Recumbent Bicycle Design by Charles Meredith Brown - November 2015
Bicycle Frame Design "If I have seen farther than others, it is because I have copied off the test papers of giants."
   
Sections:
The effect of tester bias
Idiosyncrasies in my own designs
Three of the author's best designs
Pedaling forces acting on the frame
The ground acts as a frame member!
Designing monotube frames
Asymmetric frames
 
3D Truss frames
Idler pulley
The effect of gear size
Frame materials
For more information
About the author
Also see: Steering and Ride, Air drag formula and Putting it all together


Here is how I originally got into bicycle design:  During my younger years, six of my friends died or were seriously, permanently crippled in automotive accidents.  Motorists kill over 40,000 Americans a year directly, another 30,000 through exhaust gasses.  If you add up the math, for every 30 people who drive, someone dies for it.  In addition to this you must consider the damage cars do to the planet, from getting raw materials to the pollution they cause, to turning the world from green to concrete.  It would be a better world for everyone if we had a less lethal way of getting around.  So mostly, I got into bicycles because of Paul Long, Denise Turmell, and other childhood friends that I can't talk to anymore.

So I’m a very loyal friend.  It didn’t hurt to discover that bicycles were FUN!  Because you are the engine, I don't think there is another vehicle you seem more at one with.  Since the early 1980’s I have constructed over 50 different recumbent bicycles in the search for bicycle nirvana, the ultimate ride.  This paper must be partially credited to my beloved late wife, Patricia “Blue” Keys, who put up with my nonstop experimentation for all of those years.  Listen close, my children, as I attempt to ladle my pearls of wisdom into your eagerly awaiting, outstretched hands...

This paper is primarily concerned with supine recumbent bicycles, where the rider is in a seated position.  A long wheelbase bike (LWB) has the front wheel in front of the pedals, a short wheelbase bike (SWB) has the front wheel behind.

The effect of tester bias

I started off making long wheelbase bikes and loved them.  Then I started thinking, short wheelbase bikes are more compact, almost 10% lighter in my experience, and have more weight on the front wheel for better cornering.  So SWB's became my norm for a while.  The first models pounded like the dickens, and the steering was so twitchy it seemed like one sneeze and you'd be moved to the next lane over.  I was making bike after bike to try and come up with one having a tolerable ride- wheelbases grew longer, the seat went down, and the front wheel got bigger.  I quickly got used to and soon came to prefer the steering.   After the LWB's, the steering seemed quick and positive like a good sports car.  The ride I never got so fond of, so after a decade or so it was back to the long bikes.  After all, they're only a foot and a half (40-50 cm) longer, and have a ride no SWB can match.  That gets important on a long trip.

After all that time on shorter bikes, turning a LWB seemed like trying to steer the Queen Mary.  You'd crank the steering 'way over and the scenery would very, very slowly start to turn sideways.  In a month I'd be used to the steering again and again come to prefer this more laid-back system.

It takes me about a month after switching from an upright to a recumbent before I am producing full power, and about the same amount of time when switching back.  Going from a high to a low bottom bracket, or vice versa, requires a similar adaptation period, as do slight changes in the seat to bottom bracket distance.

In other words, individual tester bias is suspect.  My preferences are probably different from yours.  It would be a pretty boring world if we were all the same.  What are you trying to build?  We all prioritize different things.  This whole article is just my opinion, and parts may not be correct for your purposes.  Listen, but think for yourself.   (Actually, such advice could apply to all of life!)

Idiosyncrasies in my own designs

Many recumbent builders allow lots of space between chain and frame, to avoid damaging the frame and rattling.  I use less clearance, but protect the frame by sticking hard plastic patches over vulnerable areas.  Black plastic looks better after a period of time.

I was unable to develop a front suspension that worked without absorbing some of the rider’s power.  This was tested by making the suspensions lockable (they could be disabled temporarily), then timing myself going uphill with suspension and without.  If anyone can do better, please let me know-  a bit of front suspension on a SWB would be wonderful.

To eliminate one variable in my testing, all bikes had tires 1” to 1-1/8” (25-28mm) wide, with inflation pressures around 100 psi (7 bar).  I think  SWB’s would, overall, be better bikes with wider tires.

About 2/3 of my test bikes had frames made of wood.  Don’t laugh, the material is easy to modify and pleasant to work with- this may have something to do with why I made so many. Eventually I could make wooden frames that were as light, strong, and stiff as those made from the finest steel.  (Gotta write an article on that someday.)

Shallow steering angles put a larger load on the fork and headset.  I've used forks that worked well at around 72 degrees steering angle, carrying 1/2 the weight.  I would bend them to greater rake and use them at around a 47 degree steering angle carrying only 1/3 the weight.  The forks then would be slightly more flexible than desired, making the steering less precise.  I've come to use 20" forks on 20" wheels for stiffness.

As another effect of how shallow steering angles put more stress on the fork, I once had the long steering tube on a fork snap in half, the front wheel was carrying only 1/3 of the 230 lb. (104 kg) (bike + rider) total. I use long head tubes on LWB bikes in order to get a reasonable lifespan out of headsets, and to make it easier to get handlebars to reach.

As a result of living in fairly flat areas, I don't need or use front derailleurs. Once while cycling in Dallas, the chain came off the chainring to the outside, fell down to the pedal, and all the excess chain flew into the back wheel, locking it up.  I would not be alive today if the bus driver immediately behind me had not been able to stop in time.  I now put chainguards on the crankset on all my bikes.  Gardner Martin once told me he put that extra idler assembly on the return chain of the Tour Easy for the same reason.

Three of the author's best designs

Well, I've been doing this for over 30 years now; you're bound to get something right sooner or later.  I'd be delighted if other people used them.   I'd like to be credited, but won't insist on it. They're included here as illustrations, when I refer to these later on, you can flip back to check on the designs.


Pedaling forces acting on the frame

Some people claim that recumbents can climb hills just as fast as upright bicycles.  In the case of most recumbents, where the drive train is long, this is simply not true.  Some of the energy the rider puts into the pedals goes into bending parts back and forth, rather than propelling the vehicle forward.  This bending energy becomes a little bit of heat, which is lost to the atmosphere.  This power loss can be reduced somewhat by smoother pedaling.   Throughout my personal R&D program, I’ve been measuring how far I can move the right pedal at my maximum effort with the back wheel locked.  (All bikes had a single, 52 tooth chainring.)  These measurements of the drive train’s flexibility agreed directly with my subjective opinion of how well the various bikes climbed hills.

Let’s say you’re going uphill, putting out about 1/2 horsepower (373 watts), which would mean pedal force peaking at about 50 pounds (222 newtons).  This drops to about 0 twice in each revolution, when your legs hit maximum and minimum extension.

Assuming a 170 mm crank and a 52 tooth chainwheel, the crankset increases the pull on the chain 62%.  Let’s round that off to a pull of 80 pounds (360 newtons) on the chain.  Flip to the diagram of Future a few pages back.   We’ll use this as example because it has a simple drive system (no idler), and because the chain passes so close to the seat, pedaling forces have about the least effect on the frame possible for a rear-drive supine.  There are 56 inches (142cm) between the bottom bracket and the rear axle.  My measurements on a piece of Sedisport chain show that this length of chain, under 80 lbs. (360 N) force, will stretch 0.04 inches (1 mm), twice every pedal revolution.

This does not seem like much, but if this could somehow be replaced by a length of non-stretchable chain, I think most of us, at least the harder-riding ones, would notice the difference.  If the side plates of the chain were given a slightly greater sectional area, though made heavier, the bike should climb and accelerate just the tiniest bit better.  Having a very short drive train, such as prones and front wheel drives, would be another way to solve this problem.

If you had a monotube frame, a frame shaped as a single, Y-shaped tube, and we could run the forces caused by  pedaling right down the center of it, the frame would compress by less than 0.01 inches (an itsy bitsy number of millimeters).

Alas, it does not work that way!  More on this later.

The ground acts as a frame member!

How the frame works is affected by where you put the wheels!  Many years ago I built a Future type vehicle with a slightly flexible monotube frame, which gave it a tiny bit of suspension.  As a long wheelbase bike, it was a very successful vehicle, but when I converted it to a SWB (reinforcing the main tube to compensate for  loss of material at the hole), suddenly I couldn't climb hills!  Felt like I was pedaling limp linguini!  What happened?

To find out, I built a test apparatus to apply pressure from the back of the seat to the pedal.  The back wheel was locked in place, and the frame was carefully measured with and without the pressure.  The dotted lines show how the frame bent.  The effect is much exaggerated in the diagram so you can see it, the actual bending was very small.

In long wheelbase form, the force bent the frame into a slight “S” shape.  When I put the fork and front wheel in the other headtube, converting it to a short wheelbase bike, the same force bent the frame over four times as much!  The bottom bracket bent ‘way down under pedal pressure.  Sideways movement was less than vertical, and was similar in both versions. 
 

 
I think a stiffer fork would make a bike climb better, as the bottom bracket would be better braced.  Would excess trail have the opposite effect?

Lesson learned:  If you're building a monotube frame for the slight, but noticeable, improvement in ride, a long wheelbase design works far better than a short. This gives only a little bit of suspension effect - too much flex in the frame takes a toll on power production.

Lesson learned:  designers of short WB bikes should pay particular attention to vertical forces acting on a frame- possibly considering a truss design. In situations where the vertical forces are high, but there is not enough space for a truss to work well, for example a lowracer, designers normally make the main tube a lot taller than it is wide.  This solution puts more of the strength and stiffness in the vertical direction, where it is needed, and saves weight on the sides.

Designing monotube frames

This is a recumbent frame consisting of a single tube, until it splits into a “Y” shape to hold the rear wheel.  There are a lot of reasons for building one- they are cheap and easy to build, they provide a little bit of passive suspension making the ride a little smoother, and they have excellent torsional stiffness for better steering.  The downside is that they can flex too much from pedaling forces, turning uphill climbs into drudgery and giving the bike a leaden feel.  Flex cannot be eliminated, but let’s learn to minimize it as much as we can.

We want to arrange the tubes so they can best take the load.  We want the loads running right down their length, where they can be handled very well.  We don’t want the loads bending the tubes, as they are far less stiff in that direction.

In the case mentioned previously of the bike heading uphill while the rider is putting out 0.5 horsepower, with the crank about straight up the chain will be experiencing 80 pounds of tensile pull, countered by the 50 pound of compressive force in the leg, and 30 pounds of compressive force provided by the frame.

Now in the engine there's a part called the "H point", where the femur connects to the pelvis.  A line straight from here to the pedal is where the leg's compressive force acts; even if you've lowered the seat as close as possible to the chain, there's still about 6" (15 cm) between the H point and the chain.  In order to counter this perfectly, the frame has to drop down quite a bit.  At the crank, the distance from the pedal to the chain, and that from the chain to the bottom bracket spindle, is here a 3:5 ratio.  The same ratio needs to be maintained, so with the H point 6" above the chain, the frame goes 10" (25 cm) below.
 


Hopefully you have noticed from the diagram how important it is for power production to have a rigid seat back.  Many makers of production recumbents don't seem to understand this.

I would advise against using aluminum for a long-wheelbase monotube frame. The fatigue life of the material is just scary in this application, though it is wonderful stuff to use in a truss frame.

Here is an alternate design, with a monotube front mated to a triangulated back end.  There is a major stress raiser where the two join, so you need lots of reinforcement here.  A telescoping connection here would allow adjustment for rider size, as well as allowing disassembly of the bike for transport.          
 


The second picture is an idea I haven't tried-  the idea is to use the flex of a monotube frame to provide a bit of suspension at the front of a SWB.  As the tubes are lined up better with the forces acting on the frame, they can be lighter and more flexible than the norm, and still be adequately stiff.
 

 
All this having been said, I must confess this whole thing is not quite right.  We have been using the example of the pedal being straight up, 90 degrees from the chain.  Try doing the math with the pedal a little before or after this point.  Eea ghads, the angle the tube wants to take gets steeper!  Shift to a smaller chainwheel, and the desired angle becomes less! 

In actually building and riding such bikes, I find monotubes with the tube angled like I describe climb hills and accelerate noticeably better than bikes where the tube is a straight shot from bottom bracket to back axle.  This angle is pretty close,  but we can't get it exactly right for all conditions.

If you're building your frame asymmetric to reduce side-to-side forces acting on the frame (see below),  as you’ve seen, the vertical forces on the frame are significantly higher than the lateral ones.  It would be best to make the main tube vertically oval, to increase strength where it is needed, and reduce weight where it is not.

Asymmetric frames

Let’s now look at the frame from the top view.  You want to keep the compressive strength of the frame as close as possible to the tensile force of the chain, so the frame bends as little as possible with each pedal stroke.  To accomplish this, just move the tubes over to the right.  I now make all my frames this way.
 


Even better would be if you could have the chainring in the middle of the tube, getting the chain as close as possible to the center.  Alas, where would you get the parts?

What would make even more sense would be to move both dropouts about 1 cm (0.4 in) to the right, and build the back wheel without dish.  Our chains are so long, this has only a negligible effect on chain angle.  In building and riding these, I find getting the rim a little past the center of the hub flanges makes the strongest drive wheel (reverse dish!).

If you can’t change the dish, since the drive side spokes carry about twice the stress, why not use stronger spokes here, and save weight with gossamer thin ones on the other side?    I have no idea  why this hasn’t become standard practice.

Even if you never build a monotube frame, I still wanted you to have a look at how the forces go before we get to other frames.  This insight helps you to design a frame no matter what you build.

Truss frames

These add triangles above and/or below the main tube to greatly stiffen it vertically. Short wheelbase bikes, as we have seen, put some serious stresses on the frame from pedaling, so a truss often works well here. Trusses like to spread out and make a tall frame in order to work their best.  If you're incorporating a head tube as part of the truss, try and make it a long one, say at least 8" (20 cm).  Low racers could really use the stiffness, but a truss generally won't fit!

This is a brilliant frame design, used on production bikes by Rans and Bacchetta:
 


This is a design of my own:
 


My bikes like this accelerated well, but had a rough ride.  Would be great with a front suspension!  The frame members shown in solid lines are mostly in tension, and could be cable or rod.  Notice how the idler pulley is solidly mounted at the intersection of three tubes!  We'll see why in a bit. 

3-D Truss frames

This is a three-dimensional truss structure. Stronger, stiffer, and lighter than a single tube. Perhaps it occurs to you that maybe this truss would be lighter if you replaced its tubes with more trusses...and the tubes of those trusses were replaced by still more trusses. The whole project explodes in complexity like some kind of 3-D Sierpinski gasket. Just the thing to ride around the perimeter of Koch island. (A little math humor there.) A marvel of efficiency, but if you could build such a frame, how would you attach anything to a structure that is almost an aero gel?
 


Here is a model of a 3-D truss frame modified for use as a recumbent frame (bottom bracket would be toward the right, the chain runs through the frame).  3-D truss frames work best when you give them some room, it's difficult to get them to work between the knees.  Note that I've used a different structural solution at the ends to transfer torsional loads to the frame.

Idler pulley

There's an easy way to work out how much force is acting on the idler pulley for the upper (tension) part of the chain.   Make a scale diagram of how the chain goes, and draw lines running  parallel to both straight parts of the chain, forming a parallelogram.   Drawing a line from the idler to the opposite corner will give you the amount of upward force acting on the idler (the forces are proportional to the length of the lines) and its direction (from the angle of the line).  Simple, but it works!

As an example, let's work out whether we want to put the idler in front of or behind the seat.  The seat, bottom bracket, and rear axle will be in the same position in both diagrams:
 


I have drawn the frames going uphill and putting 80 lbf on the chain.  You can see in these examples having the idler about midway along the chain cuts the force on the idler in half.  The less force on the idler, the less it moves, the less energy is lost, and the better the bike climbs. 

You will notice the force on the idler is considerable, you want it bolted to somewhere very solid on the frame.  You need to take idler placement seriously when you design the frame.  Look at my own designs, where the tubes are positioned with the idea of giving the idler a good, sturdy home.  Metal idlers would be preferred over plastic, as they flex less.  As would be apparent from the previous discussion of lateral forces on a frame, the chain should be as close to the frame as possible.  And of course, it would help hill climbing if the chain were bent at the least angle possible-  the ideal would be no idler at all.   All engineering is compromise.

The effect of gear size

In that example of a person climbing a hill at 1/2 horsepower, the rider was putting 80 pounds pull on the chain with each pedal stroke.  That was with a 52 tooth chainring and about a 24 tooth cog.  If the gears were instead twice the diameter, 104 and 48 teeth respectively, the rider, while still putting out the same power and same rpm, would waste half as much power stretching the chain.  The reaction force on the frame would be reduced as well, and the bike would be noticeably peppier accelerating and going up hills.  In upright bikes, there is currently a trend toward smaller, 'compact' cranksets to save weight.  This is not a good idea for our long drivetrains.

Frame materials

To get the stiffest, strongest, and lightest tubes, you want the wall thickness as thin as possible for the diameter.  Up to a point- get the walls too thin, and the tube will easily buckle, like an empty beer can.  As a rule of thumb, the limit for evenly loaded metal structures is a wall 1/50th the tube's outside diameter.  We put a few localized loads on when we clamp and bolt things on, so best to go a little thicker than this.  Thin walls may also be more difficult to weld or braze. 

Carbon fiber does not have the same strength in all directions, so its walls have to be a little thicker to avoid buckling.  High-zoot carbon bikes use a lot of thin, expensive layers so the walls can be thinner, though still not quite hitting that 1/50 of metals.

To compare the stiffness of tubes of the same material, raise the outside diameter to the fourth power, then subtract the inside diameter to the fourth power.  You can quickly see stiffness increases radically with diameter.  Compared to the outside, the material on the inside is pretty weak for its weight, which is why we make bicycles out of hollow tubes rather than solid rods.  To compare tubes of different materials, take that number and multiply it by the elastic modulus, "E" for that material.

Different materials have different characteristics, so they work best when made to different diameters and wall thicknesses. 

Titanium alloy:  of the materials listed here, this is the most similar to steel.  Increase the diameter and wall thickness to16% greater than you would for steel, and you have about the same strength, stiffness, and fatigue resistance as steel at about 76% of the weight, and it doesn't corrode.

Aluminum alloy:  with a diameter and wall thickness about 42% greater than steel, it weighs 71% as much.  It is also 40% stiffer and initially stronger, but it’s good to design it that way to help compensate for aluminum’s poorer fatigue life over time.  It ought to be heat treated after welding.  If you’re making a lot of frames, this is a fairly inexpensive way to make a quality frame.

Carbon fiber:  is in fashion right now.  Again, the fatigue life could be better.  Here is a gross oversimplification which will make any self-respecting engineer cringe:  For inexpensive carbon fiber arranged with equal strength in all directions, say a constantly repeating  0° /+ 45° /- 45° /90° layup in epoxy, figure an elastic modulus (E) of very roughly 55-60 GPa, a little less than aluminum.  I mention this only as a starting point, sources tend to list impressive numbers based on the strength of fibers in only one direction without the epoxy matrix, not as it would be used in a bike frame.   A tube thus laid up with an outside diameter 40% greater than steel and an 80% thicker wall would be about 34% stiffer and weigh 56% as much.  A beauty of the material is you can custom-place the fibers, putting the strength and stiffness precisely where you want it.

Here's one thing bicycle salespeople won't tell you: The expensive high-modulus carbon fiber they use in the lightest upright bikes, while stiffer, is actually weaker than the cheaper stuff.  For a monotube recumbent, strength is often more important than stiffness, so you might save your money here and have a better bike to boot.

Wood:  the best fatigue resistance of any material here, I’ve built recumbent frames weighing under 6 lb (2.7 kg).   My secret is to build the frame as a single large diameter, hollow tube, with the wall thinned out to under 1/2” (13mm).  The material is inexpensive, pleasant to work with, and easily modified.

Composite sandwich: The buckling issue you get when you try to lighten single-tube frames by thinning out the walls could be reduced by using a composite sandwich structure.  This would allow the tube diameter to be increased and the materials used reduced.  You still want the tube walls strong enough to withstand impacts, punctures and the like- I think for a practical tube weight reduction would be limited to 20% or so compared to a smaller tube without the core.
 

There are similarities in all these methods for reducing weight while maintaining bending stiffness with a given material, like trusses and the tube above:  They all depend on increasing the size, which is critical for their efficiency.  Notice also that as the weight is reduced, endwise compression stiffness is going down, so you are getting diminishing returns.

Next: Steering and ride roughness

For more information

"Bicycles and Tricycles" by Archibald Sharp, largely a discussion of early cycles, has a great deal of technical information of interest to the bicycle engineer.

 "Bicycling Science" by David Gordon Wilson, and in the first and second edition, Frank Whitt.  If you like this article you've got to get this book.

There are a lot of sources on mechanical engineering information in print and on the internet.  I sometimes go to the library and see what's there around the 620 section.

About the author

I am, of course, far too modest to mention my succession of victories in Michigan Human Powered Vehicle Association racing at the Waterford Rally.  I will let my comrades tell it for me:

"There was that time he entered the races equipped with flat-proof tires and a box of thumbtacks..." 
-Jon Stinson

"...Passing out incorrect route maps to the other competitors..."  
-Mike Eliasohn

....Having a friend riding an identical bike so his laps were counted twice..." 
-Wally Kiehler

"Some researchers think outside the box.  Charles thinks outside his cell." 
-Kara Colecchia

"His research is as important as Phrenology, Phlogiston or Piltdown Man"
-Terry Gerweck

"Charles thinks he is the Isaac Newton of bicycle design.  He has some pretty big shoes to fill. 
Luckily they go well with his big red rubber nose."
-Mike Mowett

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