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  1. #1
    Senior Member dauphin's Avatar
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    How do I figure out the geometry of a frame?

    I have a roughly 74 Schwinn Superior and a 79 Centurion LeMans...both of which I would like to determine their geometry. What measurements should I take besides the seat tube to come with each bike's geometry?








  2. #2
    Decrepit Member Scooper's Avatar
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    It takes a little work, but here's how I do it. It involves removing the wheels, pedals, and handlebars, and placing the frame on a sheet of butcher paper with wooden wedges between the frame and the paper as spacers so that the plane of the frame is the same as the plane of the paper.

    The only tools needed are a Sharpie marker, a yardstick with an accurate straightedge, the wooden wedge spacers, and an inexpensive ($10 - $20) 10" - 15" goniometer.

    1. Remove wheels, pedals, seatpost, and handlebar stem from frame, and lay frame on a sheet of butcher paper. Use wedge shaped wooden blocks to raise the frame above the paper so that the frame and paper are in the same plane.

    2. Ensure front fork is aligned fore-and-aft with frame.

    3. Mark centers of fork dropouts and rear dropouts on the paper, and draw a line connecting the two dropout centers using a straightedge. This is the wheelbase.

    4. Mark the center of the crank (center of bottom bracket shell) on the paper.

    5. Carefully mark the intersections of the centerlines of the top tube/head tube, down tube/head tube, top tube/seat tube, seatstay/seat tube, seatstay/rear dropout, chainstay/rear dropout, chainstay/bottom bracket shell center, seat tube/bottom bracket shell center, and down tube/bottom bracket shell center.

    6. The head tube centerline is more difficult to determine than other centerlines because it is so short. It may be helpful to turn the fork 90° to the frame, then find and mark on the paper the midpoint between the fork blades to extend the head tube centerline down to the wheelbase line.

    7. Using a straightedge, draw lines through the intersection marks for each tube. The dimensions between intersections are the center-to-center measurements of the tube lengths.

    8. Use a goniometer to accurately measure frame angles (small dime store protractors aren’t accurate enough to get precise angles).

    - Stan

  3. #3
    Senior Member Road Fan's Avatar
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    How you do it is based on what you need to know. If you want high precision such as to gain strong insight into frame design, I think Stan's method is excellent. I think I'd enhance it with a technique for actually finding the tube centers and transferring them to the paper.

    If you are just looking to start to gain general insight, and aren't planning a bike teardown at least to this degree, you can learn a lot by measuring directly on the frame and bike. Numbers that I find useful:

    Seat tube length center-center
    Top tube length center-center
    Chainstay length: bb center to the point where the chainstay and seat stay centers intersect, or to your hub center
    Wheelbase
    Front-center: bbcenter to front hub center with the front wheel straight-ahead
    Wheel radius: loaded is best but unloaded is ok
    BB height: same loading convention as for wheel radius; by subtracting this from wheel radius you can get BB drop
    Standover height
    seat lug setback; need a plumb line to find the BB center
    seat tube angle; may be measured or calculated from seat tube length and seat lug setback
    head tube length

    Now the hard stuff:

    head tube angle: need an angle finder of some sort; it's mainly hard because it's not always easy to find a surface to lay the angle finder on, plus this number needs such accuracy that you really need to calibrate your angle finder against some standard, like a good quality carpenter's level, like a Fat Max Extreme.

    Fork offset: I use a good long straightedge like a heavy yardstick or metal yardstick, and line it up on the top of the stem center and the center of the fork crown. A helper (my wife or a bike bud, not my cat) holds the straightedge still while I measure the offset with a small finely graduated scale. Combined with the wheel radius (for this, loaded radius is better), you can calculate trail.

    It's still rather involved, but less time consuming and less precise than Stan's method.

    Other useful measurements, mainly for fitting assessment:

    Handlebar top height above ground
    Saddle center height above ground
    Distance from widest point of saddle to most-used handlebar contact points
    Saddle widest-point setback

    Sorry for the long post, but it's not really a simple subject.

    Road Fan

  4. #4
    slow as I ever was Ex Pres's Avatar
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    I like the little calibrated levels/ angle finders, I'm sure they have a better name. Stand the bike straight up and put the level on the seat tube, top tube, and head tube. Easy to subtract from each other to get the main frame angles.

    You should measure measure the bottom bracket height, top tube length, and chainstay (actual and virtual) length. Also the wheelbase, and with all these measurements you could probably calculate the fork rake.

    Won't be as accurate as Stan's method above, but quick and easy.

    edit: for fork rake, I've also used the method Road Fan uses.
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  5. #5
    Senior Member Road Fan's Avatar
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    For a more accurate measurement of fork rake, I like to remove the fork and do kind of a home machinist thing. I clamp a bare front hub into the fork (a spare vintage Super Record of course!) and set it down on a level section of my kitchen counter. The Fat Max level (low cost, high accuracy) tells me what's actually level. I use books, tools, pads of paper or whatever to shim under the steer tube until it is level. With a digital or dial caliper (correctly zeroed) I measure the hub flange diameter, the distance from the bottom of the steer tube to the countertop, and the distance from the top of the steer tube to the countertop.

    The difference between the bottom distance and the top distance is the height of the steer tube center above the countertop. The hub radius divided by two is the height of the hub center above the countertop.

    The difference between the hub center height and the height of the steer tube center is ,,,, the fork offset!

    If you've done everything carefully and read the level and caliper correctly, the accuracy of the answer should be within a 10th of a millimeter or 5/1000 of an inch. Pretty good for a kitchen counter!

  6. #6
    Decrepit Member Scooper's Avatar
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    I am able to accurately find the centerline of each tube by using dividers and a compass. I spread the dividers over the tube on one end and mark the point where each side contacts the paper. Do this near each end of each tube. Then remove the frame, and using the divider contact points on the paper as locus, use the compass to find the centerline.

    - Stan

  7. #7
    Senior Member Road Fan's Avatar
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    I like it, very Euclidean! I was thinking of using a right-angle object such as a carpenter's square (the L-shaped thingie) to drop a line from the edge of the frame tube to the paper.

    Lends a new meaning to frame construction.

  8. #8
    Disraeli Gears Charles Wahl's Avatar
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    I'm sorry, but I'm not going to be measuring anything that requires using a goniometer. Who knows where that's been?

    It's better just to get pictures of several thousand bikes and stare at them for a long time. Then all measurements can be made by visual inspection.

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    Quote Originally Posted by Charles Wahl View Post
    I'm sorry, but I'm not going to be measuring anything that requires using a goniometer. Who knows where that's been?

    It's better just to get pictures of several thousand bikes and stare at them for a long time. Then all measurements can be made by visual inspection.
    Yeah I was thinking that. I thought maybe you used one of those to measure your gon...well, never mind

    But seriously this is a very informative thread. I have a completely bare frame sitting over in the corner so I should do that just to satisfy my curiosity.
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  10. #10
    Senior Member Road Fan's Avatar
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    Quote Originally Posted by Charles Wahl View Post
    I'm sorry, but I'm not going to be measuring anything that requires using a goniometer. Who knows where that's been?

    It's better just to get pictures of several thousand bikes and stare at them for a long time. Then all measurements can be made by visual inspection.
    What's the mantra that goes with that?

  11. #11
    Senior Member Road Fan's Avatar
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    Quote Originally Posted by Chuckk View Post
    Back to quick and dirty comparisons. Measurement is pretty well covered above. I always look at the BB clearance to ground, though the proper measurement is BB drop between the axles.
    I found a real quick and dirty gravity angle measure from Harbor Freight is handy:

    Just set the bike on an known level tile floor.

    Start lining up enough bikes side by side centered on the BB and say, "Wow, look at that!" Quick way to learn a lot.
    Ohh yeah, it is amazing to look at that!

    That tool is the sort of thing I meant by an "angle finder," though decent digital ones are getting cheaper all the time.

    If you use an Iphone, some of the downloadable applications are digital levels with digital angle finder functions. It's nearly free if you already have the phone.

  12. #12
    cs1
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    Quote Originally Posted by dauphin View Post
    I have a roughly 74 Schwinn Superior and a 79 Centurion LeMans...both of which I would like to determine their geometry.
    If you don't mind me asking, why do you need their geometry? It won't affect the way they perform becuase you can't change what the mfg built.
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  13. #13
    Senior Member miamijim's Avatar
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    I take pictures, print them out, draw the appropriate lines and measure the angles with a protractor.

    I also have 2 digital angle meters, the first I picked at Harbor Freight and the second is a carpenters app for my iphone.
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  14. #14
    Bicycle Adventurer banjo_mole's Avatar
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    Best yet, find old spec papers and manuals and booklets and find the geometry in those.

  15. #15
    Senior Member dauphin's Avatar
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    Quote Originally Posted by cs1 View Post
    If you don't mind me asking, why do you need their geometry? It won't affect the way they perform becuase you can't change what the mfg built.
    just for my own information. I suspect the Centurion to be too small for me and the Schwinn to be a bit too big. I believe the Centurion is probably a 53cm and I usually ride a 56 or 57.

  16. #16
    Decrepit Member Scooper's Avatar
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    I think having knowledge of the geometry of bikes you ride (seat tube angle, headtube angle, fork rake, trail, top tube length, BB drop, wheelbase and chainstay length, etc.) and how you think the bikes fit your body and riding style are a big help when looking at new bike purchases. You get a good sense of what works for you and what doesn't, and can use that information to narrow your search.
    - Stan

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    Senior Member RobbieTunes's Avatar
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    Quote Originally Posted by Scooper View Post
    I think having knowledge of the geometry of bikes you ride (seat tube angle, headtube angle, fork rake, trail, top tube length, BB drop, wheelbase and chainstay length, etc.) and how you think the bikes fit your body and riding style are a big help when looking at new bike purchases. You get a good sense of what works for you and what doesn't, and can use that information to narrow your search.
    Dead on. Saves you time and money. You go to that swap meet, see a birdy you want, and knowing what fits and what doesn't, with a few simplel measurements, is a big help for avoiding frustration and headache.

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    Quote Originally Posted by Scooper View Post
    I think having knowledge of the geometry of bikes you ride (seat tube angle, headtube angle, fork rake, trail, top tube length, BB drop, wheelbase and chainstay length, etc.) and how you think the bikes fit your body and riding style are a big help when looking at new bike purchases. You get a good sense of what works for you and what doesn't, and can use that information to narrow your search.
    The above is correct, I do laugh though at Classic Rendezvous mailing list members who provide dimensions and when they are inserted into a CAD program, it is plain to see that their bike does not exist in THIS three dimensional world. They get very defensive when called on it, including a magazine editor, but when pressed they do admit to rounding off. If the purpose of measuring is to infer how a bike responds when ridden, there is the truth, an there is opinion, but sometimes the truth is not tidy.

    So, be aware of the methods you use and where the errors might be, and of information furnished to you.

  19. #19
    Senior Member Road Fan's Avatar
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    very true, all three of you!

    To gain insight by comparing different frames you come across, I think it's enough to collect measurements by a repeatible method and to calibrate your eye. If you need to have an idea of how to identify an ideal frame, you do need accurate info. One think I always look for in a "new" frame is whether the geometry approaches what I think I want.

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    As an alternative to fancy angle measurement tools, here's a low-tech and ultra low cost method. Just get out your old high school protractor and some boxboard, to make templates. Draw angles from 72 to 74 degrees for the seat tubes and cut them out. Mark the angles on them first. Notch or cut off the pointed end, so they don't contact the lugs. Simply place the templates on the inside of the frame, against the tubes, until you find the one that fits and that's your seat tube angle. Make similar templates for the head tube angle. It's cheaper, quicker and more accurate than a gongiometer or angle level.

  21. #21
    Decrepit Member Scooper's Avatar
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    Quote Originally Posted by T-Mar View Post
    As an alternative to fancy angle measurement tools, here's a low-tech and ultra low cost method. Just get out your old high school protractor and some boxboard, to make templates. Draw angles from 72 to 74 degrees for the seat tubes and cut them out. Mark the angles on them first. Notch or cut off the pointed end, so they don't contact the lugs. Simply place the templates on the inside of the frame, against the tubes, until you find the one that fits and that's your seat tube angle. Make similar templates for the head tube angle. It's cheaper, quicker and more accurate than a gongiometer or angle level.
    While this might be simpler, I question that it's more accurate. The distance between the locus and the angular calibration marks on a high school protractor is 3 inches. While the distance between the locus and the angular calibration marks on a goniometer is the same, the goniometer has 12 inch long "legs" that can be precisely positioned over the tube centerlines. This makes the angular reading using the goniometer much more accurate than the reading using a three inch protractor.
    - Stan

  22. #22
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    Quote Originally Posted by Scooper View Post
    While this might be simpler, I question that it's more accurate. The distance between the locus and the angular calibration marks on a high school protractor is 3 inches. While the distance between the locus and the angular calibration marks on a goniometer is the same, the goniometer has 12 inch long "legs" that can be precisely positioned over the tube centerlines. This makes the angular reading using the goniometer much more accurate than the reading using a three inch protractor.

    What you say about protractors is true, however I believe the disadavantages of a goniometer are greater.

    Using a template, you can make the sides as long as want, after you have marked the angle using the protactor. The resulting template angle is as accurate as the goniometer.

    With a template the angle is fixed, while a goniometer's is variable. It can change while you're trying to hold it in place to establish the locus and end points.

    With a template, it easier to hold firmly in place against a tube than a goniometer, which is sitting on the surface of a round tube and is easily shifted.

    With a gongiometer, you are estimating the centers of the tubes and their intersection. It's far from precise. You have three possibilites for error in positioning. A template is sitting firmly against a fixed surface and has no errors in postioning.

    In summary, a goniometer has three possible errors during positioning and it can easily and inadvertently shift, in both position and angle, during the measuring process. A template eliminates all these possibilities.

    Of course, if you want, you can combine the two. Use the goniometer to mark the angle on the boxboard for your template.

  23. #23
    Decrepit Member Scooper's Avatar
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    Quote Originally Posted by T-Mar View Post
    What you say about protractors is true, however I believe the disadavantages of a goniometer are greater.

    Using a template, you can make the sides as long as want, after you have marked the angle using the protactor. The resulting template angle is as accurate as the goniometer.

    With a template the angle is fixed, while a goniometer's is variable. It can change while you're trying to hold it in place to establish the locus and end points.

    With a template, it easier to hold firmly in place against a tube than a goniometer, which is sitting on the surface of a round tube and is easily shifted.

    With a gongiometer, you are estimating the centers of the tubes and their intersection. It's far from precise. You have three possibilites for error in positioning. A template is sitting firmly against a fixed surface and has no errors in postioning.

    In summary, a goniometer has three possible errors during positioning and it can easily and inadvertently shift, in both position and angle, during the measuring process. A template eliminates all these possibilities.

    Of course, if you want, you can combine the two. Use the goniometer to mark the angle on the boxboard for your template.
    OK. I think we're talking apples and oranges. You're talking about measuring the angle of the frame tubes themselves, while I was talking about first transferring the frame tube cenerlines to paper as I described earlier, then measuring the angles on flat paper.

    Sorry for the confusion.
    - Stan

  24. #24
    Senior Member Road Fan's Avatar
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    Quote Originally Posted by T-Mar View Post
    What you say about protractors is true, however I believe the disadavantages of a goniometer are greater.

    Using a template, you can make the sides as long as want, after you have marked the angle using the protactor. The resulting template angle is as accurate as the goniometer.

    With a template the angle is fixed, while a goniometer's is variable. It can change while you're trying to hold it in place to establish the locus and end points.

    With a template, it easier to hold firmly in place against a tube than a goniometer, which is sitting on the surface of a round tube and is easily shifted.

    With a gongiometer, you are estimating the centers of the tubes and their intersection. It's far from precise. You have three possibilites for error in positioning. A template is sitting firmly against a fixed surface and has no errors in postioning.

    In summary, a goniometer has three possible errors during positioning and it can easily and inadvertently shift, in both position and angle, during the measuring process. A template eliminates all these possibilities.

    Of course, if you want, you can combine the two. Use the goniometer to mark the angle on the boxboard for your template.
    If I wanted a high-accuracy frame model, I think I'd go with Scooper's method, rather than measure the frame directly. I don't dispute one can construct accurate templates, at least as accurate as can be had with the protractor. I do understand there are large ones available. But, matching an angle template to the tubes can work very well where the seat and top tubes meet, because there is a lot of free tube length available to contact the template, after the template corner is relieved to clear the lug points. The same or similar templates can't be used to measure head tube to top tube angle, because of the short length of the head tube. This problem is even worse on small frames.

    How do you measure fractional angles, or the angular values you did not make templates for? I could envision making a set of templates in 0.1 degree increments, but sheesh. They better have more dimensional stability than boxboard, because once I got them right, I would never want to do that again.

    Then there's straightness of the tubes. In using my various bubble levels on existing C&V frames, I've seen that both seat and top tubes can have a detectable bow. As you move a sensitive indicator, such as a digital angle finder with 0.1 degree resolution, along the tube the reading can change a bit. Same for a Fat Max Extreme bubble level, while trying to level the bike. This says that measuring accurately using a real tube is difficult.

    Scooper's method sidesteps these issues. He detects the center of the END of each tube using a geometric construction technique, which I believe can be very accurate, especially if the frame is level. He draws a line to connect these points only, thus modeling the intent of the frame builder and not having to deal with the imperfections of real tubes. He measures the angle with a long-baseline instrument, which reduces error compared to low-cost instruments. I priced some goniometers a while back and found around $40 for better and bigger ones. One could also use a vernier or digital drafting machine to get a rather accurate number.

    As Repechage said in a recent posting, any such frame model or set of frame numbers could (should, if you need an accurate model) be validated by modeling the frame in a CAD program or perhaps a bike-specialized one. If the numbers model a mechanically plausible frame, they are more likely to be correct than if they don't.

    Road Fan

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    Quote Originally Posted by Scooper View Post
    OK. I think we're talking apples and oranges. You're talking about measuring the angle of the frame tubes themselves, while I was talking about first transferring the frame tube cenerlines to paper as I described earlier, then measuring the angles on flat paper.

    Sorry for the confusion.
    No, I'm the one who owes you an apology. Your post was perfectly clear, I just read it too quickly. It would certainly eliminate most of errors associated with trying to use a goniometer directly on a frame.

    Quote Originally Posted by Road fan View Post
    If I wanted a high-accuracy frame model, I think I'd go with Scooper's method, rather than measure the frame directly... The same or similar templates can't be used to measure head tube to top tube angle, because of the short length of the head tube. This problem is even worse on small frames....How do you measure fractional angles, or the angular values you did not make templates for? I could envision making a set of templates in 0.1 degree increments, but sheesh.... Then there's straightness of the tubes. In using my various bubble levels on existing C&V frames, I've seen that both seat and top tubes can have a detectable bow....
    I never stated angle templates to be the ultimate measurement, only that they could be accurate, low-tech and low cost. Certainly, they have their place, if you do not have the time to do a teardown, just to measure the geometry. They're also portable and don't require the bicycle to be a level surface. They're prefect when inspecting a prospective purchase, particularly when it's a frameset or a bicycle that may require some work before being rideable.

    Granted, templates do have restrctions measuring head angles on bicycles with short tubes. You can't get around that one.

    I don't consider fractional angles to be an an issue. I've never seen a frame where it was designed in increments smaller than 1/2 degree. Using a protractor or goniometer, it's practical to make templates in these increments. Any deviation from this on actual frame is manufacturing variation and something which very few people, if any, could detect during a ride.

    I'm also not concerned about bows in tubes, as you'll just as likely have as much bow in the straight edge used to create full scale drawings. Certainly, any floor and blockings used to lay out a frame will have detectable bow, warp and twist. The only way to be truly accurate, is to secure the frame to gauge blocks on a surface plate.

    In the end, use any method you want. I was just trying to make the members aware of an alternative that may suit their needs, time and expense.
    Last edited by T-Mar; 03-23-09 at 01:00 PM.

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