![]() ![]() One way to understand this is to imagine that theball actually started at ground level with a 45 degree launch but after itrises to the actual launch height it will be travelling at a smaller angle tothe horizontal. In cases such as the shot put where the ball islaunched from a certain height above ground level, the best launch angle isalso less than 45 degrees. If the ball has enough backspin sothat the Magnus force is greater than the force of gravity then the ball willrise up at an angle greater than 20 degrees after it is launched. ![]() In that case, the ball will travelthe maximum horizontal distance before landing if it is launched at an angle ofaround 10 or 20 degrees to the horizontal. For example,when a golf ball is projected with backspin then the Magnus force acts upwardson the ball as a lift force and holds the ball in the air for a longer timethan it otherwise would if it wasn't spinning. This force is called the Magnus force, it increases as the ball spinis increased, and it acts at right angles to both the path of the ball and tothe rotation axis. Alaunch at 45 degrees would allow the ball to remain in the air for a longertime, but it would then be launched at a lower horizontal speed at the startand it would slow down more because of the longer flight time.Īn additional aerodynamic force arises if the ball isspinning. As ball speedincreases, so does the drag force and the lower is the required launch angle. When the drag force is taken into account, maximumdistance requires that the launch angle is less than 45 degrees. The drag force can bebigger than the gravitational force if the ball is travelling fast enough,although this situation would never arise when projecting a very heavy ballsuch as the shot put. One is that the ball will also be be subject to a dragforce acting backwards on the ball due to air resistance. There are several reasons why 45 degrees is NOT thebest angle in practice. That way, the vertical launch speedis the same as the horizontal launch speed and it represents the bestcompromise between maximising V and maximising T. If the only force acting on the ball is the force ofgravity and if the ball is projected from ground level and lands at groundlevel then the ball will travel the greatest horizontal distance when itprojected at 45 degrees to the horizontal. The ball will spend a long time in theair but it will travel up and down along the same vertical path and travel zerodistance horizontally. T is a maximum whenthe ball is projected straight up in the air so it travels as high as possible,but then the horizontal speed V is zero. But then the ballwill fall to the ground quickly and T will be quite small. V is a maximum when the ball isprojected as fast as possible in the horizontal direction. For D to be as large as possible,V and T both need to be as large as possible. The horizontal distance (D)travelled before it lands is given by D = VT. When a ball is hit orthrown for maximum distance then it travels in the horizontal direction atspeed V and it remains in the air for time T. There is no single answer here that covers all casesbut the problem can be viewed in the following way. Similarly, an athlete competing in the long jump needs to jump bothupwards and forwards, but what is the best launch angle above the horizontal? For example, should a golfer hit the ball upwards at say45 degrees to the horizontal or will the ball travel further if it is projectedat a lower angle? The same question arises in baseball if a player is trying tohit a home run, or in cricket if a player is trying to hit a six over thefence, or in a soccer throw or in football or when throwing a javelin or shotput. The ball must then be launched as fast aspossible, but the interesting physics question concerns the best angle at whichto project the ball. In some ball sports, a player will want to projectthe ball as far as possible. The pictures are worth thousands of words and show how the Magnusforce can sometimes be negative. Wind tunnel photos of boundary layerseparation around various balls are included in thispdf file. The relevant aerodynamics, including atutorial on boundary layer separation and how it affects lift and drag onsports balls, is described in this pdf file on sportsballs. ![]() A pdf version of this file (but withoutthe movies) can be downloaded here. ![]()
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