The Isoceles Triangle of Jump Shots

[Snapshot9]

What I am going to bring up is something I have not seen discussed before on any forum, the Isoceles Triangle of Jump shots.

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An isosceles triangle is a triangle that has two (or three) sides that are the same length.

Supplementary angles are two angles whose sum is 180°. For instance, 130° and 50° angles are supplementary angles.

~Gustav
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When a Jump shot is performed, if one was to draw a horizontal line from the top of the maximum cue ball height (on the top of the ball) back to
your cue, it forms an Isoceles Triangle. Knowing this basic principle
can assist you in determining the angle to elevate your cue for the jump shot. I see many players elevating their cues too high to perform the jump shot that they are about to perform.

When elevating the cue higher than needed, they may get over the ball, but the cue ball will dead hit, and roll barely without a true course of direction (will drift some).

Now, visualize this Isoceles Triangle in your mind before attempting a jump shot. The further the object being jumped is from the cue ball, the lower, or wider, the Isoceles Triangle will be. The closer the object ball is, the taller, or narrower, the Isoceles Triangle will be. Balls that closer to be jumped, you usually have to jump the cue ball higher to get over the ball, and with the momentum to carry it forward, hence the taller Isoceles Triangle if you were to draw that horizontal line from the top of the cue ball at its maximum height back to your cue.

If you elevate your jump cue to, say, a 60 degree angle, visualize the cue ball going forward up at the same angle. To know how high to elevate, as a rule of thumb only, look at the base of the cue ball from the side to the top of the object ball to be jumped, and determine what the angle is, say iyou determine it to be 55 degrees (draw a line mentally from the bottom of cue ball to top of object ball and determine angle degrees), then add 10 degrees to your estimation, and this gives you an estimation of how high you should elevate your cue for the jump.

 

[TheBook]

Can you post a illustration? It would be easier to visualize. I am having a hard time trying to figure it your description.

Thanks

 

[justnum]

Diagram is not to scale

Kudos for attempting to explain math. The visualization says elevate cue a certain amount for a desired effect. And from the diagram one can observe (1 hr lecture) that there is more than one path to reach the same point, the difference being the height reached.

Pictures are a highly effective teaching tool, and they are confusing. Its better than equations at least here people can identify shapes.

 

[justnum]

More interesting in billiards is the curvature from english or masse shots. Which are results of various amounts of force exerted on a specific location of the sphere. Its pretty when you see it on the table. And beautiful when you can see the design behind it.

Thats enough math for one day dont you think, I can smell minds overheating from exhaustion of trying to imagine the isosceles triangle.

If you like stuff like that I recommend thinking the symmetry of a sphere and why it is that the motion is predictable.

Than you can all become theoretical physicists by saying well what if you eliminate the resistances of the table caused by friction and gravity and assume the motion for infinity.

Should you wish to pursue the mathematical journey than ask yourself what bounds the motion and how can one exploit those properties for desired effects.

For budding engineers try to figure out how one can measure those properties.

 

[justnum]

Just to be sure here is the diagram with more lines.

 

[Bob Jewett]

... If you elevate your jump cue to, say, a 60 degree angle, visualize the cue ball going forward up at the same angle. ...

If the angle up were actually the same as the angle of the stick pointed down, it would be sufficient to just shoot the cue ball "below" the ball you have to jump over. That is, if you imagine the table suddenly disappearing and the balls suspended in air, if you shot the cue ball below the object ball, that would be the elevation required to miss the object ball with the table present. It is the same as the mirror principle for banking.

There are two problems with this idea. The first is that the table does not bounce well. If the stick is elevated to 45 degrees, the initial path of the cue ball is considerably less than 45 degrees of take-off elevation. The second problem is that the path of the cue ball is not a straight line. It is a parabola. The height the cue ball achieves is only half of what you would calculate from its take-off point, landing point and the take-off angle, and assuming a triangular path.

The system is correct in general that you will get a higher angle from the cue ball for a higher angle on the stick, but only up to a certain point. After that point, masse sets in.

 

[seymore15074]

If the angle up were actually the same as the angle of the stick pointed down, it would be sufficient to just shoot the cue ball "below" the ball you have to jump over. That is, if you imagine the table suddenly disappearing and the balls suspended in air, if you shot the cue ball below the object ball, that would be the elevation required to miss the object ball with the table present. It is the same as the mirror principle for banking.

That is brilliant, I have not thought of jump shots this way. I always viewed the jump from the side-view, assuming (approx.) angle into the slate = angle out, and adjusted a little for gravity...

Great post.