# Terminal Velocity of the Fuel Balls

Does anyone have any estimates for the terminal velocity of the fuel balls?

Thank you,
Dikshant Sharma

Terminal velocity is the highest velocity attainable by an object as it falls through a fluid (air is the most common example, but the concept applies equally to any fluid)

With that definition, and with G23:

Shoot FUEL from your own LAUNCHPAD. A ROBOT may only LAUNCH FUEL while in their LAUNCHPAD (i.e. at least breaking the plane of the line with BUMPERS).

I don’t see any teams actually approaching terminal velocity with their fuel. So, why do you want to figure out what it is? trying to shoot the ball through the ceiling of your venue?

No, trying to calculate ball trajectory.

Terminal velocity is a simple way of incorporating air drag force into trajectory calculations.

At terminal velocity, the force of air drag is equal to the force of gravity.

If you assume air drag is proportional to velocity squared, you can then compute the air drag force at any velocity.

You can then set up an Initial Value Problem and numerically integrate it to find the trajectory.

Like this.

Mumbles something about empirically determining terminal velocity of balls by firing them out of a bench grinder

In our team’s unscientific testing of the fuel ballistics behavior (i.e…no one was writing anything down), we observed that they are pretty stable when tossed but they lose velocity rapidly and eventually just want to drop out of the air.

Dimples on golf balls are not the same as holes in a hollow ball.

I don’t think aerodynamics will be useful for modelling flight paths of fuel; the holes will let air through, and even if the interaction is significant, it wouldn’t be practical to model internal air flow.

Sidenote: I know one of the pieces of software in the KoP vouchers does airflow modelling, that might be worth looking into. Also Wolfram Alpha Pro: Amazing.

But…
Here I’ll link my projectile motion with air resistance desmos graph. I used it last year with the solid balls. It assumes that friction is proportional to velocity directly (ie not squared) which is technically an incorrect assumption, but it looks pretty.

You don’t need to model airflow in order to build a useful simulation. All you need is some good data.

For any team so inclined, here is an opportunity to provide a useful service to the community

Place the cannon against a block wall (a gym perhaps) and fire shots along the wall at different elevation angles and muzzle speeds while taking high-speed timestamped videos. Make sure there are no running fans or open doors or windows (to eliminate air currents).

The blocks act as a Cartesian grid for marking 2D (x,y) location.

Using the location vs time data, that data can be fit to a parameterized model to find values for the model parameters which provide the best fit.

Once the best-fit parameters have been experimentally determined, the model can be used by teams to help design their cannons.

I’ll volunteer to do the model fitting if the data is made available.

[EDIT] Thinking back to my boyhood, I seem to recall that Wiffle balls exhibit a profound Magnus effect. Topspin and backspin can dramatically affect the flight path. This makes the data collection and modeling quite a bit more difficult and contentious.

I think the more pressing question is the maximum fire rate of the balls before they start colliding with each other at the apex of their arc.

I wonder if that’s because of the holes in general or the fact that wiffle balls only have holes on one side. With holes more evenly spaced, it might make a difference, though I’m not entirely sure.

We did specific testing to see if spin affected ball trajectory on the order of what a wiffle ball does, and these balls are not affected in the same way as wiffle balls.

I opine that the uniform distribution of holes does not enable the very interesting aerodynamic effects that make wiffle balls so darn wiffly.

For reference.

Team 4926 conducted a ball drop experiment to measure the terminal velocity of the fuel balls. We confirm a terminal velocity of 10.16 m/s (33 ft/s). From this we calculated the drag coefficient to be 0.45. Thanks Ether for the help! If you want to see our video you can find it on our Facebook Page (Columbus Robotics) or through this link.

Mackenzie

Your thoughts are exactly right. REAL Wiffle balls (manufactured 1 mile from where I now sit) were specifically designed to curve, and that’s why the holes are only on one side.