If you’ve ever driven a golf ball (I have, many times) you may also observe that from the tee, it looks nothing like a parabola. It appears to fly off into the distance, then plummet. I dare say cannonball flights look much the same, viewed from the cannon.
Just who is demanding that “reality should behave this way”?
It appears to fly off into the distance, then plummet. I dare say cannonball flights look much the same, viewed from the cannon.
Cannonballs weigh a lot more than golf balls relative to air resistance. More importantly much of the phenonemon you describe is due to the Magnus effect. That is, when you hit a golf ball with a golf club you impart a whole lot of backspin which allows the ball to maintain elevation beyond that of a pure parabolic arc. As far as I know cannons do not consistently impart backspin on their projectiles.
Cannonballs are a lot bigger and go a lot faster than golfballs, and resistance is proportional to the square of velocity and to the cross-sectional area, hence drag deceleration is proportional to (vel*diam)^2 / mass.
Golfball: initial speed 70 m/s, diameter 1.68in, mass 1.62oz, giving in SI units a deceleration proportional to ((70*0.0426)^2) / 0.046 = 193.
So there’s not much in it. Despite weighing two hundred times as much, the initial deceleration is only about 25% less. Solving the equations numerically gives clearly asymmetrical trajectories. When fired at 30 degrees elevation, the cannonball peaks 60% of the way through its flight and lands at an angle of 50 degrees.
Oo! Oo! [Raises hand] I’ve followed the trajectory of a bullet with my own eyes! Admittedly, it was with tracers.
But, I bet in the history of firearms, there have been projectiles of such size, fired at such low velocity, that you could follow them with your eyes in the daytime.
Still, if you can’t follow the exact trajectory, all the more reason to assume that the conventional wisdom is correct.
But, I bet in the history of firearms, there have been projectiles of such size, fired at such low velocity, that you could follow them with your eyes in the daytime.
Some book I’ve read lists the ability to watch the arrow in flight as one of the advantages of the bow compared to the rifle (i.e. every round is a tracer round).
I was moderately bothered by that as well but I went ahead and trusted my memory. Continued research is not finding the section I was thinking about. This is bizarre because I don’t thing I’ve read anything else that that could have come from- maybe I had a copy that was embellished? Maybe I’ve forgotten the name of some samurai text that would have included that as a tip? The last seems most likely, since I believe that was the only time people were actually comparing the two.
Cannonballs do not travel on parabolas.
If you’ve ever driven a golf ball (I have, many times) you may also observe that from the tee, it looks nothing like a parabola. It appears to fly off into the distance, then plummet. I dare say cannonball flights look much the same, viewed from the cannon.
Just who is demanding that “reality should behave this way”?
Cannonballs weigh a lot more than golf balls relative to air resistance. More importantly much of the phenonemon you describe is due to the Magnus effect. That is, when you hit a golf ball with a golf club you impart a whole lot of backspin which allows the ball to maintain elevation beyond that of a pure parabolic arc. As far as I know cannons do not consistently impart backspin on their projectiles.
Let’s look at the numbers.
Cannonballs are a lot bigger and go a lot faster than golfballs, and resistance is proportional to the square of velocity and to the cross-sectional area, hence drag deceleration is proportional to (vel*diam)^2 / mass.
Cannonball (example): 590mph, 20 pounds, 5.5in diameter, giving ((263*0.14)^2) / 9.09 = 149.
Golfball: initial speed 70 m/s, diameter 1.68in, mass 1.62oz, giving in SI units a deceleration proportional to ((70*0.0426)^2) / 0.046 = 193.
So there’s not much in it. Despite weighing two hundred times as much, the initial deceleration is only about 25% less. Solving the equations numerically gives clearly asymmetrical trajectories. When fired at 30 degrees elevation, the cannonball peaks 60% of the way through its flight and lands at an angle of 50 degrees.
You are correct about the Magnus effect.
A golf ball is a good example of something light enough that air resistance has a high impact.
I doubt people could follow the trajectory of a cannonball with their eyes. Ever tried to follow the trajectory of a bullet?
Oo! Oo! [Raises hand] I’ve followed the trajectory of a bullet with my own eyes! Admittedly, it was with tracers.
But, I bet in the history of firearms, there have been projectiles of such size, fired at such low velocity, that you could follow them with your eyes in the daytime.
Still, if you can’t follow the exact trajectory, all the more reason to assume that the conventional wisdom is correct.
Agreed.
If you’re standing directly behind (or in front of, I suppose) the cannon/gun it gets a lot easier, since the angular rate is much lower.
At night with the flood lights behind you, it’s quite easy to watch the arced trajectory of handgun bullets.
Some book I’ve read lists the ability to watch the arrow in flight as one of the advantages of the bow compared to the rifle (i.e. every round is a tracer round).
Not Sun Tzu, surely. Dates are uncertain, but it appears that he lived at least seven centuries before the probable invention of gunpowder.
I was moderately bothered by that as well but I went ahead and trusted my memory. Continued research is not finding the section I was thinking about. This is bizarre because I don’t thing I’ve read anything else that that could have come from- maybe I had a copy that was embellished? Maybe I’ve forgotten the name of some samurai text that would have included that as a tip? The last seems most likely, since I believe that was the only time people were actually comparing the two.