Frame Geometry Primer
The dimensions and design of a bicycle's frame fundamentally determine how it will ride. Understanding which features of the frame affect corresponding aspects of its behaviour can be very helpful in determining what kind of bike is right for you. Herein, a primer on bicycle frame geometry - a look at how certain aspects of a frame's design determine how it will "handle" or ride as a bike. I'm going to examine bottom bracket drop, seat tube angle, and chain stay length.
Bottom Bracket Drop
Draw a horizontal line between the front and rear drop outs (where the wheels attach) of the frame and fork. Now, draw a perpendicular line that passes through the center of the frame's bottom bracket. The distance between the centre of the frame's bottom bracket and the first line, measured along the second, is the frame's bottom bracket drop: how far below the wheels' axles the bottom bracket sits.
Mountain, cyclocross, and track frames have little bottom bracket drop - their bottom brackets tend to sit quite high. The primary reason for this is clearance: to keep roots, rocks, or a severely sloping track from hitting the pedals, chain rings or frame, the bottom bracket is kept high and out of the way. A higher bottom bracket also shortens the chain stays and downtube of a frame - the tubes of a bicycle put under the greatest stress during riding - thereby giving a stiffer, more responsive feel.
But stiffness and clearance come at the expense of stability; the lower the bottom bracket, the lower the bike's centre of gravity, and the more stable it will ride. Touring and commuter frames should have a lot of bottom bracket drop, as their function is more practical than performance. Road bikes tend to fall somewhere between the two extremes.
Note: bottom bracket drop, rather than height, is used when talking about a frame because the height of a bike's bottom bracket depends both on the frame design and the size of its wheels and tires, while a frame's bottom bracket drop remains constant.
Seat Tube Angle
The angle of the seat tube is measured in relation to the ground, and tends to fall somewhere between 68 and 75 degrees.
A frame's seat tube angle determines the position of a bike's saddle in relation to its bottom bracket. Since the bottom bracket is the axis around which the bike's cranks and pedal rotate, this in turn affects the orientation of the rider's legs and body in relation to the bike. Seat tube angle also influences the distribution of the rider's weight between saddle and handlebar.
A steeper seat tube brings the bike's saddle more into a vertical line with the bottom bracket, thrusts the rider forward into a more aerodynamic riding position, places more of the rider's weight on the handlebars, and puts more demand on the rider's hamstring muscles. Triathlon bikes tend to have steep seat tubes, because they're built almost exclusively for speed and tend to be ridden by people who are strong runners (and therefore have well-developed hamstring muscles).
The shallower the seat tube, the further the bike's seat is pushed behind its bottom bracket. This puts the rider in a less aerodynamic position, but it also puts more demand on the thighs and glutes (which tend to be well developed in cyclists), and places more of the rider's weight on the saddle, thereby increasing rider comfort.
A steeper seat tube means a shorter seat tube for a frame of a given size, again making for a stiffer, more responsive feel, while a shallower seat tube requires longer chain stays, the effect of which I'll address later.
A steeper seat tube also allows for a more direct transfer of power through the rider's legs, although a shallow seat tube angle puts the rider in a better position to exert power at low cadence, therefore assisting with seated climbing.
Finally, seat tube angle plays a large role in bicycle frame design for women. Most production bike frames tend to be built for men of "normal" proportions. On average, women tend to be shorter than men and proportionally have longer legs and shorter torsos. The smaller the frame, the steeper the seat tube, because (all else being equal) more room is needed for the rear tire to clear the frame. Since women generally ride smaller frames, this works against their physiology - a steeper seat tube is a shorter seat tube, allowing less room for full leg extension. This conundrum is sometimes remedied by using longer chain stays or smaller wheels - both of which allow for shallower seat tubes - on frames designed specifically for women. But since this increases the cost and time of production, many companies don't bother taking it into account.
Chain Stay Length
A frame's chain stays are the tubes that run from the bottom bracket to the rear drop outs (where the rear wheel's axle attaches). One can measure either the actual length of the chain stay or the "effective" chain stay length because, all else being equal, bottom bracket drop will increase or decrease the length of a frame's chain stays without pushing the rear wheel any further back.
The modern trend, among virtually all bikes, is towards shorter chain stays. Shortening chain stays makes them stiffer and less likely to flex, enhancing power transfer from pedalling. This reduces the wheelbase of the bike, making it feel snappier and better able to handle low speed turns. It also puts more of the rider's weight over the rear wheel, thereby improving traction. Mountain bikes in particular benefit from short chain stays.
On the other hand, the longer wheelbase afforded by longer chain stays makes a bike more stable, especially at higher speed. Longer chain stays will flex more and ensure that the rider is not sitting directly over the rear wheel, thereby providing a more comfortable ride; they allow for both a shallower seat tube angle, which as previously noted, is better for seated climbing and for women's physiology. They also provide more tire clearance, allowing larger tires to be employed and making it easier to remove the rear wheel from the frame. Finally longer chain stays will keep the rider's heel away from a rear-mounted pannier. For all of these reasons, commuter and touring bikes benefit from longer chain stays.
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