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Mathline

Tim Gobber, Mountain Biker, BMX Track Designer, and Owner of Ozark Bicycles

More Career Connections

Tim Gobber Bicycles are generally described in terms of metric units. However, Americans generally think in terms of pounds, ounces, and inches. So I always do a lot of rough conversions in my head. A pound is about 450 grams. I generally use 100 grams for a quarter of a pound, even though it's a little more. One of the most common ways I use math is when I am working with someone to lighten their bike. People want to make their bikes faster. According to physics, you want to lighten the rolling mass. That means you need to lighten the tires or wheels. That could mean going with a lighter hub, rim, tube, or even a lighter tire. A full steel bead tire, full knob, weighs about 800 grams. A hi-tech kevlar bead, semi-slick tire, is about 520 grams. So that is almost a half-pound difference per tire. That only lightens the bike by a pound, but lightening the rolling mass by a pound makes you a lot faster. The wheels act sort of like fly wheels. The heavier they are, the harder it is to get them spinning. There is an analogy with weight lifting. The lighter the weight, the more times you can lift it. Well the lighter the bike, the more reps your legs can do, and so you can ride farther, climb hills easier, and go down hills faster.

Gear ratios are something that 99% of all people don't consider. But there is a real difference. On a mountain bike, the rear gear is either a six, seven, or eight speed. Each of those gears has a number of teeth that ranges from eleven to thirty-four. With a thirty-four, you will be able to climb any hill. It's a very low gear, or "granny gear." The eleven-tooth is a faster gear. You go faster with a slower pedaling gear.

On a BMX bike, you have only one speed, and the rear gear always stays the same. However, you do have some choices for the pedal gear. You can set your bike up with a pedal gear with forty-two teeth or with thirty-eight teeth. Since these are the gears on the pedals, for the BMX bike, the lower the number the quicker it is off the start. The higher the number the slower starting it is, but you have a faster top speed. Our track uses gravity a lot, so you want the higher top speed. But if you were riding on a flat course where a quicker start is needed, you would want to use the lower gear. Also, shorter crank arms can allow you to pedal faster. The crank arms connect the pedals to the bike. The longer they are, the bigger the circle that your feet have to turn, and the longer it takes to make a full rotation. The trade off is the longer the crank arms, the easier it is to pedal.

Cadence is another important factor. Cadence is the revolutions per minute that you pedal. These generally range from 70, which is pretty low, to racers that have a cadence around 110. The important thing for a rider is to find the cadence with which they are comfortable and to then have the right set of gears that work for that cadence and the type of riding they are doing. The beauty of the gears is that you shift as you ride so that you can continually keep the same cadence.

Another thing you will notice about different types of bikes is the size of the wheels. Physics would say that the bigger the wheel, the faster the bike. Road bikes have about a 27-inch wheel, where mountain bikes have 26-inch wheels, and BMX bikes have a 20-inch wheel. It makes sense that one turn of a 27-inch wheel will move you a lot farther than one turn of a 20-inch wheel.

We're building a single-track mountain bike trail and have learned quite a bit about slopes through the process. I have a tool that allows me to measure the slope of a hill. From experience, I have found if you have a 20% slope, which is way too steep to ride across it, you are at such an angle with the hill that very little of your tire, just the side of the knobs, is actually in contact with the trail. The problem then becomes to find a path around this area, or to resort to digging out a small path so you're not sliding down the hill. In general, you are looking to give the rider a range of experiences and some challenging areas without making it is impossible to ride.

On the BMX trail, there is a lot of geometry in the dirt jumps. The way the jump curves determines whether it is a good jump or not. The jumps need to be shaped so they throw you up in the air. A straight slope or constant incline, like a ramp, won't do the trick. With a bulldozer, you can create a steady incline. Then you have to dig it out in the middle and place the dirt on the top so that the jump really comes when riders hit the top. The landing ramp needs to be more of a straight incline. The spacing between the jumps also needs to be just right and is related to the riders, speed. Riders can miss jumps that are too close together. On the other hand, if the jumps are too far apart, riders can't carry their speed from one jump to the next.

As a kid, I was always on a bike. I had a Stingray. As I got a little older, it was just the easiest, cheapest, and most convenient way to travel. Today, a lot of people young and old are getting back into different types of riding. There is really quite a bit of mathematics and science involved in bikes. A lot of people don't understand the gears and the ratios, but if you work at it, think about, and watch how the bike works, it really does make sense.