- #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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The discussion revolves around a derivation from Warren F. Phillips' book on flight mechanics, specifically concerning the lift-to-drag ratio (C_L/C_D). The user is struggling to reconcile their results with the expected outcome from the equations provided. They present a series of equations and transformations but end up with a different expression for C_L/C_D. The key confusion seems to stem from the manipulation of terms and the application of the equations. Clarification on the derivation process and potential algebraic errors is sought to resolve the discrepancy.
- #2
jack action
Science Advisor
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- 9,860
$$C_L = \sqrt{C_{D_0}\pi e R_A} = \sqrt{C_{D_0}}\sqrt{\pi e R_A}$$
$$\frac{C_L}{C_D} = \frac{\sqrt{C_{D_0}}\sqrt{\pi e R_A}}{C_{D_0} + C_{D_{0,L}} \sqrt{C_{D_0}}\sqrt{\pi e R_A} + \frac{C_{D_0}\pi e R_A}{\pi e R_A}}$$
$$\frac{C_L}{C_D} = \frac{\sqrt{C_{D_0}}\sqrt{\pi e R_A}}{2C_{D_0} + C_{D_{0,L}} \sqrt{C_{D_0}}\sqrt{\pi e R_A}}$$
$$\frac{C_L}{C_D} = \frac{\sqrt{C_{D_0}}\sqrt{\pi e R_A}}{2C_{D_0} + C_{D_{0,L}} \sqrt{C_{D_0}}\sqrt{\pi e R_A}} \times \frac{\frac{1}{\sqrt{C_{D_0}}}}{\frac{1}{\sqrt{C_{D_0}}}}$$
$$\frac{C_L}{C_D} = \frac{\sqrt{\pi e R_A}}{2\sqrt{C_{D_0}} + C_{D_{0,L}} \sqrt{\pi e R_A}}$$
$$\frac{C_L}{C_D} = \frac{\sqrt{C_{D_0}}\sqrt{\pi e R_A}}{C_{D_0} + C_{D_{0,L}} \sqrt{C_{D_0}}\sqrt{\pi e R_A} + \frac{C_{D_0}\pi e R_A}{\pi e R_A}}$$
$$\frac{C_L}{C_D} = \frac{\sqrt{C_{D_0}}\sqrt{\pi e R_A}}{2C_{D_0} + C_{D_{0,L}} \sqrt{C_{D_0}}\sqrt{\pi e R_A}}$$
$$\frac{C_L}{C_D} = \frac{\sqrt{C_{D_0}}\sqrt{\pi e R_A}}{2C_{D_0} + C_{D_{0,L}} \sqrt{C_{D_0}}\sqrt{\pi e R_A}} \times \frac{\frac{1}{\sqrt{C_{D_0}}}}{\frac{1}{\sqrt{C_{D_0}}}}$$
$$\frac{C_L}{C_D} = \frac{\sqrt{\pi e R_A}}{2\sqrt{C_{D_0}} + C_{D_{0,L}} \sqrt{\pi e R_A}}$$
- #3
TonyEsposito
- 39
- 6
Many Many thanks!!!