Errata for the book The Science of Vehicle Dynamics

Errata for the book The Science of Vehicle Dynamics Massimo Guiggiani April 18, 018 These are all the errors and omissions for the book The Science of Vehicle Dynamics, published by Springer (014), reported as of April 18, 018. They are listed here in two ways: by page number (better for first reading), right hereafter; in chronological order (better for updating), beginning on page 17. Positions in the book are indicated by page and line number, where the top line of a page is number 1 and the bottom line is number 1. A running head and a page number are not considered to be lines, but all other lines are. Please report any additional errors to massimo.guiggiani@unipi.it Updates will be available at www.dimnp.unipi.it/guiggiani-m/svderrata.pdf

x x x x x x x x x x x x x x x x x x Chapter 1 - Introduction Errata ordered by page number Ch. 1, page, lines 5 and 8 Replace kart with cart. [First reported by Basilio Lenzo on 0 November 015] Ch. 1, page 4, line 15 Replace from the axis with from the longitudinal axis x. [First reported by Basilio Lenzo on 0 November 015] Chapter - Mechanics of the Wheel with Tire Ch., page 7, lines 14 17 Replace with In the lower part, the sidewalls bend and, thanks to the air pressure p a, they apply more vertical forces F a in the bead area than in the upper part. The overall effect on the rim is a vertical load F z. The higher the air pressure p a, the lower the sidewall bending. In the lower part the radial cords encased in the sidewalls undergo a reduction of tension because they no longer have to balance the air pressure p a acting on the contact patch. The net result is that the total upward pull of the cords on the bead exceeds that of the downward pull by an amount equal to the vertical load F z. [First reported in the book review by Jon W. Mooney, Noise Control Engineering Journal, Vol. 6 (3), May June, 014, added here on 31 January 015] Ch., page 8, Fig..1 The correct figure is pa pa F z pa pa lower meridian tensile stress F z

[First reported in the review by Jon W. Mooney, Noise Control Engineering Journal, Vol. 6 (3), May-June, 014, added here on 31 January 015] Ch., page 9, line 1 Replace breaking with braking. [First reported by Bengt J. H. Jacobson on 14 October 014] Ch., page 31, eqn. (.69) The correct equation is σ y tan α = 1 + σ x without the last part. [First reported by Massimo Guiggiani on 8 November 015] Ch., page 3, Fig..14 Replace x with y and y with x in the axis labels. [First reported by Cecilia Moreschini on 6 March 018] Ch., page 39, line 1 Add the sentence All forces are in kn.. [First reported by Basilio Lenzo on 6 November 015] Ch., page 41, captions of Figs..3 and.4 Replace the first two instances of F y with F x. [First reported by Massimo Guiggiani on 1 November 015] Chapter 3 - Vehicle Model for Handling and Performance Ch. 3, page 49, Fig. 3. Replace β with ˆβ. [First reported by Matteo Pergoli on 16 October 017] Ch. 3, page 49, eqn. (3.5) Replace sin ψ with sin ψ. [First reported by Basilio Lenzo on 0 November 015] 3

Ch. 3, page 51, Fig. 3.4 Replace β with ˆβ. [First reported by Matteo Pergoli on 16 October 017] Ch. 3, page 5, eqn. (3.15) Insert the unit vector j before the last =. The correct equation is a C = (a x r S ṙr)i + (a y r R + ṙs)j = r(ṙi Ṡj) [First reported by Antonio Sponziello on 13 March 014] Ch. 3, page 5, line 9 Add the sentence Actually, in most cases β ˆβ, and they can be considered as synonymous (Fig. 3.). [First reported by Massimo Guiggiani on 10 January 015] Ch. 3, pages 53 and 54 All instances of sin(β) and cos(β) should be replaced by sin( ˆβ) and cos( ˆβ), respectively. [First reported by Massimo Guiggiani on 10 January 015] Ch. 3, page 54, eqn. (3.3) A cos ˆβ is missing. The correct equation is ρ G = r + β cos ˆβ u cos ˆβ = r u + v + vu v u (u + v ) 3 [First reported by Basilio Lenzo on 3 December 015] Ch. 3, page 55, eqn. (3.40) Unit vectors i and j are missing. The correct equation is GK = a xr a y ṙ r 4 + ṙ i + a xṙ + a y r r 4 + ṙ j [First reported by Massimo Guiggiani on 3 December 014] 4

Ch. 3, page 57, eqn. (3.45) In the third and fourth equations change the sign in front of (v ra ). The correct equations are σ x1 = [(u rt /) cos(δ 1 ) + (v ra ) sin(δ 1 )] ω 1 r ω 1 r σ x = [(u + rt /) cos(δ ) + (v ra ) sin(δ )] ω r ω r [First reported by Riccardo Bartolozzi on 10 January 015] Ch. 3, page 57, eqn. (3.46) In the last equation change the sign in front of rt /. The correct equation is σ y = (v ra ) cos(δ ) (u + rt /) sin(δ ) ω r [First reported by Riccardo Bartolozzi on 10 January 015] Ch. 3, page 59, lines under eqn. (3.5) To be replaced with since J yz 0. Moreover, it is worth noting that typically J zx J z. Therefore, we can often safely assume K r G J zṙk. [First reported by Basilio Lenzo on 3 December 015] Ch. 3, page 59, line 14 Replace couple with moment. [First reported by Riccardo Bartolozzi on 10 January 015] Ch. 3, page 63, line Replace (3.63) with (3.53). [First reported by Riccardo Bartolozzi on 10 January 015] Ch. 3, page 63, eqn. (3.63) Replace Z a1 and Z a with Z a 1 and Z a, respectively. [First reported by Francesco Bucchi on 9 October 014] 5

Ch. 3, page 64, eqn. (3.65) Replace the second Z a1 with Z a. [First reported by Francesco Bucchi on 9 October 014] Ch. 3, page 64, eqn. (3.65) and (3.66) Replace Z a1 and Z a with Z a 1 and Z a, respectively. [First reported by Francesco Bucchi on 9 October 014] Ch. 3, page 65, line 14 Delete Z. [First reported by Riccardo Bartolozzi on 10 January 015] Ch. 3, page 70, line -6 Delete the sentence An alternative selection could be the roll angle ϕ and the track variations t 1 and t. [First reported by Stelios (Stylianos) Markolefas on 3 February 017] Ch. 3, page 79, eqn. (3.101 ) Change the sign in front of N Y /Y. [First reported by Stelios (Stylianos) Markolefas on 5 October 016] Ch. 3, page 80, eqn. (3.110) The last two terms in both equations must be changed. Moreover, in the denominator of the next to last term in the second equation the subscript should be. The correct equation is ] ϕ s 1 = 1 k ϕ1 k ϕ kϕ s 1 k ϕ [ Y (h q b ) k ϕ Y 1q 1 k p ϕ 1 + Y q k p ϕ [ ] ϕ s = 1 k ϕ1 k ϕ Y (h q b ) kϕ s Y q k ϕ k ϕ1 k p + Y 1q 1 ϕ k p ϕ 1 The same equation (3.110) is repeated on page 88 and hence must be corrected as well. [First reported by Daniele Calderini on 30 September 014] Ch. 3, page 85, line 1 Change m n to m u. However, throughout the book, m n and m u should be considered as synonymous. [First reported by Aurele Verne on 13 March 014] 6

Ch. 3, page 87, eqn. (3.1) The correct equation is Xij + Y ij pz ij and Z ij 0 [First reported by Marco Gabiccini on December 016] Ch. 3, page 88, eqn. (3.45 ) In the third and fourth equations change the sign in front of (v ra ). The correct equations are σ x1 = [(u rt /) cos(δ 1 ) + (v ra ) sin(δ 1 )] ω 1 r ω 1 r σ x = [(u + rt /) cos(δ ) + (v ra ) sin(δ )] ω r ω r [First reported by Stelios (Stylianos) Markolefas on 5 October 016] Ch. 3, page 89, eqn. (3.46 ) In the last equation change the sign in front of rt /. The correct equation is σ y = (v ra ) cos(δ ) (u + rt /) sin(δ ) ω r [First reported by Stelios (Stylianos) Markolefas on 5 October 016] Ch. 3, page 90, eqn. (3.16) The second equation should be M l M h 0. [First reported by Massimo Guiggiani on 7 October 016] Chapter 4 - Braking Performance Ch. 4, page 107, eqn. (4.1) In the next to last term of the third equation the subscript should be. The correct equation is 0 = (X 1 + X + X a ) h (Z 1 Z a 1 ) a 1 + (Z Z a ) a [First reported by Mauro Scalise on October 014] 7

Chapter 5 - The Kinematics of Cornering Ch. 5, page 117, line 3 Change ṙ to r. [First reported by Massimo Guiggiani on 17 July 014] Ch. 5, pages 16 130 All instances of cos(β), cos(β 1 ) and cos(β ) should be replaced, respectively, by cos( ˆβ), cos( ˆβ 1 ) and cos( ˆβ ), consistently with eqn. (3.18). [First reported by Massimo Guiggiani on 10 January 015] Ch. 5, page 17, Fig. 5.19 The correct figure is β1< 0 E C F 1 A 1 E 1 F β< 0 A β1> 0 F E 1 A 1 F 1 C E A β> 0 [First reported by Matteo Pergoli on 8 November 016] 8

Chapter 6 - Handling of Road Cars Ch. 6, page 13, eqn. (6.3) In the last two equations the sign in front of (v ra ) is +. [First reported by Massimo Guiggiani on 1 December 016] Ch. 6, page 13, eqn. (6.5) Insert a minus sign in front of mvr. The beginning of the correct equation is ma x = mvr =... [First reported by Marco Gabiccini on 15 April 016] Ch. 6, page 133, eqn. (6.8) There are the same errors as above, that is the last two terms in both equations must be changed. Moreover, in the denominator of the next to last term in the second equation the subscript should be. The correct equation is ϕ s 1 = ma y 1 k s ϕ 1 k ϕ1 k ϕ k ϕ [ h q k ϕ a q 1 lk p ϕ 1 + a 1q lk p ϕ ] = ma y ρ s 1 [ ] ϕ s 1 k ϕ1 k ϕ h q = ma y kϕ s a 1q k ϕ k ϕ1 lk p + a q 1 ϕ lk p = ma y ρ s ϕ 1 [First reported by Francesco Bucchi on 9 October 014] Ch. 6, page 134, eqn. (6.1) The mass m is missing in the last term of the second line. The correct equation is = δ 0 ij + δ v τ ij + Υ ij mρ s i a y [First reported by Niccolò Galeotti on 9 January 015] Ch. 6, page 135, eqn. (6.14) Replace a y with ma y in all last terms. [First reported by Massimo Guiggiani on 9 December 015] 9

Ch. 6, page 135, eqn. (6.17) Change the sign of both terms within square brackets. The correct equation is ( ) ] qi b i γ i ma y [ ρ s i + ρ p i = ma y χ i [First reported by Francesco Bucchi on 9 October 014] b i Ch. 6, page 135, eqn. (6.18) Delete the term cos ( δ ij (δ v ) ). [First reported by Francesco Bucchi on 9 October 014] Ch. 6, page 137, eqn. (6.3) and (6.5) Replace a y with ma y in all last terms. [First reported by Massimo Guiggiani on 9 December 015] Ch. 6, page 15, eqn. (6.59) The sign of the last term is wrong. The correct equation is mã y = Y 1 (α 1 ) + Y (α ) 0 = Y 1 (α 1 )a 1 Y (α )a [First reported by Aurele Verne on 3 September 014] Ch. 6, page 15, eqn. (6.60) Exchange a 1 and a. The correct equation is Y 1 (α 1 )l ma = ã y and [First reported by Aurele Verne on 3 September 014] Y (α )l ma 1 = ã y Ch. 6, page 15, eqn. (6.61) Exchange a 1 and a. The correct equation is Y 1 (α 1 )l = Y 1(α 1 ) mga Z1 0 = ãy g and Y (α )l = Y (α ) mga 1 Z 0 = ãy g [First reported by Aurele Verne on 3 September 014] 10

Ch. 6, page 153, eqn. (6.66) The third terms must be exchanged. The correct equation is ( ρp grad ρ p =, ρ ) p = (ρ y, ρ δ ) = ( ) K ρy, K ρδ ã y δ v ( βp grad β p =, β ) p = (β y, β δ ) = ( ) K βy, K βδ ã y δ v [First reported by Nicola Boscolo Zemelo on 6 May 014] Ch. 6, page 157, line 8 Replace two intersecting lines with the two lines intersecting at the vertical axis. [First reported by Francesco Bucchi on 9 October 014] Ch. 6, page 157, line 1 Replace In Fig. 6.15 with In Fig. 6.14. [First reported by Cristiano Pieralice on 10 February 015] Ch. 6, page 164, line 3 Replace 6.4 with 6.3 [First reported by Davide Malatesta on 31 January 018] Ch. 6, page 164, line 4 Replace 6.18 with 6.19 [First reported by Davide Malatesta on 31 January 018] Ch. 6, page 168, line 1 Replace negative with positive. [First reported by Giulio De Simone on 0 November 015] Ch. 6, page 17, line 15 Replace damping coefficient with damping ratio [First reported by Alessio Artoni on 15 May 016] 11

Ch. 6, page 17, eqn. (6.91) Delete all the last term (it is not correct), thus leaving only ω s = ω n 1 ζ [First reported by Emanuele Abbatessa on 17 April 018] Ch. 6, page 174, eqn. (6.101) The correct equation is β t + ζω n βt + ω nβ t = a b 1 + a 1 b + ḃ1 = F β ρ t + ζω n ρ t + ω nρ t = a 1 b 1 a 11 b + ḃ = F ρ [First reported by Massimo Guiggiani on 17 March 016] Ch. 6, page 176, eqn. (6.66 ) To be corrected like eqn. (6.66) [First reported by Niccolò Galeotti on 9 January 015] Ch. 6, page 183, eqn. (6.14) Replace C 1 with Φ 1 in the last equation. [First reported by Francesco Bucchi on 8 November 014] Ch. 6, page 184, Table 6.1 In the last column, replace deg/g with deg/(mg). [First reported by Massimo Guiggiani on March 016] Ch. 6, page 195, line 10 The sentence If we assume δ v = 0 should appear at the beginning of line 10, instead of line 1. [First reported by Aurele Verne on 30 September 014] Ch. 6, page 198, Fig. 6.44 Reverse the sign of α 1 and α. [First reported by Nicola Cambri on 17 February 017] 1

Chapter 7 - Handling of Race Cars Ch. 7, page 06, eqn. (7.5) In the third equation change the sign of the right-hand side term. The correct equation is X 1 = [ F y11 sin(δ 11 ) F y1 sin(δ 1 ) ] / 0 [First reported by Daniele Calderini on 15 April 015] Ch. 7, page 07, eqn. (7.13) In the denominators replace with 4. The correct equation is D 1 = 1 4 ρ as a C z1 and D = 1 4 ρ as a C z [First reported by Samuele Barsacchi on 3 February 015] Ch. 7, page 08, eqn. (7.17) In the third equation, t 1 is missing in the left-hand side term. Moreover, change the sign. The correct equation is [ Fy11 sin(δ 11 ) F y1 sin(δ 1 ) ] t 1 / = X 1 (v, r, u, δ v, N d )t 1 [First reported by Aurele Verne and Daniele Calderini on 30 September 014 and 15 April 015] Ch. 7, page 08, eqn. (7.18) In the fourth equation, t is missing twice. The correct equation is N d = ( ) F x F x1 t / = X (v, r, u, δ v, N d, ω 1, ω )t [First reported by Aurele Verne on 30 September 014] Ch. 7, page 0, caption of Fig. 7.3 Replace steer angle with lateral acceleration [First reported by Massimo Guiggiani on 15 July 016] Chapter 8 - Ride Comfort and Road Holding Ch. 8, page 46, line 17 Replace z(t) = 5y(t) with y(t) = 5z(t). [First reported by Massimo Guiggiani on 4 January 018] 13

Ch. 8, page 47, line 5 Insert a minus sign before Ω. [First reported by Giacomo Bianco on 10 April 014] Ch. 8, page 48, line 11 The correct subscript is. Therefore, it should be: ζ = 0.44 and ω 1 ζ = 77.0 rad/s for the second mode [First reported by Massimo Guiggiani on 3 January 018] Ch. 8, pages 49 5, Figs. 8.8, 8.11 and 8.1 Frequency in Hertz (Hz) is shown along the abscissa, not radians per second. [First reported by Massimo Guiggiani on 16 December 015] Ch. 8, page 58, eqn. (8.70) The correct equation is x 1 = (Z s1, 1) = ( ) zs1 (t) θ 1 (t), 1 and x = (Z s, 1) = ( ) zs (t) θ (t), 1 [First reported by Niccolò Galeotti on 9 January 015] Ch. 8, page 58, eq. (8.7) Insert a minus sign in front of the two fractions. [First reported by Cecilia Moreschini on 6 March 018] Ch. 8, page 65, eq. (8.101) Insert a minus sign in front of the last term. [First reported by Cecilia Moreschini on 6 March 018] Chapter 9 - Handling with Roll Motion Ch. 9, page 84, eqn. (9.31) Change the sign from minus to plus within the last parentheses of each row. equation is The correct K r G = [J x ṗ (J y J z )qr J xy ( q rp) J yz (q r ) J zx (ṙ + pq)]i 3 + [J y q (J z J x )rp J yz (ṙ pq) J zx (r p ) J xy (ṗ + qr)]j 3 + [J z ṙ (J x J y )pq J zx (ṗ qr) J xy (p q ) J yz ( q + rp)]k 3 14

[First reported by Oleg Yuri Giovannini on November 015] Ch. 9, page 84, eqn. (9.3) Change the sign from minus to plus within the last parentheses in the first row. The correct equation is K r G = [J x ṗ (J y J z )qr J zx (ṙ + pq)]i 3 +... [First reported by Oleg Yuri Giovannini on November 015] Ch. 9, page 87, eqn. (9.44) Change the second instance of Z a1 to Z a. The correct equation is Z = Z 1 + Z a1 + Z + Z a mg [First reported by Giacomo Bianco on 10 April 014] Chapter 10 - Tire Models Ch. 10, page 99, eqn. (10.7) Replace CP with DP. The correct equation is V P = V d + Ω sz k DP = V c + q + Ω sz k (ˆxi + ŷj) [First reported by Samuele Barsacchi on 31 January 015] Ch. 10, page 337, eqn. (10.113) Replace s xy with s yy in the last term. [First reported by Alberto Bortolini on 10 January 016] Ch. 10, page 337, line 4 Replace with in both occurrences. [First reported by Massimo Guiggiani on 16 August 017] 15

Ch. 10, page 340, eqn. (10.18) In the seventh equation replace e x by e y. The correct equation is k e y (ˆx s (t), t) = µp(ˆx s (t)) [First reported by Aurele Verne on 10 December 014] 16

Same Errata, but in Chronological Order 014 Ch. 3, page 5, eqn. (3.15) Insert the unit vector j before the last =. The correct equation is a C = (a x r S ṙr)i + (a y r R + ṙs)j = r(ṙi Ṡj) [First reported by Antonio Sponziello on 13 March 014] Ch. 3, page 85, line 1 Change m n to m u. However, throughout the book, m n and m u should be considered as synonymous. [First reported by Aurele Verne on 13 March 014] Ch. 8, page 47, line 5 Insert a minus sign before Ω. [First reported by Giacomo Bianco on 10 April 014] Ch. 9, page 87, eqn. (9.44) Change the second instance of Z a1 to Z a. The correct equation is Z = Z 1 + Z a1 + Z + Z a mg [First reported by Giacomo Bianco on 10 April 014] Ch. 6, page 153, eqn. (6.66) The third terms must be exchanged. The correct equation is ( ρp grad ρ p =, ρ ) p = (ρ y, ρ δ ) = ( ) K ρy, K ρδ ã y δ v ( βp grad β p =, β ) p = (β y, β δ ) = ( ) K βy, K βδ ã y δ v [First reported by Nicola Boscolo Zemelo on 6 May 014] 17

Ch. 5, page 117, line 3 Change ṙ to r. [First reported by Massimo Guiggiani on 17 July 014] Ch. 6, page 15, eqn. (6.59) The sign of the last term is wrong. The correct equation is mã y = Y 1 (α 1 ) + Y (α ) 0 = Y 1 (α 1 )a 1 Y (α )a [First reported by Aurele Verne on 3 September 014] Ch. 6, page 15, eqn. (6.60) Exchange a 1 and a. The correct equation is Y 1 (α 1 )l ma = ã y and [First reported by Aurele Verne on 3 September 014] Y (α )l ma 1 = ã y Ch. 6, page 15, eqn. (6.61) Exchange a 1 and a. The correct equation is Y 1 (α 1 )l = Y 1(α 1 ) mga Z1 0 = ãy g and Y (α )l = Y (α ) mga 1 Z 0 = ãy g [First reported by Aurele Verne on 3 September 014] Ch. 7, page 08, eqn. (7.18) In the fourth equation, t is missing twice. The correct equation is N d = ( ) F x F x1 t / = X (v, r, u, δ v, N d, ω 1, ω )t [First reported by Aurele Verne on 30 September 014] Ch. 6, page 195, line 10 The sentence If we assume δ v = 0 should appear at the beginning of line 10, instead of line 1. [First reported by Aurele Verne on 30 September 014] 18

Ch. 3, page 80, eqn. (3.110) The last two terms in both equations must be changed. Moreover, in the denominator of the next to last term in the second equation the subscript should be. The correct equation is ] ϕ s 1 = 1 k ϕ1 k ϕ kϕ s 1 k ϕ [ Y (h q b ) k ϕ Y 1q 1 k p ϕ 1 + Y q k p ϕ [ ] ϕ s = 1 k ϕ1 k ϕ Y (h q b ) kϕ s Y q k ϕ k ϕ1 k p + Y 1q 1 ϕ k p ϕ 1 The same equation (3.110) is repeated on page 88 and hence must be corrected as well. [First reported by Daniele Calderini on 30 September 014] Ch. 6, page 133, eqn. (6.8) There are the same errors as above, that is the last two terms in both equations must be changed. Moreover, in the denominator of the next to last term in the second equation the subscript should be. The correct equation is ϕ s 1 = ma y 1 k s ϕ 1 k ϕ1 k ϕ k ϕ [ h q k ϕ a q 1 lk p ϕ 1 + a 1q lk p ϕ ] = ma y ρ s 1 [ ] ϕ s 1 k ϕ1 k ϕ h q = ma y kϕ s a 1q k ϕ k ϕ1 lk p + a q 1 ϕ lk p = ma y ρ s ϕ 1 [First reported by Francesco Bucchi on 9 October 014] Ch. 4, page 107, eqn. (4.1) In the next to last term of the third equation the subscript should be. The correct equation is 0 = (X 1 + X + X a ) h (Z 1 Z a 1 ) a 1 + (Z Z a ) a [First reported by Mauro Scalise on October 014] Ch. 3, page 63, eqn. (3.63) Replace Z a1 and Z a with Z a 1 and Z a, respectively. [First reported by Francesco Bucchi on 9 October 014] Ch. 3, page 64, eqn. (3.65) Replace the second Z a1 with Z a. [First reported by Francesco Bucchi on 9 October 014] 19

Ch. 3, page 64, eqn. (3.65) and (3.66) Replace Z a1 and Z a with Z a 1 and Z a, respectively. [First reported by Francesco Bucchi on 9 October 014] Ch. 6, page 135, eqn. (6.17) Change the sign of both terms within square brackets. The correct equation is ( ) ] qi b i γ i ma y [ ρ s i + ρ p i = ma y χ i [First reported by Francesco Bucchi on 9 October 014] b i Ch. 6, page 135, eqn. (6.18) Delete the term cos ( δ ij (δ v ) ). [First reported by Francesco Bucchi on 9 October 014] Ch. 6, page 157, line 8 Replace two intersecting lines with the two lines intersecting at the vertical axis. [First reported by Francesco Bucchi on 9 October 014] Ch., page 9, line 1 Replace breaking with braking. [First reported by Bengt J. H. Jacobson on 14 October 014] Ch. 6, page 183, eqn. (6.14) Replace C 1 with Φ 1 in the last equation. [First reported by Francesco Bucchi on 8 November 014] Ch. 3, page 55, eqn. (3.40) Unit vectors i and j are missing. The correct equation is GK = a xr a y ṙ r 4 + ṙ i + a xṙ + a y r r 4 + ṙ j [First reported by Massimo Guiggiani on 3 December 014] 0

Ch. 10, page 340, eqn. (10.18) In the seventh equation replace e x by e y. The correct equation is k e y (ˆx s (t), t) = µp(ˆx s (t)) [First reported by Aurele Verne on 10 December 014] 015 Ch. 3, page 57, eqn. (3.45) In the third and fourth equations change the sign in front of (v ra ). The correct equations are σ x1 = [(u rt /) cos(δ 1 ) + (v ra ) sin(δ 1 )] ω 1 r ω 1 r σ x = [(u + rt /) cos(δ ) + (v ra ) sin(δ )] ω r ω r [First reported by Riccardo Bartolozzi on 10 January 015] Ch. 3, page 57, eqn. (3.46) In the last equation change the sign in front of rt /. The correct equation is σ y = (v ra ) cos(δ ) (u + rt /) sin(δ ) ω r [First reported by Riccardo Bartolozzi on 10 January 015] Ch. 3, page 59, line 14 Replace couple with moment. [First reported by Riccardo Bartolozzi on 10 January 015] Ch. 3, page 63, line Replace (3.63) with (3.53). [First reported by Riccardo Bartolozzi on 10 January 015] Ch. 3, page 65, line 14 Delete Z. [First reported by Riccardo Bartolozzi on 10 January 015] 1

Ch. 3, pages 53 and 54 All instances of sin(β) and cos(β) should be replaced by sin( ˆβ) and cos( ˆβ), respectively. [First reported by Massimo Guiggiani on 10 January 015] Ch. 5, pages 16 130 All instances of cos(β), cos(β 1 ) and cos(β ) should be replaced, respectively, by cos( ˆβ), cos( ˆβ 1 ) and cos( ˆβ ), consistently with eqn. (3.18). [First reported by Massimo Guiggiani on 10 January 015] Ch. 3, page 5, line 9 Add the sentence Actually, in most cases β ˆβ, and they can be considered as synonymous (Fig. 3.). [First reported by Massimo Guiggiani on 10 January 015] Ch. 6, page 134, eqn. (6.1) The mass m is missing in the last term of the second line. The correct equation is = δ 0 ij + δ v τ ij + Υ ij mρ s i a y [First reported by Niccolò Galeotti on 9 January 015] Ch. 6, page 176, eqn. (6.66 ) To be corrected like eqn. (6.66) [First reported by Niccolò Galeotti on 9 January 015] Ch. 8, page 58, eqn. (8.70) The correct equation is x 1 = (Z s1, 1) = ( ) zs1 (t) θ 1 (t), 1 and x = (Z s, 1) = ( ) zs (t) θ (t), 1 [First reported by Niccolò Galeotti on 9 January 015] Ch. 10, page 99, eqn. (10.7) Replace CP with DP. The correct equation is V P = V d + Ω sz k DP = V c + q + Ω sz k (ˆxi + ŷj) [First reported by Samuele Barsacchi on 31 January 015]

Ch., page 7, lines 14 17 Replace with In the lower part, the sidewalls bend and, thanks to the air pressure p a, they apply more vertical forces F a in the bead area than in the upper part. The overall effect on the rim is a vertical load F z. The higher the air pressure p a, the lower the sidewall bending. In the lower part the radial cords encased in the sidewalls undergo a reduction of tension because they no longer have to balance the air pressure p a acting on the contact patch. The net result is that the total upward pull of the cords on the bead exceeds that of the downward pull by an amount equal to the vertical load F z. [First reported in the review by Jon W. Mooney, Noise Control Engineering Journal, Vol. 6 (3), May-June, 014, added here on 31 January 015] 3

x x x x x x x x x x x x x x x x x x x Ch., page 8, Fig..1 The correct figure is p a p a F z p a p a lower meridian tensile stress F z [First reported in the review by Jon W. Mooney, Noise Control Engineering Journal, Vol. 6 (3), May-June, 014, added here on 31 January 015] Ch. 7, page 07, eqn. (7.13) In the denominators replace with 4. The correct equation is D 1 = 1 4 ρ as a C z1 and D = 1 4 ρ as a C z [First reported by Samuele Barsacchi on 3 February 015] Ch. 6, page 157, line 1 Replace In Fig. 6.15 with In Fig. 6.14. [First reported by Cristiano Pieralice on 10 February 015] Ch. 7, page 06, eqn. (7.5) In the third equation change the sign of the right-hand side term. The correct equation is X 1 = [ F y11 sin(δ 11 ) F y1 sin(δ 1 ) ] / 0 [First reported by Daniele Calderini on 15 April 015] 4

Ch. 7, page 08, eqn. (7.17) In the third equation, t 1 is missing in the left-hand side term. Moreover, change the sign. The correct equation is [ Fy11 sin(δ 11 ) F y1 sin(δ 1 ) ] t 1 / = X 1 (v, r, u, δ v, N d )t 1 [First reported by Aurele Verne and Daniele Calderini on 30 September 014 and 15 April 015] Ch., page 31, eqn. (.69) The correct equation is σ y tan α = 1 + σ x without the last part. [First reported by Massimo Guiggiani on 8 November 015] Ch., page 41, captions of Figs..3 and.4 Replace the first two instances of F y with F x. [First reported by Massimo Guiggiani on 1 November 015] Ch. 1, page, lines 5 and 8 Replace kart with cart. [First reported by Basilio Lenzo on 0 November 015] Ch. 1, page 4, line 15 Replace from the axis with from the longitudinal axis x. [First reported by Basilio Lenzo on 0 November 015] Ch. 3, page 49, eqn. (3.5) Replace sin ψ with sin ψ. [First reported by Basilio Lenzo on 0 November 015] Ch. 6, page 168, line 1 Replace negative with positive. [First reported by Giulio De Simone on 0 November 015] 5

Ch. 9, page 84, eqn. (9.31) Change the sign from minus to plus within the last parentheses of each row. equation is The correct K r G = [J x ṗ (J y J z )qr J xy ( q rp) J yz (q r ) J zx (ṙ + pq)]i 3 + [J y q (J z J x )rp J yz (ṙ pq) J zx (r p ) J xy (ṗ + qr)]j 3 + [J z ṙ (J x J y )pq J zx (ṗ qr) J xy (p q ) J yz ( q + rp)]k 3 [First reported by Oleg Yuri Giovannini on November 015] Ch. 9, page 84, eqn. (9.3) Change the sign from minus to plus within the last parentheses in the first row. The correct equation is K r G = [J x ṗ (J y J z )qr J zx (ṙ + pq)]i 3 +... [First reported by Oleg Yuri Giovannini on November 015] Ch., page 39, line 1 Add the sentence All forces are in kn.. [First reported by Basilio Lenzo on 6 November 015] Ch. 3, page 54, eqn. (3.3) A cos ˆβ is missing. The correct equation is ρ G = r + β cos ˆβ u cos ˆβ = [First reported by Basilio Lenzo on 3 December 015] r u + v + vu v u (u + v ) 3 Ch. 3, page 59, lines under eqn. (3.5) To be replaced with since J yz 0. Moreover, it is worth noting that typically J zx J z. Therefore, we can often safely assume K r G J zṙk. [First reported by Basilio Lenzo on 3 December 015] 6

Ch. 6, page 135, eqn. (6.14) Replace a y with ma y in all last terms. [First reported by Massimo Guiggiani on 9 December 015] Ch. 6, page 137, eqn. (6.3) and (6.5) Replace a y with ma y in all last terms. [First reported by Massimo Guiggiani on 9 December 015] Ch. 8, pages 49 5, Figs. 8.8, 8.11 and 8.1 Frequency in Hertz (Hz) is shown along the abscissa, not radians per second. [First reported by Massimo Guiggiani on 16 December 015] 016 Ch. 10, page 337, eqn. (10.113) Replace s xy with s yy in the last term. [First reported by Alberto Bortolini on 10 January 016] Ch. 6, page 184, Table 6.1 In the last column, replace deg/g with deg/(mg). [First reported by Massimo Guiggiani on March 016] Ch. 6, page 174, eqn. (6.101) The correct equation is β t + ζω n βt + ω nβ t = a b 1 + a 1 b + ḃ1 = F β ρ t + ζω n ρ t + ω nρ t = a 1 b 1 a 11 b + ḃ = F ρ [First reported by Massimo Guiggiani on 17 March 016] Ch. 6, page 13, eqn. (6.5) Insert a minus sign in front of mvr. The beginning of the correct equation is ma x = mvr =... [First reported by Marco Gabiccini on 15 April 016] 7

Ch. 6, page 17, line 15 Replace damping coefficient with damping ratio [First reported by Alessio Artoni on 15 May 016] Ch. 7, page 0, caption of Fig. 7.3 Replace steer angle with lateral acceleration [First reported by Massimo Guiggiani on 15 July 016] Ch. 3, page 88, eqn. (3.45 ) In the third and fourth equations change the sign in front of (v ra ). The correct equations are σ x1 = [(u rt /) cos(δ 1 ) + (v ra ) sin(δ 1 )] ω 1 r ω 1 r σ x = [(u + rt /) cos(δ ) + (v ra ) sin(δ )] ω r ω r [First reported by Stelios (Stylianos) Markolefas on 5 October 016] Ch. 3, page 89, eqn. (3.46 ) In the last equation change the sign in front of rt /. The correct equation is σ y = (v ra ) cos(δ ) (u + rt /) sin(δ ) ω r [First reported by Stelios (Stylianos) Markolefas on 5 October 016] Ch. 3, page 79, eqn. (3.101 ) Change the sign in front of N Y /Y. [First reported by Stelios (Stylianos) Markolefas on 5 October 016] Ch. 3, page 90, eqn. (3.16) The second equation should be M l M h 0. [First reported by Massimo Guiggiani on 7 October 016] 8

Ch. 5, page 17, Fig. 5.19 The correct figure is β1< 0 E C F 1 A 1 E 1 F β< 0 A β1> 0 F E 1 A 1 F 1 C E A β> 0 [First reported by Matteo Pergoli on 8 November 016] Ch. 6, page 13, eqn. (6.3) In the last two equations the sign in front of (v ra ) is +. [First reported by Massimo Guiggiani on 1 December 016] Ch. 3, page 87, eqn. (3.1) The correct equation is Xij + Y ij pz ij and Z ij 0 [First reported by Marco Gabiccini on December 016] Ch. 3, page 70, line -6 Delete the sentence An alternative selection could be the roll angle ϕ and the track variations t 1 and t. [First reported by Stelios (Stylianos) Markolefas on 3 February 017] 9

Ch. 6, page 198, Fig. 6.44 Reverse the sign of α 1 and α. [First reported by Nicola Cambri on 17 February 017] Ch. 10, page 337, line 4 Replace with in both occurrences. [First reported by Massimo Guiggiani on 16 August 017] Ch. 3, page 49, Fig. 3. Replace β with ˆβ. [First reported by Matteo Pergoli on 16 October 017] Ch. 3, page 51, Fig. 3.4 Replace β with ˆβ. [First reported by Matteo Pergoli on 16 October 017] Ch. 8, page 48, line 11 The correct subscript is. Therefore, it should be: ζ = 0.44 and ω 1 ζ = 77.0 rad/s for the second mode [First reported by Massimo Guiggiani on 3 January 018] Ch. 8, page 46, line 17 Replace z(t) = 5y(t) with y(t) = 5z(t). [First reported by Massimo Guiggiani on 4 January 018] Ch. 6, page 164, line 3 Replace 6.4 with 6.3 [First reported by Davide Malatesta on 31 January 018] Ch. 6, page 164, line 4 Replace 6.18 with 6.19 [First reported by Davide Malatesta on 31 January 018] 30

Ch., page 3, Fig..14 Replace x with y and y with x in the axis labels. [First reported by Cecilia Moreschini on 6 March 018] Ch. 8, page 58, eq. (8.7) Insert a minus sign in front of the two fractions. [First reported by Cecilia Moreschini on 6 March 018] Ch. 8, page 65, eq. (8.101) Insert a minus sign in front of the last term. [First reported by Cecilia Moreschini on 6 March 018] Ch. 6, page 17, eqn. (6.91) Delete all the last term (it is not correct), thus leaving only ω s = ω n 1 ζ [First reported by Emanuele Abbatessa on 17 April 018] 31