### Flying disks and mathematical models

An exploration of mathematical models and flying disks form the core of laboratory fourteen.

Laboratory fourteen explored the use of data to determine mathematical models and to test whether flying disks and rings outperform the theoretic performance of a non-flying object.

The first question examined was the nature of the mathematical model - does a horizontally thrown disk or ring travel a horizontal distance d that is linearily related to the horizontal throw velocity v? The velocity will be the independent variable on the x-axis, the distance will be the dependent variable on the y-axis.

The second question was whether a disk or ring can outperform a ball or rock. A ball or rock travels a distance d equal to the horizontal distance times the square root of two times the height divided by the acceleration of gravity.

horizontal distance = sqrt(2h/g)*horizontal velocity

One should not get confused by the square root sign, the quantity sqrt(2h/g) is a constant that is roughly 0.45 seconds if h is one meter. That suggests a linear relationship.

If the disk or ring actually generates lift, then the distance should be greater than predicted by sqrt(2h/g)*horizontal velocity and the resulting slope should be greater than sqrt(2h/g).

Note that a throw velocity of zero meters per second generates a zero distance, thus (0 m/s, 0 m) is also a data point.

Along the way I discovered that some students had either never thrown a flying disk or had only thrown a flying disk once or twice. In hindsight I should have given instructions on how to throw a flying disk and flying ring. Aim was also an issue, very few students - even when they tried - could put the flying disk or ring dead onto the radar gun.

Williamson captured this photo of a lawn visitor who some of the female students find frightful. If some of the male students frightful of toads, they did not let on.

Vancyleen Wichep, Jerisse Salvador, Amabella Soram with disks

Laboratory fourteen explored the use of data to determine mathematical models and to test whether flying disks and rings outperform the theoretic performance of a non-flying object.

Marlynn Fredrick, Natasha Edwin

The first question examined was the nature of the mathematical model - does a horizontally thrown disk or ring travel a horizontal distance d that is linearily related to the horizontal throw velocity v? The velocity will be the independent variable on the x-axis, the distance will be the dependent variable on the y-axis.

Isako Sohar, Vancy, Kepueli Kurabui,and Marlynn

The second question was whether a disk or ring can outperform a ball or rock. A ball or rock travels a distance d equal to the horizontal distance times the square root of two times the height divided by the acceleration of gravity.

horizontal distance = sqrt(2h/g)*horizontal velocity

My directions were to throw the disks at my head

One should not get confused by the square root sign, the quantity sqrt(2h/g) is a constant that is roughly 0.45 seconds if h is one meter. That suggests a linear relationship.

If the disk or ring actually generates lift, then the distance should be greater than predicted by sqrt(2h/g)*horizontal velocity and the resulting slope should be greater than sqrt(2h/g).

Isako throws

Note that a throw velocity of zero meters per second generates a zero distance, thus (0 m/s, 0 m) is also a data point.

Marlynn, Isako, Jerisse

Along the way I discovered that some students had either never thrown a flying disk or had only thrown a flying disk once or twice. In hindsight I should have given instructions on how to throw a flying disk and flying ring. Aim was also an issue, very few students - even when they tried - could put the flying disk or ring dead onto the radar gun.

Williamson captured this photo of a lawn visitor who some of the female students find frightful. If some of the male students frightful of toads, they did not let on.

I have a calculator in my right hand, I forgot to print out the kph to m/s conversion table for the 8:00 class

The morning 8:00 data was surprisingly linear and exceeded the 0.45 to 0.55 estimated slope for a thrown ball or rock. I suppose to really complete this laboratory tennis balls ought to be thrown, but how to get them thrown arc free? With zero launch angle? Ideally a discus would be used, being double curved the lift cancels out. No discus. Maybe I can find a round barbell free weight to be flung. That would bring a new urgency to getting out of the way of the throw.

Bilrose Optaia records data

Lesleena ready to throw a flying ring