# Bicycle Mechanics - Head Tube Angle question

Bikeforums.net is a forum about nothing but bikes. Our community can help you find information about hard-to-find and localized information like bicycle tours, specialties like where in your area to have your recumbent bike serviced, or what are the best bicycle tires and seats for the activities you use your bike for.

View Full Version : Head Tube Angle question

DOS
11-11-10, 09:19 AM
I understand that as far as reach is concerned a 1 degree difference in seat tube angle equals approximately 1 CM in ST length (that is a 57 CM ST at 73 degrees = 58 CM at 74 degrees more or less). Does that math hold ture for head tube angle wher two bikes have same ST angle but different ST lengths and HT angles?

FBinNY
11-11-10, 09:34 AM
Only if the head tube is in the e57cm range, so realistically no.

The horizontal deflection from vertical of the end of an angled tube is equal to the cosine of the angle times the length of the tube. Here's a link to a cosine table (http://www.grc.nasa.gov/WWW/K-12/airplane/tablcos.html). Calculate the the difference between the ends of two tubes by multiplying their length by the difference in their respective cosines.

Also calculating where head tubes may end up as angles change is a bit more complex than with seat tubes, because you need to know which other dimension is kept constant, ie. the headtube/downtibe joint, the front axle, or the HT/top tube lug.

BTW- if the position of the front axle with respect to the bottom bracket is kept constant, then since they're at similar heights, your original assumption would work out, but it isn't anything to count on without checking.

DOS
11-11-10, 09:39 AM
Only if the head tube is in the e57cm range, so realistically no. The horizontal deflection from vertical of an angled tube is equal to the sine of the angle times the length of the tube

I knew I should have paid attention in Trig class.

FBinNY
11-11-10, 09:46 AM
I knew I should have paid attention in Trig class.

Me too I typed faster than I thought, but went back and corrected the prior post. Don't call it Trig and it'll be easier, Draw yourself a quick sketch, do the simple math (the guy who made the cosine chart did all the hard work for you), and you'll quickly know where you stand (or sit).

Sample seat tube distance behind BB line calculation for 74/57cm vs 73/58cm degrees.

57cm x .2756 (cosine 74) = 15.71cm
58cm x .2924 (cosine 73) = 16.96cm

11-11-10, 09:56 AM
DOS, Hopefully I understood your post correctly... If there's an official answer it is 'sometimes'. It'll depend on the top tube length, which I think of as the critical frame measurement. Using my 56 cm '89 crit Cannondale as an example the 1.25 deg. steeper HT angle required a longer TT than a same sized non crit road frame. It could have also been achieved by using the same TT, but shortening the DT, which would've kept the reach the same for the two frames. When I wanted a newer frame to build I found the 58 cm 2.8 frame had nearly the same TT length as the '89, within 1/2 cm. A difference in ST angle will have the same 'maybe' effect.

The reason I researched the 2.8 is that I read the same, or nearly the same info as you. I think the info is valid, but again it depends where the steeper HT or ST angle was accomodated.

DOS
11-11-10, 11:04 AM
This is why I have never bought a frame online, "ride the bike" is best answer to any question about how something will fit. But I am exploring online purchasing. Here are some real numbers.

Frame A (Current ride):57.5cm TT with 73.5 HT angle and 73 degree ST angle. ST is 58

Frame B (potential online purchase): 58.1cm ST with 71.7 HT angle and 72.7 ST angle. ST is unknown but claimed frame size is 59 so perhaps ST is 59 (cant really assume that however)

Lets just say for sake of simplicity that the .3 degree difference in ST angle is unimportant and all other things are equal (which they are not but both do have 17.5cm HT). Using FBINY formulas

Frame A: 57.5 x .2840 = 16.33CM
Frame B: 58.1x .3134 = 18.2CM

What have I just learned about reach on each bike ( if anything)?

I am concluding that Frame B, with same 110mm Stem I have on Frame A, will have me more upright than Frame A (which is what I am looking for since this will be used for commuting vice the hammering I do on the other bike on weekend rides).

DaveSSS
11-11-10, 11:23 AM
Your comparison is not accurate. You put in the wrong angle for frame B. When comparing the two frames, the suggested method is still wrong, even if you had used the correct STA. To make this comparison properly, requires more complicated calcs to bring one of the frames to the same vertical height as the other.

To make the comparison more accurately, all you need to do is consider the TT length of frame B to be 58.1mm minus 3mm for the 72.7 degree STA, or 57.8mm. The slightly more slack angle decreases the frame reach.

The botton line is that the actual frame reach is only about 3mm longer on frame B, ignoring the HTA difference. If you figure in the difference in reach due to the HTA, the two frames will fit almost identically, once the saddle is placed in the same position, relative to the BB. The difference in reach due to the change in HTA is only 1-2mm per degree, but since you've got a large 2 degree difference, it's actually significant.

What I would also compare is the head tube lengths, with the headset. That tells you the true difference in vertical size, assuming that both frames are of the same type, like road bikes. If one is a road bike and the other a cross bike with an entirely different fork length, then this is not a proper comparison. The ST dimension on both frames may not be measured the same (c-c versus c-t).

HillRider
11-11-10, 11:32 AM
....(the guy who made the cosine chart did all the hard work for you),.....
You really don't need that guy any more. Any \$10 "scientific" calculator has all of the trig functions and their inverses available at the push of a button.

11-11-10, 11:41 AM
DOS, A lot harder for you to compare than what I went through. I'll be interested in what the gurus write about this.

DOS
11-11-10, 11:50 AM
Your comparison is not accurate. You put in the wrong angle for frame B.

I did? I got .3134 as cosine for HTA of 71.7 (I mistyped anlges in post as 71.5, it actually 71.7). But your way, add 3mm for slacker ST angle, the take away approx 3mm for 2 degrees of HTA, is way simpler. So thanks.

San Rensho
11-11-10, 11:59 AM
Don't worry too much about reach being determined by the HT or ST angle, reach is easily set and ajusted by the seat set back and stem legnth. The angle of the frame determines how the bike handles. Decide what handling you want then dial in reach with set back and stem legnth.

DOS
11-11-10, 12:47 PM
Don't worry too much about reach being determined by the HT or ST angle, reach is easily set and ajusted by the seat set back and stem legnth. The angle of the frame determines how the bike handles. Decide what handling you want then dial in reach with set back and stem legnth.

Yeah, I am looking for a bit more comfy ride than I have with Frame A. In addition to HTA angle, Frame B has longer wheelbase and chain stays.

DaveSSS
11-11-10, 01:39 PM
I did? I got .3134 as cosine for HTA of 71.7 (I mistyped anlges in post as 71.5, it actually 71.7). But your way, add 3mm for slacker ST angle, the take away approx 3mm for 2 degrees of HTA, is way simpler. So thanks.

You would never multiply the cosine of the HTAs times the frame size. That makes no sense at all. To Figure the change in reach due to a difference in the HTA, you take the cosine of the HTAs and multiply by the distance from the TT/ST interesection point to the top of the stem. That length is very short in comparison to the frame size and that's why the HTA has little effect on fit.

When you mulitply the c-c frame size (not always the same as the ST length) times the cosine of the STA, all you've done is calculate the frame setback or the horizontal distance between a vertical line through the BB and the TT/ST intersection point.

What you really want to know, with regard to fit, is the frame reach, which is the distance from a vertical line through the BB center to the HT/TT intersection point. That value is the TT length minus the frame setback. Once again, you can't directly compare frames that are different in size.

Here's a link to some info from Cervelo, the orginators of the reach and stack concept. They use a different reference point - the top-center of the head tube. Even with this definition, you can't directly compare the reach of frames with a different stack height.

http://www.cervelo.com/en_us/bikes/2011/R3/geometry/

DaveSSS
11-11-10, 01:44 PM
Don't worry too much about reach being determined by the HT or ST angle, reach is easily set and ajusted by the seat set back and stem legnth. The angle of the frame determines how the bike handles. Decide what handling you want then dial in reach with set back and stem legnth.

Ignoring the effect of the STA can be quite significant. I've had frames with a 2 degree difference in the STA, so the one with the steeper STA could have nearly a 2cm shorter TT and still fit the same as the other.

Reach should be dialed in mostly with stem length and very little (5mm or less) with saddle setback.

DOS
11-11-10, 02:08 PM
You would never multiply the cosine of the HTAs times the frame size. That makes no sense at all. To Figure the change in reach due to a difference in the HTA, you take the cosine of the HTAs and multiply by the distance from the TT/ST interesection point to the top of the stem. That length is very short in comparison to the frame size and that's why the HTA has little effect on fit.

When you mulitply the c-c frame size (not always the same as the ST length) times the cosine of the STA, all you've done is calculate the frame setback or the horizontal distance between a vertical line through the BB and the TT/ST intersection point.

What you really want to know, with regard to fit, is the frame reach, which is the distance from a vertical line through the BB center to the HT/TT intersection point. That value is the TT length minus the frame setback. Once again, you can't directly compare frames that are different in size.

Here's a link to some info from Cervelo, the orginators of the reach and stack concept. They use a different reference point - the top-center of the head tube. Even with this definition, you can't directly compare the reach of frames with a different stack height.

http://www.cervelo.com/en_us/bikes/2011/R3/geometry/

Type-o. I wrote 58.1 ST; meant that Frame B is 58.1 TT. Wouldn't distance from intersect of TT/ST to top of stem be pretty much equivelant to C-C TT measurement

I get what your saying about vertical line of BB. Generally when setting up a bike, first thing I do is measure from back of my saddle (aka where my ass would be) on a bike already fitting well to hoods of the handlebars (aka where my hands would be), then set up new bike with same reach. From there I correct with stem if I want to be more upright or if other differences change relative height of handlebars and saddle.

Edited to add: BAsed on DaveSSS's formular for calculating reach, it appears the two bikes have exactly the same reach. 40.7cm. I made some assumptions but I dont think they a big difference:

Setback of frame A seems to be 17.4. I arrived at this by assuming 59cm size imeans C-C ST measure of approx 58.5 because I dont know what the actual measure is so I estimated low. Cosine of 72.7 STA is .2974. 58.5x.2974=17.4

Setback of Frame B is 16.8 based on ST C-C of 57.5 (actual measure) and STA of 73. Cosine of 73 is .2924. 57.5x.2924=16.8

Frame A reach: 58.1-17.4=40.7
Frame B Reach: 57.5-16.8=40.7

DaveSSS
11-11-10, 02:28 PM
Your setup technique is sound, if the saddles are the same model and the saddle setback, relative to the BB is set first. Different saddle models leads to errors.

Trust my frame analysis, I'm a mechanical engineer and I've been doing this for a long time. There should be little difference in the fit if the TT/STAs are as posted - 57.5/73 and 58.1/72.7. The slack STA reduces the reach by about 3mm and the HTA angle difference reduces the reach about 3mm, so the net difference is about zero.