Measuring Air Resistance
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.
Bamline Controls & Data Acquisition Group
Avanced Photon Source, Argonne National Laboratory
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?
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.
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.
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
Click here to return to the Engineering Archives
Update: June 2012