Before you start in on this, I want to make a couple of things clear. Firstly, none of this is the result of any formal education in engineering, it's just information that I've put together from wondering why we do what we do. Secondly, I'm not writing this to provide you with any easy answer. It's just intended to clear up some of the mysteries and help you to make a better informed decision of your own.

So, you're going to build or modify a frame, you know what style you want and you've rounded up the tools. But what size tube do you get? Well if you're modifying a frame the OD (outside diameter) is dictated by the existing rails. It's all going to look a lot happier if the rails are the same OD all the way along, rather than having bulges where the new bits meet the old. If you're scratch building a frame then the "look" you're trying to achieve is going to have some influence on your choice though the size and weight of the finished bike are important factors too.

This is my CB 750 chop. It dates from about 1980 and was built by Uncle Bunt's Chop Shop. this was John Reed's old business when he was building bikes in England and when I have a minute to spare (and a K series CB motor to hand) I'm planning on "restoring" it. But it's an old school chop with a fairly serious rake and reasonably high headstock. But the frame is built from 1" OD tube.

That's what gives it the spindly look that makes it so obviously an old school chop. If you look at the front down tubes they are pretty long, and it's not hard to see that if you had a piece of 1" OD tube that long in your hands you could probably flex it a little.

Fig. 1

That's not a good thing for a motor cycle frame. Which is why you can see that the gussetting around the headstock is very deep, and it also has a tube brace that is quite low on the down tubes. Both of these are there to reduce the unsupported length of the down tubes as well as to brace the headstock area. The other thing about this frame is that it is built of 1/8" wall tube, that and the care that was taken with the gussetts and the bracing are all due to the fact that this is a frame with long runs of tube of relatively small OD.

Fig. 2

The frame in Fig. 2 is one I built. This is more of a Euro chop than an old school job, and it has 1 ¼" OD down tubes and rails with the actual length of the down tubes being something like two third of the length of the Honda ones in Fig. 1

Simply the fact that they are shorter is going to make them stiffer, but because they are also fatter then the stiffness is increased again. A look at the bracing round the headstock will tell you that there is a lot less of it than there is on the Honda simply because it doesn't need it.

The wall thickness is also less at 2.5mm as opposed to 3.2mm. So how can I tell that the tube is stiffer if it's thinner?

Well there's a formula that will give you the moment of inertia (basically bending stiffness) of any given size of tube. What that means is that as long as you're comparing like for like (i.e. 1020 Dom against 1020 DOM and not 1020 DOM against schedule 40 water pipe!) you get a comparison of how stiff the different tube sizes are.

And what is this magic formula? Well it's ((π/64) x (D⁴-d⁴)) of course. Where D is the OD, d is the ID and π is a well known number from Greece. Now I personally took ages to remember that, which really annoyed me as I can run it through without a calculator, and if I wasn't lining the pockets of a brewer the night before I've even been known to do it in my head. So, on one of my more together days I wrote this...

Just enter the OD and the wall thickness for a tube and it will turn out some numbers to let you do some comparisons. There are a few things though, first off it works in decimal inches, so it understands 1.5 but not 1 1/2" OK? Secondly, it makes you write the numbers down before you can actually do a comparison. Well tough, you ain't paid for it, you ought to expect a little work.

So what are we comparing? Well the moment of inertia figure will tell you the difference in deflection (bending!) for a given load from one size of tube to the other. The weight in pounds per foot is going to let you compare the weight of similar structures. That just leaves the cross sectional area.

You ever hear figures being bandied around like "Yeah its got a strength of 45,000 PSI"? that's the tensile strength of a material, and the PSI doesn't refer to a pressure. it refers to the amount of pull a piece of that material can stand in Pounds per Square Inch of cross sectional area. So you multiply the cross section figure off the calculator by the tensile strength of your chosen material and that's how hard you have to pull it to break it!

Word of caution here. Go too thin in the wall and stuff like stones being chucked up off the road, or Bob accidentally hitting the frame with a hammer WILL dent the tubes. If you don't think that's a problem get four empty, undented, beer cans and a square of ply about 12" by 12" and thick enough to take your weight. Place the cans in a square on a level floor, place the ply on top of them so it's supported at each corner, and place a helmet on your head and fasten it up. Now, carefully stand on the ply. Takes your weight no problem huh? Now get Bob to poke one of the cans with a pen or screw driver. See why I said put a helmet on?

Punch the mumbers for 1" OD .120" wall tube, and 1.25" OD .097" wall tube in to the calculator and compare the weight per foot, cross sectional area, and moment of inertia. Interesting huh? These are the sizes of tube used for the rails on the bikes in Figs 1 & 2. Here's another interesting fact, if you double the length of a tube it will bend eight times as far under a given load. That is the deflection of one end will be EIGHT times greater than a piece of tube half the length if you clamp one end in a vise and hang a weight off the free end.

See how long tube runs in a frame might cause a problem? And choppers typically have long runs of tube. Part of my personal fondness for tube braces on the headstock stems from the fact that by running the brace halfway along the top tube I'm making it eight times stiffer than it would be if it were unsupported.