Aerodynamics: Optimization of an aircraft engine

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SUMMARY

The discussion focuses on the derivation of the aerodynamic drag equation, specifically the formula \( F_d = \frac{1}{2}\rho u^2 A C_d \). The drag coefficient \( C_d \) is defined through dimensional analysis, particularly the Buckingham π Theorem, and varies with flow conditions such as Reynolds and Mach numbers. Resources like 'Aerodynamic Drag' by Hoerner provide extensive data on \( C_d \) values for various shapes. Understanding the variability of \( C_d \) with geometry is crucial for optimizing aircraft engine performance.

PREREQUISITES
  • Understanding of aerodynamic principles and equations
  • Familiarity with the Buckingham π Theorem
  • Knowledge of flow conditions affecting drag, including Reynolds and Mach numbers
  • Basic grasp of dimensional analysis
NEXT STEPS
  • Research the derivation of the aerodynamic drag equation in detail
  • Study the impact of Reynolds number on drag coefficient variations
  • Explore the relationship between geometry changes and \( C_d \) values
  • Read 'Aerodynamic Drag' by Hoerner for comprehensive data on drag coefficients
USEFUL FOR

Aerospace engineers, aerodynamics researchers, and students studying aircraft design and optimization will benefit from this discussion.

dd5139
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New user has been reminded to always show their work on schoolwork problems.
I am writing an essay about optimization of an aircraft engine. I have to show the derivation of aerodynamic drag eq. I need help about it because i couldn't find where it came from.
 
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Hi there, welcome to the forum! :welcome:

It is probably better to start a new topic on this next time instead of replying to an old thread (last post almost a year ago). We try to keep threads limited to the original topic.

But do you mean by 'the aerodynamic drag eq.' this one:
$$
F_d = \frac{1}{2}\rho u^2 A C_d
$$
If so then you ought to know that this is just the inverse of the definition of the drag coefficient (##C_d = \frac{2 F_d}{\rho u^2 A}##). The drag coefficient comes from dimensional analysis (The Buckingham ##\pi## Theorem). This drag coefficient is found to be similar for similarly shaped object. There are whole books written that give (a range of) ##C_d## values for differently shaped objects (most notably the historic 'Aerodynamic Drag' by Hoerner). But please note that ##C_d## is not always constant for even the same object in different flow conditions (like for different Reynolds numbers or different Mach numbers). Also, the million dollar question is how ##C_d## varies for small changes in the geometry.
 
dd5139 said:
I am writing an essay about optimization of an aircraft engine. I have to show the derivation of aerodynamic drag eq. I need help about it because i couldn't find where it came from.
Welcome to PF.

Please show us your Google search terms that you have been using so far. This seems like a pretty easy search, so we would like to help you learn how to do searches like this better in the future. :smile:
 

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