Project 1Analysis of a Golf Ball

Project BackgroundA Golf ball manufacturing company, Golf Ball Inc. (GBI), has plans to approach the USGA and the LPGA and propose that the ladies be allowed to use a modified golf ball to even the field.

Basic problemGBI has contracted your engineering team to do the analysis of their new ball and to get your recommendations on the further re-design of the ball. You devise a simple device using a video camera, a strobe light and a vertical launcher to measure the position of the ball as it travels up and down again. This data is contained in the file H:\Golf_Fall03.txt and shows the position of the ball above the ground in meters.

Basic Data (excerpt)Time (s)Position (m)000.14.270.27.420.39.940.412.010.513.750.615.230.716.490.817.580.918.5119.28

Team TaskYour team must produce a formal report that will be submitted to your instructor as if he is the supervising engineer at GBI.As a minimum the report must include the items on the task list along with any supporting calculations, data, theory, etc.

Quick Process PreviewDrag and Numerical Methods

Concept of DragDrag is the retarding force exerted on a moving body in a fluid mediumIt does not attempt to turn the object, simply to slow it downIt is a function of the speed of the body, the size (and shape) of the body, and the fluid through which it is movingSee Foundations pages 266-267

Dropping a Ping Pong BallIf you dropped a ping pong ball down the stairwell in this building (height 50 feet), and the stairwell had a vacuum in it, how long would it take for the ping pong ball to hit the floor?If you left the air in the stairwell would it take longer, shorter, or the same time to hit the bottom?

Looking at the ball in detailDrawing a Free Body Diagram (FBD) of the ball is shown to the rightSince all the drag force is doing is slowing the ball down, it is directly vertical and upwards

Numerical AnalysisIf you have two data points (time, position), then you can approximate the velocity of the body.Given the points (2 s, -15m) and (2.1 s, -17m), what is the approximate velocity at 2.1 seconds?If the next data point is (2.2 s, -19.05m), what is the velocity at 2.2 seconds?

Solution

Now Find AccelerationGiven the velocities at 2.1s and 2.2s, what is the acceleration at 2.2s?Data points are (time, velocity):(2.1s, -20 m/s)(2.2s, -20.5 m/s)

Acceleration Solution

Continuing the processThe ultimate goal of this numerical analysis is to find the drag force on the bodyNow that we have the acceleration, we can find the total force acting on the body (F=ma), the force of gravity (Fg=mg), and Drag Force (F=Fg+FD)

Back to the ProjectExplicit Task List

Task List1. Produce three graphs: position, velocity, and drag force vs. time for the data obtained on the vertical launch.2. Given that the actual value of n is 2, estimate the appropriate value for k.3. Predict the "terminal velocity" (that velocity which the ball will reach if it is left in free fall indefinitely).

Task List4. Using numerical methods, determine the trajectory of the golf ball when it is launched with an initial speed of 225 ft/s and an initial angle of 45 degrees. Produce a graph of the position in X vs. Y coordinates.

Task List5. For the given velocity (225 feet per second), what initial angle will produce the maximum range (distance down range while airborne)? What is the maximum range?

Task List6. When a ball is traveling through air and rotating, there is a force created by the flow of the air around the sphere that is perpendicular to the direction of travel. This force is called the Magnus force. Top spin tends to make the ball dip and backspin makes it carry. This force is related to the rate of spin and the velocity of the ball. It is this force that allows a baseball to curve. The lift force has the same form as drag, but operates perpendicular to the velocity vector. Add this parameter to your solutions and repeat steps 4 and 5 for various angles to account for lift if the ball is hit with backspin spin resulting in a Magnus parameter of 6.388 x 10-6.

Example Graph

Due Dates:

Grading: