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Name: Andrew
Status: Student
Age: 6-8
Location: FL 
Country: United States
Date: February 2006

I am doing a science project dealing with golf. My teacher says I need to measure the air resistance of the golf balls based on the fact that some have round dimples, some have square dimples, etc. How do I measure the air resistance of a golf ball being hit by a golf club as it travels through the air?

You could suspend a golf ball on a string and blow on it. The amount by which the ball is deflected would depend sensitively on its air resistance. You could vary the sensitivity of the measurement by varying the string length.

Tm Mooney
Bamline Controls & Data Acquisition Group
Avanced Photon Source, Argonne National Laboratory

Dear Andrew,
The only reasonable way I can think of to measure the air resistance of a golf ball is by using a wind tunnel. It has to be a rather fancy wind tunnel, since a golf ball travels at speeds around 70 mi/hour = 30 m/s. I got this from the range equation R = (v^2/g)sin (2a) where a is the initial angle of the golf ball's motion relative to the horizontal, g is the acceleration due to gravity, and v is the initial speed of the ball. I assumed a 100 m drive with the initial angle being 45 degrees. This calculation ignores air resistance, but gives you a good idea of the physics. This speed is approaching the speed of hurricane winds and if you get access to such a windmill, you should be very careful.

I would think a fan capable of producing such a wind velocity would be difficult to obtain (though I could be wrong). I guess if I had to design and build such a wind tunnel, I would use an evacuated tank which then sucks the air through the tunnel. Using a standard compressed air tank (about 6 in diameter by 5 ft high) and a 2 in diameter tunnel, a wind speed of 30 m/s would fill the tank in 0.1 s! So you would need a rather large tank.

You could also just drop the golf ball from a tall building and measure the time it takes for the ball to reach the ground. Comparing to the time without air resistance (y = gt^2/2) would give you a good idea of the air resistance. Unfortunately, you need a rather tall building to attain these speeds. The height needed to attain a speed of 30 m/s (ignoring air resistance) is about 50 m or 150 ft (a 15 story building). This uses the equation v^2 = 2gy, which I presume you have seen. Not an easy measurement! Good luck! If you manage a measurement, I would be delighted to hear about it.

Best, Dick Plano, Professor of Physics emeritus, Rutgers University

Hi, Andrew. Resistance changes with the speed the ball is moving through the air. The best way to measure the resistance of the balls is to mount them on something that can measure force, and blow air across them at a several speeds, then write down the resistance at each airspeed. Then you can draw a curve of resistance versus speed.

Without a wind tunnel, this can be hard to do, but I imagine mounting the ball to a mechanism that would push backward on a hinged arm would work. Put the whole shebang into a plastic tube about the size of the ball to keep the flow undisturbed, and mount the arm to a sensitive fish scale or some other sort of scale capable of measuring forces down into the ounces. Put the whole thing on a car and drive at various speeds. use the same mechanism and car for consistency. To eliminate the effects of the wind, take averages of measurements taken going two opposite directions. Look at the ways models are mounted in wind tunnels for help in designing the mechanism.

I will stop there to avoid "spilling the beans" on your experiment, but you might want to ask yourself if the drag versus speed of a golf ball is the same or different than that of a smooth ball the same size, and why or why not?

David Brandt

The air resistance of a golf ball (or other object) does depend upon the shape of the surface, but I do not know of a simple way to determine that. Because the flow of air is turbulent, the mechanics of the flow is very complicated mathematically.

Vince Calder

Wow, that is one heck of a project you are undertaking!

Let us see if we can apply some scientific reasoning to it. First, we will need to controll all factors not directly related to the surface of the ball itself. This means you will need some controlled way to throw the golf balls consistantly. (In other words, something other than a golfer swinging the club) I would recomend some type of slingshot, as it will allow you to fire ball after ball with consistancy. (provided you mount it to some type of fixed position) Once you have controlled the firing speed and angle of the golf balls in question, You should need only to run a series of tests. Fire each type of ball downrange several (many) times, and record the distances they travel. Since initial velocity and angle are controlled, the only thing that should change the range would be air resistance.

Alternately, I suppose you could try building a simple wind tunnel, and measuring the force of moving air on the balls more directly, such as by suspending them from a string and seeing how far back they are pushed by moving air. Unfortunatley, building a wind tunnel is a fairly extensive science project in itself.

Ryan Belscamper

The ball spins, that is part of the reason for the different dimples. By their shape and location the manufacturers can control the elevation, the curing and distance. There are a lot of formulas on projectiles, which branch out to weapons, I might start there for formulas for air resistance.

James Przewoznik

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