- #1
TonyEsposito
- 39
- 6
- TL;DR
- cant figure it out equations
Why Do My Cl/Cd Derivations Differ from Phillips' Equations?
- Thread starter TonyEsposito
- Start date
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SUMMARY
The discussion centers on discrepancies in the derivation of lift-to-drag ratios (C_L/C_D) from Phillips' equations in flight mechanics. The user is attempting to reconcile their results with those presented in Warren F. Phillips' work. Key equations discussed include the lift coefficient (C_L) expressed as $$C_L = \sqrt{C_{D_0}\pi e R_A}$$ and the lift-to-drag ratio derived as $$\frac{C_L}{C_D} = \frac{\sqrt{\pi e R_A}}{2\sqrt{C_{D_0}} + C_{D_{0,L}} \sqrt{\pi e R_A}}$$. The user seeks clarification on potential errors in their calculations.
PREREQUISITES- Understanding of flight mechanics principles
- Familiarity with lift and drag coefficients
- Knowledge of the equations of motion in aerodynamics
- Basic proficiency in algebraic manipulation of equations
- Review the derivation of lift and drag coefficients in aerodynamics
- Study the implications of the aspect ratio (R_A) on lift-to-drag ratios
- Examine the impact of induced drag on overall drag calculations
- Learn about the assumptions made in Phillips' equations and their applications
Aerospace engineers, flight mechanics students, and anyone involved in aerodynamic analysis will benefit from this discussion.
- #2
jack action
Science Advisor
- 3,553
- 9,895
$$C_L = \sqrt{C_{D_0}\pi e R_A} = \sqrt{C_{D_0}}\sqrt{\pi e R_A}$$
$$\frac{C_L}{C_D} = \frac{\sqrt{C_{D_0}}\sqrt{\pi e R_A}}{C_{D_0} + C_{D_{0,L}} \sqrt{C_{D_0}}\sqrt{\pi e R_A} + \frac{C_{D_0}\pi e R_A}{\pi e R_A}}$$
$$\frac{C_L}{C_D} = \frac{\sqrt{C_{D_0}}\sqrt{\pi e R_A}}{2C_{D_0} + C_{D_{0,L}} \sqrt{C_{D_0}}\sqrt{\pi e R_A}}$$
$$\frac{C_L}{C_D} = \frac{\sqrt{C_{D_0}}\sqrt{\pi e R_A}}{2C_{D_0} + C_{D_{0,L}} \sqrt{C_{D_0}}\sqrt{\pi e R_A}} \times \frac{\frac{1}{\sqrt{C_{D_0}}}}{\frac{1}{\sqrt{C_{D_0}}}}$$
$$\frac{C_L}{C_D} = \frac{\sqrt{\pi e R_A}}{2\sqrt{C_{D_0}} + C_{D_{0,L}} \sqrt{\pi e R_A}}$$
$$\frac{C_L}{C_D} = \frac{\sqrt{C_{D_0}}\sqrt{\pi e R_A}}{C_{D_0} + C_{D_{0,L}} \sqrt{C_{D_0}}\sqrt{\pi e R_A} + \frac{C_{D_0}\pi e R_A}{\pi e R_A}}$$
$$\frac{C_L}{C_D} = \frac{\sqrt{C_{D_0}}\sqrt{\pi e R_A}}{2C_{D_0} + C_{D_{0,L}} \sqrt{C_{D_0}}\sqrt{\pi e R_A}}$$
$$\frac{C_L}{C_D} = \frac{\sqrt{C_{D_0}}\sqrt{\pi e R_A}}{2C_{D_0} + C_{D_{0,L}} \sqrt{C_{D_0}}\sqrt{\pi e R_A}} \times \frac{\frac{1}{\sqrt{C_{D_0}}}}{\frac{1}{\sqrt{C_{D_0}}}}$$
$$\frac{C_L}{C_D} = \frac{\sqrt{\pi e R_A}}{2\sqrt{C_{D_0}} + C_{D_{0,L}} \sqrt{\pi e R_A}}$$
- #3
TonyEsposito
- 39
- 6
Many Many thanks!!!
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