In this design, there is a relationship between the length of the rubberband, the diameter of the axels and the diameter of the wheels because all three act as a single component in this design.

The rubberbands provide both power and distance. However, the longer the rubberband, the longer the distance travelled but with less force. The axels are important because they are the component that transfers the energy from the rubberband to the wheels. The diameter of the axels determines the number of rotations of the rubberband around it which, in turn, determines the distance travelled by the wheels. The diameter of the wheels is important in the present design because the distance travelled is directly related to its size.

By way of example, in the two wheeled model (refer appendix 1), the rubberband was able to be twisted about 8 time around the skewer axel but the distance travelled was approximately 3 meters. This was due to the size of the wheels. In other words, each full turn of the skewer was also a full turn of the wheel. There is, therefore, a balancing act that must be performed having regard to the performance criteria for this project and the materials available.

# | # | F | d | F=kd | W=Fxd | W=0.5k(d^2) |
---|---|---|---|---|---|---|

Load(kg) | Extension(mm) | Load(N) | Extension(m) | k | Joules | x2Joules |

0 | 210 | 0 | 0.21 | 0 | 0 | 0 |

0.8 | 360 | 7.848 | 0.36 | 21.8 | 2.8253 | 2.8253 |

1.3 | 510 | 12.753 | 0.51 | 25.01 | 6.5040 | 6.5040 |

1.8 | 645 | 17.658 | 0.645 | 27.38 | 11.3894 | 11.3894 |

2.8 | 750 | 27.468 | 0.75 | 36.62 | 20.601 | 20.601 |

This table uses the rubberband test results (ie. load and extension) to determine the energy stored in the rubberband at various extensions.

Have a go yourself by entering a value for load and extension.

0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |

The next table provides details of the initial acceleration available for varying levels of rubberband extension and overall weight.The last column of the table indicates that if the rubberband is cut into two, both pieces acting in parallel will deliver the same amount of work as one whole rubberband. It also follows that if the rubberband is cut once to double its length, it will halve the force delivered. To compensate, more rubberbands will need to be added in parallel.

a=(kd)/m | k=21.8 | k=25.01 | k=27.38 | k=36.62 |
---|---|---|---|---|

mass(kg) | a1(m/s^2) | a2(m/s^2) | a3(m/s^2) | a4(m/s^2) |

0.80 | 9.81 | 15.94 | 22.07 | 34.34 |

0.85 | 9.23 | 15 | 20.77 | 32.32 |

0.90 | 8.72 | 14.17 | 19.62 | 30.52 |

0.95 | 8.26 | 13.42 | 18.59 | 28.91 |

1.00 | 7.85 | 12.75 | 17.66 | 27.47 |

Acceleration reduces as rubberband extension decreases (as expected). Initial acceleration reduces as mass increases (as expected).

I expected the overall weight of the model and the load to be approximately 1kg. The highlighted portion of the table sets out the likely acceleration that may be available at various points as the rubberband unwinds. This also provides an indication as to the force available at various points of the travel.

Based on the table, it seems to me that a rubberband with a single cut that doubles its length should be the maximum length. This size rubberband will need to be looped around a central dowel in order to be effective. If it were longer, a lot more loops would be required and the risk of entanglement increases and there is also the possibility that full extension may not be achieved. This problem would be compounded by the fact that several such rubberbands would be required in parallel to achieve the force needed to complete the track.

So, to answer the first question about the length of the rubberband for our model, a single rubberband cut once to double its length should suffice. I will deal with force requirements separately later.

This now leads me to deal with the diameter of the axels. I propose to use off the shelf dowel cut to appropriate lengths for the axels. There are two sizes available for our purposes; 6mm and 12mm. The 6mm will enable more turns upon winding up than the 12mm. However, I also propose to drill holes through the dowel in order to secure the rubberbands to them. This will invariable weaken the dowel. In addition, the width of the rubberband is 4mm. These factors make it impractical to use 6mm dowels for the axels. As such, the axel diameter will be 12mm in our design.

Finally, we need to determine the size of the wheels. To do this I have used the following equation:

Number of turns about axel x wheel circumference = distance travelled.

By experimentation, I have determined that it is possible to achieve 15 to 16 rotations of the rubberband about the 12mm axel. The distance required to be travelled is 6000mm.

This means that the size of the circumference is: 6000mm / 15 turns = 400mm.

The diameter of the wheel is therefore: 400mm / π = 127mm.

The calculation gives a minimum wheel diameter of 127mm.

The final detail to be ascertained is the number of rubberbands required to propel the model car. This requires calculations to determine forces and work done.

I have estimated the weight of the vehicle will be approximately 1 kg. The model will also have to carry a load of approximately 150g giving a total weight of 1.15kg. The rubberbands will release their energy over 6 meters (refer distance calculations above).

Weight(N) | P1=P3 | P2 | Work done on incline | Work done on lead up | Work done on follow on | Total work done |
---|---|---|---|---|---|---|

8.829 | 7.408 | 9.981 | 9.981 | 7.408 | 29.634 | 47.023 |

9.320 | 7.820 | 10.536 | 10.536 | 7.820 | 31.280 | 49.636 |

9.810 | 8.232 | 11.090 | 11.090 | 8.232 | 32.926 | 52.548 |

10.301 | 8.643 | 11.645 | 11.645 | 8.643 | 34.573 | 54.861 |

10.791 | 9.055 | 12.199 | 12.199 | 9.055 | 36.219 | 57.473 |

11.282 | 9.466 | 12.754 | 12.754 | 9.466 | 37.865 | 60.085 |

11.772 | 9.878 | 13.308 | 13.308 | 9.878 | 39.512 | 62.698 |

12.263 | 10.289 | 13.863 | 13.863 | 10.289 | 41.158 | 65.310 |

The above table sets out the force required to move an object along the planes and incline and the work done along each plane. I have assumed an angle of friction of 10 degrees for the purposes of this design (which subsequent testing confirmed). Further, given that I was keeping the design relatively simple and not using spacers or bearings around wheels, there would inevitably be some rubbing. As such, I added a further 30 degrees to compensate for tractive resistance. Using a spreadsheet to do these calculations is a quick and efficient way to generate a range of options.

The following table expands on the last row of data relating to work done by identifying how much work is required to be done per meter of distance travelled. It also identifies the work done by up to 4 rubberbands (of the size determined earlier) in parallel and equates that work done to meters covered given that our ultimate distance is fixed at 6 meters.

1 rubber | meters | 2 rubbers | 3 rubbers | 4 rubbers | Work required per meter |
---|---|---|---|---|---|

0 | 0 | 0 | 0 | 0 | 0 |

20.601 | 2.99145 | 41.202 | 61.803 | 82.404 | 9.055 |

11.389 | 1.65385 | 22.778 | 34.168 | 45.558 | 12.199 |

6.504 | 0.94444 | 13.008 | 19.512 | 26.016 | 9.055 |

2.825 | 0.41026 | 5.651 | 8.476 | 11.301 | 9.055 |

9.055 | |||||

9.055 | |||||

41.320 | 6.000 | 82.639 | 123.959 | 165.279 | 57.473 |

By equating work done by the rubberbands with work required to be done, we can see that a single rubberband will not be enough to do the work required. A minimum of two rubberbands will be necessary.

Continue to Construction, Finishing and Testing

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