From: lwcamp@gmail.com   
      
   On Wednesday, March 15, 2017 at 3:09:09 PM UTC-7, MrAnderson wrote:   
   > Hi, Mr Campbell!   
   > How is this is possible? The meteors, burning satellites, go well beyond 100   
   their lenght when in atmosphere I think.    
      
   That's because they start to disintegrate up in the mesosphere, where the air   
   density is 10 million to 10 trillion times less than at sea level.     
      
   > But if that's true, are there any heat shield ways to overcome this?    
      
   It's not a matter of heat shielding, but of material strength.  At high   
   speeds, the ram pressure of pushing through the air overcomes the material   
   strength of the projectile, and it breaks up.  You need heat shielding, too,   
   but it needs to be both strong    
   and refractory.   
      
   > Also, wouldn't such thing make kinetic bombardment idiotic?   
      
   If the initial ablation part of the descent causes the projectile to slow down   
   to where it is no longer being ablated, then you have a perfectly serviceable   
   projectile that is still moving at 1 to 4 km/s when it hits the ground.   
      
   > On penetration, why is that? The kinetic energy of 2 km/s rod is smaller   
   than of 50 km/s rod, so why would it be this way?   
      
   Kinetic energy doesn't give you penetration.   
      
   Consider the case where the projectile is moving so fast that the dynamic   
   pressure at the interface between the projectile and the target greatly   
   exceeds the material strength.  Call the speed of the impact V.  Imagine that   
   you are moving along with this    
   interface layer, watching as the projectile burrows into the target.  Call the   
   speed at which the interface layer propagates into the target U.  From this   
   vantage point, you see the target material coming from the right with speed U,   
   and the projectile    
   material coming from the left at speed V-U, creating a stationary region where   
   they collide into each other.  The dynamic pressure is given by Bernoulli's   
   principle, and is the fluid's density times the square of its speed (where,   
   because we can neglect    
   material strength, both the projectile and the target can be considered   
   fluids).  Since the interface is stationary, the pressures must be equal.  So   
   (target density) x (V-U)^2 = (material density) x U^2.  You can see that the   
   rate at which the    
   projectile is being ablated (the (V-U) term) is related to the rate at which   
   the target is being penetrated (the U term) by the ratio of the square roots   
   of their densities.  Multiply this ratio by the length, and you find that the   
   distance the target is    
   penetrated is the length of the projectile times the square root of   
   (projectile density)/(target density).   
      
   Thus, at high speeds where material strength is irrelevant, the distance of   
   penetration of a long rod is constant, and has no dependence on speed.   
      
   If you use a very strong material (like tungsten carbide), then at around 1.5   
   to 2 km/s you can be in a regime where the strength of the projectile still   
   matters but the strength of the target does not.  This increases the   
   penetration of the projectile.     
   If you start going faster than this, the superior strength of the projectile   
   no longer comes into play and the penetration decreases.   
      
   There are some second-order effects that can introduce some speed dependence   
   to penetration but for long rods they are small.   
      
   Luke   
      
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