# The Longest Scoring Shot in the History of the NBA in SOLIDWORKS Motion

On February 17, 2001, a basketball game was played between the Hornets and the Bucks. It was in this game that a world record was set. As time expired in the third quarter, a teammate passed the ball to Baron Davis who hurled it 89 feet landing right into the basket. This is the longest scoring shot in NBA history. Sixteen years later, at the time of this writing, the record still stands. Is it really that hard to break? Let’s use SOLIDWORKS Motion Analysis to find out!

### Setting Up the Court in SOLIDWORKS

To begin, I modeled the basketball, the hoop, and the court. The hoop and the court were straightforward. Using the standard dimensions found online, I created models with arbitrary materials and added a large emblem onto the court to help visualize where Davis was standing at the time of his legendary shot. For the basketball, I set the material to rubber and tuned the mass of the ball with a shell feature. Now it’s time to bring all the assets into an assembly and let the real fun begin!

### Preparing the Motion Study With SOLIDWORKS Simulation

With our court to play in, let’s next prepare the motion study using SOLIDWORKS Simulation. First, I created a plane using Davis’s location point and the axis of the center of the hoop. This way we have a plane representing the plane of motion of Davis’s shot. Using this new plane, I created a sketch by drawing a line heading upwards and placing one endpoint right on top of Davis’s location and one 6 feet above the ground. I set the angle of this line to be 30 degrees with respect to the horizontal datum.

I chose these values as an educated guess because there are no other measurements or documents existing other than the fuzzy video of his shot and the 89-foot record you can view above. This study should retain some validity because I am determining how sensitive this shot is to deviation (and therefore how difficult it was to pull off) rather than trying to determine absolute measurements. With the initial direction vector established, I then added two mates with the ball. One places the origin right at the end of the line, the other orients the front plane of the ball perpendicularly to the line. The ball is now in place.

### Creating the Motion Study

Next, we’ll move onto the actual Motion Analysis. First, I need to create a new Motion Study, and to do that I’ll start by selecting “Motion Analysis” for the type (make sure you have the SOLIDWORKS Motion Add-in enabled!) I now need to edit some of the Motion Study Properties for this motion analysis. For the framerate, I used 120 frames per second, checked the “Use Precise Contact” checkbox for interactions with the rim, and set the accuracy to medium (0.00001). I set Gravity in the Y-direction with a magnitude of 9.81 m/s2. For my solid body contacts, I set one for the ball and court and the other for the ball and hoop (including the rim). I left the contact sets both as acrylic due to another assumption I made.

Reviewing the video, we can see that Davis did not make use of the backboard at all during his shot. Luckily, this greatly simplifies our analysis by allowing us to neglect the coefficient of restitution between the ball and the backboard that is affected by the material of the ball, material of the backboard, and ball inflation pressure among other things. In short, we are looking for what it takes to get the ball right into the rim.

Next, it is time to apply a force. Studying the video once more, we see that Davis holds the ball for approximately 0.3 seconds, but only for about 0.1 seconds he appears to be applying a force. Therefore, I use 0.1 seconds as the duration of the force applied. I set the direction to “Action only” applied at the origin of the ball and used the sketched direction vector as the direction.

### Running the Motion Study

It was only a matter of trial-and-error before the correct amount of constant force could be determined. Approximately 20 minutes later, that value was found. With 111 Newtons (N) of force applied for 0.1 seconds, launched at 35 degrees starting 6 feet off the ground, we get this shot:

It practically hits the rim dead center, although it clips the back of the rim on the way down. What is more amazing is to see what it takes to ruin the shot. Setting the force to 110 N or 112 N (still both at 0.1 seconds duration) misses the shot. To illustrate how mind-bogglingly minuscule a change like that is, consider this: it takes 1 Newton of force to flip a light switch. This is truly a legendary shot, not only in the sense of what it takes to make it happen but the fact that Baron Davis made it happen with 0.7 seconds left on the clock to claim the title of the longest scoring shot of the NBA. As a record that has stood for 15+ years, we all knew that it was an amazing shot, and I hope you all enjoyed quantifying a little bit about what makes it amazing with SOLIDWORKS Motion!

Author: Robert Maldonado, Application Engineer at DesignPoint

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