Extreme Efficiency: Secrets Behind Miserly Solar Cars Part III (Tires)

Solar cars designed specifically to race in competitions such as the North American Solar Challenge or the Green Global Challenge (previously the World Solar Challenge) must somehow move at freeway speeds with less power than a typical hairdryer. Building these vehicles is a grand exercise in energy efficient design, and demonstrates what’s possible when engineers focus on producing maximum results with very limited power consumption. This is the third installment in a series that discusses several strategies solar car designers use to squeeze the most performance out of a vehicle-sized solar array. As with the larger energy system that powers our homes, vehicles, and factories, the best solution is not necessarily to focus only on producing more (ideally renewable) power, but also to identify and eliminate waste in systems that use energy. Designing for energy efficiency is a very cost-effective strategy to addressing energy problems.

One significant source of energy consumption in cars is tire rolling resistance. Basically, it takes some amount of force to roll a tire forward, even if you are not accelerating or going uphill. A simplified model of rolling resistance is:

This equation describes how much force is required to roll a tire forward at a constant speed on a flat road; this force is called rolling resistance . It depends on two things: the vertical load supported by the tire (i.e., the normal force ), and the coefficient of rolling resistance . The normal force depends on how weight is distributed in your car, and the rolling resistance is a function of tire design (and is also influenced by things like temperature, speed, and tire slip). Rolling resistance goes up proportionately with both normal force and with . We would like to reduce rolling resistance in order to reduce the energy consumed while driving. It’s easy to see that one way to do this is to reduce how much a car weighs, which reduces . Suppose we’ve eliminated as much vehicle mass as possible, and still want to reduce rolling resistance further. How do we reduce ? To understand this, let’s have a look at where rolling resistance comes from.

When rubber tires roll over the road they deform. The spot that touches the road (the contact patch) is flattened just a little due to the force of the car pushing down. Imagine what happens to one piece of rubber in your tire as the tire rolls on the ground. Looking at the drawing below, at position 1, the piece of rubber is slightly curved. As the tire rolls, the piece of rubber moves into position 2, and it starts to deform. By the time it gets to position 3, it’s pretty much flat, and then as it moves through position 4 to position 5, it returns to its original shape.

All the rubber in the tire tread and sidewalls goes through some type of deformation with each revolution of the tire. It takes energy to deform rubber. We get most of that energy back when the rubber ’springs’ back into shape. But rubber is not exactly like a spring; you don’t get back all the energy you put into it. Rubber is what we call viscoelastic. The elastic part of viscoelastic is the springy part. Something has elastic behavior if it springs back into shape after being deformed. The viscous part means that when something is deformed, energy is lost, and resistance to deformation increases with how fast you try to deform it. Think of stirring a pot of honey; if you stir it slowly it doesn’t take much effort, but if you try to stir it fast the viscosity of the honey makes it harder to stir. Where does all the energy go from stirring? The honey doesn’t ’spring back’, so you can’t recover the energy like you can with a spring. The energy from stirring was converted to heat; the honey became a little bit warmer.

Tires exhibit both viscous and elastic behavior. Some of the energy is recovered when the rubber springs back into shape after rolling through the contact patch (point 3). Due to the viscous nature of rubber, there is extra resistance to deformation, as well as resistance to returning to its normal shape. The energy used to overcome this extra resistance is converted to heat; bending rubber back and forth makes it heat up (sort of like stirring the honey). Have you ever noticed how tires get warm after driving? The energy that warms your tires is energy lost. How can we minimize this lost energy (and reduce rolling resistance)? There are three main approaches:

• Reduce tire deformation: if tire rubber is deformed less, then less energy will be consumed. This can be accomplished by increasing tire pressure (one important reason to make sure your tires are inflated properly). It’s important not to over-inflate tires, however, as this could degrade handling and ride quality, compromise safety, and accelerate tire wear. Tire deformation can also be reduced by adjusting tire design, that is, changing its shape and what it’s made of.
• Reduce how much tire is deformed: narrower tires and tires with thinner tread have less rubber that moves in and out of the contact patch, reducing how much energy is lost from tire deformation. There are tradeoffs, however. Narrow tires may not handle as well, and thinner tread reduces durability.
• Reduce rubber ‘viscosity’: using a harder rubber compound can help shift tire behavior closer to purely elastic, meaning that a greater proportion of energy that goes into deforming rubber is elastically recovered. Again, there is a tradeoff. Harder rubber compounds may not grip the road as well as softer compounds.

Some tire manufactures have created tire specifically for solar cars, with emphasis on ultra-low rolling resistance. Solar car tires are thin, high-pressure tires with hard rubber compounds. They have rolling resistance coefficients as low as 0.0025, whereas high efficiency passenger car tires have coefficients near 0.006, and typical passenger car and light truck tires have coefficients much higher than that. To give you a sense of the legendary efficiency of solar car tires, I was contacted by engineers interested in using solar car tires on bicycles they were developing for breaking human-powered speed records. Solar car tires are more efficient than racing bicycle tires.

Below is a photo of a solar car tire along with a view of the suspension (this is a photo of the Stanford solar car from several years ago). Notice the electric hub motor just to the right of the wheel. There is a direct connection between electric motor and wheel; no drive shafts, gears, belts or chains to sap energy.

The next photo shows a pile of solar car tires. Since these tires are optimized for energy efficiency, they don’t last very long. They must be replaced frequently, and it takes a large pile of tires to make it through a long cross-country solar car race.

Solar car tires are intended for specialized racing vehicles, and are obviously impractical for passenger vehicle applications. Nevertheless, we can take lessons from their design to help improve efficiency of production vehicles. Maybe we could move toward higher pressure tires, and use more advanced suspension design to help counteract the harsher ride from stiffer, high pressure tires. As we make other vehicle aspects more efficient (such as aerodynamics or powertrain design), the energy lost through rolling resistance will become an increasingly important factor, and is an opportunity for improvement.

Posted: August 11th, 2009 | Filed under: Design, Energy, Sustainability, Transportation |

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