Nerf ball starting at 12m/s 45 degree angle ending at 8ft 6in w/ air resistance

[Nathan Pell]

Originally Posted by Ethulin

We already have something to base the air friction on, FIRST told us that it will travel 35feet at 30 degrees. That is WITH air resistance. We should be able to base our calculations off that.



The 35ft at 30 degrees is with no spin, so we can do some tests with spin afterwards, but lets get the basics first, i.e. without spin.

Just curious.. where did you find this?

[Tatsu]

Taken from Section 4 - The Game

<S02> Muzzle Velocity - No ROBOT may throw a ball with an exit velocity of greater than 12 m/s (26.8 mph).
As a reference, a ball traveling at this velocity when leaving the ROBOT at an angle of 30º from
horizontal with no spin will travel approximately 35 feet. A robot that violates this rule will be
considered unsafe per <S01>.

[Rick TYler]

Originally Posted by Bill Moore

Has anyone done weight checks to determine the the population range and median?

And the mean, mode and standard deviation? I also want to see a scatter plot to check to see if it is a one-tail or two-tail population, or even one with more than one mode. Some sort of 3D modelling of mass density would be nice, too.

[Tatsu]

I massed 6, using a mean of .18 ... the mass deviations dont significantly affect the range..

[Ethulin]

Originally Posted by Tatsu

Not sure what I'd need.. I just need someone with Mathematica 5.1 that can execute my notebook.. if not I'll just have to run it overnight or something.. not that big of a problem.

Tatsu.

Anyway, the equation isn't that bad if you dont try to make it a diffeq problem.. its just small timestep modeling.. and yes, you probably cant do this by hand (and thus the RC wouldnt be able to either.)

so if you want accurate trajectories, you'll need lookup tables.. (I cant think of any other way to calculate air resistance trajectories on the fly..)

When I posted this all I wanted was that distance. So we can make a "no one can shoot past here arc" on our field.

[Tatsu]

oh, is THAT what you want?

I think that's 6.5 meters. well, I'll just generate the full table and find the max, faster that way =p.

*edit* - wow, finals studying is making me drowsy.. but the max should be around 8.8 meters.. give or take maybe .5 meters.. (sorry, I dont have a full lookup table, but this seems pretty close..)

*edit 2* - does anyone still want the lookup tables?

[Ethulin]

Originally Posted by Tatsu

oh, is THAT what you want?

I think that's 6.5 meters. well, I'll just generate the full table and find the max, faster that way =p.

*edit* - wow, finals studying is making me drowsy.. but the max should be around 8.8 meters.. give or take maybe .5 meters.. (sorry, I dont have a full lookup table, but this seems pretty close..)

*edit 2* - does anyone still want the lookup tables?

I might if I knew what they were... all I know that I need is that one length, what will that table give me?

Also, is there any way to calculate what the best angle would be instead of 45 degrees?

[Tatsu]

Well, a standard lookuptable is something like this..

y axis - theta
x axis - v

the entry for some v and theta gives you the distance (in this case from 5 ft to 81/2 ft).. therefore you reverse-lookup to find a theta. Lets say you keep v constant at 12 m/s Now just find an entry in the table which is equal do your distance from the goal... that gives you your fireing angle. Fire.

Otherwise you have to calculate angle depending on your distance, that's not possible when you factor air resistance.. (at least not to my knowelege).. so you have 2 options

a). use lookup tables to find an angle that matches your distance

or b). use a model without air-resistance and be off by a large amount the farther away you get.

Either way its not pretty, but I think our team wants to do a). (psst.. dont tell them I already made the lookup table, I want to see how fast our programmers get it =p )

[Ethulin]

Originally Posted by Tatsu

Either way its not pretty, but I think our team wants to do a). (psst.. dont tell them I already made the lookup table, I want to see how fast our programmers get it =p )

LoL! So mean... so mean....

[billbo911]

Originally Posted by Ethulin

When I posted this all I wanted was that distance. So we can make a "no one can shoot past here arc" on our field.

Here is a picture that show a theoretical max distance. It ignores the effects of drag and spin.
It shows the theoretical max distance, when the ball is launched from ground level, at 12m/s and 45 deg. elevation to be about 37.2 ft/11.34m.

[David Brinza]

In another thread, I posted a link to a paper that describes how to calculate the trajectory of a ball, including air resistance. I also attached an Excel file that allows the user to vary launch speed, angle and height as well as ball mass, diameter, drag coefficent. It produces a trajectory plot with the upper and lower heights for the goal shown on the graph. It's pretty easy to use and gives you a tool to determine how sensitive the trajectory is to the various parameters.

See:
http://www.chiefdelphi.com/forums/sh...710#post429710

[Greg Perkins]

Im no math whiz, but would this work? have your launcher (for instance turret like a snowblower) and mount the cam so its on the top of the launcher, then proportionally program the offset of cam-turret to greenlight-hole? that way when your bot drives the cam always tracks the greenlight and your launcher is always aimed there. Me=mechanical and not too electrically intuitive, is this possible?

[obitusis]

By the way billbo911's calculations were provided by:
www.hyperphysics.phy-astr.gsu.edu

We got:
From 1.4 meters off ground to center of goal, we calculated that max range 11.1 meters at 48 degrees. That includes drag coefficient of 0.3 - constant drag coefficient. The proof is left for an exercise for the reader.

[Tatsu]

How'd you get that number? you're off about 3 meters from my calculations.. weird. want to run your caclulations again with a coefficient of .416 (should be more accurate)? I might be wrong..

[Mirza95vx]

Air resistance is not a factor unless you are going 75+ mph. So you dont have to account air resistance into the equation.