Golf Balls

Posted on 2003-03-03
Medium Priority
Last Modified: 2007-12-19
I'm a grade 8 student and I'm trying to find out ways I could test the tragectory of a golf ball when hit and how to calculate the reasons it did that(It is also the winter). I know it sounds like a gay question but im not very smart. Please help me!!!!!!!!!!
Question by:DoughBoy_666

Accepted Solution

lj8866 earned 100 total points
ID: 8061498
The trajectory is a parabola that opens down.

To get this we have to use the physics equations:

x(t) = xo + (vo)t

and y(t) = yo + (vo)t + 0.5g * t^2

where g is the acceleration due to gravity = -9.8 m/s^2

so let's assume we start on the ground and we hit the ball at an angle z with an initial velocity V.

vo in the x-direction is V*cos(z)
vo in the y-direction is V*sin(z)

If we plug these values into the equation, we have

x(t) = 0 + V*cos(z) * t
y(t) = 0 + V*sin(z)*t + 0.5g * t^2

This is only value as long as y(t) >= 0 because you can't have a ball going under the ground, so

-2Vsin(z)/g = t when y(t) = 0 the second time around.

That means that the ball hits the ground when time = -2Vsin(z)/g.

so the equations

x(t) = V*cos(z) * t
y(t) = V*sin(z)*t + 0.5g * t^2

will give you the respective height and range of the ball at a time t that is between 0 and -2Vsin(z)/g.

Hope that helps,


Author Comment

ID: 8061514
um...................Ij8866 can you say that agian only in english, i mean something i can understand okay!
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Expert Comment

ID: 8065978
Unfortunately he did say in it English.  

The math involved in describing the arc is fairly complex.

An object when thrown or hit will travel in an upside down parabolic arc.

To describe the arc you need to angle of ascent and the speed at its start.  

Since you are in the 8th grade I suspet you haven't studied either physics or trigonometry in any detail.  Without that knowledge it is very difficult t explain the math.

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Expert Comment

ID: 8066679
His nic is DoughBoy_666, I would be he has not studied anything very much. HEHE
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Expert Comment

ID: 8066737
naughty guys ;-)
I don't understand his fear of "a gay question" :D but anyway, it's not my life 8-))

It's true that the answer involves the computations above. The trajectory, as already said too, is a parabole. I hope you do understand that the ball quits the ground, goes into the air, and touches the ground again after some time has elapsed ? :D
(everything must go to the ground if subject to Earth's Gravity, hence the "g" in the maths)
So now I think you should re-read the first answer to your question and think about it 5 minutes.
And let that pop-corn box in the kitchen!
Concentrate !
You can do it !

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Expert Comment

ID: 8074581
The equations given describe the path of a golf ball (neglecting air resistance) very well.
I am not sure what you want to do. However if you want to see  the path that a golf ball takes, look at a stream of water from a hose. The path will be almost a parabola. (Not quite because of air resistance.) the smaller the stream the better. (but not a spray.) You might take a large balloon, fill it with water, and place a drinking straw in the neck. Squeeeze the water out steadily without moving the straw. You will be able to see the trajectory of the water. You can vary the speed (V in the equations) by the strength of your squeeze. You can vary the initial direction (z in the equations) by changing the angle of the straw. You will then become familiar with the possible paths of a golf ball (or any other hit object).
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Expert Comment

ID: 8082931
I do not understand, maybe I be gay since this all is both meaningless and minimally oversimplified if not poppycock.

"Well, of course to use pretty formula looks good on a test we'll neglect the impact of tides, wind, air resistance, temperatures, ball shape and components, club, swing, twist, etc."

I claim it all BS, so there! (feisty one today, huh?)

Think of moisture, and meaning of words like shank, hook, and slice. How many dimples on ball where? Is it a spheroid? Such answers above a typical here in this TA of how Math-ers or scientist quoters try to talk about real world by simplifying it into fitting things they've learned such as quotes. Sure, the path may look more like parabola to untrained eye that doesn't watch, or to one comparing whether shape of path better fits square or parabola or triangle or circle. But it remains unreal, even if a real goal of some golphers. Reality is different.

So, I go up to the green on a par 4 having 3 strokes already, I takes out my putter and... I certainly hope the groundskeeper did not prepare topology for weird parabola to sink my putt!

So many assumptions made, including that ball goes forward. While true that good experienced golphers can produce the forward result well over 90% of time, it is not a given that ball flight will always be so for all (visit a practise range and you'll be able to witness such events more frequently).

Ball shape and spin is variable that impacts flight, the ball is not statically positioned in flight, and atmospheric exposure is not precisely the same at each point throughout flight.

So much for saying I rather dispute much of the above.
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Expert Comment

ID: 8083227
So what's "a grade 8 student" to do? One problem is when you watch a pro with a driver, the flight is too fast and distant to get a good view, and you can't very well attach a long rubber band to it that will mark the path in the sky. Here's some ways you can validate my disputes, or invalidate them:

a) Give ball and club to five year old. watch path. This should be simpler to observe than watching a pro tee off (which, btw, was not a given in question, just assumption surmised by some). Once done, try same with 2 year old and 8 year old. Try to map results to fit a curve. parabola? Probably a better one than flight of a ball. Certainly not triangle or square.

b) Visit local golf course. Do not go inside. Walk around edges of course, including along fence lines. Be observant and watch ground where you walk. If it is like any couse I visited in grade 8, you will likely fins an assortment of balls. Some balls will be missing part of their coating. Some will have obvious nicks that could explain their failure to follow a straight and forward parabolic shaped path. Yet some will also appear to be perfectly new. Now, before you take those over to the nearby golfers of the day to see how much you can get for your booty, take a look at the current lie of the ball, and where the flight began (tee), and imagine a variety of flight paths, especially parabolic. I guarantee you won't find a perfect fit.

Now If you are really interested in trajectories, and reality, here's my offer for answer to your desires:

Answer: Pay a visit to a local hangout where some people gather to play billiards or pool or snooker. Watch and observe the paths of the balls for awhile. Then ask some participants inquisitively about english, and projecting the path of balls. You will likely get some interesting answers.

As a hint, sneak preview, there is much to do in these ball games with the spin of a ball. In pool, the top four are essentially top, bottom, left, and right. For more on that, well, I've given you your assignment, hmm? Don't trust me, ask around among people where you can also watch their expressions, their proof of claims in physical reality, not pencil + paper flatland, maybe even people you know. It is minimally a trust building exercise for all parties. If offered a beer, smile and say thanx, but for now you'd prefer a soda.

Before leaving the hall or parlor, add a bit of fun and ask them about table-roll. That can also impact path of a ball. The exercise here is to learn more how there's really a lot of things involved in even simple questions, that some answers are not so simple yes/no or black/white. There are many choices, many colors in the world in which we live. Thankfully, IMO, less boring that way, much more interesting to have variety than simple lookup tables for solutions.
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Expert Comment

ID: 8083281
having fun alone, SunBow ? :D

Expert Comment

ID: 8120367
Gravity will be essentially a constant under your test conditions so you can ignore it. You should record temperature, humidity and pressure for each set of experiments. Hot air is less dense (less resistance) than cold air. Moist air is less dense than dry air. Airplanes lift off faster on cold, dry days.

Build yourself a test platform with a pivoting arm. You could use a 2 x 4 piece of wood with a hole to pivot on at one end and a metal plate fastened to the other end, because the wood will deform. Make it so you can adjust the force with which this arm will strike the ball. You could use a spring or rubber bands.

Make a jig to hold the ball so that you can adjust AND measure the relative angle at which the arm strikes the ball. Theoretically, a 45 degree launch angle will provide the greatest distance.

A golfer tries for a 13 degree launch angle for greatest distance, because a lot of factors like backspin and surface characteristics come into play at higher speeds.

Good luck with your science fair project. Do some research and credit your sources. Now get to work.

Expert Comment

ID: 8134529
It depends on if you are asking this question as a golfer or a physicist.

If you are asking this as a golfer, I can answer this. Loft of club, angle of approach, speed of club, type of ball ( a softer ball will stay in contact with the club for a longer time, causing more spin ), club shaft, club head material, type of grooves on clubface, wind, and that's all I can come up with right now, all will affect ball flight.

You're only in the 8th grade! Go take a golf lesson and don't waste your time on a computer!!!!

I'm out! Peace.
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Expert Comment

ID: 8134562
true, and the fly of a bird too can affect the ball's trajectory :D
Theoretically, even the beat of the wings of some Brasilian butterfly should also affect it :D

Those minor and random effects should be neglicted in an "ideal" mathematical model

Expert Comment

ID: 8134654
Those are not minor and random effects. The loft of the club determines launch angle. The angle of approach will impart spin, which will affect the distance, height and curvature of the shot. Who really gives a rat's ass about the parabola of the shot? All that matters is if you are on target. The end.

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Expert Comment

ID: 8137624
Some golfers aim to end the flight path and total distance by a pin on the green. How do they get it to land on green and stop, and not continue rolling on off the green at increasing distance and poorer surface? I venture that the manipulation upon ball is significant, and the impact of this upon flight is not negligible. Handle a dogleg?

> take a golf lesson

Ditto, but on-the-cheap if you select the right time, you can get yourself a bucket of practise balls, and at the practise range there may be many to provide you a fair amount of advise for free.

Expert Comment

ID: 8164466

call tigar wood

Expert Comment

ID: 8269136
My personal approach to this problem whould be to get hold of a fairly decent camera (which allow you to set exposure time) find a big flat place (field, car park) thats deserted at night and not well lit.

Set your camera up at one end and have a friend ready to take a picture, now take a club and bucket of balls to the other end of the area.

Cover the balls with some luminuos paint (you can use petrol and a match too (but I didn't tell you that :) ).

set the camera exposure time to about 2-3 secs and get your mate to press the button.

smack off a ball,

do this quite a few times (it might be worth swapping with you friend half way though the film, so you have 2 lots of results)

If you've got everything right (well lit ball, right exposure, etc) You should end up with a film of arc's. The cool thing is you can then hold all the negatives together and compare the different hits.

To actually make this scientific you should make a machine like jbuttery suggested so you have repeatable forces involved.

I would steer clear of the usual trajector calculations, because the dimples in the golf ball produce very different paths to smooth balls.

In fact you should really use a smooth ball and golf ball during you tests, this will allow you to make good results and have a control set.

Hum sounds like a fun project to me, good luck mate


PS If you can't be bothered with that, get hold of a good golf game, most of them have good replays and graphs built in.

Expert Comment

ID: 8325691
You could try using a camcorder to record the flight of a golf ball.  Feed the video into a PC and examine frame by frame.

The parabolic trajectory is a straightforward analysis of a projectile in a vacuum but in the real world aerodynamic forces play a big part.

Even smooth balls are affected by spin but not as much as dimpled ones.  If you really want to learn about the aerodynamic effects other than drag (air resistance) then try a Google search on "Magnus effect".
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Expert Comment

ID: 8367322
There's nothing bad about any good engineering/math problem.  Many millions of people make good livings in the areas of golf, engineering, and math.
(1) There are a number of companies that manufacture golf simulator games.  I'm talking about the games in which the user actually swings a club and hits a ball.  These are widely available in larger video-game / entertainment clubs in my area (Denver, CO).  Searching on "golf simulator" reveals many.  (You want a manufacturer, not a reseller.)  Perhaps you could start an email discussion with one of their programmers to determine all the factors they take into account.

(2) This site: http://www.pinggolf.com/fitting_step2.html mentions something called "impact tape", which is used to indicate impacts on the head of the golf club.  It could be useful to determine the reason for various trajectories.  I'm not a golfer, but perhaps a local golf club or golf trainers would know about "impact tape".

(3) You could design a club-swinging jig similar (but MUCH simpler) to the device at this site GolfTek: http://www.golftek.com/robotAchiever.html

(4) Here's some guys (college-aged) who designed a simple swing-analyzer, won a contest prize, and came out ahead.

(5) Here's a video tracking device.  Perhaps someone there could provide better advice.

(6) You could set up an indoor testing cage.  Use a rigid frame and VERY LOOSE, STRONG netting.  (Tight netting or solid backing will act like a trampoline and will probably cause holes in your head or worse.  Also use protective eyewear and adult supervision.  DISCLAIMER: You're responsible for yourself, not me.)

(7) Here's an interesting (and not too expensive program) that could do most of the mathematical computations you'd need.  You'll still need to understand the required factors.  (You could probably find free or shareware software to do this, too.)  http://www.hanleyinnovations.com/aerotraj.html

I'm not sure if your question is a simple idealized math problem, or something based on performing actual experiments, but I hope the ideas above give you something to think about.

> It is also the winter.
What do you mean?  Isn't is spring or fall everywhere?  I'm guessing you're in a non-coastal far-north area.  Canada, Alaska, N. Asia, N. Europe?  Where are you?
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Expert Comment

ID: 8367591
ruuman> I would steer clear of the usual trajector calculations, because the dimples in the golf ball produce very different paths to smooth balls.

I really agree. All things must be considered. Consider ball with fewer but larger dimples and a large hollow core (whiffle ball).
LVL 12

Assisted Solution

farsight earned 100 total points
ID: 8367702
To help with lj8866 's answer:

t is time.  Generally assume that time starts at 0 when the ball leaves the club.
x is the horizontal position (distance from starting position).
y is the vertical position (height).
v is velocity.
V is the initial velocity in the initial direction.
z is the initial direction. (On a computer, the argument to sin() and cos() is typically radians, so you may need to convert from degrees if you're using a computer/calculator for this.  Check for your particular computing device.)

x(t) is the distance at a given time.
xo is the initial horizontal position (the position at time 0).  The value is probably 0 for your example.
yo is the initial vertical position (height at time 0).  The value is probably 0 for your example.
vo is the initial velocity.  The velocity has a components in both the horizontal and vertical directions.
y(t) is the height at a given time.

>>  x(t) = xo + (vo)t
Distance at a given time is the initial horizontal position (zero) plus the x component of the velocity times the time.  He doesn't specifically mention the x-component here.  Essentially:
Distance = HorizontalVelocity * Time

>>  y(t) = yo + (vo)t + 0.5g * t^2
This is similar to the horizontal equation, except it also takes gravity into account.
Height at a given time is the initial vertical position (zero) plus the y component of the velocity times the time plus the gravitational effect: 1/2 g t squared.  He doesn't specifically mention the y-component here.  Essentially:
Height = VerticalVelocity * Time + (g * Time^2)/2

>> g = -9.8 m/s^2

The negative is because the initial velocity upwards is indicated as positive and the acceleration of gravity is down, and they're in opposite directions .  The units is meters per second squared.  Make sure you either (1) use compatible units for other variables (meters, seconds), or (2) convert all units to be compatible.

You might wonder why we're multiplying by t^2 (t squared) instead of just t for the effect of gravity.  One way to understand is to look at the units of all the variables.  Look back a the formula for height.  Height is a linear distance, so it's measured in meters.  VerticalVelocity is in meters per second.  Time is in seconds.  When we multiply meters per second by seconds, we get meters, which is just what we need for linear distance.  Now looking at the gravity part of the equation:  g is in meters per second squared.  To get that to meters, we must multiply by seconds squared, which is why we use Time squared instead of just Time.

>>  vo in the x-direction is V*cos(z)
>>  vo in the y-direction is V*sin(z)

I won't go into it here, but it would be useful to really understand WHY cos() and sin() are used here.  Ask your teacher to explain cos() and sin() using a right triangle in a circle.
[ Triangle ABC, point A is at the center of the circle.   Points B and C are on the curcumference of the circle.  AB is a radius.  BC is vertical.  AC is horizontal. ]

lj8866 then uses calculus to derive:
>>  ball hits the ground when time = -2Vsin(z)/g
>>  y(t) = 0 + V*sin(z)*t + 0.5g * t^2
(Keywords: calculus, integrate, derivative, velocity)

Everything above basically just describes how to come up with the final two formulas.  These two formulas are all you need to determine the distance and height of the ball at any time, given the the initial velocity, the initial angle, and knowing the gravitational constant g.  These formulas are only valid until the ball hits the ground.

>>  x(t) = V*cos(z) * t
>>  and
>>  y(t) = V*sin(z)*t + 0.5g * t^2

I hope that helps clarify in "English".
Please, let me know if this helped.

Expert Comment

ID: 8475536
That helped me farsight...
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ID: 9129690
It's been at least a month since you asked this question.
Please assign points.

Expert Comment

ID: 9136827

to get data on the trajectory it is best to write a simulation programme.
then you can assume different initial conditions and look at the results
after you run the simulation.

the simulation approach will be far better than going out on a wet, cold
golf course to watch real people hitting real balls.

>(It is also the winter).

gay people do not play golf in the winter so it is better to do the simulation
if you need an answer before spring.


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