Any geometry nerds want to give this a go?

JamesShort · **Posted:** Thu Aug 19, 2010 9:12 pm

I'm trying to prove this (relating to a alignment web gui some guy wrote and I'm double checking his methods before I trust it).

EDIT:

asin ( (a - b - c + d)/(2*l) )

sorry, trying to make the parenthesis clear.

RodneyWright · **Posted:** Thu Aug 19, 2010 9:43 pm

math, highly over rated.....

I used to be able to knock this stuff out, but years behind an IT desk and I've lost yet another skill set. Guess it's time to break out the automotive math book I have and start feeding the brain again.

JamesShort · **Posted:** Thu Aug 19, 2010 9:46 pm

RodneyWright wrote:

math, highly over rated.....

I used to be able to knock this stuff out, but years behind an IT desk and I've lost yet another skill set. Guess it's time to break out the automotive math book I have and start feeding the brain again.

I know right? I'm a bit less displaced from high school than you

but I dicked around with this page and a square/ruler for about 2 hours and I can't get phi in terms of ONLY a,b,c,d and l

.

This gist of this problem is determining the 'thrust' angle between a car and a set of parallel lines only knowing the wheel base and the perpendicular distances from said parallel lines to the middle of the hubs on all 4 corners (since not all cars have equal front and rear tracks, I made it a trapezoid for the generic case).

Basically with the thrust angle between the car's centerline and the parallel lines, you can get the toe angle of each wheel relative the parallel line and add/subtract out said thrust angle to get the toe angle relative the chassis....makes self alignments SIGNIFICANTLY easier if the math is true

.

JamesShort · **Posted:** Thu Aug 19, 2010 9:58 pm

The 'edge' cases work:

Car is already parallel to the parallel lines:

asin (0/blah blah) = 0 true

Car is not necessarily || to lines but front and rear track are the same:

phi = asin( (d-b)/l) or asin( (a-c)/l) true

Steven Carter · **Posted:** Fri Aug 20, 2010 8:56 am

So I am about as far away from being a math nerd as possible, but this sounds interesting...

This is all based on the premise that front and rear track are the same, right? So if track widths are unequal front/rear, then could you just make the appropriate adjustment (distance from wheel to lines drawn beside car) and still have this work?

JamesShort · **Posted:** Fri Aug 20, 2010 9:18 am

Steven Carter wrote:

So I am about as far away from being a math nerd as possible, but this sounds interesting...

This is all based on the premise that front and rear track are the same, right? So if track widths are unequal front/rear, then could you just make the appropriate adjustment (distance from wheel to lines drawn beside car) and still have this work?

No, this is incredibly generic such that front and rear track need not be the same (nor known).

In fact you could pull a tricycle between these parallel lines (ie 0 front track) and that equation above should hold.

I purposefully made the above diagram a trapezoid (ie unequal front and rear track) so that I can check the general case...2 posts ago I showed that the formula is valid in the equal track case.

Steven Carter · **Posted:** Fri Aug 20, 2010 10:02 am

what you said:

JamesShort wrote:

The 'edge' cases work:

Car is already parallel to the parallel lines:

asin (0/blah blah) = 0 true

Car is not necessarily || to lines but front and rear track are the same:

phi = asin( (d-b)/l) or asin( (a-c)/l) true

What I understood:

JamesShort wrote:

The 'edge'

blahblahblahblahblahblah

... are the same:

blahblahblahblah somethingsomething blahblah true

Dammit, Jim!

Kevin Allen · **Joined:** Thu Aug 28, 2003 6:42 pm **Posts:** 3479

What is this I don't even.

JamesMilko · **Posted:** Fri Aug 20, 2010 10:30 am

I just had a brief flashback to geometry proofs. Coincidentally I just informed my boss that I'll be taking a half day so I can drink heavily.

KouroshNeshat · **Posted:** Fri Aug 20, 2010 11:19 am

What is this asin u speak of? Arcsin?

JamesShort · **Posted:** Fri Aug 20, 2010 11:24 am

Ahhh, I figured it out....of course it was MUCH easier than it seemed to be

.

Yes asin = arcsin = sin^-1(x) etc....asin is the Math.func form or arcsin in javascript.

Graham Jagger · **Joined:** Fri Aug 29, 2003 12:53 am **Posts:** 1718

Actually the answer is even easier than that...

sin = Performance Chassis + http://www.hunter.com/alignment/winalig ... /index.cfm - $100

JamesShort · **Posted:** Fri Aug 20, 2010 11:38 am

For those who care:

Steven Carter · **Posted:** Fri Aug 20, 2010 11:54 am

So is your conclusion that his math is good? If so, maybe post up the link so we (rather, I) can use the $100 that was going for an alignment to instead maintain my beer fund. (Priorities, you know..tough economic times and all....)

/geometry=headache
//glad math nerds figure this stuff out instead of me

JamesShort · **Posted:** Fri Aug 20, 2010 11:56 am

This is the tool in question:

http://aligned.hostcell.net/

The nice thing is that unlike most alignment methods, the car's centerline need not be parallel to your lines....only the lines themselves need to be parallel. The only extra bit of info needed is an accurate wheel base dimension.

The toe values are relative to the chassis and not the lines (since the angle b/t the chassis centerline and the parallel lines is added/subtracted out).

I also like this tool because the toe angle is on a per wheel basis and relative to the chassis so getting your rear thrust angle to 0 is quite simple.

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Any geometry nerds want to give this a go?

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