Textbook Errata:

p. 3:

The final sentence of Section 1.2.1 is misleading. It states "Gases, on the other hand, change their weight or mass per unit of volume appreciably under the influences of pressure or temperature and therefore must be considered compressible." For aerodynamic flows at low to moderate values of Mach number, the pressure changes are sufficiently small that the resulting density changes can usually be neglected. I.e., it is perfectly reasonable to talk about "incompressible aerodynamics" -- in fact, we used to offer a graduate course with that title at Cornell.

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p. 3:

The value of R for air in "American" units is 1717 ft^2/(sec^2 R)

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p. 4:

The second sentence in Section 1.2.5, which states that "Both liquids and gases possess viscosity, with liquids being much more viscous than gases," is misleading. While it is true that the values of dynamic viscosity coefficients for liquids generally are much larger than those for gases, their densities also generally are much larger, and it is the kinematic viscosity that determines the relative effect of viscosity in a fluid flow. That is, the Reynolds number, which determines the relative importance of viscosity to the dynamics of a flow having velocity U and length scale d, is Re = Ud/\nu, where \nu is the kinematic viscosity. For example, the (SI) values of dynamic viscosity for air (at SSL) and water are about 1.8e-05 and 1.0e-03, respectively, but the corresponding values of dynamic viscosity are about 1.5e-05 and 1.0e-06, respectively. Thus, from the standpoint of Reynolds number, water is less viscous than air!

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p. 5:

In Eq. (1.10) it is important to realize that the "constant" S_1 in Sutherland's formula is different for different gases. The value S_1 = 198 R is for air.

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p. 8:

The sentence at the end of the first paragraph at the top of this page: "Therefore, the pressure in a static fluid is equal to the weight of the column of air above the point of interest." is a non sequitur (and is dimensionally inconsistent). It would be better to say, "Integrating Eq. (1.16) from any point to very large h (where the pressure is negligibly small), shows that the pressure at any point in a static fluid is equal to the weight of air above that point in a column having unit cross-sectional area."

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p. 11:

The second sentence in Section 1.4.2: "As speed is increased the air undergoes a compression and, therefore, the density cannot be treated as constant." is misleading. It would be better to say "As speed is increased, pressure changes become large enough that they cause significant changes in density, which must be taken into account."

Also, in Eq. (1.33) it should be noted that the variable c is a constant.

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p. 15:

Several values in Table 1.2 are misprinted and/or are inconsistent with the (correct) sea-level values in Table 1.3. In particular, the accepted ICAO Standard values for sea-level pressure, temperature, and viscosity are: 1.01325e05 N/m^2, 288.15 K, and 1.789e-05 N s/m^2, respectively.

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p. 17:

The statement, between Eqs. (1.54) and (1.55), that the variable "... \lambda is ... called the lapse rate." is inconsistent with the usual convention that defines the lapse rate as minus the vertical temberature gradient -- i.e., the rate at which the temperature decreases with altitude. With this convention, the variable \lambda in Eqs. (1.53-59) is minus the lapse rate. Note that the equations are all correct as long as \lambda is taken to be the temperature gradient itself -- e.g., it will be a negative number in the standard troposphere.

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p. 21:

The sketch illustrating the sideslip angle \beta in Figure 1.11 is slightly misleading. Consistent with Eq. (1.68) the angle should be measured in a plane normal to the symmetry plane that contains the velocity vector. In this way, the sideslip angle \beta is independent of the choice of the x- and z- axes in the symmetry plane.

Also, the annotation below the lower object in Fig. 1.11 should, of course, be that "V_p is the projection of V onto the x_b, y_b plane."

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p. 25:

The quantity plotted in Fig. 1.13 is (Q_c - Q)/Q, i.e., the fractional error (due to compressibility) in dynamic pressure caused by interpreting the pressure difference (p_0 - p) as the dynamic pressure.

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p. 42:

The author launches into a discussion of static longitudinal stability in Section 2.3.1 without first describing why it is reasonable to consider longitudinal stability independently of lateral and/or directional stability. Of course, the answer is that, for a vehicle possessing bi-lateral symmetry, an initially longitudinal motion will remain purely longitudinal if only longitudinal disturbances (or control inputs) are allowed.

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p. 45:

Figure 2.7 is misleading. The variable z_{cg} as used in Eqs. (2.4) and (2.5) represents the distance between the c.g. and the wing aerodynamic center (not the fuselage reference line, as indicated in the sketch). Of course, terms involving z_{cg} are neglected from Eq. (2.6) on.

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p. 48:

The tail lift coefficient should be proportional to (\alpha_t - \alpha_{0_t}), and the \alpha_{0_t} is missing from Eq. (2.19). Of course, in fairness to the author, \alpha_{0_t} is usually zero for tail planes, since symmetric sections usually are used.

Also, Eq. (2.21) for the downwash angle at the tail assumes the tail is far downstream of the wing -- hence the factor 2 in place of the 1 < \kappa < 2 used in lecture and the notes.

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p. 56:

Equations (2.33)-(2.35) are a bit sloppy, as pointed out in class. The angle of attack \alpha is not defined here, but it is clear from later sections (see, e.g., Eq. (2.37) and Figure 2.20) that it is an absolute angle of attack -- i.e., is zero when the configuration lift is zero. Thus, C_{m_0} should be independent of c.g. location since the force system at zero absolute angle of attack must be a pure couple. These equations can be made consistent with those in lecture (and in my lecture notes) if in Eq. (2.35) C_{L_\alpha_w} is replaced by C_{L_\alpha} of the configuration, V_H is based on the distance between wing and tail aerodynamic centers, and Eq. (2.34) also is suitably modified. Equation (2.36) for the neutral point should then have these same changes, and it is not necessary to have "ignored the influence of center of gravity movement on V_H" when determining the location of the basic neutral point.

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p. 63:

I cannot find a formula for the variable C_{L_\alpha} appearing in Eq. (2.38) anywhere in the text. Of course, the correct formula taking into account both wing and tail lift was derived in class and appears as Eq. (3.7) in the lecture notes.

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p. 67:

The next-to-last sentence on this page should read "Note that when C_{m_\alpha} = 0 ( ... ) Equation (2.52) equals 0." That is, the reference should be to Eq. (2.52), not (2.53).

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p. 69:

The parameter C_{L_{\delta_e}} appearing in Eqs. (2.57 -- 2.60) must be interpreted as \frac{\partial C_{L_t}}{\partial \delta_e}, not as defined in Eq. (2.44). I.e., it is the derivative of the tail lift coefficient, not the vehicle lift coefficient, with respect to elevator deflection.

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p. 81:

In the paragraph describing the fuselage contribution to dihedral effect, the penultimate sentence should read: "For a low wing position, wing-fuselage interference contributes a positive (de-stabilizing) dihedral effect; the high wing produces a negative (stabilizing) dihedral effect."

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pp. 109-111:

Nelson's equations (3.51) and (3.52) are inconsistent with the usual definition of C_X. The best resolution is to take Eq.(3.51) as the definition of C_{x_u} as Nelson uses it, and to ignore Eq. (3.52). Then, use a similar definition for C_{T_u}, instead of that found in Eq. (3.58). In this way, the statements about C_{T_u} following Eq. (3.59) are correct (although the statement for piston/prop power is true only for initially horizontal flight, \theta_0 = 0).

Similarly, equation (3.61) is correct only if the derivative C_Z_u is defined analogously to equation (3.51). It is unfortunate that Nelson defines the force coefficient derivatives C_X_u, C_Z_u, and C_T_u in a way that is fundamentally different from the standard definitions of the aerodynamic derivatives C_L_u and C_D_u.

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pp. 116:

In Table 3.3, the parameters c in the factors (\ell_t / c) of the expressions for C_{m_\dot{\alpha}} and C_{m_q} should, of course, be \bar{c}, the wing mean aerodynamic chord.

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pp. 178:

The word 'ratio' is mis-spelled (as 'ration') in the first line of text on this page.

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pp. 179:

The exponent in the third-from-last equation, immediately before the References section, should be e^{\eta t} (not e^{n t}), where \eta is the real part of the characteristic root, as given in the equation immediately following.

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pp. 330:

The upper limit on the integral in Eq. (9.42) should, of course, be "t" (not "1").

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pp. 347:

There should be a minus sign before the 'k^T x' term in Eq. (9.82) for consistency with Eq. (9.83) and the block diagram in Fig. 9.3.

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pp. 349:

The text immediately following the displayed equation evaluating the augmented matrix A* should read "The eigenvalues of the augmented matrix ..." (not the augment matrix).

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pp. 350:

The final element in the vector B is Eq. (9.86) should, of course, be b_n (not b_k).

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pp. 351:

the text immediately following Eq. (9.88) should read "where the variables a_i are the coefficients of the characteristic equation of the plant matrix A: \lambda^n + a_1 \lambda^{n-1} + ... + a_{n-1} \lambda + a_n = 0."

The text immediately preceding Eq. (9.92) should read "The eigenvalues of the desired system can be used to write the characteristic equation of the augmented matrix A^* as:"

The sum of the terms appearing in Eq. (9.92) should, of course, be set equal to zero.

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pp. 416:

The value of C_{L_\dot{\alpha}} for the Mach 0.90, 40,000 foot altitude condition in Table B.27 is incorrect. A more realistic value is 5.53 (derived from the dimensional data in the cited report).

The value of C_{n_p} for the Mach 0.90, 40,000 foot altitude condition in Table B.27 is incorrect. A more realistic value is 0.0053 (derived from the dimensional data in the cited report). Unfortunately, the incorrect value in the table produces very unusual dynamics (in which increasing dihedral effect or reducing weathercock stability stabilizes the Dutch roll mode!).

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