22 April 2002

This errata can be reached on the web at http://www.bioe.umd.edu/artjohnson/books/biomechexphys.html

Biomechanics and Exercise Physiology

Errata p Vii line 21. Delete the extra space after "compensations." p xiv line 30. Should read "5.12 Active Responses/363" p 3 Table 1.2.1. Time Range should be "sec (min)" Values for a should be:

sec/kmb (min/kmb) ______

137.9 (2.299) 154.1 (2.569) 170.5 (2.841) 192.2 (3.204) 219.2 (3.654) 155.9 (2.598) 596.2 (9.936) 634.7 (10.578) 170.2 (2.836) 213.9 (3.565) 95.3 (1.589) 60.9 (1.015) 76.0 (1.266) 194.3 (3.238)

x(1-b) p 4 Equation 1.2.2 should read: s = ab p 8 line 13. Delete "strong." p 9 line 22 should read: "This pyruvic acid, in turn, can form lactic acid and other products. ATP is formed in this process. All these reactions" p 10 line 9 should read: "greater is the amount of oxygen required to . . ." p 11 Figure 1.3.3 Time scale is really in minutes, not seconds. -2- p 15 Equation 1.3.6 should read:

V˙   02 max  t wd = 7200 - 7020  ˙   V 02 

where twd = endurance time for dynamic work, sec

 = oxygen uptake, m3/sec V O2  3 V O2 max = maximum oxygen uptake, m /sec

Equation 1.3.7 should read:

2.42  MT max  t ws = 11.40    MT 

where tws = static effort endurance time, sec MT = muscle torque, Nm

MTmax = maximum muscle torque, Nm p 17 two lines before equation 1.3.8. The word "constant" should be replaced by "nearly constant and at a low level." p 23 Equation 1.3.21 should read:

  

VL  M LA (h  l V O2 max )

and the line beneath should read:

"where M˙ LA = constant related to maximal rate of lactic acid production, m2/sec” p 30 line 17. Citation should read: "69:285-290." p 35 Figure 2.2.4. Caption line 1 should read: "... The class 3 lever is a very common arrangement ..." p 36 First paragraph, first sentence, should read: "Muscles are capable of generating large forces of about 7x10 5 N/m 2 . . ."

second paragraph, second sentence should read: "The biceps muscle is attached as a class 3 lever. p 43 line just above equation 2.2.25 should read: " . . -2- . The energy expended during each step is" -4- p 65 Table 2.5.1. Replace heading speeds with 1.1, 1.3, and 1.6 m/sec. p 73 line below Table 3.2.1 should read: "In addition, hemoglobin saturation at an oxygen partial pressure of 11.2x103 N/m 2 . . ." p 74 line 14. Should read: "... response to changes in pCO2 p 75 Equation 3.2.5 should read:

i 7  pO - 3.6663   2 std  S std =  Ci   i=0  pO2 std + 3.6663 

p 77 line 17. Should read: "... accurate below a pO2 of 253 N/m 2 ..."

Add below the definition of B = base excess:

The base excess is the concentration of bicarbonate ion at pH = 7.4 less the standard concentration of bicarbonate corrected for hemoglobin concentration (Jones and Campbell, 1982)

B[c  (8.2 15.6cHb )(7.40pH)23.8][1.00.125cHb ]1.0 HCO3 (3.2.6b)

c  where HCO3 = concentration of bicarbonate ion, mole/m3 3 cHb = concentration of hemoglobin, kg/m p 87 line below equation 3.2.26 should read: "because v 2 = 0 at ri = ro and ri vi = 0 when ri = 0." p 90 line 16. Should read: "where τ = tensile stress in vessel wall, N/m2" p 91 last line above footnote should read: "age of the elasticity of arterial walls . . . "

last line, first paragraph should read: " . . . reduces the average tensile stress in the wall."

sixth line below equation 3.2.38 should read: "wall tension (shear stress) and thickness. It is . . ." p 93 Table 3.2.6. Values in the table should read: -5-

Aorta 16,000/10,700 Large arteries 16,700/10,300 Small arteries l3,100/10,900 p 94 Replace the sentence just before equation (3.2.42) with:

“In each of these cases, maximum oxygen uptake corresponds to a maximum heart rate29 for men or women given by (Jones and Campbell, 1982)

HRmax = (210 – 0.65y)/60 (3.2.42)

Equation (3.2.39) should be:

V˙ (4.2 0.032y) / 60,000 O2max (3.2.39)

Equation (3.2.40) should be:

V˙ (2.6 0.014y) / 60,000 O2max (3.2.40)

The blank line below equation (3.2.41) between V˙ symbol definitions for O2max and y should be eliminated.

Add below the definition of the symbol “y”:

“Note that without the 60,000 in the denominator, these equations have units of L/min.” p 96 Equation 3.2.48 should read:

V s V s W =  pdV +  1/ 2  v2 dV V d V d p 99 Equation 3.2.51 should read:

te J =  ( p2 +pV˙)dt 0 p 100 Table 3.3.1. Units on Mean Blood Pressure should be kN/m 2. p 115 Table 3.4.1, line 4:

Font size for Rs value on the right should be smaller. -6- p 118 Equation 3.4.7 should read:

dV d 2V p - p = ( Rav + Rb ) + I b a dt dt 2

and two lines below equation 3.4.7 should read:

2 "pa = pressure in ascending aorta, N/m " __

dV r p - R p = 0 a dt p 119 Equation 3.4.9 should read: p 121 Line beneath Equation 3.4.23 should read:

2 "pao = aortic pressure at the beginning of systole, N/m " p 122 Table 3.4.2, line 11 should read: "Compliance of arterial system 1.34x10 -8 m5/N (1.78 mL/mm Hg)"

Table 3.4.2. Value for α1 should be:

-5 3 3 α1 357x10 m /(Nsec) (0.0357 cm /(dynesec)) p 125 line 16. Should read: "Equation 3.2.39, 3.2.40, or 3.2.41 ..." p 128 line above equation 3.4.32 should read: "environmental changes with" equation 3.4.33 should read:

HRw = l.08 + (HRf - 1.08) . . . p 133 in parentheses four lines below equation 3.5.7, 1/3 2 5 should read: "(Ib is given as 400 VLV kNsec /m in Table 3.4.2)." p 148 13th line from bottom should read ". . . and heart rate all gave cardiac output changes . . . "  p 160 line 6 should read "W external work rate, Nm/sec" p 162 Add to the references in Chapter 3, between Johnson (1980) and Jones and Johnson (1980): Jones, N.L., and E.J.M. Campbell. 1982. Clinical Exercise Testing, W.B. Saunders, Philadelphia, PA. p 177 Table 4.2.4. Minute volume during heavy exercise should be: -7-

1.7x10-3 m3/sec (100,000 cm3/min) Table 4.2.4. Inspiratory reserve volume should be: 4.4x10-3m3 (4,400 cm3)

Sixth line from bottom should read: "ventilation-to-perfusion ratio is nearly five times smaller at the bottom of the lung . . ." p 178 Table 4.2.2. Units in heading should be: Capillary Volume Cardiac Output Transit Time m3x104 (cm3) m3/sec x 104 (cm3/sec) sec p. 179 List of symbols beneath equation 4.2.4: R = gas constant, N·m/(kg mol·K) p 180 Table 4.2.6. Units of molecular mass should be: kg/kg mol note beneath Table 4.2.6 should read: "Universal gas constant is 8314.34 Nm/(kg molK)" In Table 4.2.6, the units of the Gas Constant should be Nm/(kgK) ( ˙ ) p 183 line 2. Should read:"dioxide expired V CO2 to oxygen ( ˙ ) :" used V O2

Footnote:

All energy density values given should be 106 N·m/kg, or MN·m/kg

The energy density value for fat should be 37.7 x 106 N·m/kg p. 185 line just above equation 4.2.21 should read: “(Ganong, 1963), and the caloric equivalent of carbohydrate has been give as 17.2 x 106 N·m/kg and that of fat is 37.7 106 N·m/kg, then

6 -3 6 -3 (17.2 x10 )(1.23x10 ) XCHO + (1-XCHO)(37.7x10 )(0.50 x 10 ) U = O2 1000

= 2.306XCHO + 18.85 (4.2.21) -8- p 186 Table 4.2.10. Heading should read: "Diffusion Constants of Gases and Vapors in Air at 25oC and 10 5 N/m2 Pressure" p 187 Equation 4.2.29 should be:

-22 1.75 1/2 (1.013x10 )T (l/ M i +l/ M j ) Dij = 1/3 1/3 2 p V i +V j  p 189 Table 4.2.14 heading, line 2 should read: "(37oC) at 1 Atm Pressure (101.3 kN/m2)" Equation 4.2.32 applies when ij p 193 line 5 should read " . . . blood pCO2 is 5333 N/m2 . . ." ____ p 195 two lines above equation 4.2.45 should read:

"Values of pK and  CO2 may be taken as constant values of 6.10 and 0.236 mol/(kN m) . . ." p 199 Figure 4.2.13 Caption line 3 should read: "... is very low and similar for women ..."

Equation 4.2.63 should read:

 V CO Q˙ = 2 eff c c vCO2 effCO2 p 202 Footnote 38 line 2 should read: "... tissue of the lung, the parenchyma.) ..."

Footnote 38 line 4 should read: "... T = 310oK, and R  286.7 Nm/(kg mol oK) ..." p 213 Equation 4.2.81 should read:

 

pe = pˆ i + K 4 /(1-V e / V L ) p 215 The labelling of the ordinate of Figure 4.2.24 should place the zero at the bottom of the graph instead of FRC. p 219 Beginning at Time Constant should read:

When inertance is ignored, the product of resistance times compliance, which has units of seconds, is called the time constant of the lung: -9-

 = RC (4.2.109) where τ = time constant, sec R = resistance, Nsec/m5 C = compliance, m5/N

Lung time constant .... The time constant of exhalation is RC and has a value of about 0.66 sec (Mead, 1960). p 221 line 15 should read:

"positive expiratory pressures become more positive, the loops widen. From Equation 4.2.110 we" p 222 line 5 should read: "... nearly constant at about 20.2 Nm/cm3 ..." p 225 line 12 delete "Carotid bodies are much more sensitive to changes in pO2 than to changes in pCO2." ______p 227 Figure 4.3.8. Units at the bottom are really mmHg. Multiply numbers by 0.13332 to obtain kN/m2. p 230 twelfth line after Mechanoreceptors should read:

"bronchodilation/bronchoconstriction, secretion of mucus, and the diving reflex (see footnote 34," p 245 Line below equation 4.3.8 should read: "where β = parameter in Equation 4.3.7, N/m2" p 246 Equation 4.3.9 should read:

V˙ E = .... p 260 Figure 4.3.30. The lower right-hand arrow should be shifted rightward to match the horizontal placement of the upper right-hand arrow. p 265 fifth line from bottom: Change (Figure 4.2.19) to (Figure 4.2.20). p 268 line 21 should read: " . . . oxygen saturation of blood hemoglobin" p 286 Figure 4.4.9 bottom horizontal axis numbers to the left of zero should be negative. p 302 Replace all subscripts "T" with "t" in equations 4.5.7, 4.5.8, and 4.5.9, and in the four lines below equation 4.5.9. p 305 Replace all subscripts "T" with "t" in equations 4.5.35, 4.5.36, 4.5.37, 4.5.38, 4.5.39, 4.5.40, 4.5.41, 4.5.42, 4.5.43, 4.5.44, 4.5.45 and 4.5.46, and in the definitions below equations 4.5.35, 4.5.36, 4.5.37, -10-

4.5.40 and 4.5.41. p 306 Replace all subscripts "T" with "t" in lines 1, 3, and 4. p 307 Replace all subscripts "T" with "t" in equations 4.5.60, 4.5.61, and 4.5.62 and in the definitions below equation 4.5.62. p 308 Replace all subscripts "T" with "t" in equations 4.5.64, 4.5.65, 4.5.66, 4.5.68, and 4.5.70 and in the definitions below equation 4.5.66. p 310 Replace subscripts "T" with "t" in Table 4.5.1. Line below Table 4.5.1 should read: "Compiled from Grodins et al., 1967." -11- p 321 beginning at line 10, should read:

"included. At rest the total transit time is 60 sec (cardiac output = 1.0x10-4 m3/sec), but at an elevated cardiac output of 3.3x10-4 m3/sec, transit time decreases to 18 sec." p 324 Replace all subscripts "T" with "t" in equation 4.5.109. p 325 Replace all subscripts "T" with "t" in equations 4.5.110, and 4.5.111, and in definitions at the top, below equation 4.5.110, and below equation 4.5.111. p 333 line 9 should read: "The extremum was found by simultaneously solving for all i:" p 344 Replace "BT" with "Bt". p 345 Replace "CT" with "Ct", "CvT" with "Cvt", "CT" with "Ct". p 346 Replace "kTc", "kTe", and "kTi" with "ktc", kte", and "kti". p 348 Replace "PT", PTa", "PTc", "PTe", PTi", and "QT" with "Pt", "Pta", "Ptc", "Pte", "Pti", and "Qt". p 350 Replace "VT", "VTE", and "VTI" with "Vt", "Vte", and "Vti". p 351 Replace "αT", "αTc", "αTe", "αTi", "τaT", and "τvT" with "αt", "αtc", "αte", "αti", "τat", and "τvt". p 355 Reference should read:

Johnson, A. T. 1984. Multidimensional Curve Fitting Program for Biological Data. Comp. Prog. Biomed. 18:259-264.

and, reference for Johnson and Masaitis should end with:

IEEE Trans. Biomed. Eng. 23:376-380. p 361 line 8 should read: "muscular exertion generate large amounts of heat, which ..." p 363 line 1 should read: "5.1.2 Active Responses"

line 17 should read: "heat because the still air layer . . . " p 367 line 22 should read: "Values of fc are given by Equation 5.2.18 or 5.2.19."

footnote 6 line 3 should read: "Lv is upper calf circumference in cm." -12- p. 370 Equation 5.2.17 should be replaced by:

1 R th (0.494Ccl  0.0119) / A men (5.2.17a)

1 R th (0.524Ccl  0.0053) / A women (5.2.17b)

Insert below equation 5.2.17b:

Convection and radiation also contribute to heat loss from clothing. Convection and radiation are parallel heat loss processes, and, likewise, the thermal resistances corresponding to convection and radiation are in parallel with one another. The combination of these parallel resistances is in series with the conduction thermal resistance of the clothing. Thus the overall thermal resistance limiting heat through clothing is

Rtot = R th  R c || R r

1 1 (1.24Ah c ) (1.2h r A) = R th  1 1 (1.2h c A)  (1.2h r A)

1 = R th 1.2A(h r  h c ) (5.2.17c)

o where Rtot = total thermal resistance, C sec/(N m)

o Rc = convection thermal resistance, C sec/(N m)

o Rr = radiation thermal resistance, C sec/(N m)

2 o hc = convection coefficient, N m/(sec m C)

2 o hr = radiation coefficient, N m/(sec m C)

Convection coefficients are discussed in Section 5.2.1 and values may be obtained from Tables 5.2.3, 5.2.4, and 5.2.5. The velocity of “still” air is usually taken to be 0.15 m/sec. Radiation coefficients are discussed in Section 5.2.3, and a value of 4.7 N m/(sec m2 oC) is often used for people inside a room.

Clothed people subjected to radiant heat gain or loss at radiant temperatures different from mean ambient temperature must be treated somewhat differently from those with ambient and radiant temperatures essentially the same. -13-

The line below equation 5.2.19 should be:

“ for clothing ensembles. The increase of surface area due to clothing has been found to be between 15 and 25%.” p 374 Equation 5.2.28 should read:

-1  1 1 2  4 4 qr(1-2) =  + +   T1 - T 2  A11 A2 F 2-1 A2 2 

Equation 5.2.30 should read:

-1  A2 2 1 2  4 4 qr(1-2) =  + +   A2 T1 - T 2  A11 F 2-1 2  p 375 The last part of equation 5.2.36 should be

3 2 2 3 = GE[To - To Te + ToTe - Te ] p 378 Equation 5.2.40 should read:

d = (4 Anude f c  z )/ p 379 Table 5.2.10 heading should be:

γd for Solar Angle of: γz γh ______

Position 30o 45o 60o 75o p 382 Equation 5.2.54 should be:

qevap = hv A ( psat - pH 2 0)

line 10 should read: "pH2O = partial pressure of water _____ vapor in surrounding air, N/m2"

Equation 5.2.56 should be:

hd A ( sat -  a ) H = hva A ( psat - pH 2 O)

Figure 5.2.6 dark lines in the Figure should be labelled, from top to bottom: 40C, 30C, 20C, OC, -10C, -20C. p 383 Equation 5.2.57 should be: -14-

hc H ( sat -  a ) = hva ( p - pH O) Le C sat 2

Beneath equation 5.2.59 insert:

2 "where pa = atmospheric pressure, N/m " ______p 384 Equation 5.2.63 should be: ˙ qevap, res = 0.001 V (59.34 + 0.53  a - 0.0116 pH 2 O)

The second line below equation 5.2.63 should read: 2 pH2O = ambient water vapor pressure, N/m . ____

Equation 5.2.64 should read:

m˙ = 1.67x106 M / A

Second line below equation 5.2.64 should read:

"M/A = metabolic rate per unit body surface area, Nm/ (m2sec)" p 385 Equation 5.2.66 should read:

-5 hvr = 1.725x10 M/A

where M/A = metabolic rate per unit body surface area, Nm/(secm2) p 389 line 10 should read: "1967; Nishi and Gagge, 1970) is"

Equation 5.2.79 should be:

im ( hva / hc )( psat - pH 2 O) A qevap = 1/( hr + hc ) + Lc1 / kc1

Equation 5.2.80 should be:

qevap = w P hva ( psat - pH 2 O) A

p 390 line 2 should read: " ... clothing are compared (Nishi and Gagge, 1970)." -15-

line 3 should read: " ... loss through clothing, Nishi and Gagge (1970)" p 391 The Arrhenius equation 5.2.85 should read:

-/T M  = M o e p 399 Table 5.5.22. left hand margin for Cycling, Dancing, and Gardening should be the same as for Horseback riding and Gymnastics. p 402 Table 5.2.25. Heading should say: "Mass" p 409 last line above footnote should read:

" . . . and found that hypothermic individuals" p 415 line 9 should read:

". . . subcutaneous fat becomes the chief insulative layer. A"

line 20 should read:

". . . found necessary for shivering to occur . . ." p 420 Equation 5.4.4 should be:

˙ qstored,sk = ( C sk A+ cbl V bl )(r  sk ) - ( qr + qc ) - ( qevap - qevap,res )

Equation 5.4.5 should be: ˙ qstored,core = M - qevap,res - qc,res - ( C sk A+ cbl V bl )( r - sk )

Equation 5.4.7 should be:

3 hr = 4FA  (0.5  o +0.5  e + 273 ) (1+1/ Ccl )

Add Equation 5.4.8f:

= 2.9 (rest)

Equation 5.4.10 should be:

hr  rad - hc  a  e = hr + hc

Equation 5.4.11 should be: -16-

-5 qevap, res = 1.725 x 10 M tot ( psat - pH 2 0) p 421 Insert before line 2:

2 "psat = saturated vapor pressure of water, N/m 2 pH2O = water vapor pressure, N/m "

line 10 should read:

3 V˙ bl = volume rate of skin blood flow, m /sec

entries in Table 5.4.1 should be:

6 3 o Specific heat of blood (cbl) 4.187x10 N  m/(m  C)

Specific heat of body (c) 3.5 x 10 3 Nm/(kgoC)

Latent heat of water (H) 2.4 x 10 6 Nm/kg

2 Total evaporative heat loss ( qevap /A) 5.0 N  m/(m sec)

2 Resting metabolic rate (Mr/A) 58.2 Nm/(m sec) p 422 line l should read:

"if θsk>34, (θsk-34) becomes 0, and if θr37, (θr-37) becomes 0."

Equation 5.4.16 should be:

m˙ sw = 250A[ ( sk - 34)+(1-  )( r - 37)] exp [( sk - 34)/10.7]

Equation 5.4.18 should be:

qevap = qevap, res + 250 HA(1- d )( sk - 34)

+ (1 -  )( r - 37) exp [( sk - 34)/10.7]

+ 0.0165 d hc A( psat - pH 2 O)/(1+0.922 hc / Cc1 )

Equation 5.4.19 should be:

 6 V˙ bl   = 0.0442 + 0.3509/ 3.6x10 - 0.01386   A 

line 19 should read:

2 "pH2O = ambient water vapor pressure, N/m " ____ p 424 Equation 5.4.25 should be:

0.37 qevap = 0.0161 A v ( psk K e - pH 2 O) -17-

line 13 should read:

2 "pH2O = partial pressure of water vapor in air, N/m " ____ p 432 Equation 5.4.40 should be:

-4 qevap, res = (86.4+ M)(1.725x10 )(5866 - pH 2 O)

line 22 should read:

2 "pH2O = ambient vapor pressure, N/m " ____ p 433 Equation 5.4.42 should be:

qevap, max = 0.0165 hc A ( psat - pH 2 O)  qevap, sk p 436 Equation 5.5.1 should be:

M = 0.10 W{2.7 +3.2 (s -0.7 )1.65 + 100 G [0.23+0.29 (s -0.7)]} - WsG p 439 Equation 5.5.9 should be:

Emax = 0.0165 A im ( psk - pH 2 0) p 440 line 2 should read:

"psk = vapor pressure of water at the average skin o temperature; for θsk = 36 C," ___

line 4 should read:

2 "pH2O = water vapor pressure in air, N/m " ____

Equation 5.5.10 should be:

-6 -0.455 m˙ sw = 7.75x10 Ereq ( Emax /A )

50 < ( Ereq /A) < 360;

20 < ( Emax /A) < 525 p 447 Delete line 21:

2 "MA metabolic rate per unit area, Nm/(m sec)"

2 Insert before line 35: "pa = atmospheric pressure, N/m "

line 35 should be: -18-

2 "pH2O ambient water vapor pressure, N/m " ____ p 463 line 18 from bottom, right column, should read:

"mechanics 71, 100, 115, 122, 131" p 484 line 5, right column, should read:

"arterial 100, 115, 122, 144"

insert above line 9, right column:

"and cardiovascular work, 118-125" p 489 Insert before line 9: "maximum, 385, 418" p 491 add under "transit time:"

"blood, 32l"