as L·min-1. One can use a slash such as L/min. However it is not acceptable to use more than one slash in an expression so milliliters per kilogram per minute is not to be abbreviated as ml/kg/min. Acceptable abbreviations are ml·kg-1·min-1 or ml/kg·min.

Variables and Units of Measure Mass – an SI base quantity represented by the SI base unit kilograms (kg). Mass is the quantity of matter in an object. Under normal circumstances (gravitational pull of the earth) mass is equivalent to weight. One of the most common measurements in exercise physiology is body mass. Body weight is a common term but mass is more appropriate. Since body weight is used much more frequently in the United States we will typically list weight as the measurement in labs. Most of the time we will require that you enter the measurement in kg and lb. Pounds are a ‘customary’ unit and do not fit the SI system. 1 lb = 0.45 kg 1 kg = 2.2 lb Sample calculation: ? kg = 151 lb * (0.45 kg/lb) = 68.5 kg

Length and Distance – also a base quantity; is typically described with the SI base unit the meter (m). Longer lengths are described in kilometers (km), shorter lengths may be described in centimeters (cm) or millimeters (mm). For very small units micrometers (µm) may be used. Height describes vertical length expressed in m or cm. Sample calculation: ? cm = 72 in * (2.54 cm/in) = 183 cm or 1.83 m

Force – is the product of mass and acceleration. Force changes or tends to change the state of an object. Muscular activity will generate force, thus when we discuss muscles generating tension it is often linked to the application of a force. Mass and force are often linked because one’s mass will often be applied as a force. For example, a football player will move his mass at a high rate (acceleration) and apply that force to a runner to make a tackle. Force is commonly measured in newtons (N). N is the SI unit derived from mass (kg), length (m), and time (s). It is not uncommon to have to convert kg·m-1·s-1 to N. Even though the former term may be more appropriate because of the nature of the quantity, N is used as a tribute to a great scientist. Even though kg is a unit of mass people often use it to describe force. 1 kg = 9.8 N = 2.2 lb Sample calculation: ? N = 8.9 kg * (9.8 N/kg) = 87 N

Work – is the product of two base quantities, force and length or distance (displacement). Work is often thought of as movement against the force of gravity, such as in weight lifting. The movement against gravity is termed positive work, while movement with gravity is negative work. Thus, walking upstairs is positive work and walking down stairs is negative work. In everyday activities negative work is estimated to be about one-third that of positive work. So what about a person lifting weights, they move the weight upward against gravity then lower the weight. The force is equal to the weight, displacement is the distance the weight moves from starting to ending position. Positive work (+w) is the product of these two variables, negative work (-w) is one-third +w. Total work (w) is the sum of +w and –w, or the product of positive work and 1.33. Positive work - +w = F x D Negative work - -w = (F x D)/3 Total work - w = F x D X 1.33

Work is commonly expressed in units called joules (J); larger volumes of work may be expressed as kilojoules (kJ) or even megajoules (MJ). When using the individual components of work (F and D) we will come up with units like N·m or kg·m. 1 J = 1 N·m = 0.10197 kg·m 1 kg·m = 9.8 J Sample calculation: ? J = 325.5 kg.m * (9.8 J/kg.m) = 3192 J

Work can only be demonstrated when working against gravity. When a person is walking on a flat grade the contralateral movement of the arms cancels out the other side and no measurable work is performed. An individual on a treadmill on which the deck is set to a grade is moving against gravity. The grade is expressed as a %. The % is an expression of the vertical displacement for every 100 units of distance traveled horizontally. Thus a 1% grade on a treadmill set at a speed of 100 m.min-1 is yielding 1 m.min-1 of vertical displacement.

Power – is an expression of the rate at which work is done. When a given amount of work is done in a shorter period of time a greater amount of power is generated. Power is work divided by time or: Power (P) = w/t = w · t-1

This term is also applied when discussing the rate at which one transforms metabolic energy to physical performance. The terms anaerobic and aerobic power apply to the discussion of this transformation. The recommended unit for power (P) is the watt (W). W describes the power in totality rather than describing each of the components. Joules per second is an acceptable expression of P and is equivalent to watts. It is not uncommon that in an exercise physiology lab one will encounter the term kg · m · min-1 which is not an acceptable SI term. 1 W = 1 J · s-1 = 6.12 kg · m · min-1 1 kg · m · min-1 = 0.1635 W Sample calculation: ? W = 975 kg.m.min-1 * (0.1635 W/ kg.m.min-1) = 159 W

Energy – describes the amount of metabolic energy released to perform mechanical work and release the heat of the body. The terms energy and work are strongly related to the extent that the same unit J may be used to describe each. Energy is commonly expressed in kilocalories, but this is not an acceptable SI term. We estimate energy expenditure through indirect calorimetry during which an oxygen uptake is calculated. Oxygen uptake or oxygen consumption (vO2) may be expressed in absolute or relative terms. Absolute terms do not consider mass, whereas relative terms consider mass. Absolute oxygen consumption is commonly expressed as liters per minute (L · min-1). The most common relative expression is milliliters per kilogram body mass per minute (ml . kg . min-1). The energy expended per unit of oxygen consumed varies slightly depending upon the substrate . -1 . -1 being utilized to produce the energy but is very close to 5 kcals LO2 or 21 kJ LO2 . 1 kcal = 4.186 kJ Sample calculation: ? kJ = 2137 kcal * (4.186 kJ/kcal) = 8945 kJ

Speed and velocity – defined as the product of distance or displacement divided by time. Distance and displacement have different meanings and are not technically supposed to be interchangeable. The most appropriate unit for expressing speed and velocity is m . s-1, however there are several acceptable SI units derived from any unit of length and time. Examples include m . min-1 and km . h-1. The term miles per hour (mi . h-1) is not an acceptable SI term. 1 m . s-1 = 2.2 mi . h-1 1 mi . h-1 = 1.6 km . h-1 = 26.8 m . min-1 = 0.447 m . s-1 Sample calculation: ? m . s-1 = 61 mi . h-1 * (0.447 m . s-1/ mi . h-1) = 27 m . s-1

Volume – the acceptable SI unit is the liter (L). The lower case l is acceptable but the capital L is commonly used to eliminate confusion with the number 1. Several volumes will be discussed in exercise physiology labs the most common of which has been described above, liters of oxygen.

Meteorological Units Temperature – the base unit of temperature is the kelvin (K). The kelvin scale is based on an absolute zero, the lowest temperature possible. Most laboratories do not use kelvin, the preferred way of providing temperature is in degrees Celsius. Degrees Celsius are acceptable SI units. Fahrenheit is not an acceptable SI unit. F° to C° conversions are not uncommon since Fahrenheit is so commonly used in the US. The conversion requires the movement of the zero point and an adjustment for the size of the degree. Most people are aware that 0 degrees Celsius is at 32°F and this must be corrected. Because there are 9 Fahrenheit degrees for every 5 degrees Celsius we simply divide 9 by 5 to get 1.8 or 1.8 degrees Celsius for every degree Fahrenheit. °F to °C: X °C = (X °F – 32)/1.8 °C to °F: X °F = (X °C * 1.8) + 32 Sample calculation: ? °C = (98.6 °F – 32) / 1.8 = 37.0 °C

Relative Humidity – an indication of the amount of water in the air relative to how much water the air could hold at a given temperature. This value is displayed as a percentage. At 100% RH the air contains the most amount of water vapor that it can hold at that temperature.

Barometric Pressure – is the pressure being exerted by the ‘weight’ of the atmosphere under the pull of gravity. This value is measured by a barometer, thus the common term barometric pressure (PB). The derived term for pressure is pascals (Pa). A pascal (N . m2) is equivalent to the force exerted (N) per unit area (m2). Pascals are very small units and are commonly expressed in hectopascals (hPa; 100Pa) or kilopascals (kPa; 1000 Pa). hPa are equivalent to millibars. The millibar is not an acceptqable SI unit. The expression of PB in mmHg is also unacceptable. At sea level the standard PB is 1013 hPa or millibars and 760 mmHg. According to the American College of Sports Medicine it is acceptable to make exceptions to SI units for blood pressure and lung pressures. Thus, these values are expressed in mmHg. mmHg to hPa: X hPa = X mm Hg * 1.333 hPa to mmHg: Xmm Hg = X hPa * 0.75 Sample calculation: ? hPa = 126 mmHg * (1.33 hPa/mmHg) = 167hPa

Solve the following (show all work)

1. Your subject weighs 178 pounds and is 69.5 inches tall. This subject runs up a set of 5 stairs with 6 inch risers in 1.5 seconds. Express his mass, height, and vertical distance traveled in SI terms. What was the work and power output of your subject?

2. If the temperature is 72 °F and the PB is 755 mmHg, what is the temperature in Celsius and pressure in SI terms?

3. Mr. A is walking on a treadmill at 3.25 mi.h-1 and his oxygen consumption is 0.95 L.min-1. What is his energy expenditure?

4. If the grade of the treadmill on which Mr. A is walking is changed from 0 to 2%, what is his vertical displacement per minute? What is his work output?

5. Convert each of these values to the appropriate SI unit: a. 127 lbs

b. 1515 yd

c. 750 kg.m

d. 1250 kg.m.min-1

e. 2100 kcal

f. 4.3 mi.h-1

g. 120 mmHg

h. 87 kg

6. You observe that as subject A runs on a treadmill his oxygen consumption increases 0.3 L · min-1 with each unit increase in miles per hour. At the same time, his blood pH drops by 0.05 units with each mile per hour increase. Graph these changes. Identify which is an inverse and which is a direct relationship.