Why in baseball the optimal angle for a home run is a lot less than 45 degrees?
In high school physics (okay, this is no longer 5 year old level) to throw something to the most distant, you throw it at 45 degrees.
But why in baseball the optimal angle for hitting a home run is a lot less than what is taught in physics?
I kind of understand it has to do with air resistance, but why does air resistance change the angle by that much?
In: Physics
The ball is being thrown at the bat. It is not stationary. The bat needs to counteract the balls momentum.
Three factors:
1) Air resistance slows the ball down over time, so time spent in the air is not worth as much as in the airless case, pushing the optimal angle lower
2) The ball does not start at ground level. Granted a home run generally arcs much higher than the batter, but the added initial height does push the angle down a bit.
3) The 45° optimal angle from intro physics assumes that the initial speed is fixed. For the case of a bat hitting a ball that is not the case. You actually get the most speed if you hit the ball straight back. You still want to angle it upward so that it gets time in the air, but that really pushes the optimal angle downward
For professional baseball, the strength of those three is probably 3>1>2.
The ball is pitched horizontally, and the swing of the bat is mostly horizontal. It’s easy to put a lot of horizontal speed into the ball by bouncing it off the front of the moving bat.
To get the ball to leave the bat at 45 degrees, you have to either swing the bat in a more upward direction, which sacrifices body mechanics and makes the ball harder to hit, or glance the ball off the top of the bat which imparts less speed to it.
It’s mainly because the air resistance increases in proportion to the square of the velocity. So if something is going twice as fast, it has 4x the air resistance.
The ball leaves the bat going very fast (120+ mph), so at the beginning of its flight it slows down quickly because the air resistance is much higher. If we want the ball to go far, it needs to cover more horizontal distance while it’s going fast, so it’s better for it to be moving at an angle shallower than 45 degrees during that time. If it leaves at a 45 degree angle, the horizontal velocity is lost more quickly (edit: more quickly in terms of how far the ball has moved horizontally over a period of time)
Distance comes from energy transference. Centre of the heaviest part of the bat meeting centre of the ball transfers the most energy. Every degree from perfectly flush loses energy that would direct it straight. It is not about angle, it is just entropy.
1 is correct. 2 is irrelevant with respect to angle, and 3 assumes there is no resistance due to air. I don’t really understand what you are trying to say about the initial speed of the ball, but there is an initial speed moments after the ball bounces off the bat.
The optimal launch angle of a projectile in atmosphere is based on many things, including drag, stability in flight, direction of spin, and momentum.
In short, a 45 deg angle for a baseball will result in a ball that runs out of forward momentum before it hits the ground, so you can get additional range by reducing the launch angle so that you balance height over the wall with loss of forward momentum.
A 45 degree angle is the optimal angle for distance in a vacuum. In an atmosphere it heavily depends on the mass of the object. A baseball doesn’t have very much mass so it is affected by air resistance much more than something heavier or denser would be and you want it to travel as much distance as possible before it slows down.
There’s a lot of good replies about energy transfer and such. But there’s also the angle and distance to consider.
To get a traditional home run, the ball just has to make it over the back wall. The minimum required angle for that is usually far less than 45 degrees. Using math (Pythagoram theory), the ground (a) and wall (b) make the right angle, and the hypotonuse is the flattened average of the ball’s flight path (c).
So, hitting at an angle smaller than 45 degrees shortens the distance of the ball’s flight from the plate to the back wall. This also means it doesn’t take as much energy to get the homerun at the flatter angle.
If you hit it more than 45 degrees, most of the energy will make the ball go high, but not far.
If you hit the ball less than 45 degrees the ball will go far, but not high.
You need the prefect balance, because gravity is also reducing the height of the ball in both cases.
**Air resistance can really be ignored.
>In high school physics to throw something to the most distant, you throw it at 45 degrees.
In high school physics you ignore air resistance.
That’s it, air resistance is complicated as hell so you just ignore it in high school.
But in the real world it has a huge impact so sports such as Baseball, Golf, Discus, Javelin, Frisbee etc. where you are supposed to throw or hit things far need to adapt to the air resistance to find optimal angles.
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