OCCRA [more] FRC Kickoff : 24d 17h 46m ...
JVN, thanks for working with me. You will make a great MC anywhere. Folks, he actually loosened up and fit right in. - Steve W [more]
 Chief Delphi Physics: ball launch using gravity
 CD-Events CD-Media CD-Spy FRC-Spy
The Chief Delphi Forums are sponsored by Innovation First International, Inc.

#1
02-16-2006, 07:17 PM
 JoeXIII'007 Perpetually Stunned Speechless AKA: Joeseph Smith FRC #0066 Team Role: Alumni Join Date: Feb 2004 Rookie Year: 2001 Location: Ypsilanti, MI (Ann Arbor's shadow) Posts: 752
Physics: ball launch using gravity

OK, before I get into what I'm looking for, here's my assignment:

I have to build a device that will launch a ball approximately 10 grams in weight to a 10 cm wide hoop 1 meter away and 1 meter high.

Now, what I really want to do is build a ramp system that will use gravity to accelerate the ball and then redirect its direction so that it will launch high and far enough to get into the hoop. In my thinking, if I build it just right, it should work 100% of the time.

Question is, how do I successfully transfer the vertical motion of the ball at start into horizontal and vertical motion good enough to get the ball into the hoop?

Thoughts?
Other suggestions are really welcome.

-Joe

 in the case that this involves complex math and you must use it, I'm currently enrolled in a pre-calc class. So go for it. [/edit]
__________________
Joeseph P. Smith
University of Michigan - Informatics
#2
02-16-2006, 11:47 PM
 David Brinza Lead Mentor, Robot Inspector FRC #0980 (ThunderBots) Team Role: Mentor Join Date: Feb 2003 Rookie Year: 2003 Location: Glendale, CA Posts: 1,247
Re: Physics: ball launch using gravity

Using conservation of energy, you should be able to determine from what height you will need to start rolling the ball down a "ski jump" in order to achieve enough velocity to launch the ball at some angle to make it through the hoop. Don't forget to include the rotational energy of the ball in your calculation...
__________________
"There's never enough time to do it right, but always time to do it over."
2003 AZ: Semifinals, Motorola Quality; SoCal: Qtr-finals, Xerox Creativity; IRI : Qtr-finals
2004 AZ: Semifinals, GM Industrial Design; SoCall: Winners, Leadership in Controls; Championship: Galileo #2 seed, Quarterfinalist; IRI: Champions
2005 AZ: #1 Seed, Xerox Creativity; SoCal: Finalist, RadioShack Controls; SVR: Winners, Delphi "Driving Tomorrow's Technologies"; Championship: Archimedes Semifinals; IRI: Finalist
2007 LA: Finalist; San Diego: Q-finals; CalGames: Finalist
2008 San Diego: Qtr-finalist; LA: Winners; CalGames: Finalist
2009 LA: Semifinals; Las Vegas: Qtr-finalist; IRI: #1 Seed, Finalist
2010 AZ: Motorola Quality; LA: Finalist
2011 SD: Qtr-finalist; LA: Qtr-finalist
2013 LA: Xerox Creativity, WFFA, Dean's List Finalist
#3
02-17-2006, 12:59 AM
 Tom Bottiglieri Custom User Title FRC #0254 (The Cheesy Poofs) Team Role: Engineer Join Date: Jan 2004 Rookie Year: 2003 Location: San Francisco, CA Posts: 2,869
Re: Physics: ball launch using gravity

Quote:
 Originally Posted by David Brinza Using conservation of energy, you should be able to determine from what height you will need to start rolling the ball down a "ski jump" in order to achieve enough velocity to launch the ball at some angle to make it through the hoop. Don't forget to include the rotational energy of the ball in your calculation...
As David said...

Total energy is a system is constant.
Code:
```Potential Energy (U)  = (mass) * (height) * (acceleration of gravity)
Linear Kinetic Energy (T) = 1/2 * (mass) * (velocity ^ 2)
Rotational Kinetic Energy (KR) = 1/2 * (moment of inertia) * (velocity ^ 2)

I for a sphere: 2/5 * Mass * Radius^2

EA = EB (E is total energy, A and B are arbitrary points in time.)

E = T + U + KR```
So what I would do first is a simple kinematics/projectile motion problem (there might be some handy tools in the white paper section ) to find what velocity is needed on the launch. (In this case, you would arbitrarily chose the angle theta of the launch. I would chose 45 degrees.)

Once you have your needed velocity and launch angle, figure out how much kinetic energy it will have at launch. Plug the velocity, mass, and Moment of Inertia (I) into the equations above, and add the 2 values together to find net kinetic energy. Then, set that equal to the potential energy (You can assume this if your reference frame has the balls launch point as (0,0) and the ball is starting from a stop, aka no kinetic energy.)

So now you have U = T + KR and U = mgh. Simply solve for U, and divide by 0.098 (g * m) to find how high (in meters) your ball should start in the y direction above the launch point.

Voila.
__________________
Team 254 | San Jose, CA | Mentor (2010 - Present)
Team 125 | Boston, MA | College Student (2007 - 2011)
Team 195 | Southington, CT | Student (2002 - 2006)
#4
02-17-2006, 10:16 AM
 JoeXIII'007 Perpetually Stunned Speechless AKA: Joeseph Smith FRC #0066 Team Role: Alumni Join Date: Feb 2004 Rookie Year: 2001 Location: Ypsilanti, MI (Ann Arbor's shadow) Posts: 752
Re: Physics: ball launch using gravity

Quote:
 Originally Posted by Tom Bottiglieri As David said... Total energy is a system is constant. Code: ```Potential Energy (U) = (mass) * (height) * (acceleration of gravity) Linear Kinetic Energy (T) = 1/2 * (mass) * (velocity ^ 2) Rotational Kinetic Energy (KR) = 1/2 * (moment of inertia) * (velocity ^ 2) I for a sphere: 2/5 * Mass * Radius^2 EA = EB (E is total energy, A and B are arbitrary points in time.) E = T + U + KR``` So what I would do first is a simple kinematics/projectile motion problem (there might be some handy tools in the white paper section ) to find what velocity is needed on the launch. (In this case, you would arbitrarily chose the angle theta of the launch. I would chose 45 degrees.) Once you have your needed velocity and launch angle, figure out how much kinetic energy it will have at launch. Plug the velocity, mass, and Moment of Inertia (I) into the equations above, and add the 2 values together to find net kinetic energy. Then, set that equal to the potential energy (You can assume this if your reference frame has the balls launch point as (0,0) and the ball is starting from a stop, aka no kinetic energy.) So now you have U = T + KR and U = mgh. Simply solve for U, and divide by 0.098 (g * m) to find how high (in meters) your ball should start in the y direction above the launch point. Voila.
Thank you. This should work really well.

-Joe
__________________
Joeseph P. Smith
University of Michigan - Informatics
#5
02-17-2006, 11:56 AM
 David Brinza Lead Mentor, Robot Inspector FRC #0980 (ThunderBots) Team Role: Mentor Join Date: Feb 2003 Rookie Year: 2003 Location: Glendale, CA Posts: 1,247
Re: Physics: ball launch using gravity

Quote:
 Originally Posted by Tom Bottiglieri So what I would do first is a simple kinematics/projectile motion problem (there might be some handy tools in the white paper section ) to find what velocity is needed on the launch. (In this case, you would arbitrarily chose the angle theta of the launch. I would chose 45 degrees.)
I posted an Excel spreadsheet that computes the ball trajectory for Aim High. You can adjust the launch angle, velocity, and see the effect of air resistance (which should be really small) for your problem. To "turn off" air resistance, you can set the drag coefficient (Cd) to zero. The spreadsheet can be downloaded from this post:

http://www.chiefdelphi.com/forums/sh...5&postcount=19

Have fun...
__________________
"There's never enough time to do it right, but always time to do it over."
2003 AZ: Semifinals, Motorola Quality; SoCal: Qtr-finals, Xerox Creativity; IRI : Qtr-finals
2004 AZ: Semifinals, GM Industrial Design; SoCall: Winners, Leadership in Controls; Championship: Galileo #2 seed, Quarterfinalist; IRI: Champions
2005 AZ: #1 Seed, Xerox Creativity; SoCal: Finalist, RadioShack Controls; SVR: Winners, Delphi "Driving Tomorrow's Technologies"; Championship: Archimedes Semifinals; IRI: Finalist
2007 LA: Finalist; San Diego: Q-finals; CalGames: Finalist
2008 San Diego: Qtr-finalist; LA: Winners; CalGames: Finalist
2009 LA: Semifinals; Las Vegas: Qtr-finalist; IRI: #1 Seed, Finalist
2010 AZ: Motorola Quality; LA: Finalist
2011 SD: Qtr-finalist; LA: Qtr-finalist
2013 LA: Xerox Creativity, WFFA, Dean's List Finalist
#6
03-02-2006, 01:27 PM
 JoeXIII'007 Perpetually Stunned Speechless AKA: Joeseph Smith FRC #0066 Team Role: Alumni Join Date: Feb 2004 Rookie Year: 2001 Location: Ypsilanti, MI (Ann Arbor's shadow) Posts: 752
Re: Physics: ball launch using gravity

It's been a while since I posted here, but a few things have changed with the project, which is working quite well. First, here's the criteria for the ball launcher from the sheet my physics teacher gave:

Quote:
 Build a machine that will project a ball (current weight is roughly 30-40 grams, it is no longer 10) through a hoop that is ~ 10 cm wide, 1 meter in the x direction, and 1 meter in the y direction. Rules:you will have three tries to get the ball through the hoop.The ball must move at least 1 meter in the +x direction once it leaves the bounds of the machine.Calculations to support your design must be completed in report form. Include the following in the calculations:Force of the mechanism acting on the ball.Graph showing the path of the ball once it leaves the mechanism.Speed the ball is traveling through the air Grades will be determined by the accuracy of calculations and physics50pts Mechanics of the machine (does it work)35pts Creativity of the design15pts Extra points may be earned for distances traveled through the air > 1 meter.
So, here's the status of the project, which is due next Wednesday. I have it launching the ball 10-15 cm short of the 1 meter height and 1 meter away requirement. HOWEVER, I have been able to consistently get the ball through the hoop, which is in vertical orientation, between 84-94 cm high. The angle, which I am yet to measure is about 45-55 degrees. Do not trust the protractor like device in one of the pics, for I do have the ramp a bit higher than 45.

The device consists of a vertically standing PVC pipe that is 1.9 meters long. It provides the ball gravity acceleration. At the end of the pipe, I have 2 'hot-wheels' flexible tracks that end about .75 horizontal meters away, pointing the ball 45-55 degrees to the hoop.

I need to know how exactly to measure the curve, circular or not. It was never drafted, and was tweaked SEVERAL times that any rough/initial draft with any accuracy would be no longer accurate. Pictures are attached of the device, or should I say ramp.

As far as calculations are concerned, I know that I can get the speed and force before the ball hits the curve using v = gt and f = ma respectively since it's a relatively straight vertical drop. It's the curve that I need measured, and the angle I can get easily.

Thanks again, and any ideas on how to get the ball just a wee bit higher would be really great.

-Joe
Attached Thumbnails

__________________
Joeseph P. Smith
University of Michigan - Informatics

Last edited by JoeXIII'007 : 03-02-2006 at 02:10 PM.
#7
03-02-2006, 04:56 PM
 David Brinza Lead Mentor, Robot Inspector FRC #0980 (ThunderBots) Team Role: Mentor Join Date: Feb 2003 Rookie Year: 2003 Location: Glendale, CA Posts: 1,247
Re: Physics: ball launch using gravity

Joe:

Does your calculation of drop height consider the rotational kinetic energy of the ball? (If not, this would explain why you are coming up short.)

You may also be losing some energy due to flexure of those "hot wheels" tracks and perhaps some friction losses as well. So, you will need to drop the ball from a greater height to offset some of these loss factors. If you need the ball to go higher, you can increase the angle (with loss in distance traveled).
__________________
"There's never enough time to do it right, but always time to do it over."
2003 AZ: Semifinals, Motorola Quality; SoCal: Qtr-finals, Xerox Creativity; IRI : Qtr-finals
2004 AZ: Semifinals, GM Industrial Design; SoCall: Winners, Leadership in Controls; Championship: Galileo #2 seed, Quarterfinalist; IRI: Champions
2005 AZ: #1 Seed, Xerox Creativity; SoCal: Finalist, RadioShack Controls; SVR: Winners, Delphi "Driving Tomorrow's Technologies"; Championship: Archimedes Semifinals; IRI: Finalist
2007 LA: Finalist; San Diego: Q-finals; CalGames: Finalist
2008 San Diego: Qtr-finalist; LA: Winners; CalGames: Finalist
2009 LA: Semifinals; Las Vegas: Qtr-finalist; IRI: #1 Seed, Finalist
2010 AZ: Motorola Quality; LA: Finalist
2011 SD: Qtr-finalist; LA: Qtr-finalist
2013 LA: Xerox Creativity, WFFA, Dean's List Finalist
#8
03-02-2006, 05:09 PM
 Richard Wallace I live for the details. FRC #3620 (Average Joes) Team Role: Engineer Join Date: Jan 2003 Rookie Year: 1996 Location: Southwestern Michigan Posts: 2,564
Re: Physics: ball launch using gravity

Quote:
 Originally Posted by JoeXIII'007 Thanks again, and any ideas on how to get the ball just a wee bit higher would be really great. -Joe
This may be a bit late in your project and a bit too abstract to be useful, but..

Neglecting friction, the problem of finding the curve of steepest descent rate (which would maximize velocity at the bottom) is called the brachistochrone problem. The solution is a cycloid curve.

The problem can be generalized using calculus of variations to include friction, rotational KE, etc.

The descending section of your Hot Wheels track appears to be very close to a cycloid.
__________________
Richard
Whirlpool Corporation, Benton Harbor, Michigan
Mentor since 2011 for FRC 3620 Average Joes (St. Joseph, Michigan)
Mentor since 2002 for FRC 931 Perpetual Chaos (St. Louis, Missouri)
since 2003

I believe in intuition and inspiration. Imagination is more important than knowledge. For knowledge is limited, whereas imagination embraces the entire world, stimulating progress, giving birth to evolution. It is, strictly speaking, a real factor in scientific research.
(Cosmic Religion : With Other Opinions and Aphorisms (1931) by Albert Einstein, p. 97
#9
03-02-2006, 06:32 PM
 JoeXIII'007 Perpetually Stunned Speechless AKA: Joeseph Smith FRC #0066 Team Role: Alumni Join Date: Feb 2004 Rookie Year: 2001 Location: Ypsilanti, MI (Ann Arbor's shadow) Posts: 752
Re: Physics: ball launch using gravity

Quote:
 Originally Posted by David Brinza Joe: Does your calculation of drop height consider the rotational kinetic energy of the ball? (If not, this would explain why you are coming up short.) You may also be losing some energy due to flexure of those "hot wheels" tracks and perhaps some friction losses as well. So, you will need to drop the ball from a greater height to offset some of these loss factors. If you need the ball to go higher, you can increase the angle (with loss in distance traveled).
Actually, the 1.9 meter length of the pipe was arbitrary, because I bought over at a hardware store, and they cut it there. I do have the other half, however. I have actually gone the experimental route in developing the launcher.

Increasing the angle I have tried, but the loss of x-distance is too great.

And yes, I have been trying to stiffen the tracks so that they would not absorb energy needed to launch. As far as height, we have considered going to the second floor and drilling a hole large enough to do that, but I do not think the administration and especially the custodial staff would like that. The top of the pipe is 10-15 cm from the drop ceiling though, and perhaps if I could convince someone to let me move the tiles... hmm... yes. I'll have to do some good old fashined negotiating.

Quote:
 Originally Posted by Richard This may be a bit late in your project and a bit too abstract to be useful, but.. Neglecting friction, the problem of finding the curve of steepest descent rate (which would maximize velocity at the bottom) is called the brachistochrone problem. The solution is a cycloid curve. The problem can be generalized using calculus of variations to include friction, rotational KE, etc. The descending section of your Hot Wheels track appears to be very close to a cycloid.
I'm studying Pre-calc, not calculus quite yet, that's a problem. But if I were to sit down and take some time with it, maybe I could figure it out. Otherwise I do not need to bother my physics teacher with more stuff to read over, since he was assuming everyone was going to build a simple catapault or trebuchet. Plus, he's got a hockey team, robotics team, TV productions, and this physics class to handle (a lot of people need help on simple physics stuff, I always try to help out). SO, I'll have to ask him what exactly he would like as far as calculations for the device.

Interesting stuff though, can't wait until I learn it all, and thank you very very much for the insight.

-Joe

PS: I wonder what my partner in this project is going to think of all this...
__________________
Joeseph P. Smith
University of Michigan - Informatics

Last edited by JoeXIII'007 : 03-02-2006 at 06:41 PM.

 Thread Tools Display Modes Rate This Thread Linear Mode Rate This Thread: 5 : Excellent 4 : Good 3 : Average 2 : Bad 1 : Terrible

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts vB code is On Smilies are On [IMG] code is On HTML code is Off
 Forum Jump User Control Panel Private Messages Subscriptions Who's Online Search Forums Forums Home Announcements     User Announcements FIRST     General Forum         FIRST E-Mail Blast Archive     Rumor Mill     Career     Robot Showcase     Moderated Discussion Technical     Technical Discussion     Robotics Education and Curriculum     Motors     Electrical         CAN     Programming         NI LabVIEW         WindRiver C++         Java         MATLAB & Simulink         Python     intelitek easyC/REC information         easyC v2 for Vex         easyC for FRC         REC/Learnmate         WPILib         easyC PRO     Control System         IFI Control System         FRC Control System         Sensors         USB Chicklet     Pneumatics     Kit & Additional Hardware     CAD         Inventor         SolidWorks         Pro ENGINEER / Creo     IT / Communications         3D Animation and Competition         Website Design/Showcase         Videography and Photography         Computer Graphics     National Instruments LabVIEW and Data Acquisition         LabView and Data Acquisition Competition     Awards         Chairman's Award     Rules/Strategy         Scouting         You Make The Call     Team Organization         Fundraising         Starting New Teams         Finding A Team         College Teams     Championship Event     Regional Competitions     FIRST in Michigan     Mid-Atlantic Robotics     Off-Season Events         Chief Delphi Invitational     Thanks and/or Congrats     FRC Game Design     OCCRA         OCCRA Q&A         OCCRA Programming Other     Unsung FIRST Heroes     Chit-Chat         Games/Trivia             Fantasy FIRST     Car Nack's Corner     College & University Education     Dean Kamen's Inventions     FIRST-related Organizations         Western Region Robotics Forum         Robot Chicks Union (RCU)         Southern California Regional Robotics Forum         FIRST Interactive Rural SupporT         FIRST Scouting Network         The Grand FIRST Team         FloridaFIRST         FIRSTwiki         Ultimate Robot Challenge         Team San Diego         Dream FIRST         The Blue Alliance             Video Archives     FIRST Historians     FIRST-A-Holic's Anonymous Mailbox     FIRST In the News...     FIRST Lego League         Lego Mindstorm Discussion     FIRST Tech Challenge     VEX         VEX Robotics Competition         VEX IQ     Televised Robotics     Math and Science         NASA Discussion ChiefDelphi.com Website     CD Forum Support     Extra Discussion Old Forum Archives     1999     2000     2001

 Similar Threads Thread Thread Starter Forum Replies Last Post White Paper Discuss: Physics Analysis of a Ball Launcher coastertux Extra Discussion 0 02-01-2006 05:58 PM White Paper Discuss: Analysis of Ball Drag from Fundamental Physics coastertux Extra Discussion 0 02-01-2006 04:49 PM Ball Recirculation Question Nuts4FIRST Rules/Strategy 23 01-15-2006 03:35 PM Experimental Ball Drive Sepsis900 Technical Discussion 16 10-31-2005 04:59 PM 2004 Game BBFIRSTCHICK General Forum 112 04-19-2003 05:12 PM

All times are GMT -5. The time now is 06:13 AM.

The Chief Delphi Forums are sponsored by Innovation First International, Inc.

 -- English (12 hour) -- English (24 hour) Contact Us - Chief Delphi - Rules - Archive - Top