Ball Flight Model

[DavisDad]

Care to compare?

Modified spreadsheet model from here: University of Illinois

[adlasa]

Very nice. Could you please explain what CD means?

[themccannman]

Originally Posted by adlasa

Very nice. Could you please explain what CD means?

Chief Delphi obviously

/s

actually though, it's probably coefficient of drag.

[DavisDad]

Originally Posted by adlasa

Very nice. Could you please explain what CD means?

Hi adlasa

This baseball model, posted by University of Illinois, accounts for air drag and lift forces from backspin. Cd is coefficient of drag. The data are calculated with modelling for air resistance. This is a comparison of spinning ball vs. no spin.

[Ether]

Originally Posted by DavisDad

Care to compare?

What values did you use for launch angle, initial speed, ρ, C_D, and C_L?

[RSchorr]

The calculation of drag first requires the computation of Reynolds number. With my initial assumption of 30 degree angle the Initial velocity needed to travel 30 ft to the high goal is about 253 inches/second. This makes the Reynolds number of 2.60E06. My fluid mechanics book is a bit dated (1977) but this would result in a drag coefficient of 0.4 to 0.42.

Using the density of air at 70F of 0.00238 slug/cubic ft and the 24"diameter

Fd = Cd*Rho*V^2/2 *(projectedArea) the initial drag force is 0.65 lbs.

As speed decrease the drag force falls, but this seems to show that drag forces will not be "insignificant".

Can someone confirm please?

[DavisDad]

Originally Posted by Ether

What values did you use for launch angle, initial speed, ρ, C_D, and C_L?

Hi Ether,

Sorry for the illegible chart.

Launch angle- 60deg
Init. speed- 22 f/s
Cd - 0.5
Density- 0.074 lb/m^3
Cd is a calculated function; see U of IL spreadsheet: http://baseball.physics.illinois.edu...culator-v2.xls

I haven't worked through the calculations completely and still need to adjust Re (spreadsheet is 100 mph,147 f/s)

[NotInControl]

I have developed my own model which only accounts for air resistance, I currently ignore spin because I don't think we will be adding spin to our ball.

But I pluged your numbers into my model: using your launch angle of 60 degrees and inital velocity of 22ft/s the results seem very comparable. Note: I DID NOT change my air density of 1.2 kg/m^3, mass of 1.2474kg or Cd which is 0.47 to yours so that is why the number differ slightly.

But here are my results. The Green line represents the center of the top goal, and the red line represents the white zone.

Note again this is only with air drag, not spin.

Remember this is only a simulation, and while our simulations may agree, I would urge you to do some data validation experiments, before you use the results of the simulation to drive your design.

Hope this helps,
Kevin

[DavisDad]

Originally Posted by NotInControl

I have developed my own model which only accounts for air resistance, I currently ignore spin because I don't think we will be adding spin to our ball.

But I pluged your numbers into my model: using your launch angle of 60 degrees and inital velocity of 22ft/s the results seem very comparable. Note: I DID NOT change my air density of 1.2 kg/m^3, mass of 1.2474kg or Cd which is 0.47 to yours so that is why the number differ slightly.

But here are my results. The Green line represents the center of the top goal, and the red line represents the white zone.

Note again this is only with air drag, not spin.

Remember this is only a simulation, and while our simulations may agree, I would urge you to do some data validation experiments, before you use the results of the simulation to drive your design.

Hope this helps,
Kevin

Thanks Kevin for the data, much appreciated!

I am still brushing up on my fluids (humbling exercise) and going through the U of Il theory. My thinking is that simple calcs (no drag) would provide a good enough estimate of velocity required to design shooter. I'm interested in aerodynamic effects for two reasons:

1. Is there much benefit in back-spin for increasing apex height
2. Will back-spin reduce any knuckle-ball effect? I.e., is there enough benefit to invest in more complex back-spin design?

For Rebound Rumble (Nerf basketball), backspin had a significant advantage for range and accuracy.

[NotInControl]

No problem,

I will try to post some datasets from my model later so that you can compare more than just one data point.

In terms of design, it will be hard to ignore drag and obtain meaningful numbers. The ball is relatively large in size, and if you reduce your Cd in your model to 0, you should be able to see the numbers reported for the "No Drag" case.

At shallow launch angles the No drag model will report the ball traveling a lot further then it will in reality.

As for spin, the magnus effect on a ball is very real, and if you plan to put significant spin on the ball then you should at least consider modeling it if your model will be used to help narrow your design parameters.

For my case all the ideas my team has come up with so far are of the type of sling-shot, or catapult launcher, and in most cases will not impart spin on the ball.

For any object traveling though a fluid, spin does offer greater stability which leads to better accuracy. So without spin repeatability will decrease. By how much I can not say cause we are still testing the flight behavior of this ball on our prototypes.


Hope that helps,
Kevin

[DavisDad]

Originally Posted by NotInControl

No problem,

I will try to post some datasets from my model later so that you can compare more than just one data point...
Kevin

That'll be great! I'll be working on sorting out the baseball theory...

We worked on this catapult design for Rebound Rumble:

Rolling Release Catapult

We got it shooting 35' fixed hard to the ground, but ran out of time and the design was questionable re rules and safety. If interested I could post some videos of the last prototype (not in thread).

Craig

[Mike Schreiber]

I've attached a simple to use iterative model that can be edited including comments on how everything is calculated and a FBD. I'm confident the no drag calculation is right because it is simple kinematics, I could use a reality check on the drag included portion because it seemed a little drastic to me, but I checked all my calculations.

I assumed the drag coefficient to be constant, I calculate the Reynolds number but I could not find a look up table online for Re versus Cd of a sphere, if someone knows of one I can easily add it in to recalculate and interpolate to this table on each iteration (probably won't make a significant difference).

I did not include spin because I don't believe many teams will intentionally put spin on the ball (I could be wrong).

Hopefully this can be helpful to someone.

[pfreivald]

It jives well with my Mathcad model.

[Ether]

- Free-body force diagram

- Derivation of differential equations of motion

- C pseudo-code for the difference equations for 2nd order numerical integration

- Includes drag and spin

- Example graphs

http://www.chiefdelphi.com/media/papers/2725

[DavisDad]

pfreivald, Ether & Mike,

Thanks for the replies, much appreciated!