Suspension geometry math

[Rough Edge racing]

  I hear all the time how raising or lowering the bike affects steering geometry. For you guys who like math,I do not , lol, how about this example.....A bike with 57 inch wheelbase, 27 degrees fork rake and 4.5 inches trail...Raise the rear one inch, how much rake and trail change?  Suppose instead you drop the front end half an inch? 

[Huzo]

If the wheelbase is 57” and you raise the arse by 1”.
You have a triangle whose sin is 1 and cos is 57.
The tangent is therefore sin/cos= tan
And that is 1/57=0.0175
So an angle whose tan= 0.0175
Is 1 degree.
You have altered the rake by 1 degree...
If a line drawn down the angle of the headstem to the ground and the distance from that point to the contact patch is the sin of the angle change.
You’ve to take the sin of 1 degree and multiply it by the distance of the axle to the imaginary point where the line of the forks will touch the road. This will be the radius of the rim plus the depth of the tyre...(near enough)
For an 18” rim that’s ...
9”+3”=12”
So the alteration to trail is about 12x sin 1 degree, which is 12x 0.0174 = 0.21”
So that’s a change in trail of about 1/4”

[kingoffleece]

Uh, let's see.  Multiply the first by the second, minus the fourth and divide by, what, again?  Or is it second from first minus third......crap, I don't know.

Oh, HUZO figured it out.  Thank goodness.  Well done, mate.  Good on ya!

Having done that mod to a few bikes I always wondered-now I know.

[Groover]

What Huzo said

[cloudbase]

Gotta break out the old slide rule for that one.

[John Croucher]

Better jump in here before Lannis.

Huzo's explanation is good, to a point.  When a rider gets on the bike, weight is added, passenger added, road surface imperfections that change the shock lengths.  In a perfect world of smooth consistency the math works.  In the real world, it is constantly changing in a range.  Some times close is good enough.

[kirby1923]

Yes, especially in the case of SAMs.

:-)

[kingoffleece]

Or horseshoes and hand grenades 

[Rough Edge racing]

  I bent conduit for years as an electrician. With multiple pipes on a rack the starting point of bending each pipe if making a bend had to be adjusted so the pipes remained the same distance apart from each other .Sin and all that business. Generally we just  memorized about 5 situations and made adjustments based on past experience.
  Pretty much the same when I modify a bike. I jack the bike up or down and using angle levels and marks on the work platform to keep track of trail changes. But it,s handy to see it written down, Thanks..

[Huzo]

Yes, especially in the case of SAMs.

:-)

Or P factor...

[malik]

Or P factor...

You don't want to let any of those factors get in the way of a good story.

[dguzzi]

  I bent conduit for years as an electrician. With multiple pipes on a rack the starting point of bending each pipe if making a bend had to be adjusted so the pipes remained the same distance apart from each other .Sin and all that business. Generally we just  memorized about 5 situations and made adjustments based on past experience.
  Pretty much the same when I modify a bike. I jack the bike up or down and using angle levels and marks on the work platform to keep track of trail changes. But it,s handy to see it written down, Thanks..

   I have a Suspension Engineering Handbook if it would help you. Its old but math and geometry doesn't change much!

[Huzo]

You don't want to let any of those factors get in the way of a good story.

Kirby straightened me out on some old knowlege that needed some polish years ago.
Sometimes you don’t know what you don’t know...

[Huzo]

You could draw a schematic diagram at 10:1 scale and plot the angle with a protractor.
Then raise the back by 0.1” and plot the new angle.
Similar triangle theory says the angle change will be the same, but the change in trail will be 1/10 th of my calc.
A 1/2 or 1/4 scale drawing will yield more accurate results, but don’t look too closely...
You might discover that I’m full of shit.....(but I think not..) 

[Harryc]

I did a spreadsheet a while ago to work this stuff out. I can't see a way to attach it to the post, but if you want a copy, message me with your email & I can forward it.

[Rough Edge racing]

  Harry ,thanks ,but this was a one shot theoretic question.....For me, using a bike and measuring tools seems to be best....

[twowheeladdict]

http://www.thompsonchoppers.com/rake-and-trail-calculator/

Found this website when I was considering a raked front end on my Mean Streak.

[dguzzi]

    The book says, Raising or lowering the chassis at either end by one inch will generally change the angle by almost one degree.