Math and Fit Question

[Dr. Doofus]

ok....Doof has a chance to pick up something good for dirt, dirt, dirt cheap, in addition to the Lobster project.

Here are the geos

Seat tube Top tube Seat angle Head angle

57 56.8 72.4 73.3
58 57.3 72.3 73.3
59 57.8 72.1 73.0


Doo'f 59 Giordana is identical to this 59. It is a little long in the f-c, and our bozoboy should probably be on a smaller frame (seat height 79cm, only a 120 stem on that 59).

the decrease in STA will require moving the saddle back on the rails
the increase in head angle with affect the reach, so,

question:

will the 57 or 58 allow I, Doof, to use a 120 or 130 stem and have the same setup (7cm saddle setback, height 79cm, 56 cm reach to bar center, 9cm of drop) as on the 59 Giordana?

al these numbers much confuse...cannot just snag one and build it up to see...Too Tall? Dave? Anyone?

[Fixed]

Bro Where is the Jerk? Good luck Doc. Cheers :beer:

[Dr. Doofus]

yeah

somebody needs to just yell at doof to shut up

that and bikes should not have weird tube lengths and angles

they should be like shirts: S, M, L, XL

wait

they do that

and it sucks

never mind


wait -- solved it


all three have the same "reach," as Cervelo calls it (TT minus frame setback).

hmmmm......

[chrisroph]

Seat of the pants calculations, use a 13 on the 57 (Merckx); 12.5 on the 58 (Pego) for roughly the same contact point fit as on your giordana. The merckx will be marginally longer (3mm or so) and the pego also (2mm or so). All stems are not created equal. The ritchey or cinelli even sizes are equal to some other's 1/2 sizes, like 3ttt. You could make 'em all fit and both will have shorter front centers than the goirdana.

[Louis]

I've done the easy part. The other stuff related to the stem and HTA is more complex.
This should be enough to get you going.

Drop a plumb line down to the BB.

Let L1 be the horizontal distance from the line to the ST-TT intersection. (going aft)
Let L2 be the horizontal distance from the line to the HT-TT intersection. (going fwd)

Let H be the vertical distance from the center of the TT to the center of the BB.

The frames line up as follows:

ST TT STA L1 L2 H
57 56.8 72.4 17.24 39.56 54.33
58 57.3 72.3 17.63 39.67 55.25
59 57.8 72.1 18.13 39.67 56.14

(The formating looks fine now, but looks buggered when I post it)

The math:

L1 = ST*cos(sta)
L2 = TT - L1
H = ST*sin(sta)

Louis

[Dave]

Louis, your calculations are correct, but don't make a valid comparison of the three frames. Your L2 dimension is the only one of importance. That is the "reach" of the frame. Reach is the TT length minus the frame setback. Setback is the c-c frame size (probablywhat Doofus is calling the seat tube) times the cosine of the STA.

A comparison of the reach of several frames is only accurate if the frames are all the same size. Your comparison suggests that all three frames have a reach (L2) that is within 1mm of the same. This is not really the case.

For example, the smallest frame has a setback (L1) of 17.24 as you correctly calculated, but this setback is not the being measured at the same vertical height as the other two frames. To make an accurate comparsion, one of the frames has to be selected as a "reference" size, and the dimensions of the other frames calculated from the same reference points.

If the 59cm frame is selected as the reference, then the setback of the 57cm frame is actually 59cm times cosine72.4, or 17.84cm, not 17.24. Fortunately, the difference in HTA of the frames is so small that it can be ignored (not always the case). The reach of the 57cm frame then becomes 56.8 - 17.84 = 38.96, which I would call just 39cm. This makes it about 7mm shorter in reach than the 59cm frame. A one size longer stem would probably be required.

Performing the same calculation for the 58cm frame yeilds a reach of 39.4cm, which is about 3mm less than the 59cm frame. This frame would use the same stem length as the 59cm frame.

What Doofus may not have considered is the head tube length, with the headset installed. Whether the smaller frames are a good choice may depend on the amount of steering tube spacer and stem angle that will be required to produce the desired bar height with the smaller frames.

[chrisroph]

Dave, that's what I said, but in English. ;)

[Louis]

Louis, your calculations are correct, but don't make a valid comparison of the three frames.

Dave, you comment seems a bit harsh to me ("not valid" etc.), considering that I put in a caveat that what I showed was the easy part, and just the beginning of the comparison. My post was not intended to be a complete comparison of the entire deal.

I was at work, and since Doof had not provided a charge number for the analysis :) I spent just a few seconds putting the simple equations in an Excel spreadsheet. For a full comparison, included a true apples-to-apples visualization, you'd need more info.

Louis

[Needs Help]

Dave, you comment seems a bit harsh to me
You're kidding, right?

[Dave]

Just pointing out that things get a bit more complicated when you try to compare the fit of different sized frames.

[Louis]

Just pointing out that things get a bit more complicated when you try to compare the fit of different sized frames.

I certainly agree with that.

Take care,
Louis

[Dr. Doofus]

makes


head


hurt


(those frames can sit...this is too hard)

[Dave]

Just read the conclusion. The smallest frame takes one size larger stem and the middle sized proabably needs the same size stem.

Any time you change frame sizes you need to consider the head tube length. That's a common mistake, getting the "perfect" TT length and a head tube that's 2cm too short.

If you're looking at frames that take a conventional threadless headset, then the HT lengths can be compared directly. If integrated headseta are involved, you have to know if the stack height is 5mm, or 15mm, compared to the 25-30mm height for a conventional.

[chrisroph]

Doof--Think of it this way. In your size, a .5 degree st variance equals a 5mm effective tt difference.

[Ozz]

Maybe you could send the question over to a math teacher at your school and see how the geometry class does at solving the problem? :beer: