Deriving trail from partial data
 

Is there a way to derive a bike's trail if the manufacturer's published geometry specs are incomplete? If so, what would be the minimal data or combination data needed to do the calculation?

For example. Bob's bike has a HT angle of 71 and fork offset of 50mm and tires are 700/35c. What is the trail?

Can other data be put to work to solve for unknown trail?

Bicycle Trail Calculator. Awesome! Thanks Spoonrobot.

Now, can it also be derived if no offset is given, say, by some other means? It's very spotty with bike manufacturers, a lot them not including that offset spec. What if you know the front-centre measurement and HT angle? Not enough data?

Trail is the distance on the ground between the line of the steering angle and a vertical line from the dropout, which requires the outer diameter of the tire.

So you would derive it by drawing a picture of the above and measuring, measuring the actual bike, or writing a math formula - which is what that website does.

Thanks Kontact. Actually measuring the bike wouldn't be a derivation, but I get your point. Not a math guy, the formula, whatever that might be, is above my pay grade. The online calculator is helpful.

The online calculator is the formula. You can probably "show source code" and read is, but all the formula is doing is drawing an imaginary point, a horizontal, vertical and angled line and measuring the result. It is all the same thing measuring a few points and lines or measuring the real thing.

What if fork offset is unknown? Could trail be derived from Front Centre, HTA, Tire size, and Reach?

You could use reach, STA, HTA, BB drop and front center to take a stab at rake. And you can derive front center if you have the rest of the numbers. If all the numbers were accurate your rake would be within 2mm.

In practice, some posted geometry is not accurate enough, but most modern bikes are designed on CAAD so they are more likely to be on. I tried figuring out some missing numbers on an old Cannondale and found that the published dimensions didn't work together.

But deriving trail without rake isn't going to work because all trail is is a "ratio" between rake and HTA.

Juggling variables, thanks Kontact. In a my little database of 15 or so bikes in the adventure/gravel/touring genres, about half publish rake/offset, and only a couple give trail numbers (Vivente Gibb, Soma Grand Randonneur). Perhaps this is because there seems to be very little variation in offset, most makers somewhere in the 45mm-55mm range. The Soma GR is an outlier, on purpose, making low trail (32mm) a marketing feature, and offset is predictably higher at 69mm.

Although my sampling of relaxed geometry bikes is tiny, it suggests that the "industry", generally speaking defaults to a medium rake/medium trail. And if that's the case, the front end handling of these bikes ought to be fairly similar among them, other variables being reasonably equivalent. Would you agree or disagree with this theory.

Another spotty metric among bike makers I've noticed is BB Height. Most firms report BB drop, but lot of them don't publish BB height, Salsa for example.

I'm drifting off-topic here, so I'll start a new thread in the Fit section.

BB height is dependent on tires, but drop is not.

Most roadish bikes are medium to high trail, unless it is designed for loads like a touring bike. There are many exceptions, of course.

One thing you'll find is that trail is often variable between frame sizes - one or two rakes are used with a variety of frame sizes and HTAs.

the formula is TRAIL = (DIAMETER * COS (HTA) - OFFSET)/ SIN (HTA). I use millimeters for all lengths and degrees for the angle.

You measure wheel diameter with a ruler. The head tube angle is hard to measure if you don't have a good digital angle measuring device. Fork offset, well my method is kind of intricate, I'll let others chime in.

If you delve into the code this is what you should find as a kernel.

But i think the Yojimbo tool is accurate if you have accurate inputs.

I really don't know any rules of thumb or other estimates.

How does this estimate work?

Thanks for pitching in the Trail formula. It's exactly what I was fishing for, i.e, a derivation. Looks like I'm gonna need a trig refresher!

You would just use those whichever of those numbers necessary to find where the front dropouts would be if the fork had no rake. You just follow the angles and lengths around to where it would be, using drop to calculate the head tube to dropouts as a fraction of the seat tube. Then you take that forth leg and compare it to the front center. The difference will be very close to rake.

I have a mistake in the equation! Instead of diameter, it should be calling for radius.

Apologies to all!

Ok, that sounds pretty decent. Have you checked it against exact using the equation? How close did you come?

You can find some other bike math at Liegerad, HPV, Fahrrad: technische Informationen.

I've checked similar derivations and they are, like I said, within 2-3mm. I'd suggest using a triangle calculator tool like this one to work your way from bb to seat cluster to head tube to dropout. Remember when you subtract for the BB drop that it is a vertical number and you'll need to make a right triangle to use it as when subtracting from HTA.

Just to clarify, Road Fan, the site says diameter, not radius. Is the site wrong? Is that your site? The sketch certainly seems to illustrate radius, not diameter, but the text says diameter.

The site is not wrong and it is not my site. It asks you for inputs that seem convenient: rim bead seat diameter spec (622, 630, etc) and tire width (22, 28, 42, etc). With those inputs the code can compute wheel radius in a code unit. The writer shows us how to input the numbers he needs rather than teaching the mathematics. The Wiki article "Bicycle and Motorcycle Geometry" uses radius, but it is trying to show the science.

Sorry for my typing, i'm in a cast due to a broken wrist.

I've taken bike specs from the literature together with my measurements, and run the numbers both on thw site and on the equation, validating against specs. If I use wheel radius, the site result will agree with the equation, with my measurements, and the published specs.

I'd suggest reading Chapter 8 of "Bicycling Science 3rd edition" by Wilson and Papadopous for a detailed discussion of what influences bike handling. It does not explain popular terms such as "twitchiness."

recap:

not my site
site is correct because it checks with my measurements, specs, and calculations
wheel radius is correct because it results in the agreement mentioned above
suggest delving into the Wiki site and the text "Bicycling Science."

What I can't steer you toward is a derivation of the formula based on pure geometry.

Are you talking about calculating trail from scratch? You don't need to reference a circle at all. You need to plot two right triangles, one with a leg that is rake and has the HTA in it to get the hypotenuse, then you take that hypotenuse an subtract it from the total hub to ground distance (total wheel radius), and use what's left and the angles provided to get the length of the leg parallel to the ground.

That's all trail is. You can make the calculation more involved if you want the formula to derive your total wheel radius from your rim radius and tire size, but you can also just get that off a chart or with a ruler.

Physical measurement of bike in front of you?

Head Tube Angle axis line, crosses Axle plumb line down to the ground , above the ground plane.

the distance between those 2 points is Trail..






....

I challenge anyone to accurately extend the head tube axis line to the ground. Your suggestion is completely impractical.

got a laser pointer?

And do what with it? Got special laser pointer clamping system?