Frame & Geometry Variables

Yo Baby, what’s your Sine? The meaning of rake, trail, and other bicycle geometry conundrums.

I get a lot of questions about the different effects that changing the angles or geometry has on a frame.  So as a reference, I cobbled this together – remember, these are generalizations, not etched in stone.  Some are accepted standards and some are products of my experience.

The primary frame/fork dimensions/angles and that affect handling are and their typical ranges:

Variable Road (700c) MTB
Bottom Bracket Drop (below axle centerline) 50-85mm -20 to 50mm
Seat Tube Angle 72-76 degrees – steeper for TT or Tri bikes 70-74 degrees
Head Tube Angle 72-75 degrees 69-72 degrees
Rake 26-55mm 35-55mm
Trail 50-70mm 50-70+mm
Chainstay length 390-430mm 410-450mm
Front Center Dimension all over the board all over the board

Of course frame build and tube stiffness affects handling and bike feel also but we’ll not discuss those at this point.

Bottom Bracket Drop directly effects your center of gravity.  Less drop results in a higher and stiffer bottom bracket (shorter down tube), shorter chainstays, and more cornering clearance but less stability.  More drop adds compliance (longer down tube), reduces driveline rigidity, lengthens chainstays, and adds stability by lowering the center of gravity (CG), but provides less cornering and tire clearance.

Seat Tube Angle has a significant impact on your center of gravity also.  Shallow angles generally result in a softer ride and place more weight over the rear wheel but can be more difficult for some people to spin at a high cadence.  Steeper angles produce often produces a stiffer ride, moves the CG forward, and is easier to spin.  This is highly variable on the rider and his positioning on the bike.  Effective seat tube angle can be increased or reduced by using a seatpost with or without setback (the seatpost’s clamping mechanisms relationship to the centerline of the seat tube).

Head Tube Angle: For a given trail dimension, as the head tube angle gets steeper, steering responsiveness increase but transmits more road shock.    Steeper head tube angles also shorten the wheelbase of the bike and require less rake in a fork to achieve a given trail number.  The opposite is also true.

Rake or Offset is the distance the axle center is from the steerer tube centerline measured perpendicular to the steerer tube. For a given trail dimension, less rake increases steering response, shortens wheelbase (moves CG forward), and lessens shock absorption.  More rake causes steering response to slow, lengthens wheelbase (moves CG rearward), and offers more shock absorption.

Trail is the principle component of steering traits and handling.  More trail causes a tendency toward more stability at higher speeds.  Less trail causes a tendency toward more stability at lower speeds.  It is the product of tire radius, head tube angle, and rake.  If you use MS Excel and want to set up a spreadsheet to calculate trail, then the formula will look like this:

Trail =(tire radius*COS(headtube angle*PI()/180)-rake )/SIN(head tube angle *PI()/180)

Substitute tire radius, headtube angle, and rake with the cell references you enter those numbers into or just enter your values into the formula.  For example if your bike has a tire radius of 336mm, a headtube angle of 73 degrees and a rake of 45mm the calculation should result in a trail of 55.7mm.  The actual formula would look like this:

Trail =(336*COS(73*PI()/180)-45)/SIN(73 *PI()/180) = 55.7mm

Or if you want to take my word for it, you can download a nice little spreadsheet that will calculate trail based on the variables you apply here. If you don’t have a computer (and just how are you reading this) or don’t have Excel, then you can use this formula:

Trail = (tire radius x cosine of the HTA – rake) / sine of the HTA

Chainstay Length: Shorter chainstays means a stiffer bottom bracket, shortens the wheelbase, provides less tire clearance and shock absorption, but are more efficient.  They also move the CG to the rear.  Longer stays are more shock absorbent, provide more tire clearance, lengthen the wheelbase and move the CG forward.

Front Center Dimension is the distance from the center of the bottom bracket to the center of the front axle.  This changes with any change made to fork length, rake, top tube length, and headtube angle.  This dimension is used to determine CG on a frame as it considers the effects of fork variables.  It is very useful in solving toe overlap problems.

That’s it, those are the basics. Pretty simple, eh? The hard part is juggling it all so you get a bike that rides tthe way you want it to ride!

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