What do we know about the formula for air drag force?

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Discussion Overview

The discussion revolves around the understanding of the formula for air drag force, exploring both theoretical foundations and practical applications. Participants examine the complexities involved in deriving the formula, especially at varying speeds, and the implications of the Navier-Stokes Equations in this context.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants question whether the formula for air drag is derived from fundamental principles or if it is primarily an approximation based on empirical data.
  • Others argue that at speeds greater than Mach 0.3, the drag coefficient (Cd) becomes a function of velocity, requiring interpolation from measured values.
  • A participant mentions that while the Navier-Stokes Equations provide a theoretical framework, they often lack analytic solutions, leading to reliance on computational fluid dynamics (CFD) or empirical methods.
  • There is a reference to the uncertainty surrounding the existence of solutions to the Navier-Stokes Equations, highlighting its significance in the field of mathematics.
  • One participant humorously suggests that a solution to this problem could be worthy of a Nobel Prize.

Areas of Agreement / Disagreement

Participants express differing views on the derivation of the air drag formula, with some emphasizing empirical methods and others focusing on theoretical foundations. The discussion remains unresolved regarding the balance between these approaches.

Contextual Notes

The discussion touches on the limitations of current understanding, particularly regarding the Navier-Stokes Equations and the conditions under which the drag coefficient is considered constant or variable.

victorhugo
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Is it the typical "get some results and stack the maths together and chuck in some constants to make it fit to get some approximation" or do we understand the rules behind it to derive the formula, such as how the molecules repel each other and how energy is transferred depending on temperature, velocity, etc
 
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If you're considering speeds greater than Mach 0.3, it gets complicated. In order to use the simple formula where drag force = Cd v2, Cd becomes a function of v, interpolated from measured or calculated values in a table. Wiki article, note table showing how drag coefficient varies with Mach (speed). In the wiki example, Cd is near constant until Mach 0.4 (it's also possible that when the table was generated, values of Cd for speed less than Mach 0.4 weren't important, so a constant Cd was chosen, not measured).

http://en.wikipedia.org/wiki/External_ballistics#Doppler_radar-measurements
 
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victorhugo said:
Is it the typical "get some results and stack the maths together and chuck in some constants to make it fit to get some approximation" or do we understand the rules behind it to derive the formula, such as how the molecules repel each other and how energy is transferred depending on temperature, velocity, etc
It is both.
We do understand the rules quite well, see Navier-Stokes Equations, unfortunately most of the time they do not have analytic solutions (*) so it's either heavy-duty number crunching CFD or back to method #1.

(*) And we don't even know if solutions exist. It is quite literally a million-dollar question, see http://www.claymath.org/millennium-problems
 
Probably. Sure worth a try :rolleyes: ... twice therefore !
 

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