Trail Calculator
Steering Trail Calculators
Online tools to help you design your recumbent bicycle steering geometry
By Warren Beauchamp
High Speed trail   Actual Trail  Notes  Disclaimer   What's trail, and why do I need it?

Optimal High Speed Trail Calculator
This calculator finds the "optimal high speed trail" for a specific design. Note that in many cases this may be more trail than is practical for general use. A trail value greater than 5 inches will generate excessive fork flop. The trail calculator should be used as a design aid to give you a good idea of how changes in your bikes geometry effect the need for additional trail. This equation is still being developed. Calculator updated 9/11/06 to provide more realistic trail values. Personally I feel that the numbers generated with the "Jet Fighter" K5 value are the best for me. YMMV.

 

Horizontal distance between rear axle and cg  = Inches or Centimeters
Vertical distance between ground and cg  = Inches or Centimeters
Mass of bike and rider  = Pounds or Kilograms
Seat back angle from horizontal  = Degrees
K5 - Steering feel 
English
Metric
Theoretical Trail =   Inches or Centimeters

Actual Trail Calculator (English or Metric)
This tool allows you to calculate the actual trail of a bike, given the wheel size, the fork's offset, and the head tube angle.

Wheel Radius = Fork Offset (rake) = Headtube angle =
Actual Trail = 1.67200362597166
Notes:
cg = Center of gravity, generally your belly-button is at the bike's cg.
Kx = radius of gyration for a specific seat back angle. - 35 @ 90,  .345 @ 80,  .335 @ 70,  .32 @ 60,  .30 @ 50,  .275 @ 40,  .24 @ 30,  .20 @ 20

The equation with which this page calculates is:

T = K5 B/M (1/Kx2 + 1/h2)

K5 = steering feel, the calculator here uses values of 0.5, 1.0, 1.2, and 1.5
B = horizontal distance of the cg from rear axle 
M = mass 
Kx = radius of gyration
h = cg height fom ground
2 means squared.
All units in meters and kg.
Bikes that are ridden by more than one person should be designed for a 160 pound rider.
The trail equation is only one design value and can seldom be used alone.

Bill Patterson notes that he does recommend K5 values under 1.2, but that for high performance vehicles that do not need to be ridden by the general public, it can go lower (as it does in the "Normal Fast" and "Jet Fighter" settings on this calculator).


Thanks to all the work that Bill Patterson put into creating the equation behind this page. This equation is just a small part of a book on bike handling that is available for:

$48 plus $2.50 s.h in  North America. Shipping is $6.50 elsewhere.

From:

Bill Patterson
3058 Lancaster
Santa Maria CA 93455

Also see the following links for more information on Bill Patterson and his Single Track Vehicle design course at Cal Poly.

 Single Track Vehicle Design   and    1998 class photos 


What's trail, and why do I need it?
Trail is the distance between the bottom end of a line drawn through your headtube to the ground, and the point where your tire contacts the ground. In general to make the bike handle well, it's a good idea to have some positive trail. This means the line through the head tube ends up in front of your tire patch. Too much trail and you get excessive fork flop, not enough, and the bike is too twitchy.
trail.gif (4361 bytes)
Note that trail is not the only thing that effects a bike's handling. The head tube angle, wheelbase and well, pretty much every other aspect of the bike effects how it handles. Your job is to make a series of compromises to get the bike that does what you want it to. These tools are designed to help you do that.

Disclaimers:
  • The equations used in the "optimal high speed trail" calculator are still being refined. 
  • By using these tools, you agree to release all parties involved in the creation, translation, and publishing of this information of any responsibility for anything bad that may happen.

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