Bongle

04-16-2006, 10:12 PM

Hmmm... title should read "ATTEMPTS to work out the coefficient of drag"

Edit: And if this should be in a different forum, tell me. I couldn't figure it out.

A few people from 1281 were bored this afternoon, so we decided to go about and try to figure out the coefficient of drag of a poofball to potentially increase the accuracy of shooters or shooter software everywhere.

Guided by the experiment I had devised a few days ago and armed with a van, some string, a poofball, and a combination level/protractor, we terrorized the streets of richmond hill at 40km/h for an hour or so. And by streets I mean empty parking lots. But really, I mean the suspension and brakes of the poor van we used.

Materials:

1. Vehicle capable of 40km/h with a spedometer

2. Protractor/level tied to a poof ball

Procedure:

1. Accelerate van to 40km/h (~12m/s), have passenger lean out window

2. While driver attempts to maintain a constant velocity, try to measure the angle that the string makes with the protractor

3. Stop van, record angle, goto step 1. Try to go up and down in opposite directions so that any wind or hilly bits cancel out

All in all, it should look something like this.

http://www.student.cs.uwaterloo.ca/~ahare/robotics/PICT3482s.JPG (http://www.student.cs.uwaterloo.ca/~ahare/robotics/PICT3482.JPG)

Results:

With one member doing the measuring, we found deflection angles of 65, 65, 65, 69, 69, 69, and 68 degrees from horizontal. With another member (me), we had 59, 63, 66, 59, and 62 degrees from horizontal.

Calculations:

Mass of poof ball: 0.175kg

Surface area of poof ball: 0.0245m2

Density of air: 1.29kg/m3

Velocity: 11.1m/s (40km/h)

Free-body diagram and sum of forces (we assume that the ball was essentially in equilibrium since it was oscillating about a certain angle and we were trying to find that angle)

http://www.student.cs.uwaterloo.ca/~ahare/robotics/drag.PNG

So from that triangle we can determine Fdrag. Once we know Fdrag, we can do this:

Fdrag = tan(90-measured angle)*Fg <-- from triangle

Fdrag = 0.5*C*A*P*V2 <-- equation for aerodynamic drag from wikipedia

We know Fdrag, A (0.0245), P (1.29), and V (11.1m/s). Thus, we can solve for C, which is the coefficient of drag of a poofball

tan(90-measured angle)*1.715 / 1.95053576025 = C

tan(90-measured angle)*0.879 = C

So if we take the average of my measurements, we get 61.8 degrees from horizontal, which means that my result is 0.479 as an approximate upper bound on what C actually is. If we take the average of dave's measurements, we get 67.1 degrees and a result of 0.371 as an approximate lower bound. If we take the average of these two informed guesses, we get 0.423.

Verifying

In order to make sure that whatever we got for 40km/h wasn't totally wrong, we did two runs at 60km/h. If our result for 40km/h successfully predicted the deflection at 60km/h, then we would know that our result was somewhere in the ballpark of correct.

So at 60km/h, our results predict that we should get an Fdrag of 1.85N. Taking the triangle formed with Fg = 1.715, we can use arctan to find the angle of deflection. In the end, we predict we should get 42 degrees of deflection. Our actual results were wildly varying, at 38 and 49 degrees. However, since our 40km/h result predicted our 60km/h result, we feel that our 40km/h result is somewhat accurate.

Sources of Error

1. It's difficult to drive at exactly 40km/h

2. It's even more difficult when we know that spedometers are only mandated to only be accurate within 5%

3. Wind, hills, speedbumps

4. The front of the van probably disrupts air at the point that the poof ball goes through it

5. Eyeballing whether or not the protractor is correct is harder than it looks, especially for the 60km/h runs, which were kinda terrifying (and we drove through a swarm of bugs while I was holding the ball :mad: )

6. The mass of the string or drag on the string might be significant, though with so little string this is unlikely.

Edit: And if this should be in a different forum, tell me. I couldn't figure it out.

A few people from 1281 were bored this afternoon, so we decided to go about and try to figure out the coefficient of drag of a poofball to potentially increase the accuracy of shooters or shooter software everywhere.

Guided by the experiment I had devised a few days ago and armed with a van, some string, a poofball, and a combination level/protractor, we terrorized the streets of richmond hill at 40km/h for an hour or so. And by streets I mean empty parking lots. But really, I mean the suspension and brakes of the poor van we used.

Materials:

1. Vehicle capable of 40km/h with a spedometer

2. Protractor/level tied to a poof ball

Procedure:

1. Accelerate van to 40km/h (~12m/s), have passenger lean out window

2. While driver attempts to maintain a constant velocity, try to measure the angle that the string makes with the protractor

3. Stop van, record angle, goto step 1. Try to go up and down in opposite directions so that any wind or hilly bits cancel out

All in all, it should look something like this.

http://www.student.cs.uwaterloo.ca/~ahare/robotics/PICT3482s.JPG (http://www.student.cs.uwaterloo.ca/~ahare/robotics/PICT3482.JPG)

Results:

With one member doing the measuring, we found deflection angles of 65, 65, 65, 69, 69, 69, and 68 degrees from horizontal. With another member (me), we had 59, 63, 66, 59, and 62 degrees from horizontal.

Calculations:

Mass of poof ball: 0.175kg

Surface area of poof ball: 0.0245m2

Density of air: 1.29kg/m3

Velocity: 11.1m/s (40km/h)

Free-body diagram and sum of forces (we assume that the ball was essentially in equilibrium since it was oscillating about a certain angle and we were trying to find that angle)

http://www.student.cs.uwaterloo.ca/~ahare/robotics/drag.PNG

So from that triangle we can determine Fdrag. Once we know Fdrag, we can do this:

Fdrag = tan(90-measured angle)*Fg <-- from triangle

Fdrag = 0.5*C*A*P*V2 <-- equation for aerodynamic drag from wikipedia

We know Fdrag, A (0.0245), P (1.29), and V (11.1m/s). Thus, we can solve for C, which is the coefficient of drag of a poofball

tan(90-measured angle)*1.715 / 1.95053576025 = C

tan(90-measured angle)*0.879 = C

So if we take the average of my measurements, we get 61.8 degrees from horizontal, which means that my result is 0.479 as an approximate upper bound on what C actually is. If we take the average of dave's measurements, we get 67.1 degrees and a result of 0.371 as an approximate lower bound. If we take the average of these two informed guesses, we get 0.423.

Verifying

In order to make sure that whatever we got for 40km/h wasn't totally wrong, we did two runs at 60km/h. If our result for 40km/h successfully predicted the deflection at 60km/h, then we would know that our result was somewhere in the ballpark of correct.

So at 60km/h, our results predict that we should get an Fdrag of 1.85N. Taking the triangle formed with Fg = 1.715, we can use arctan to find the angle of deflection. In the end, we predict we should get 42 degrees of deflection. Our actual results were wildly varying, at 38 and 49 degrees. However, since our 40km/h result predicted our 60km/h result, we feel that our 40km/h result is somewhat accurate.

Sources of Error

1. It's difficult to drive at exactly 40km/h

2. It's even more difficult when we know that spedometers are only mandated to only be accurate within 5%

3. Wind, hills, speedbumps

4. The front of the van probably disrupts air at the point that the poof ball goes through it

5. Eyeballing whether or not the protractor is correct is harder than it looks, especially for the 60km/h runs, which were kinda terrifying (and we drove through a swarm of bugs while I was holding the ball :mad: )

6. The mass of the string or drag on the string might be significant, though with so little string this is unlikely.