XPost: rec.arts.comics.strips   
   From: ted@loft.tnolan.com   
      
   In article ,   
   Paul S Person   wrote:   
   >On Thu, 16 Oct 2025 20:18:07 -0400 (EDT), kludge@panix.com (Scott   
   >Dorsey) wrote:   
   >   
   >>Mark Jackson   wrote:   
   >>>On 10/15/2025 5:04 PM, Scott Dorsey wrote:   
   >>>> But time of arrival is more difficult since the projectile velocity   
   >>>> isn't constant at every point along that parabola.  Vectors and the   
   >>>> calculus make these simple problems but they would be difficult to   
   >>>> solve without them.   
   >>>   
   >>>Again, why would you need calculus?  The time to arrival depends on the   
   >>>distance to target and the horizontal component of the muzzle velocity,   
   >>>both of which are constant.  Only the vertical component of the shell's   
   >>>velocity varies, and that doesn't enter into things.   
   >>>   
   >>>(For negligible air resistance, of course, and - to be precise - firing   
   >>>at a target at the same height as the cannon.  Firing uphill the shell   
   >>>will land a bit earlier, downhill a bit later.)   
   >>   
   >>That's the point of indirect fire!  You're firing upward and the shell   
   >>travels often higher vertically than it travels horizontally.  The enemy   
   >>may not be very far away but they are on the other side of a barrier.   
   >>You can shoot over the barrier with artillery, while you are protected   
   >>from small arms fire.  Angles of 75 to 85 degrees are not uncommon.   
   >   
   >Modern indirect fire, which does indeed require some form of spotting.   
   >   
   >But the ancients shot arrows up and over the enemy, not because they   
   >could not see them, but because they wanted to wound/kill /all/ of   
   >them, not just those in the front line. The ones behind the front line   
   >were, not hidden, but covered.   
   >   
   >The Roman testudo    
   >was used to protect the troops against indirect arrow fire. (And also   
   >to protect them from items falling off the walls of besieged cities --   
   >things like stones, burning oil, and other nasties).   
   >   
      
   	I shot an arrow into the air,   
   	It fell to earth, I knew not where;   
   	For, so swiftly it flew, the sight   
   	Could not follow it in its flight.   
      
   --   
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   What's not in Columbia anymore..   
      
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