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Super Dork Out Geometry Formulas

djjohnr

Turbo Monkey
Apr 21, 2002
3,107
1,799
Northern California
Okay, we all know the best way to find your next frame is to test ride everything that floats your boat. However, it’s usually much easier said then done – finding frames in your size and in stock is not easy. Standard manufacturer data doesn’t usually tell me enough about how a bike will ride, so I dorked out and put together a set of formulas that uses manufacturer data to spit out more usable geometry info. The default data is for mini-dh/all-mountain frames in medium size, but you can plug in whatever frames you want.

How to use this -

First, download the file at - Bike Geometry Formulas (you can view the file right on the site, but to enter in additional frames you'll need Excel)

Plug in the following data – head angle, top tube (inches), static bb height (inches), wheelbase (inches), chainstay length (inches) and rear travel. There’s a millimeter to inches converter formula in the sheet if you need it, as well as a formula for converting BB drop to static bb height.

Output:

The resulting data is for COMPARISON use only. The data without a reference point isn’t very useful. It’s best to use bikes you have ridden as controls to compare other bikes to. Also, remember garbage in = garbage out, the data is dependent on it’s source – if you use crap measurements you’ll get crap accuracy.

BB/WB: Ratio of sagged bb height to overall wheelbase. This is a tricky data point because rear travel is not usually measured vertically. That said, bikes with a lower percentage may have a lower center of gravity.

Front to Center: Front axle to the center of the BB. Gives you an idea of how much room you have in the front end.

Standing Horizontal Reach: Similar to top tube measurement but starts at a point directly above the BB and ends at the center of the stem on the steerer. This is much more useful then a top tube measurement as it reflects reach when you're standing. To make the data comparable the calculation uses the same height between the BB and the stem on all frames. You can enter a control value for preferred stem height, but if it’s too low it won’t be realistic – the point you’re measuring would be in the headtube or lower. The default measurement is 24”. Use your own measurements from your current bike if you wish (measure floor to the center of your stem on the steerer and subtract static bb height).

Front to Bar: Horizontal measurement from the front axle to the center of steerer tube based on preferred bar height. Gives you an idea how far out in front of your bars your front wheel will be.

Rider Center vs True Center: Center between bb and bar reach versus center point between the axles. Gives you an idea about the forward/rearward bias of the bike.

Once you have the sheet loaded with the frames you're interested in, just sort the list by column criteria to find the bikes that meet your preferred specs.
 
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Gridds

Monkey
Dec 18, 2008
266
0
Great Britain
Um, from what I understand he didn't find it - he made it. Right?

Nice one.

Can you make it so it produces a side profile simple image of the frames/bikes so you can compare different frame geometries visually?
 

Tracer Tong

Chimp
Mar 21, 2009
77
0
This is a great tool, thank you.

Not to hijack the thread, but do you know where I can dig up the geometry for the OLD bullit? That's what I ride and I'm interested to see how it stacks up.
 

djjohnr

Turbo Monkey
Apr 21, 2002
3,107
1,799
Northern California
Can you make it so it produces a side profile simple image of the frames/bikes so you can compare different frame geometries visually?
Unfortunately that's not a skill I have. I may make a web front end that lets you just plug in the numbers without having to use the spreadsheet. It would be cool to have an interface where users could enter in real world measurements from their bike into a database that anyone could access and review.

Not to hijack the thread, but do you know where I can dig up the geometry for the OLD bullit? That's what I ride and I'm interested to see how it stacks up.
You're in luck - http://web.archive.org/web/20010605214558/www.santacruzmtb.com/specs.htm
 

Bicyclist

Turbo Monkey
Apr 4, 2004
10,152
2
SB
I think that a stickied thread with this + REAL WORLD bike geo would be a great resource...I suggested that to Transcend a while back but did not hear anything back. Oh well.

EDIT: for some reason I'm not getting output. I tried using both Excel and Open Office, to no avail. Should the output numbers be automatic, or do you have to run something?
 
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djjohnr

Turbo Monkey
Apr 21, 2002
3,107
1,799
Northern California
Bicyclist, the easiest thing to do is copy on of the rows and edit it.

I just uploaded a revision including a blank row with the formulas in it.
 

Tracer Tong

Chimp
Mar 21, 2009
77
0
Do you mind going into a little detail about how you approached the math? Some of the formulas are really obvious, but the ones involving actual geometrical stuff(I seem to remember seeing radians and tangents and stuff) are a little cloudy to me.

Just a thought.
 

djjohnr

Turbo Monkey
Apr 21, 2002
3,107
1,799
Northern California
To figure out the standing reach you first need to figure out the front to bar. To do that, imagine a right triangle with angles A, B and C. Angle A is at the stem, angle B is directly below it along the wheelbase (this is the 90 degree angle), and angle C is the head tube angle at the front hub. You can use this data to figure out the rest of the triangle's dimensions. Specifically you want to find length BC. The question is what length to use for the equation. You could use the axle to crown of the fork plus the head tube length as the hypotenuse (length AC). However the combo of head tube angle and differing head tube lengths would mean comparing bikes at their minimum stack height, which wouldn't be very even for comparison. It would be easier to use a constant bar height for comparison purposes, so I use length AB (floor to bar minus static BB height). The equation is Length BC = TAN(angle A) x Length AB. If you want to know why to use tangent instead of sine or cosine read this - http://homepages.cambrianc.on.ca/tutorial/thetutorialcentre/mathscience/math/trig.htm. Angle A will always be 90-angle C (3 angles in a triangle always add to 180). Now that you've solved the bar to front distance you can subtract it and the chainstay length from the wheelbase to figure out standing reach.
 
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W4S

Turbo Monkey
Mar 2, 2004
1,282
23
Back in Hell A, b1thces
really cool tool! thanks for making this spreadsheet, it makes it really easy to analyze the bikes characteristics. What would be also cool is to see notes on why designers choose those Geo's, too, what was the thinking behind a 68.5 head angle tied to a 13.5 BB with short CS, reach, wheel base, etc on a 6" shredder? some kinda weird numbers all over the place but still no straight on mini-DH numbers, imo. any way to include frame weights, too?
 

Bicyclist

Turbo Monkey
Apr 4, 2004
10,152
2
SB
If you could make an online portion that would be perfect. Input values, or look at other bikes. You could even have a "bank" of select bikes you want to look at at one time.