Ratio Math and Mechanical Advantage. It’s Pretty Helpful.

Ratio math may not sound like an exciting subject to discuss in a blog, but it is very important to recognize the relevance of ratios.  Much of the machinery we use everyday take advantage of ratios to offer us some benefit.

So what exactly is a ratio?  A ratio is a measurement of mechanical advantage in a drive system.  An easy example is to think about a bicycle.

The pedals on a bicycle are attached to a toothed disc called a sprocket.  Attached to this sprocket is a chain that drives a sprocket attached to the rear wheel.  If both sprockets are the same size, the rear wheel will turn 1 revolution for every 1 revolution you pedal.  However, if we make the sprocket twice as large on the rear wheel, you now have to make two revolutions on the pedal to turn the rear wheel once.  It’s easier on the person pedaling, but it moves the rear wheel slower.  Increasing the amount of force output at the sacrifice of speed.  This example is a 2:1 ratio.

If you think of a truck that is trying to tow a heavy load, you can imagine the mechanical advantage a ratio can offer.  Vehicles that haul heavy loads often times have a wide range of ratio options through a transmission.  To get the heavy load moving, they will put the transmission in low gear (numerically high).  It’s called low gear because it is the very first gear ratio in the transmission and will result in very slow movement of the truck.  By putting the transmission in low gear, the engine will make more revolutions for every single rotation on the output of the transmission.  This results in an output on the transmission that has more force than the engine output, but will move slower than the engine output.  This allows the truck to move a heavy load, at slower speeds.

Other places where ratios are used are in belt and pulley systems, chain and sprocket systems, hydraulic cylinders, transmissions, planetary gearboxes and other gear drive systems.

For more information on the math behind ratios, try some of the online calculators at CalcuNATION.com.

Machinery and Engineering Calculators

Hydraulic Cylinder Force Calculator

Belt and Pulley Drive Ratio Calculator

Chain and Sprocket Drive Ratio Calculator

Gear Reducer Calculator and Gear Increaser Calculator

CalcuNATION is a website featuring online calculators and educational resources for mathematics.  Other Mathematical Blogs ( CalcuNATION on EduBlogs and CalcuNATION on Blogger)

 

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