Modeling Meteorite Re-Entry Speeds: A Study of Drag and Impact on Earth

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Discussion Overview

The discussion revolves around modeling the re-entry of a meteorite into Earth's atmosphere, focusing on the drag forces experienced at high speeds and Reynolds numbers. Participants explore the applicability of the quadratic drag equation and consider alternative approaches for calculating drag at supersonic and hypersonic speeds.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant presents a scenario involving a meteorite with specific weight and speed, questioning the validity of the quadratic drag equation at high Reynolds numbers.
  • Another participant asks about the background in aerodynamics of the original poster, indicating a potential gap in knowledge.
  • A suggestion is made to search for information on supersonic drag, hinting at the complexity of the topic.
  • The original poster clarifies their lack of aerodynamics background and expresses concern that different equations might apply due to the meteorite's high speed and Reynolds number.
  • One participant explains that at high velocities, wave drag becomes dominant due to shock waves, while other forms of drag may become relevant as speed decreases.
  • Another participant mentions Newtonian impact theory as a potentially useful approach for estimating forces on hypersonic objects, despite its historical inaccuracies.
  • A request for references on Newtonian impact theory is made, indicating a desire for further reading and understanding.
  • Participants share links and references to resources that discuss Newtonian impact theory and related concepts.

Areas of Agreement / Disagreement

Participants express varying views on the applicability of the quadratic drag equation and the significance of wave drag at high speeds. There is no consensus on a single approach or equation to use for modeling the meteorite's re-entry.

Contextual Notes

Participants acknowledge the complexity of drag forces at different Mach numbers and the limitations of using a single drag coefficient across a wide range of speeds. The discussion reflects uncertainty regarding the best modeling approach for the scenario presented.

PeterH
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I have been given the assignment to model the entrance of meteorite in Earth's atmosphere, and ultimately it's impact with earth.
The meteorite weighs 0.025kg, and has the speed 28.6km/s 50km vertically above the surface of the earth, giving it a Reynolds number of approximately 3.5*10^7.

The quadratic drag equation, F_d = 0.5*p*C_d*A*v^2, is used for Re > 1000.
My question is: Will this equation still give a reasonable approximation of the drag, experienced by the meteorite, or do you know of any other equations used at such high Reynold numbers and speeds?

Thanks!
 
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What sort of class is this for? What is your background in aerodynamics?
 
Search for supersonic drag.
 
I have no background in aerodynamics, I have physics in high school (in Denmark).
I ask, as I am to model the motion of the meteorite as it moves through the atmosphere, and as it not only moves at a supersonic speeds, but at more than 3 times the lower limit of re-entry speeds (according to http://en.wikipedia.org/wiki/Hypersonic_speed#Classification_of_Mach_regimes), it was my thinking that a different equation might apply with regard to drag force.
I have searched for super- and hypersonic drag, and it is my understanding that the equation itself will not change, but the drag coeffecient will, due to change in or layers piling up in front of the boundary layer.
 
For the most part that is true depending on how accurate you would like your solution to be. Basically, at such high velocities, the drag is going to be dominated by drag due to the large shock wave that forms, called wave drag. Once it slows down, other forms of drag become increasingly important. I doubt it would ever slow to under the speed of sound, so wave drag will likely still always be the dominant form of drag, but there are others that may start to be appreciable. It would be difficult to find one drag coefficient to cover that whole Mach number range with any degree of accuracy. You could probably just treat the whole problem considering only wave drag and get a decent approximation, however. You might look into Newtonian impact theory. It was Newton's original theory of fluid motion in Principia that turned out to be spectacularly wrong in terms of describing fluids in general, but a fairly good estimate for hypersonic objects. It usually gives a pretty decent estimate of the forces on a body at high Mach numbers. You could run the numbers using that technique the whole way and then worry about correcting it for lower Mach numbers if your final answer even shows the Mach number dipping below 5 or so.
 
Thank you very much, truly helpful.
Lastly; is it possible for you to list some references or link some pages, that concern this Newtonian impact theory or Newton's original theory of fluid motion?
 
Great! Very helpful.
 

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