# paper: Ball Trajectory Calculations

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Ball Trajectory Calculations
by: JesseK

Tailored for FTC’s 2009-2010 game, this shows the estimated ball trajectory relative to the two goals. Inputs are in yellow.

Tailored for FTC’s 2009-2010 game, this shows the estimated ball trajectory relative to the two goals. Inputs are in yellow. It is possible to re-simulate FRC 2006, 2008, and to a lesser extent 2009.

Here is the Microsoft Office 2007 converter if it’s needed.

BallTrajectory.xlsx (66.6 KB)

Cool spreadsheet. I did one for our bot back when it was a shooter. One thing I found valuable was estimated time from release to score. Tracking this variable, there was a sweet-spot for our bot where shots would land in a minimum amount of time.

Hi Jesse,

I like your spreadsheet. Very cool. A number of questions and suggestions.

Instead of asking the user to enter wind resistance which is hard to estimate, you can calculate it. It is based on diameter of ball, coefficient of drag (shape constant) and density of air. Also since you are asking the user to enter number of spinning shooter sides, if it is only 1, it will create top spin or back spin. Based on my spreadsheet calculation, that can affect the trajectory quite a bit depending on weight to diameter ratio of the ball. Ask a tennis player and you will see.

A question for you. Do you take into account the speed of motor when it is under load or are you using free speed? From your experience, how much difference is there?

I am going to show your spreadsheet to my son. He is doing science olympiad this year and he will be doing the trajectory challenge. Your spreadsheet will be very useful for him. Thanks.

Ed Law

The motor speed shown is free speed, yet the trajectory calculations show that only a % of that maximum speed is used due to torque loss in the gearing. The reasoning behind this is that these balls do not compress without a substantial amount of force, thus I was unable to figure out a way to properly calculate a torque load. Hence I had to throw that idea out for this FTC game and estimate the trajectory based on the old-fashioned method that gearbox losses determine maximum speed. The idea behind the bottom of the sheet with feeder speed really comes from my watching the success of many 06/09 shooters who had feeder systems that were just as fast as the shooter wheels. In experimenting with the wiffle balls, the same principle holds true that the shooter only accelerates the ball by a certain amount, and the only way to consistently get that acceleration (thus overcoming the inconsistency in ball-shooter contact) is to have a high feeder speed.

Additionally, I don’t know of the equations to calculate losses from wind, nor do I know where to find it or any of the constants for the medium (air), ball properties, etc. So I left wind resistance as a percentage so it’s intuitively simple to adjust after some experimenting. I’m also not great at Excel, so the preferred method of drop down boxes and lookup tables for the topspin/backspin/no spin will have to be implemented when I have time.

I am working on a “mother of all spreadsheets”, due out at the end of FRC competition season 2010. The hope is that I can take what I’ve done with JVN’s drive train calculator and extend it into arms, elevators, etc. The new ones will attempt to graph position as a function of discretized time based upon the inputs and our favorite physics equation v = a * t (or … v(k+1) = a(k) * h + v(k) …). The hope is to be able to graphically relate power, time, and systems engineering-type requirements to really make the design portion of the build season fly.

If anyone is interested, the following link explains how to calculate projectile motion with air resistance.

http://wps.aw.com/wps/media/objects/877/898586/topics/topic01.pdf

I can’t find the paper online that talks about effect of spin on the motion of a ball. It is basically calculating the Magnus force which creates lift for back spin and dive for top spin. You just add that force to the gravity force and the air resistance when you calculate the acceleration/deceleration. When I find it, I will send it to you. It is just an approximation since the minor details like dimples in a golf ball and stitches of a baseball can have a significant effect at high speed. However in FRC applications, the speed of objects and amount of spin that can be created is limited, and that approximation is qute valid in that range.