Bicycle geometry affects how a bike fits and rides. It doesn't tell you everything; components and materials are at least as important. And it's less prescriptive than some would have you believe. Bike geometry grew out of practical considerations rather than pure maths. To fit comfortably, the saddle went here, the bars went there, and the front wheel had to be there so it wouldn't hit your feet. Nevertheless, the numbers do tell you useful things about what a bike will be better or worse at, and whether it will suit you.
Will it fit me?
In the days when bikes had horizontal top tubes and short seat posts, the seat tube length told you whether you'd be able to reach the pedals and stand over the frame when you stopped – in short, whether it would fit. So that's how bikes were sized. This idea hasn't died, despite the fact that most bikes now have a downward sloping top tube and 200mm or more of saddle height adjustment.
Assuming that you can comfortably stand over the frame, the most important frame measurement for fit is the effective top tube length (ETT). This is the length the top tube would be if it ran horizontally from the top of the head tube to the seat post. It tells you how stretched out you will be on the bike, subject to a given handlebar type and stem length.
Once you know the ETT of a bike you find comfortable, you can use this to size up other bikes with the same kind of handlebar. If your 600mm ETT hybrid feels just right and you're in the market for a new one, you want one with something close to a 600mm ETT, irrespective of whether the bike is described as Medium or Large or has 530 or 550mm seat tube. To fine tune the fit, see the Bike Fit Basics article in issue 11 of Cycle Commuter. And don't forget you can try for size before buying at your local bike shop.
Seat tube angles range from about 70-75 degrees. A steeper angle moves the saddle forward while a shallower angle moves it back. Steep is fine for racers. It allows them to ride hard in an aero crouch, as the more open hip angle doesn't constrain breathing or power transfer. It's not so good for more relaxed riding as it transfers more of your weight from your backside to your hands, which can cause aches and pains.
You can change the effective seat tube angle by sliding the saddle forward or back in the seat post clamp, or by fitting a different seat post with more or less 'layback' (the distance the clamp is behind the seat post centreline).
Head tube angles range from about 66 degrees (gravity-oriented mountain bikes) to 74 degrees (razor-sharp road bikes). Other things being equal, a bike with a steeper head angle with steer more sharply and a bike with a slacker head angle will be more inclined to travel in a straight line. Small-sized bikes often have a slacker head angle too, not to change the steering (although it does) but too keep the front wheel from hitting the rider's feet.
The head and seat tube angles on bikes with suspension change as the suspension compresses. Riders cope easily with this, which shows that small differences in geometry aren't critical.
How a bike steers
The biggest influence on how a bike steers is not head angle alone but a measurement that head angle helps determine: trail. This can be calculated if it's not listed. Trail is the distance that the contact patch of the front tyre on the ground trails behind a line drawn through the steering axis (the head tube) to the ground.
Trail figures for bikes range from the low thirties to the high nineties in millimetres, with sixty-something being typical. Lower is good for a more immediate steering feel but can feel 'nervous'; higher is for good for holding a line on bumpy trails but can feel 'lazy'.
These things produce more trail: a larger diameter wheel; a shallower head angle; a smaller amount of fork offset (which is the distance between the fork dropouts and a line through the steering axis). A smaller wheel, steeper head angle, and increased fork offset all reduce trail. Have a look at the diagrams of trail on Wikipedia to see how this works.
This isn't the whole story. Steering feel is also affected by the wheelbase of the bike, your weight distribution relative to the front wheel, the weight of the wheels themselves, the size of the front tyre, the length of the stem, and the width of the handlebar. These things change enormously between types of bike but not so much within types.
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Other useful numbers
Wheelbase is the distance between the wheel axles. It's determined by the front centres (the distance between the centre of the front axle and the centre of the bottom bracket) and the chain stay length (the distance between bottom bracket and rear axle). The modern trend is for shorter wheelbases and particularly shorter chain stays. Shorter makes the bike feel more lively. Longer improves stability and, since you're not 'on top of' the rear wheel as much, comfort; it also provides heel clearance for panniers.
The bottom bracket needs to be high enough that the pedals don't hit the ground and low enough that you can still get a toe down. Bikes ridden off-road benefit from extra clearance – a bottom bracket height of more than 300mm – whereas commuter bikes ridden in stop-start traffic are more manageable with a low bottom bracket (270mm or so).
There's more to bike geometry than this, not least because of how the different measurements interact. Just don't be blinded by pseudo-science or someone else's opinion: if your bike feels right, it is right.
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