Math whiz needed

[Jarlaxle]

Do we have any here? I am trying to figure out a geometry problem and all I am getting is a headache.

[Crackpot]

Not a whiz but semi capable

[Bicycle Bill]

Not a whiz but semi capable

Ditto.  Lay it on us, we can't do any worse than you seem to be doing on your own.

-"BB"-

[Jarlaxle]

OK, here it is. It is complicated, which is why I'm hoping for a math whiz. (Or someone with the appropriate computer program.)

A Harley-Davidson Sportster 1200T has 31 degrees of fork rake, and 5.7"/140mm of trail. Wheelbase is 59"/149cm. Visual aid:


The rear shocks mount at about a 45 degree angle, and attach to the frame about 2" behind the strap that runs across the seat. If I were to install shocks 2.5"/65mm longer than stock (10.5"/267mm to 13"/330mm) with no other changes, how much would that reduce rake and trail?

For those totally unfamiliar with motorcycles...
Rake: angle of the forks, with 0 being vertical and 90 degrees being horizontal. Rake on the Captain America chopper from Easyriders is 42 degrees, for an extreme example. (I recall bicycle head angle is measured the other way, with 90 degrees being vertical.)
Trail (caster) is something easier to explain with a LINK, rather than posting a wall of text.

[RayThom]

OK, it's a Harley you're talking about. Do you think the rate of the usual oil leak should be factored in?

Regardless, math was never my strong suit. I'm lost without a calculator. So maybe this "Professional Rake and Trail (Trail?) Calculator" will work for you.

http://www.whosyadaddy.com/rake_trail_calculator.htm

[Jarlaxle]

I saw that...but it's for people building extended-fork choppers. I'm trying to do the OPPOSITE, by raising the rear of the bike, which that site does not have any way to figure.

[rubato]

Get a piece of paper. scale your dimensions so the motorcycle fits on it.

Draw a straight line near the bottom.

Draw a second line through the wheel hubs.

Now use a protractor to draw a line representing the forks at the correct angle and continue the line upwards past where the handlebars are. Draw a line parallel to that one by a distance equal to the offset. Measure the trail and use the scale you have chosen to convert it into real-world dimensions.


Now measure forward from the center of the rear hub to the center of the shock/strut attachment. Use a protractor to measure the angle.

Now on your drawing draw a line representing the centerline of your struts and extend it through the line for your forks. Use the scale you have chosen to convert 2.5in to scale and measure that distance forward from the current fork centerline on the shock centerline an make a mark. Draw a straight line through this mark and the hub center to the ground. To a first approximation this should give you the new head angle. To calculate trail you need to draw a second line parallel to the fork centerline off set by the distance of the offset between the steerer tube (bicycle terminology) and the forks.

yrs,
rubato

[Jarlaxle]

I have the same chance of doing that as I do flapping my arms and soaring to the planet Frimerbee.

[rubato]

Suit your self.

It is a simple graphical method. But if you don't care about the result its your business.


yrs,
rubato

[RayThom]

Suit your self.
It is a simple graphical method. But if you don't care about the result its your business.
yrs,
rubato

They call this Passive/Aggressive behavior. It's one of the best way to keep people at a distance.

You're winning!

[Bicycle Bill]

First, visualize the motorcycle frame as a triangle.  We already know the length of the base of the triangle — the wheelbase, 59 inches — and two of the three angles, given as 45° and 59° (determined by subtracting the 31° of rake from 90°).

Now you could figure this by calculating sine and cosine, but I found this website — Triangle Calculator.  Plug in the known values in the appropriate spaces to get the length of the other two sides of our theoretical triangle — 52.121" and 42.996".

Swapping out the shocks for ones 2.5 inches longer will obviously lengthen that leg ... so add 2.5 to 52.121"; this now makes that leg 54.621" long.  Input this new number, along with the other newly-calculated side length of 42.996 inches and the wheelbase of 59 inches.  Voila!  The new rake angle is 27.55°.

-"BB"-

[RayThom]

First, visualize the motorcycle frame as a triangle.  We already know the length of the base of the triangle — the wheelbase, 59 inches — and two of the three angles, given as 45° and 59° (determined by subtracting the 31° of rake from 90°).

Now you could figure this by calculating sine and cosine, but I found this website — Triangle Calculator.  Plug in the known values in the appropriate spaces to get the length of the other two sides of our theoretical triangle — 52.121" and 42.996".

Swapping out the shocks for ones 2.5 inches longer will obviously lengthen that leg ... so add 2.5 to 52.121"; this now makes that leg 54.621" long.  Input this new number, along with the other newly-calculated side length of 42.996 inches and the wheelbase of 59 inches.  Voila!  The new rake angle is 27.55°.

Damn, BB. That amazing. Math can make everything sound great. I'd believe this even if it turns out to be seriously flawed.

[ex-khobar Andy]

Jarl - I have been looking at this on and off for a couple of days in between doing other stuff - my trigonometry isn't bad (I got an A at A Level maths which might impress some of the UK folk here but it was a very very long time ago) but I think I need a little more info. I know nothing about motor bikes. I think I need either (a) the length of the fork from where it attaches to the frame to the center of the wheel or (b) the length of the frame from the top of the strut to the point at which the fork is attached to it or (c) can I assume that the frame from the top end of the strut to the top of the fork is horizontal - i.e., parallel to the ground? I assume that both the strut and the fork are attached to the frame with some sort of bushing which allows free rotation.

[Jarlaxle]

No, the frame is nowhere near straight-it angles down under the fuel tank, then levels off at the seat. The triple tree (where the forks attach to the frame) is a good 6" higher than the rear upper shock mount

I don't know it offhand, but can probably get the fork tube length easily enough. (I THINK it is 30 inches on a Super Low, but am not sure.)

[ex-khobar Andy]

I think that 6" off horizontal is a good enough piece of information. It may be a day or two before I can get back to it.

[Jarlaxle]

In the picture, the rear shocks mount about level with the brightwork on the upper part of the saddle bag, about the same height as the mounting screws on the air filter housing. The forks mount to the triple tree just above the front turn signal, the bottom of the triple tree is about even with the bottom windshield bracket on the fork.

6" is a total wild guess.

[Bicycle Bill]

You're overthinking it, xKA.  Occam's Razor, you know?

The frame of the motorcycle is four sided, but it is still just the lower portion of an (imaginary) triangle ABC —

(and if you want you can draw a line from side AB to side BC,
about ⅓ of the way up, to simulate the top of the frame)

— created by taking the wheelbase (side AC) and then completing the triangle by extending the sides defined by the rear shocks (side AB) and front fork blades (side BC), using 59" for the length of side AC and 45° and 59° for angles A and C respectively, until they meet at a theoretical point somewhere above the rider's head.

Then, since the frame is rigid between the shocks' attachment point and the area where the fork fits (in bicycling terms, the headset), this means the wheelbase is going to remain constant..... so extending the length of side AB of the imaginary triangle (and leaving side BC unchanged) will move the apex of the triangle (B) slightly forward as well as changing the measurements of angles A, B, and C.  And we're only concerned about angle C.

-"BB"-

[Jarlaxle]

Confirmed: the forks are 30" from triple tree to wheel hub.

[RayThom]

Confirmed: the forks are 30" from triple tree to wheel hub.

That's really close to what BB calculated -- a "new rake angle is 27.55". An inch here, an inch there -- it's all close enough for government work.

BB must be some kind of mathlete.

[Econoline]

I just wanted to compliment Bill for not only finding the angle, but also explaining clearly how he did it.