Effect of air resistance on angle yielding max displacement

[sskkiilleeff]

Considering simple projectile motion, would the effect of air resistance cause the angle for maximum horizontal displacement to change? Would the maximum angle then be greater or less than 45 degrees? Just a conceptual question, don't really need equations (though wouldn't mind either).

 

[cjl]

Less. When you factor in air resistance, it becomes favorable to cover proportionally more ground early, while the speed is highest, and hang time becomes less important (because late in the flight, the horizontal speed is substantially decreased anyways). Because of this, a higher initial horizontal speed at the expense of hangtime will increase range compared to a 45 degree shot (assuming only drag and no lifting forces). In other words, a lower angle.

 

[DickL]

I'm going with - it depends. Back in WWI, the German Paris gun was aimed at something around 50 or 55 degrees to be the maximum range. The explanation was that at high altitudes (45,000 ft and above) the air was thinner and offer less resistance and most of the projectile's flight was above 45k ft. If I remember the article correctly, the angle of flight at 45k ft. was 45 degrees.

For less extreme ballistics, I go with cjl's opinion.