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

[PeterH]

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!

 

[boneh3ad]

What sort of class is this for? What is your background in aerodynamics?

 

[A.T.]

Search for supersonic drag.

 

[PeterH]

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.

 

[boneh3ad]

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.

 

[PeterH]

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?

 

[boneh3ad]

The reference I used for learning that stuff was https://www.amazon.com/dp/1563477807/?tag=pfamazon01-20 by Anderson.

I've seen a few bits about it just from using Google, too. For example, there is a section in this link about it:
http://homepages.wmich.edu/~y3yang/files/handouts/chap14082.pdf

 

[PeterH]

Great! Very helpful.