Ballstic Tragictory

[tylerbrowner]

I want to make a golf ball launcher just beacuse it sounds like fun to see how far i could gat a golfball to go. anyway to make the golfball launcher i and going to get a 3000 rpm moter and make a wheel that will spin on the shaft of the moter. the top of the wheel will be inside a pvc tube so as the wheel spins a golfball will be droped in to the pvc pipe and be forced between a spinng wheel and the inside of the tube. this should force the golf ball foword. Like a soccerball launcher. If i use a 1 ft in cicumfernce whell than the ball will be moving at ruffly 22 mph. so i want to know how far the ball will be launched if shot at a 45% angle. how do i do this. at what rate will the ball fall towereds the ground??

[swansont]

22 mph is just under 10 m/s

 

We can analyze this in terms of kinematics or conservation of energy (we'll get the same answer either way). The horizontal and vertical speed components at 45º will be the same, since sin(45º) and cos(45º) = .707, so the ball is moving up at ~7 m/s and moving horizontally at ~7 m/s. Looking at the vertical motion only, 1/2 v² = gh if we can ignore the effects of the air. h = 2.5 meters, which is not particularly high (22 mph isn't very fast for a golf ball) Again ignoring air resistance, the ball will have the same speed when it gets back to the height at which it was launched.

 

In reality its impact speed will be slower, and it will not go as high as predicted, owing to the effect of the air, so the above is the best-case scenario. A spinning ball will also see some deflection owing to the Magnus effect, which further complicates the analysis.

[Bignose]

TaylorMade (a golf equipment manufacturer) was using the slogan "17 degrees, 1700 rpm" in its ad copy this past year. Specifically, this is means that a launch angle of 17 degrees from vertical, with a backspin of 1700 rpm yields maximum distance.

 

It made for good ad copy, but wasn't exactly true. If someone hits with a lower speed, then they need higher than 17* launch angle and more spin for lift. If someone hits with a very high swing speed, then need a lower launch angle and lower backspin otherwise there will be too much lift. However, we're talking launch angles of 12 or 14* for the very high swing speed players, and launches of 20 or 22* for the very low swing speed players.

 

In short, 45* is no where near the maximum distance launch angle for a golf ball, for the various fluid dynamic effect swansont mentioned above. 45* launch angle is like hitting a golf ball with a 9 iron or pitching wedge. Guys hit driver off the tee when they want maximum distance.

 

There actually is software out there, TrajectoWare http://www.trajectoware.com/wrap.php?content=description.htmlthat takes into consideration how an actual golf ball interacts with the air. The equations it is based on are in the physics literature (I wrote one of these myself for a project and it agrees pretty closely with the other models out there). The real ones used in industry are proprietary -- i.e. TaylorMade is not sharing code with Titleist who isn't sharing with Calloway, etc. Each of them are trying to eek out as much distance as they can from their own club designs and ball designs. But, this software will quickly show that 45* launch angle for a golf ball is far from maximum distance.

[imatfaal]

Great post Bignose. But 17 degrees from VERTICAL? With backspin that would end up coming back over your head. Or is this a transatlantic language problem. I am presuming that TaylorMade would suggest that you hit the ball at 17 degrees elevation above the horizontal. Doesn't seem enough to me - but gonna play with that software a bit

Or is that the angle that the face of the club makes with the vertical at point of impact? That seems likely

[Bignose]

Yeah, oops. 17* above the horizon. My bad. For reference, the loft on a typical driver is between 8* and 12*, and modern instruction asks players to try to hit up ever so slightly... between the inelasticity of the impact and this slight hit up, that's where the launch in the high teens comes from.

[Waleed]

I think 22 mph is just under 10 m/s

 

Or is that the angle that the face of the club makes with the vertical at point of impact?