Ball Trajectory Planning

[mikegrundvig]

Hi all; thanks for all the feedback. I just got off with phone with Rhett Allain (http://www.wired.com/wiredscience/author/rhettallain/) - he is a physics professor and the friend-of-a-friend. He feels that the Magnus Effect can be effectively ignored in these foam basketballs because of their size, density, and low RPM of spin. Likewise, while air resistance will certainly be a measurable amount, it's exceptionally hard to calculate and also likely to be within the inconsistency of the machine itself in the best case scenario. This also means temperature, pressure, etc. can all be ignored.

Looks like you guys were right and I was wrong - no need to over-complicate it. This is good news for us though as the physics problem is now just one of projectile motion and nothing too nasty.

-Mike

[sometimestommy]

Ive worked on finding a good formula to make a good curve but to no avail. I think im just going to make a chart when our launcher is working what maps out various distances and initial velocities/theta. This way you can just either create a curve in labview or just store the data on the crio to have the code refer to

[DjMaddius]

Thats great news, I'm glad you went ahead and did a lot of research and posted it all here.

The information you are giving may be very vital to some of the games played this year!

[Rocketeeringer]

I hear from some of my basketball friends that you want to aim for the square on the backboard, and that will guarantee you a basket.

Assuming you are shooting a basket straight on, could you just calculate the normal angle of the plane that would give you the most area between the uppermost point of the backboard and outward most point of the hoop that would give you the greatest chance of scoring?

[Basel A]

I've been doing some basic physics on shooting the ball with near-optimal trajectory (still working on the equation for optimal trajectory) and have found that in some situations, essentially a full-field shot, ball initial velocities will need to exceed 10 m/s without accounting for air resistance (or spin, for that matter). As such speeds, wouldn't air resistance come into play?

Honestly, I'm doing this for fun without expecting accuracy, but I'd love to get as accurate as possible.

Ether, if you happen to be around, I'd love to get your input on this problem, since you know pretty much everything.

[shuhao]

Originally Posted by Basel A

I've been doing some basic physics on shooting the ball with near-optimal trajectory (still working on the equation for optimal trajectory) and have found that in some situations, essentially a full-field shot, ball initial velocities will need to exceed 10 m/s without accounting for air resistance (or spin, for that matter). As such speeds, wouldn't air resistance come into play?

Honestly, I'm doing this for fun without expecting accuracy, but I'd love to get as accurate as possible.

Ether, if you happen to be around, I'd love to get your input on this problem, since you know pretty much everything.

Using the viscosity of the air, I'm able to estimate the resistive force on the sphere (since it is a sphere, it makes this calculation much simpler instead of using the drag calculations.. which is okay, but i just prefer this one).. at 10m/s you will encounter significant drag.

Here's an Octave/Matlab script that does the estimation (working with iterative solution... no calculus involvement yet.. which seemed rather difficult to do)

https://bitbucket.org/ultimatebuster...12/bbairdrag.m

[Dan.Tyler]

Originally Posted by shuhao

Using the viscosity of the air, I'm able to estimate the resistive force on the sphere (since it is a sphere, it makes this calculation much simpler instead of using the drag calculations.. which is okay, but i just prefer this one).. at 10m/s you will encounter significant drag.

But, it's NOT a sphere. The little bumps? They change the boundary layer behavior and aerodynamic effects.

This both increases the effective diameter of the ball and changes every other aerodynamic factor. The bumps will act to actually REDUCE overall drag by reducing pressure drag significantly; but it increases skin friction drag which increases the affect of most aerodynamic forces, including magnus effects. (same way that the little holes in a golf ball work... increase range, make it harder to remain accurate).

Just saying... if you want to be ultra accurate, you're forgetting some stuff.
And to anybody that thinks it won't end up coming down to testing and evaluation... well... good luck with that. Most of these simple equations are made with some extreme aerodynamic simplifications that will introduce an error of 10-25% in your calculations anyways.

Drag WILL be important. Magnus effect MIGHT be (depends on your launching mechanism). Being able to adjust your scaling factors (you should definitely have these) on the fly, mid-match, will probably be a nice thing to have.


I'd give you the math... but you either wouldn't understand it, or already know it.

[Tom I]

I think the general agreement by most is that the math is VERY complex if you include all the contributing factors, but in reality it's not that important in the long run. I think teams should definitely put thought into the trajectory of their throwers, but anything beyond simple kinematic equations is going to be wasted effort. I think the quote from Ian Curtis put it best,

Entire books have been written on drag, but FIRST robots tend to operate pretty well on the back of a napkin.

Rather than worry about every little detail that could potentially throw off a throw, people need to realize that this game, by it's nature, is going to be full of variables. Heck, the balls are going to get sliced up, no doubt, so that right there is going to throw off any calculations of drag. The best thing to do is to do basic calculations to get a good idea, then build a shooter that is consistent, and try to get as accurate as you can but accept the fact that there will always be percent error. The old expression goes "measure with a micrometer, mark with chalk, cut with an ax."

[Dan.Tyler]

Originally Posted by Tom I

I think the general agreement by most is that the math is VERY complex if you include all the contributing factors, but in reality it's not that important in the long run. I think teams should definitely put thought into the trajectory of their throwers, but anything beyond simple kinematic equations is going to be wasted effort. I think the quote from Ian Curtis put it best,

Rather than worry about every little detail that could potentially throw off a throw, people need to realize that this game, by it's nature, is going to be full of variables. Heck, the balls are going to get sliced up, no doubt, so that right there is going to throw off any calculations of drag. The best thing to do is to do basic calculations to get a good idea, then build a shooter that is consistent, and try to get as accurate as you can but accept the fact that there will always be percent error. The old expression goes "measure with a micrometer, mark with chalk, cut with an ax."

I'd have to fervently agree with the sentiment here.

But, some people still like to do the math. So I thought I'd hand over a few more tidbits of information like the word "boundary layer" to open a world to as much math as they could possibly want (and the realization that all the math in the world can't describe how air behaves)

[Michael Hill]

See this thread: http://www.chiefdelphi.com/forums/sh...ad.php?t=99485

[kws4000]

I cooked this program up a while ago... more like more than a year ago, and I'm not sure how it still works, but it does. Based entirely on the metric system, uses meters/kilograms/seconds/degrees/jouiles/etc std SI units.

I planned on making it able to work backwards using given variables but never got that far. Feel free to edit, compile and post. Executable in the zip, scource in the .c file.

[mikegrundvig]

Originally Posted by DjMaddius

The information you are giving may be very vital to some of the games played this year!

Heh, thanks. I'm trying to get this whole cooperation thing though it goes against my extremely competitive nature

[mathking]

I hear from some of my basketball friends that you want to aim for the square on the backboard, and that will guarantee you a basket.

You don't want to aim for the square on the backboard in general in basketball if you are shooting from a distance from in front of the rim. You aim for the backboard (and banking the shot in) when you are in close to and below the basket, particularly from the side. For shots from more than a few feet basketball players are taught to aim for the hoop itself and not the backboard.

[Rocketeeringer]

Originally Posted by mathking

You don't want to aim for the square on the backboard in general in basketball if you are shooting from a distance from in front of the rim. You aim for the backboard (and banking the shot in) when you are in close to and below the basket, particularly from the side. For shots from more than a few feet basketball players are taught to aim for the hoop itself and not the backboard.

ooooh got it, thank you!

[DjMaddius]

http://hyperphysics.phy-astr.gsu.edu...traj.html#tra7

This should do work for you! Gives you everything you need to know. As long as you know the speed at which the ball is launched and the angle it will tell you how far it will launch. With some manipulations with the equation you can determine much other stuff also.