Wheels+Distance

Worksheet: Wheels and Distance Be sure that you follow the steps in each project, and answer the questions at the appropriate times. (Immediately after you do the step.)Create a wiki page called "Wheels and Distance." Fill out all your answers on this page of your wiki.

Condition 1: Standard Wheels - Calculate Distances Record your measurements in the data table below. Diameter (cm) ||  || Wheel Circumference (cm) ||  || Number of wheel rotations in program ||  || Theoretical (predicted) Distance traveled in program (cm) ||  || Actual distance traveled (cm) in each trial ||  || Average actual distance traveled (cm) || 17.58 cm |||| 2 |||| 35.17cm || 1.37.5cm ||^  || 38.17cm || Wheel |||||| 3.0cm |||| 3.0x3.14+ 9.42cm |||| 2 |||| 18.84cm || 1. 21.3cm ||^  || 20.83cm ||
 * Condition ||  || Wheel
 * Standard Wheel |||||| 5.6cm |||| 5.6x3.14=
 * ^  ||||||^   ||||^   ||||^   ||||^   || 2.38.5cm ||^   ||^   ||
 * ^  ||||||^   ||||^   ||||^   ||||^   || 3. 38.5 ||^   ||^   ||
 * Small
 * ^  ||||||^   ||||^   ||||^   ||||^   || 2.20.7cm ||^   ||^   ||
 * ^  ||||||^   ||||^   ||||^   ||||^   || 3.20.5cm ||^   ||^   ||

6. Look at the data in your table. i. Did the robot go the exact same distance in all three trials? Why or why not?

ii. Calculate the average distance that the robot went with these wheels and this program.

iii. What is the purpose of averaging the three distances?

7. How far off was the experimentally measured average from the predicted value? Find the Percent Error (% error) of the measured value compared to the predicted value using the following formula:


 * __ 35.17 - 38.17 __ || = || -8.53 ||  ||
 * 35.17 ||  ||   ||   ||

8. Look back at your table.

i. Was the average of the distances you measured close to what Dr. Turner’s hypothesis predicted it would be?

ii. Does this support the hypothesis? Why or why not?

iii. Is this set of trials alone enough to prove or disprove how valid the hypothesis is, in general?

9. The instructions tell you to measure from the front of the robot to the back of the line. Why shouldn’t you measure the space “between” the robot and the line (from the back of the robot to the front of the line)?

1. Find the Percent Error (% error) of the measured average compared to the predicted value using the following formula




 * __18.84cm - 20.83cm__ || X ||  || 100 = ||   || -10.6 ||
 * 18.84 ||  ||   ||   ||   ||   ||

17. Look at the data in your table.

i. Were the average measured distances about what Dr. Turner’s hypothesis predicted they would be?

ii. Do you think you have enough evidence to reasonably accept or reject how valid the hypothesis is now?

iii. If so, do you accept or reject it? If you are not sure, what additional testing could you do to help you decide?

Analysis and Conclusions: Conclusion

18. In her fax, Dr. Turner proposes a relationship for calculating distances traveled by a robot, based on the robot’s wheel size. You have been testing this hypothesis to see how well it predicts the distance your robot travels.

iii. Summarize the steps you took and data you gathered to investigate, and explain how they led to your conclusion.

19. Configure your robot using what you feel are the best all-purpose wheels for your classroom. Measure the wheels on your robot.

i. How many cm does your wheel travel per 360 degree rotation?

ii. In order to travel 10 cm, how many degrees does the wheel need to turn? (Show your work.)

iii. In order to travel 20 cm, how many degrees does the wheel need to turn? Show your work.

iv. How many degrees to travel 30 cm?

20. What is the advantage of being able to control your robot’s movement distance in centimeters as opposed to rotations?

21. Technically, the Wait For block in your program waits for motor rotations, and not wheel rotations.In this Investigation, we have been considering them to be interchangeable. What physical characteristics of the robot allow us to make this simplification? Analysis and Conclusions: Exercises 22. Tracy measures the wheels on her robot and finds that they are 2.3 cm in diameter. Her program is shown in the picture below. i. How far should her robot go? 2.3cm * 3.14 = 7.22cm


 * 720d || = || X * ||  || __360d__ ||   ||
 * ||  ||   ||   || 1 ||   ||

2 = Rotations
 * __1__ || 720d || = || Rotation ||  || __360d__ || * __1__ ||
 * 360d ||  ||   ||   ||   || 1 || 360d ||

7.22cm * 2rots= 14.44cm

ii. Is her robot likely to go exactly that distance when she runs it? Why or why not?

23. Rodney likes monster trucks. He replaces the wheels on his robot with wheels that are four times as large (in diameter) as the wheels on his old one, but leaves the program the same. How many times farther (or shorter) will his robot run than the old one?

24. Many wheels are constructed from a tire (black) and a hub (grey). Mark’s robot runs 720 degrees using the assembled (hub+tire) wheel. However, he wants to run the robot using just the grey hub as a wheel, without the black tire. i. How many // degrees // must the new hub-only wheel turn in order to go the same distance?

ii. What other issues might he encounter in using the hub as a wheel by itself?

iii. How would these other issues affect the actual distance the robot travels?

25. New wheel on terrain. New diameter.

26. Diana’s robot travels 7.85 cm using the program shown below. Assume that the comment is correct.

i. What size are the wheels on her robot? diameter = 7.85cm
 * 7.85cm = Cir * 360d ||  || * || __1rot__ ||   ||   ||   ||   ||
 * ||  ||   || 360d ||   ||   ||   ||   ||

ii. How far will her robot go with the following program, assuming the comment is correct? Show your work.



27. Jeanne’s robot travels 65 cm using the program shown below. Assume that the comment is correct.

i. What size are the wheels on her robot?


 * || 65cm = ||  || __2040d__ ||   || X ||   || Cir ||   ||
 * ||  ||   || 360d ||   ||   ||   ||   ||   ||


 * __360d__ || X || 65cm = ||  || __2040d__ || X || __360d__ || X ||   || Cir ||   ||
 * 2040d ||  ||   ||   || 360d ||   || 2040d ||   ||   ||   ||   ||

11.47cm = Circumference

diameter x 3.14/3.14 = 11.47/3.14 Diameter = 3.65cm

ii. Jack’s robot goes the same distance with the program below. Assume that the comment is correct. What size are his wheels?


 * || 65cm = ||  || __1020d__ ||   || X ||   || Cir ||   ||
 * ||  ||   || 360d ||   ||   ||   ||   ||   ||

22.94cm = Circumference
 * __ 360d __ || X || 65cm = ||  || __1020d__ || X || __360d__ || X ||   || Cir ||   ||
 * 1020d ||  ||   ||   || 360d ||   || 2040d ||   ||   ||   ||   ||

diameter x 3.14 = 22.94

diameter x 3.14/3.14 = 22.94/3.14

Diameter = 7.3 cm

28. You are your team’s lead programmer hard at work refining your robot’s movement code the day before it needs to compete in a hallway navigation challenge. Your friend, the team’s mechanic, stops by and informs you that he seems to have misplaced the wheels for your robot during cleanup last night. He also says the local Wheels R Us will not have any replacements in stock for at least two weeks. There are several sets of 3-inch diameter wheels lying around the workshop, but they are not the same as the 2.7cm diameter ones that you had been planning to use. Your old code is shown below. What must you do in order to get your robot in working order to perform the challenge tomorrow?

2.54cm/1 inch x 3.0 inch = 7.62cm

The code must be changed by setting the rotations of the wait block to 3401 degrees.
 * || __2.7cm__ ||  || x ||   || 9600d = 3401d ||   ||   ||   ||
 * || 7.62cm ||  ||   ||   ||   ||   ||   ||   ||