Techies - Summer Biking

Now that spring is in full swing, I decided to break out my bicycle to start burning away some of that winter fat.  However, when I finally hit the trails, I saw that both my tires were visibly under pressured (I later found it to be at 20psi).  Remembering that only a month ago, I did a Tire Pressure Lab as part of my Mech 305 course at UBC, two thoughts came to mind.  For motor vehicles, the reduction in tire pressure causes the following two major concerns:

1. loss of stability;
2. reduction in fuel efficiency.

Shot of Vancouver from Canada Line Bridge

The US Department of Energy claims that for every 1psi drop below the recommended tire pressure rating, gas mileage can be reduced by 0.3%¹.  My focus today is on fuel efficiency and how the reduction of tire pressure reduces the efficiency of my bicycle. Of course, when we’re looking at efficiency, we’re looking at energy input vs energy output.  What better way to demonstrate the “feeling” of efficiency than physically being the energy input.  As I powered my bicycle, I realized that I reached fatigue much sooner than I used to.  At first I thought, “I must be so out of shape.”  However, once I made it to a gas station and pumped up my bicycle to the proper tire pressure (between 40-60psi) I soon felt a major difference.  Back on the road with optimal tire pressure and a brief break, I soon found powering my bicycle was a lot easier and that I made it home without reaching fatigue at all.

When I arrived home, as an engineering student, I eventually thought, “why does this even happen?”  So I set out to find some answers.  In an ideal case, we make several assumptions as the wheel rolls:

1. the wheel is perfectly circular;
2. there is a single point of contact;
3. the wheel is rolling without slipping.

However in real life, only rolling without slipping is true (unless you're trying to do a burnout).  In real life, the wheel actually deforms at the point of contact into a surface of contact.  Here I will offer two definitions:


Contact Patch:  Flat area of the tire that is in contact with the ground.²
Hysteresis:  During the deformation of a material, the energy of deformation is great than the energy recovered when the material returns to its original state.³
  
Because of losses to heat, sound and other forms of waste energy, hysteresis occurs.  Therefore, a loss of energy occurs.  Now you might ask, "why don't we pump the tire to it's maximum so that the deformation is minimum?"  There are two reasons for this⁴:a

1. Increased stress concentrations result in increase wear at the centerline of the tire;
2. high tire pressure stiffens the interface between road surface and car.

To explain the first reason, we see that if a tire is inflated to the point where it can almost be approximated by a circle, then the entire weight of the car is essentially sitting on zero contact patch.  The pressure in the tires approaches infinity (P = F/A where area is approaching a very small number)!  This high pressure results in high wear and the tires fail faster.


The second reason why we don't run tires at maximum pressure is more of a luxury.  Thinking back to Mech 364 - Mechanical Vibrations, the wheels of the car can be thought of as a bunch of springs: the higher the pressure, the stiffer the spring, the lower the pressure, the flimsier the spring.  At high stiffness, you can assume that there is no spring at all (a rigid connection).  As a result, you will feel every bump and pebble that your tires roll over, which serves as a very uncomfortable ride!



References:

1. US Department of Energy: http://www.fueleconomy.gov/feg/maintain.shtml - Retrieved April 27th, 2011.
2. How Stuff Works: http://auto.howstuffworks.com/tire4.htm - Retrieved April 27th, 2011
3. Wikipedia: http://en.wikipedia.org/wiki/Rolling_resistance - Retrieved April 27th, 2011
4. How Stuff Works: http://auto.howstuffworks.com/tire5.htm - Retrieved May 10th, 2011