I haven't posted here in a while because it seems like nobody is paying attention. I checked the counter today and noticed this blog is starting to show up on Google search in the top 10 of 37,000 for several searches and it is starting to get some good web traffic. Not bad!
I always chart my fuel economy in my car. For every tank of gas I record the amount of fuel used, cost of the fuel, approximate outdoor temperature, the miles driven, miles with the air conditioner on, highway miles, interstate miles, city miles, the weight I am carrying, and any other significant notes. I have a big Excel sheet with all of this information and I do many calculations with the data.
Last weekend I drove about 420 miles round trip to visit family and achieved my highest fuel economy ever: 46 mpg! The car is a Toyota Corolla S with manual transmission. It is rated with the old mpg rating system to have 32 city/41 highway mpg. The awesome thing about the high fuel economy is about 40% of the miles were on the interstate at higher speeds, and 70% of the miles required the air conditioner.
My lifetime average fuel economy with the car is about 36 mpg. Most of the miles I have driven between 3 and 5 mph over the speed limit. This past weekend was different, I never exceeded the speed limit on highways or the interstate.
The benefits of going slow was high fuel economy. The downside was mostly psychological. Driving 55 seemed like I was going very slow and I could be going faster. In reality, the difference was minimal. Driving just a few mph faster does very little for short trips, but for long trips a few mph can easily add up. I actually found the extra time required was negligible. It took me 3h 45min to make the drive one way at the posted speed. My previous trip was 5 mph over the speed limit for most of the time and it took me 3h 35min. I saved 10 minutes, but my fuel economy was about 8 mpg less.
In addition to driving slow, I do use mild hypermiling techniques that I have used regularly over the past several years. The main thing to do is just pay attention to driving, which you should be doing anyway. If you see a stop sign ahead, don't hold the gas pedal down until the last moment and then brake hard. You would be surprised how far your car can coast. For one highway stop sign on the route, I put my car in neutral 0.6 miles away from the sign and coasted in. When I hit my brakes as I neared the stop sign, my car was still doing 45 mph and had only dropped 10 mph from my previous speed. If there is a slight downhill grade, I can put the car in neutral even sooner. The extra time this added to my trip was very small, probably less than 5 seconds, but I was able to coast for 0.6 miles at probably 200 mpg or higher.
A similar technique can be used for stoplights. If one turns red, brake early to slow down, and then coast in. If you time it right, you will still be rolling and nearing the car in front of you as the light turns green. Slowing early will actually help you maintain a higher speed when the light turns green.
Two other things I do are slow acceleration and using my cruise control. These are simple things that will save you several mpg. I would not recommend drafting other vehicles as some others suggest. Drafting is unsafe and illegal.
The biggest time lost in the trip is not from the highway driving speed; city driving is the worst. As I travel through small towns, it is only 4% of the total trip miles but it takes 10% of the trip time. Doing the math, it only saves 12 minutes over the whole trip to drive 4 mph over the speed limit, which agrees with my observed results.
Changing interstate speeds back to 55 mph might not be such a bad idea. Even if people still go over the speed limit, the net effect will be lower overall speed and people using less fuel. For my 210 mile trip, the difference in time between current speed limits and if all roads were 55 mph is about 25 minutes. The benefits of increased safety and reduced foreign dependence on fuel are probably worth the extra time.
Wednesday, July 2, 2008
Sunday, March 16, 2008
26 vs 29er Mountain Bikes - an Engineering Analysis
When I was researching bikes last fall I ultimately settled on a 29er, which refers to the tire size. Instead of a traditional 26 inch wheel, a 29er has a 29 inch wheel. The idea is lower rolling resistance, better traction, and a ton of other benefits. The bigger wheels seem to be the trend of the future with mountain bikes.
There is a lot of differing opinions on the internet about the tire size, ranging from people hating 29ers to people who never ride a 26 inch wheel bike after changing. The one big argument against larger wheels is slower acceleration and heavier weight. The wheels weigh more due to the bigger size and more material, and with the larger diameter and resulting higher moment of inertia, it will take more energy to spin a 29er wheel up to speed. My initial reaction was the effect is probably minimal, but I never got around to calculating the difference until today.
The following is a comparison of energy required for acceleration of a 26 vs 29er bike based on calculations only. For the analysis, specifications from manufacturers are used. Both bikes will use Bontrager Rythm Elite Tubeless Disc wheels at 1,835g and 1,955g for the smaller and larger size respectively. Bontrager Jones ACX Aramid Clincher 2.2 width tires are used, with a weight of 520g and 650g respectively. Tubes are assumed to weigh 200g for each size tire. I am assuming the wheel has of its weight at the ISO bead seat diameter of 559 and 622 mm for the two different wheel sizes. This is not completely accurate, but I am not going to mathematically integrate the individual wheel parts to account for density gradients and variable geometry. The moment of inertia calculation should be within 10% using my approximation, and the comparison between the two bikes should be nearly identical with less than one percent error based on using the same assumption for both.
The wheels are on a bike frame that weighs 8,000g for both tire sizes. The total weight of the wheels with tubes and tires is 3,275 and 3,655 for the 26 inch and 29 inch wheels respectively. The total bike weight is therefore 11,275g (24.8 lbs) and 11,655g (25.6 lbs) with the bigger wheel bike being heavier. The moment of inertia of the wheels is 0.256 and 0.354 kg-meters squared. The small change in diameter is squared, which makes the seemingly small change in diameter have a large affect on the moment of inertia.
Now for the results. Lets assume both bikes start from a stop and accelerate to 8 meters per second (17.9 mph) on flat ground. The calculation is only for energy to bring the bike up to speed, and does not consider rolling resistance or other losses. It will take 436 Joules to bring the bike up to speed for the 26" wheels versus 457 Joules for the 29" wheels for an increase of about 4.9%. 29ers are claimed to have decreased rolling resistance. Assuming both tires have the same coefficient of rolling friction since they are using the same tire, the 29er should have a 10% lower rolling resistance due to the larger wheel diameter, which more than makes up for the losses due to weight and tire diameter.
This analysis isn't quite complete. In the calculation, a common error was made as I ignored the weight of the rider. Bicyclists, bicycle magazines, and other sources always talk about bike weight without including the rider effect on the performance. If one bike weighs 24 lbs and another weighs 25 lbs, the simple calculation would be one bike is 4% lighter than the other. If you include a 175 lb rider, the difference in weight of the complete bike and rider together is only 0.5%. Only considering bicycle weight exaggerates the performance enhancement.
If I recalculate the results again assuming a 155 lb rider (me) the difference is even smaller than before. The total energy required to bring the bike and rider to 8 meters per second velocity is 2,690 Joules for the 26" bike versus 2,711 Joules for a 29er bike, or about 0.8%. The rolling friction difference is for the most part not affected by rider weight. There will still be a 10% benefit of lower rolling resistance with the bigger wheels, therefore the losses from a heavier and larger diameter wheeled bike should be completely outweighed by lower rolling resistance.
If you are going to drag race the two bikes in real life, the 29er should win if both riders weigh the same, have the same energy output, and both bikes are built from similar quality components. The difference between the two is very small. The weight argument is certainly not valid.
NOTE: The calculations above do include the effect of rotating mass, which is the reason why I had to calculate the moment of inertia of the wheels. The larger diameter wheels spin slower, so the amount of energy required to spin the wheels only up to speed is only about 12% different. The amount of energy required to accelerate the wheels up to rotational speed is only about 17% of the total energy to accelerate the whole bike (ignoring rider). The majority of the energy to accelerate the bike is due to bike mass.
UPDATE 3/23/08: In response to a comment, I was asked to recalculate the numbers based on slightly heavier tubes for the 29er. A 29er wheel is about 11% bigger in circumference, so I am going to calculate the tube to have an 11% higher mass, or 222g versus 200g for the 26er. The results change by 2 Joules, or 459 Joules to accelerate the bike and wheels up to speed, or about 5.4% more than a 26er (versus 4.9% with the same mass tubes analysis). The rider and bike combined will require 0.87% more energy to accelerate than a 26er with the heavier tubes, with a roughly 10% lower rolling resistance.
There is a lot of differing opinions on the internet about the tire size, ranging from people hating 29ers to people who never ride a 26 inch wheel bike after changing. The one big argument against larger wheels is slower acceleration and heavier weight. The wheels weigh more due to the bigger size and more material, and with the larger diameter and resulting higher moment of inertia, it will take more energy to spin a 29er wheel up to speed. My initial reaction was the effect is probably minimal, but I never got around to calculating the difference until today.
The following is a comparison of energy required for acceleration of a 26 vs 29er bike based on calculations only. For the analysis, specifications from manufacturers are used. Both bikes will use Bontrager Rythm Elite Tubeless Disc wheels at 1,835g and 1,955g for the smaller and larger size respectively. Bontrager Jones ACX Aramid Clincher 2.2 width tires are used, with a weight of 520g and 650g respectively. Tubes are assumed to weigh 200g for each size tire. I am assuming the wheel has of its weight at the ISO bead seat diameter of 559 and 622 mm for the two different wheel sizes. This is not completely accurate, but I am not going to mathematically integrate the individual wheel parts to account for density gradients and variable geometry. The moment of inertia calculation should be within 10% using my approximation, and the comparison between the two bikes should be nearly identical with less than one percent error based on using the same assumption for both.
The wheels are on a bike frame that weighs 8,000g for both tire sizes. The total weight of the wheels with tubes and tires is 3,275 and 3,655 for the 26 inch and 29 inch wheels respectively. The total bike weight is therefore 11,275g (24.8 lbs) and 11,655g (25.6 lbs) with the bigger wheel bike being heavier. The moment of inertia of the wheels is 0.256 and 0.354 kg-meters squared. The small change in diameter is squared, which makes the seemingly small change in diameter have a large affect on the moment of inertia.
Now for the results. Lets assume both bikes start from a stop and accelerate to 8 meters per second (17.9 mph) on flat ground. The calculation is only for energy to bring the bike up to speed, and does not consider rolling resistance or other losses. It will take 436 Joules to bring the bike up to speed for the 26" wheels versus 457 Joules for the 29" wheels for an increase of about 4.9%. 29ers are claimed to have decreased rolling resistance. Assuming both tires have the same coefficient of rolling friction since they are using the same tire, the 29er should have a 10% lower rolling resistance due to the larger wheel diameter, which more than makes up for the losses due to weight and tire diameter.
This analysis isn't quite complete. In the calculation, a common error was made as I ignored the weight of the rider. Bicyclists, bicycle magazines, and other sources always talk about bike weight without including the rider effect on the performance. If one bike weighs 24 lbs and another weighs 25 lbs, the simple calculation would be one bike is 4% lighter than the other. If you include a 175 lb rider, the difference in weight of the complete bike and rider together is only 0.5%. Only considering bicycle weight exaggerates the performance enhancement.
If I recalculate the results again assuming a 155 lb rider (me) the difference is even smaller than before. The total energy required to bring the bike and rider to 8 meters per second velocity is 2,690 Joules for the 26" bike versus 2,711 Joules for a 29er bike, or about 0.8%. The rolling friction difference is for the most part not affected by rider weight. There will still be a 10% benefit of lower rolling resistance with the bigger wheels, therefore the losses from a heavier and larger diameter wheeled bike should be completely outweighed by lower rolling resistance.
If you are going to drag race the two bikes in real life, the 29er should win if both riders weigh the same, have the same energy output, and both bikes are built from similar quality components. The difference between the two is very small. The weight argument is certainly not valid.
NOTE: The calculations above do include the effect of rotating mass, which is the reason why I had to calculate the moment of inertia of the wheels. The larger diameter wheels spin slower, so the amount of energy required to spin the wheels only up to speed is only about 12% different. The amount of energy required to accelerate the wheels up to rotational speed is only about 17% of the total energy to accelerate the whole bike (ignoring rider). The majority of the energy to accelerate the bike is due to bike mass.
UPDATE 3/23/08: In response to a comment, I was asked to recalculate the numbers based on slightly heavier tubes for the 29er. A 29er wheel is about 11% bigger in circumference, so I am going to calculate the tube to have an 11% higher mass, or 222g versus 200g for the 26er. The results change by 2 Joules, or 459 Joules to accelerate the bike and wheels up to speed, or about 5.4% more than a 26er (versus 4.9% with the same mass tubes analysis). The rider and bike combined will require 0.87% more energy to accelerate than a 26er with the heavier tubes, with a roughly 10% lower rolling resistance.
Wednesday, March 5, 2008
The GT Lives!
Tonight I attended a bicycle maintenance class put on by the outdoor recreation program at Iowa State. The class was definitely worth it. For two hours, we talked about bikes and worked on our own. I already knew most of the topics we covered, and every adjustment talked about in the class I had already done to one of my bikes at some point, but it was good to learn a few new techniques.
We were told to bring our bikes to work on in the class. I brought the old mountain bike, a GT hardtail. My GT now works better than ever. I adjusted the derailleur so it shifts perfectly. I even did a little bit of truing of the rear wheel and some general cleaning.
I can now adjust a rear derailleur in about 1/3 the time it took me before, and with better results. Not bad, considering the class only cost $3.00!
We were told to bring our bikes to work on in the class. I brought the old mountain bike, a GT hardtail. My GT now works better than ever. I adjusted the derailleur so it shifts perfectly. I even did a little bit of truing of the rear wheel and some general cleaning.
I can now adjust a rear derailleur in about 1/3 the time it took me before, and with better results. Not bad, considering the class only cost $3.00!
Tuesday, February 26, 2008
First Ride
Snow has been on the ground here in Ames since the end of November, which is now about three months ago. We repeatedly get snowstorms and sub zero Fahrenheit weather resulting in very little snow melting. The roads have been a mess; they will still have a layer of ice and snow several days after the most recent snowstorm.
Finally, last weekend, we had a period of about a day where the sun cleared the roads and the ice and snow was gone. Of course, this didn't last long as another snowstorm arrived Monday with a slushy mix of three inches of snow. The latest snow left another layer of ice covering sidewalks, bike trails, and streets.
During the brief moment without ice on the roads, I took the new road bike out on the road. The bike is a Trek 1600 SLR. It has an aluminum frame, carbon fiber fork and seatpost, and Shimano 105 and Ultegra components with a 30 speed setup. I'm very impressed with its performance and ride. Power is transfered to the ground very efficiently. I was cruising between 22 and 27 mph while on flat or slightly uphill road. I'm excited to see the performance when I'm not sick and we have good weather (it was 15 degrees when I was riding).
The controls are awesome. New road bikes have shifters built into the brake levers requiring a simple sideways movement of one or two fingers for an indexed shift. Shifting is instant and precise. I added a Cateye Cadence cycle computer, which provides basic speedometer, odometer, and timing functions, and it also displays my cadence (pedaling rpm).
The bike weighs around 20 lbs, which is not super light for a race bike but within a few pounds of the lowest weight bikes available. The cost of removing a few more pounds of weight is spending about four times as much on a carbon fiber frame and other lighter components. Aluminum is fine with me. I'm not ready for carbon fiber due to cost and durability issues.
I will add more details once I get more miles on the bike.
Finally, last weekend, we had a period of about a day where the sun cleared the roads and the ice and snow was gone. Of course, this didn't last long as another snowstorm arrived Monday with a slushy mix of three inches of snow. The latest snow left another layer of ice covering sidewalks, bike trails, and streets.
During the brief moment without ice on the roads, I took the new road bike out on the road. The bike is a Trek 1600 SLR. It has an aluminum frame, carbon fiber fork and seatpost, and Shimano 105 and Ultegra components with a 30 speed setup. I'm very impressed with its performance and ride. Power is transfered to the ground very efficiently. I was cruising between 22 and 27 mph while on flat or slightly uphill road. I'm excited to see the performance when I'm not sick and we have good weather (it was 15 degrees when I was riding).
The controls are awesome. New road bikes have shifters built into the brake levers requiring a simple sideways movement of one or two fingers for an indexed shift. Shifting is instant and precise. I added a Cateye Cadence cycle computer, which provides basic speedometer, odometer, and timing functions, and it also displays my cadence (pedaling rpm).
The bike weighs around 20 lbs, which is not super light for a race bike but within a few pounds of the lowest weight bikes available. The cost of removing a few more pounds of weight is spending about four times as much on a carbon fiber frame and other lighter components. Aluminum is fine with me. I'm not ready for carbon fiber due to cost and durability issues.
I will add more details once I get more miles on the bike.
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