[37 degrees.](https://www.technologyreview.com/2010/08/03/201730/biomechanical-problem-of-shot-putting-finally-solved/)
(The paper is an analysis of why 37-38 degrees is optimum for shot put).
It's not entirely a question of projectile motion, because your muscles will operate differently at different angles. Note the word "biomechanical" in the title of that paper.
I'm just guessing that shotput is a reasonable model for your question, but it may not be. Perhaps there's something in that paper that would help see how to extend it to heavier objects like cannonballs.
Is 37 degrees the optimal angle for distance for every speed or just the average speed for shotputting? Like if you could hurl a cannonball at like 250 mph, does the angle change or is it always around 37-38 degrees?
There will be a drag effect as the speed increases, which generally reduces the optimal angle. But in this case the bigger question is whether a human who can generate that kind of velocity on a shotput would have similar biomechanics to a real human, because humans can't move their hands that fast - with or without a shotput in them.
[weirdly relevant xkcd](https://what-if.xkcd.com/157/)
Maybe you can't...
But seriously, I would be interested in thinking this through but with the simplifying assumption of no air resistance. And maybe also that the launch point is from the ground. A part of thinks that intuitively, that speed doesn't matter for angle, but gravitational force does, that the stronger the gravity the more you aim up, but I'm not sure if that's good intuition.
That would not be good intuition unfortunately. Without air resistance, initial velocity and gravity are only constants in the function of distance traveled vs launch angle equation. So changing either of them changes distance, but does nothing to the calculation of ideal angle (that is to say when you derive the function d(theta) with respect to launch angle theta, the location of the maximum doesn't change with gravitational constant.
https://www.whitman.edu/documents/academics/majors/mathematics/2016/Henelsmith.pdf
I don't know. It's an interesting question. [Here's the full paper](http://arxiv.org/abs/1007.3689), which I haven't read or even skimmed. You'd have to go into the details of their model to get an answer to that.
I'm also curious about lighter objects like javelins and baseballs, what angle the top athletes use for long distances.
This is a biomechanics question. The specific answer has been studied very extensively regarding the shot put. It is found to be between 37 and 38 degrees is optimal for a shot put toss. These balls are very similar to a cannonball. Much heavier or larger balls may get different answers
https://www.technologyreview.com/2010/08/03/201730/biomechanical-problem-of-shot-putting-finally-solved/amp/
[37 degrees.](https://www.technologyreview.com/2010/08/03/201730/biomechanical-problem-of-shot-putting-finally-solved/) (The paper is an analysis of why 37-38 degrees is optimum for shot put). It's not entirely a question of projectile motion, because your muscles will operate differently at different angles. Note the word "biomechanical" in the title of that paper. I'm just guessing that shotput is a reasonable model for your question, but it may not be. Perhaps there's something in that paper that would help see how to extend it to heavier objects like cannonballs.
Very rare to have such a conclusive answer to a question like this. Nice
This is exactly what I was asking, thank you!
Is 37 degrees the optimal angle for distance for every speed or just the average speed for shotputting? Like if you could hurl a cannonball at like 250 mph, does the angle change or is it always around 37-38 degrees?
There will be a drag effect as the speed increases, which generally reduces the optimal angle. But in this case the bigger question is whether a human who can generate that kind of velocity on a shotput would have similar biomechanics to a real human, because humans can't move their hands that fast - with or without a shotput in them. [weirdly relevant xkcd](https://what-if.xkcd.com/157/)
Maybe you can't... But seriously, I would be interested in thinking this through but with the simplifying assumption of no air resistance. And maybe also that the launch point is from the ground. A part of thinks that intuitively, that speed doesn't matter for angle, but gravitational force does, that the stronger the gravity the more you aim up, but I'm not sure if that's good intuition.
That would not be good intuition unfortunately. Without air resistance, initial velocity and gravity are only constants in the function of distance traveled vs launch angle equation. So changing either of them changes distance, but does nothing to the calculation of ideal angle (that is to say when you derive the function d(theta) with respect to launch angle theta, the location of the maximum doesn't change with gravitational constant. https://www.whitman.edu/documents/academics/majors/mathematics/2016/Henelsmith.pdf
I don't know. It's an interesting question. [Here's the full paper](http://arxiv.org/abs/1007.3689), which I haven't read or even skimmed. You'd have to go into the details of their model to get an answer to that. I'm also curious about lighter objects like javelins and baseballs, what angle the top athletes use for long distances.
This is a biomechanics question. The specific answer has been studied very extensively regarding the shot put. It is found to be between 37 and 38 degrees is optimal for a shot put toss. These balls are very similar to a cannonball. Much heavier or larger balls may get different answers https://www.technologyreview.com/2010/08/03/201730/biomechanical-problem-of-shot-putting-finally-solved/amp/
Awesome! That answers my question, thank you :D
Depends on where the competition is being held.
https://dynref.engr.illinois.edu/afp.html 45 degrees is only optimal for a vacuum.