I always wanted to know how fast we sling and how the air drag changes the speed of various projectiles. As far using a camera I was able to calculate average speeds at given distances at the best. The average speed actually doesn't say much about how fast you launches a projectile and how fast it hits a target - especially when we are talking about tennis balls, that are affected by the air drag very much. Lately inspired by a Slingermedia's video and having in my hands a better (not very good one) camera I did deeper "researches" of a video. As a result I got some interesting numbers and charts.

First, a few very short words what and how I did.

1. I filmed from the side a few shots with tennis ball against a steel door. I used my regular 75 cm long sling and several somewhat worn-out tennis balls. The shots were of moderate power. They were like in my regular slinging for accuracy. The camera was located symmetrically 28-29 m from the line of slinging. The distance between the point of the releases and the door measured with a measuring wheel as 86 feet, what is 26,2 in meters.

2. Using the Audacity I chose the shot that had the shortest time of flight.

Here is the video: http://www.youtube.com/watch?v=xJooCQldw0M

3. Using a video and graphical program I got a picture with marked location points of the tennis ball in each frame, where measured precisely each section between the marked points in pixels.

http://i0.simplest-image-hosting.net/picture/trajektoria.png




4. Using a spredsheet and knowing both the real slinging and the camera distance, corrected the parallax errors of each section - because of the camera looks at the sections at various angles and actually they are longer then the measured from the picture.
Next, knowing the frame rate of the camera (30fps) and the all needed lengths either in pixels or meters, I calculated the average speeds of the ball between each frame and assumed that they were momentary speeds in the middle times between the frames. In this way I got a series of the speeds together with corresponding times.



5. I put the results into a plotting program, where I did a "curve fitting" for them.







Sounds short and simple. Actually it took a while to find some tools and put it all together
Anyway, finally I got I wanted the most A nice pretty accurate chart that says a lot about a flying tennis ball.



I got more interesting charts from the first one. I am going to share them in next posts.


Yurek

Gold star award wining post

First, Yurek you sling those tennis balls fast... Yikes.  Second, isn't it amazing how quickly they lose speed? I would love to see how tennis balls compare on average to stones and lead glandes for how quickly each loses velocity to drag.  Maybe one day we can get all that data together.  Great job on this Yurek.  Very interesting stuff.

Beautiful work. I've realized from practical experience that tennis balls lose speed very rapidly. Extrapolating the graph shows why it's virtually impossible to sling a tennis ball 100m.

I was going to say that the flight of the ball would be the same whether launched from a sling or struck by a tennis racket. Of course that may not always be true as tennis players usually put a lot of spin on thir shots. This alters the flight path but may not actually affect the rate at which the ball loses speed.



BTW It was very interesting to see the slow motion of you slinging from the side view. Perhaps you could post another video so we can better see the details of your style.

This is great stuff, Yurek.

I've tried to get data like this and failed to get anything satisfactory, so it's wonderful to see some clear results.

Eyeballing the gradient of your curve to get the deceleration at the beginning, it looks like close to 50m/s². That puts it at five times the acceleration due to gravity, and suggests a terminal velocity (where weight matches the drag forces) at  51/ sqrt(5), of  about 23m/s.

This is amazingly close to the drag predicted for a sphere with the size and weight of a tennis ball, and suggests the ball behaves like it has a drag coefficient of about 0.5  even at the high speed of launch, no evidence of the 'drag crisis' at least. If anything, it looks from the continuation of the graph like the effective drag coefficient decreases as the ball slows down, although perhaps that is the trajectory of the ball?

Can't wait for further experiments!

That's some serious speed for a tennis ball! Cool stuff and well done.

The last chart I posted is the most important as is a base for all other ones. But I think more intuitive for most of us is an information how the speed changes along the trajectory.

Chart 2


Chart 3


You can read from the charts that when you going to destroy a target with a tennis ball, it is much better to approach close and sling gently than sling hard from a bigger distance, not mentioning accuracy. I have to shorten my practice range

Great results Jlasud. You most probably right, but maybe it would be worth of a try to test stones. We could increase the distance, stones can fly fairly flat at 50 m or more. But in this case a good camera would be needed to see the stones.

Next two charts about deceleration of the ball due to the air drag:

Chart 4


Chart 5


Just after the release a deceleration of the ball is bigger than 6g - quite impressive.  There is a strange inflection of the curve at ca. 0.07 s. But I don't think it is due to the "drag crisis". Most probably it is due to overall accuracy of the method... or maybe not?

Next charts tomorrow, time to the bed.

In regard to spin's effect on drag I remember reading on the NASA education pages (and I think in their FoilSim program) that if the spin is generating lift then there is some lift-induced drag, but I don't know how to calculate that.