Geometry: A lot of people make a big deal about a frame's geometry and for good reason - because it effects bike fit and handling. Changing a bike's geometry can make a bike more capable at climbing or descending; turning; more or less stable; more or less comfortable; and more or less efficient.*
There are a lot of variables to consider when designers develop a frame and, like chaos theory, changing one little variable can drastically effect the outcome of the overall fit and handling of a bike. The good news is, as long as you are within the ballpark of frame size and type, you can change what I'll call the "effective geometry" of a bike without cutting up the frame and welding (or gluing) it back together. I call it the effective geometry because you are not changing the geometry, just the angles in relation to the rider. This is accomplished by changing or adjusting some of the parts that bolt onto the bike. I'll touch on those areas as I explain them in relation to the frame.
For beginners, disecting a frame's geometry can be a little too far in the weeds when choosing a bike. View the following as an extremely generalized guide to help you understand why one bike may feel different than another and give you an idea as to what people are talking about when they throw around esoteric terms while discussing the mystery of frame design.
For the most part, certain categories of bikes have a specific type of geometry and each is within a pretty close range of one another. Cross country bikes are pretty close to other cross country bikes' geometry and same goes for all mountain vs AM and down hill compared to other DH bikes. But cross country bike geometry is a lot different than a down hill bike's geometry. Manufacturers tweak their designs within each category to give specific types of fit and handling because some people prefer a certain type of geometry over another because of their body dimensions or riding style.
There are four basic areas of a frame's geometry that will effect the way it rides: head tube, top tube, seat tube and chainstay. See diagram below:
Let's start with the front of the bike.
The head tube. There are two measurements to be concerned with: the head tube length and the head tube angle.
Head tube length can be important if you want a really aggressive (low) handlebar position or a really relaxed (high) handle bar position. You can alter the handlebar position with more or less spacers on the steering tube, but only within limits (the steering tube is the part of the forks that goes through the head tube and connects to the stem and handlebars). So, for the most part, a short head tube, with no spacers, will allow you to get lower than a longer head tube with no spacers.
Since the number of spacers you can use has limits, some people need or want a longer head tube to get a sufficiently upright position, just as some prefer the short head tube to get a sufficiently aggressive riding position. Some bikes with a short head tube ship with a long steering tube and a lot of spacers to allow you to determine how aggressive of a riding position you want. Others will cut it low assuming you want an aggressive riding position.
Note: You cannot lengthen a steering tube once it has been cut - you must buy a new set of forks, so, make sure you like the handlebar position before you go cutting off that steering tube! If the bike comes with a short head tube and steerer tube and you want a more upright position, you can buy a set of riser bars. Or, if it's too high, you can go the other way and cut the steerer tube or buy a set of flat bars. Because 29ers' head tube sits higher than a 26ers' head tube, some people are slamming the stem and/or turning it upside down with flat bars to get the aggressive riding position they are used to having with a 26er.
This begs the question, "what's the difference between an aggressive and relaxed riding position?" In short: aerodynamics, leverage and comfort. The lower you are, the more aerodynamic with greater leverage to pull up on the front wheel (and arguably less comfortable and less stable) compared to more upright. So, it's a trade and depends on what is more important to you.
Head tube angle. For the most part, the more a bike looks like a chopper, the more stable it will be while riding in a straight line. This is why downhill and all mountain bikes have "slack" HT angles - for stability. The less chopper-like the bike gets, the faster it will steer and turn. Careful though, not enough head tube angle and the bike will be twitchy (difficult to ride with no hands) and you'll also likely to be over the bars often.
Depending on the category of riding a bike is designed for, the angle of the head tube will be within a certain range. XC bikes have a steeper HT angle compared to All Mountain (AM) and Downhill (DH) bikes. Generally, entry-level XC bikes will be a little more slack than race XC bikes.
However, one can change the "effective" HT angle (slackness/stability and steering speed) by increasing or decreasing the length of the forks. Not all forks are adjustable. However, some are designed and built to allow a rider to change the fork length (travel) by +/- 20mm. This is typically accomplished by altering the travel, or, the distance a suspension fork can compress. A segment of adjustable forks even have a way to adjust the travel (and therefore fork length) with a couple twists of a knob. When you increase or decrease the travel, you are raising or lowering the head tube. In doing that, you are increasing or decreasing the "effective" head tube angle and changing the angle of the forks. Comparatively longer travel will make a bike more slack. Be careful though - if you change the travel more than +/- 20mm, you will void the warranty because you are putting additional stress on the head tube and you might cause it to break.
Another way is to buy a special "adjustable" headset. The headset is the compilation of bearings and spacers in the head tube. An adjustable headset allows one to adjust the steerer tube angle within the head tube +/- 1.5 degrees. It might not sound like a lot, but 1.5 degrees in either direction can really change the way a bike rides.
It is also possible to speed up or slow down the steering or twitchiness a couple of ways without changing the travel or HT angle. Putting a longer stem on a bike and/or widening the bars slows the steering down just as a shorter stem and/narrower bars speed it up. This is like the difference between a small steering wheel on a sports car and a big steering wheel on an 18-wheeler. It doesn't actually change the ability of the bike to steer quicker or slower, it just feels like it.
Changing either the stem or handlebars, or both, will also change your effective reach and put you in a more or less aggressive riding position. Longer stem means you have to bend over farther to reach the grips. Wider bars have the same effect. This may or may not be what you want. You can counter this by moving your saddle forward or backward to compensate for the change in reach. Again, you have to be careful making changes because moving your seat position also changes your effective seat tube angle and, in an essence, also changes the effective top tube length.
There are a lot of variables to consider when designers develop a frame and, like chaos theory, changing one little variable can drastically effect the outcome of the overall fit and handling of a bike. The good news is, as long as you are within the ballpark of frame size and type, you can change what I'll call the "effective geometry" of a bike without cutting up the frame and welding (or gluing) it back together. I call it the effective geometry because you are not changing the geometry, just the angles in relation to the rider. This is accomplished by changing or adjusting some of the parts that bolt onto the bike. I'll touch on those areas as I explain them in relation to the frame.
For beginners, disecting a frame's geometry can be a little too far in the weeds when choosing a bike. View the following as an extremely generalized guide to help you understand why one bike may feel different than another and give you an idea as to what people are talking about when they throw around esoteric terms while discussing the mystery of frame design.
For the most part, certain categories of bikes have a specific type of geometry and each is within a pretty close range of one another. Cross country bikes are pretty close to other cross country bikes' geometry and same goes for all mountain vs AM and down hill compared to other DH bikes. But cross country bike geometry is a lot different than a down hill bike's geometry. Manufacturers tweak their designs within each category to give specific types of fit and handling because some people prefer a certain type of geometry over another because of their body dimensions or riding style.
There are four basic areas of a frame's geometry that will effect the way it rides: head tube, top tube, seat tube and chainstay. See diagram below:

Let's start with the front of the bike.
The head tube. There are two measurements to be concerned with: the head tube length and the head tube angle.
Head tube length can be important if you want a really aggressive (low) handlebar position or a really relaxed (high) handle bar position. You can alter the handlebar position with more or less spacers on the steering tube, but only within limits (the steering tube is the part of the forks that goes through the head tube and connects to the stem and handlebars). So, for the most part, a short head tube, with no spacers, will allow you to get lower than a longer head tube with no spacers.
Since the number of spacers you can use has limits, some people need or want a longer head tube to get a sufficiently upright position, just as some prefer the short head tube to get a sufficiently aggressive riding position. Some bikes with a short head tube ship with a long steering tube and a lot of spacers to allow you to determine how aggressive of a riding position you want. Others will cut it low assuming you want an aggressive riding position.
Note: You cannot lengthen a steering tube once it has been cut - you must buy a new set of forks, so, make sure you like the handlebar position before you go cutting off that steering tube! If the bike comes with a short head tube and steerer tube and you want a more upright position, you can buy a set of riser bars. Or, if it's too high, you can go the other way and cut the steerer tube or buy a set of flat bars. Because 29ers' head tube sits higher than a 26ers' head tube, some people are slamming the stem and/or turning it upside down with flat bars to get the aggressive riding position they are used to having with a 26er.
This begs the question, "what's the difference between an aggressive and relaxed riding position?" In short: aerodynamics, leverage and comfort. The lower you are, the more aerodynamic with greater leverage to pull up on the front wheel (and arguably less comfortable and less stable) compared to more upright. So, it's a trade and depends on what is more important to you.
Head tube angle. For the most part, the more a bike looks like a chopper, the more stable it will be while riding in a straight line. This is why downhill and all mountain bikes have "slack" HT angles - for stability. The less chopper-like the bike gets, the faster it will steer and turn. Careful though, not enough head tube angle and the bike will be twitchy (difficult to ride with no hands) and you'll also likely to be over the bars often.
Depending on the category of riding a bike is designed for, the angle of the head tube will be within a certain range. XC bikes have a steeper HT angle compared to All Mountain (AM) and Downhill (DH) bikes. Generally, entry-level XC bikes will be a little more slack than race XC bikes.
However, one can change the "effective" HT angle (slackness/stability and steering speed) by increasing or decreasing the length of the forks. Not all forks are adjustable. However, some are designed and built to allow a rider to change the fork length (travel) by +/- 20mm. This is typically accomplished by altering the travel, or, the distance a suspension fork can compress. A segment of adjustable forks even have a way to adjust the travel (and therefore fork length) with a couple twists of a knob. When you increase or decrease the travel, you are raising or lowering the head tube. In doing that, you are increasing or decreasing the "effective" head tube angle and changing the angle of the forks. Comparatively longer travel will make a bike more slack. Be careful though - if you change the travel more than +/- 20mm, you will void the warranty because you are putting additional stress on the head tube and you might cause it to break.
Another way is to buy a special "adjustable" headset. The headset is the compilation of bearings and spacers in the head tube. An adjustable headset allows one to adjust the steerer tube angle within the head tube +/- 1.5 degrees. It might not sound like a lot, but 1.5 degrees in either direction can really change the way a bike rides.
It is also possible to speed up or slow down the steering or twitchiness a couple of ways without changing the travel or HT angle. Putting a longer stem on a bike and/or widening the bars slows the steering down just as a shorter stem and/narrower bars speed it up. This is like the difference between a small steering wheel on a sports car and a big steering wheel on an 18-wheeler. It doesn't actually change the ability of the bike to steer quicker or slower, it just feels like it.
Changing either the stem or handlebars, or both, will also change your effective reach and put you in a more or less aggressive riding position. Longer stem means you have to bend over farther to reach the grips. Wider bars have the same effect. This may or may not be what you want. You can counter this by moving your saddle forward or backward to compensate for the change in reach. Again, you have to be careful making changes because moving your seat position also changes your effective seat tube angle and, in an essence, also changes the effective top tube length.
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