6 Factors Affecting Bicycle Transmission Efficiency

Recently I had been thinking about what kind of gear ratios I would need to climb Mount Washington on my derailleur equipped bike. Being an engineer, efficiency is a staple word in my daily mingling with other engineers.

So I started to think about gear to gear effect on a multi speed road bike, such as one with 30 speeds (3 gears up front, 10 in the back). If one could save a bit of power by choosing the most mechanically efficient gearing, that'd be a relief on a long climb (lesser energy expenditure) and could translate into quicker times.

Most people you talk to about this subject would snap that the well oiled bicycle chain is 98% efficient and the discussion would end there. However, missing from that discussion is several factors that could skew it one way or the other.

One factor may be obvious - chain tension. If the chain is too long for the job, the slack side tension is now more, which will subtract from the tight side tension in the power equation. You wont be riding for a long time this way because there is higher tendency for the chain to 'jump' or skip gears. Efficiency for a given cadence will be lower.

The second factor is the selected gear. When you move away from a single speed setup and loop your chain through a derailleur and a cog containing several sprockets, efficiency is not really constant per se from gear to gear. Some gears happen to be more efficient than others, perhaps because of what you can call lesser system 'restrictions'.  

If you picture yourself as a link on the chain and think about the challenge of having to maintain chain tension while bending around big and small gears alike, you'd carry power more easily the lesser you'd have to twist and bend. Atleast that's my theory. I'd like to think that a 11T small cog presents a bigger restriction to chain-link movement than a 17T cog.

Other things are less obvious. What could the effect on drivetrain wear be? I've written about an effect called chordal action when using high gears.

To measure gear to gear efficiency loss with any degree of high accuracy takes a dyno setup, load cells, a data acquisition system and lots of time. Fortunately, Chester Kyle, a mechanical engineering professor at Cal State Long Beach and founding father of IHPVA, did some very relevant work on this stuff back in the day. In Vol 52-2001 of the Human Power magazine, he describes using a single setup, with varying loads to measure efficiency in multiple drivetrain systems including hub gears.

Some of the findings were -

1) Efficiency generally increased with load : As you drive the crank to higher power inputs, the frictional factors eating away at that input becomes a lesser percentage as the input goes up. So frictional effects go up less rapidly. (Ofcourse, we're talking about mechanical efficiency here. If the human body is less efficient at oxygen intake and clearing away lactate at higher loads, there's really no point in trying to hammer away with higher gears. But that's a subject for another day)

2) There is generally a 1-3% difference in efficiency between adjacent gears. Prof. Kyle wrote that "an average of 2% difference in efficiency is thus easily possible if the wrong gears are chosen".

3) The efficiency (for all loads tested) tends to fall with higher gear ratios for all transmission systems tested.

Since I was thinking about my own road bike setup, I was particularly interested in the test he performed on the 27 speed Shimano system. The efficiency curve for this setup looked like this from the study :

A Shimano Ultegra 27-speed mountain- bike transmission with three front chainrings (44/32/22 teeth) and a 9-speed rear cluster (12, 14, 16, 18, 20, 23, 26, 30, and 34 teeth). Input cadence is constant at 75 rpm. Driven load power selected were 80 W, 150 W and 200 W. Dotted trend line shows average efficiency of setup tested at all loads decreasing with gear number.

Since Prof. Kyle ran out of time, only 15 of the 27 gears were tested.

I constructed the legend of the data points below. Gear ratio, calculated as driven teeth divided by driving teeth, decreases from top to bottom. Smaller gear ratio means "high gear" while the opposite is "low gear". Generally, the former is important if you wanted top speed and the latter would be if you cared for acceleration.

The graph show interesting things and I'd like to highlight a couple that caught my eye:

1) I'm seeing that higher gears and hence lower gear ratios mean you can lose efficiency but some perspective is important here. Between the lowest gear and the highest gears tested in this setup, there's a 1 point drop in average efficiency.

2) The 44/34T gear, which is a  big front-big rear cross chained scenario, shows the worst efficiency. Generally, cross chaining is not a good thing so this might be the proof of that.

3) The 44/12T gear, which is a big front-small rear cross chained scenario interestingly shows about the same efficiency at 75 rpm as a 44/26T. Why is this so, given that I said driving a chain around a smaller cog is probably worse for transmission efficiency? No idea. Perhaps its more straight chained than the latter. Moreover, this type of cross chaining shows higher efficiency than a big-front-big rear cross chain.  

4) 44/20T shows the highest efficiency of 95%, and if you included the 1-2% in friction loses in Prof. Kyle's study, that translates to 96-97% efficiency.. It must be straight chained as well. Could anyone verify this?

This study is truly interesting and has implications for performance improvement. I wonder if anyone else from another part of the world had a chance to investigate this more. It paves way for some interesting discussion.

CONNECTED READING : 

52/12T vs 52/11T Gearing : A Look At Chordal Action

*  *  *

6 Electronically Balanced Bicycles & Unicycles

"..The wheel consists of a ring of small rubber wheels overlapping a single large wheel. When the large wheel rotates, the U3-X moves forward or backward.."

Hundreds of years ago and approaching the Industrial Revolution, we had all sorts of genius and madmen tinkering with devices to propel an age of moving devices by virtue of mechanics. Plethora of gears, linkages and energy conversion schemes gave us the printing press, the mechanical wristwatch, the steam engine, the bicycle and calculators.

We're now quite deeply embedded in the Age of Electronics, where smart, sensible electronics in the form of boards, kits, controllers, sensors etc seem to be well within the affordability of average Joe. Has the age of invention really died? I argue not. Did you check next door?

Anyway...there is something existential in seeing a machine able to balance itself, isn't it? Well that's the topic for today.

Some years back while in college, I saw the murata boy riding his bicycle and smirked - that's it, the Japanese are going to take over the world. The motto behind the design effort was 'when you fall off a bicycle, get right back on' and so Murata Manufacturing packed gyro tilt angle sensors, power giving capacitors and other position sensing hardware into the robot to ride a bike. Two wheels.

To give company to the 'male' robot came an agile murata 'girl' and her stance was on one wheel saying 'ha, look at me' and out she came out more looking more heroic than her cousin balancing a unicycle while managing to avoid obstacles.

A video from Hacked Gadgets shows the impressive capabilities of the two creations.



The principles behind these electronics for basic work are not that hard to understand. And for an average guy to get his hands wet in application, you don't have to go far these days. LEGO has for a number of years been marketing the Mindstorms NXT kit which comes with a microprocessor, motors and several sensors to teach you motor control, object detection and so on.

Then if you listened to Cornell prof. Andy Ruina's wise words and had an itch to create, you could take that NXT to the next level :



Elsewhere, people were doing challenging work. The question probably was - could you extend this idea of robot-ism to humans and create a unicycle for propulsion? Dean Kaman's Segway seems to have inspired a string of inventors from all over the world to do exactly that.

The concept would be similar to the Segway - so you would take a chassis and mount an electronic gyroscope capable of measuring vertical angle. If you leaned far forward or back, an electronic motor controller would send a signal to the motor to rev it up or slow down so as to to put the bike back in balance.

The challenge would be to get your filtering right or you'll be leaning forwards and the sluggish machine would toss you off, or there would be introduction of positional errors, gyroscopic "drift" in your system and so on which would also not be good for tracking. Sampling rate is the other thing that's quite important. 100 Hz means sampling every .01 seconds, but on an electric unicycle, is that good enough?

An electrical engineer from Slovenia seemed to have got it right with his Enicycle. Works quite like a Segway and if you wanted to turn left or right, you simply put pressure on the left or right side footrests, then watched where you were going as the 1000 W motor raced the device to 15 kmph. A prototype was featured on the Gadget Show :



Perhaps Honda didn't want to run out of publicity as well and displayed the Honda U3-X, also a personal mobility electric unicycle, to a throng of reporters in Tokyo (2009-ish).

The uninteresting bit was, yeah they  had tilt sensors for balance control and so on. What really captivates is the portability of the machine - the bit looks like a sleek boombox and you can haul it around like a pullman. And then came the closely guarded "omnidirectional wheel" in the device.What was that?

A writer for the electronics journal IEEE described the legend of the wheel as such : 'The wheel consists of a ring of small rubber wheels overlapping a single large wheel. When the large wheel rotates, the U3-X moves forward or backward. When the small wheels rotate, the machine moves left or right. And when both the large and small wheels turn at the same time, the U3-X moves diagonally."   How does Honda come up with stuff like this?

So here's that video demonstration that Honda did for IEEE reporter in NY. Its a good one.



Focus Designs from Washington was probably inspired by the Enicycle to create something very similar - the SBU (self balancing unicycle).  Other than the fact that it costs 1400 cold cash, it can go 12 miles single charge with its 1000W motor and has the capacity for regenerative braking, something I'll have to look more into to assess its potential. (In the past, I wrote a post looking into the regenerative capabilities of MIT's Copenhagen Wheel)




Stephen Boyer, a computer science student at MIT also flexed his creative muscles to see what he can come up with. He validates the fact that anyone these days with decent electronics knowledge can make a forward-backward balancing unicycle. He didn't complete his project since he was unsuccessful at sideways balancing but he's brought some fresh ideas into the picture, like a pressure actuated killswitch that the rider would hold in his hand to kill the machine. Lots more interesting details into the engineering of his "Bullet" and a video of Stephen riding that bike can be found on his blog entry.

Steve Jobs may have passed on with a final look at an iPhone. And Segway's owner J. Heselden may have met his end over a cliff riding a Segway. But these individuals and technologies inspire hundreds of derivative technologies daily. But some part of me wants to see progress from investigative tinkering.

I can't wait for the day when the local pizza joint dishes away with their automobiles and hires a Murata Girl to deliver my pizza. Boy, I think if Google cars can drive around Nevada for 200,000 miles without a single accident, perhaps robots on electric unicycles can do a better job of delivering pizza without fatality. I mean, I do think of how many kittens were killed in the process of getting my pizza, you know.

Happy new year! Here's hoping we see more interesting things in 2012.

*  *  *

RELATED RESOURCES ON THIS BLOG :

Energy Costs of Riding a Unicycle

Four Part Series On Bicycle Stability
An All-Automatic CVT Based Bicycle

1 Merry Christmas & A Fabulous New Year

Readers,

After I got hired by Cummins to help engineer/integrate their turbochargers to diesel engines earlier this year, I haven't had much time to concentrate on the blogging aspect. I'm still as passionate about cycling as I ever was, infact I try to commute the 6 miles to work in cold temperatures whenever I can. And I try to ride with colleagues from work.

Here's hoping you all have a joyous Christmas and new year. If it weren't for Christmas, we'd all be Jewish right? Na just kidding. Speaking of Jewish, happy Hanukkah! And Boxing Day to you rest of the bunch, whatever floats your boat.

Hopefully I can kickstart 2012 with some fresh articles relevant to cycling. Keep the rubber side down. Cheers.

-Ron George
Columbus, Indiana

3 Self Inflating Bicycle Tire Shows Up Again

William Powers, a team member of a new start-up group called PumpTire LLC, informed me a few days ago of their self inflating tire idea. James of Bicycle Design had posted on his blog that he received the same email as well so I figure that this made the rounds to many bloggers in a mass email.

The idea appears to be the brainchild of Benjamin Krempel. The internet describes him as a CEO of Aqueduct Medical, a company that develops "safe, effective, user-friendly products that improve patient recovery from facial and cosmetic surgical procedures."

In the video below, he describes the idea (although somewhat vaguely) :



So its basically a pump that operates every time its squished by rolling motion. "The tire is a 26” x 1.5” tire with a set pressure valve", says the product website. Reportedly, the tire inflates from zero guage pressure.  "The pumping mechanism will pump from a flat up to 65psi."

In a blog entry back in 2008, I listed some "new" cycling ideas that would be serve as cool thought experiments, without exploring any technical or economic aspects. An "on the go tire inflation/deflation system" was first on my list and it had an almost science fiction aspect to it - the idea that the tire would have a feedback system to it to monitor pressure while riding and adjust itself after sampling pressure.

One application where this would be attractive is in public bicycles used for bike share programs where a self inflating mechanism could possibly add to some convenience. It avoids the necessity of adding an extra infrastructure for pumping air by the sidewalk or the need for individuals to carry pumps. For utility cyclists, terms like "rolling resistance" or "wheel inertia" are usually unimportant. Most just want to get from point A to B.

Having said that, a safety feature in the system is a must. The tire shouldn't injest water along with air. It also shouldn't over-pressurize and lead to tire bursts. Things like that. In the end, an interesting thought experiment ends up consuming time being developed, tested, re-tested, re-designed, at the same time needing to raise funds for the development and meeting the demands of consumer standards and regulations. By the end of it all, the inventor will want to go for a serious ride to breathe some air.

The idea of a self-inflating tire doesn't appear to have sprung up now. A few others tried to do something on similar lines, one of them if I remember correctly was an entry for the Specialized : Innovate-or-die" contest that happened a few years ago.

Here's Sean Conley back in 2007 :



And here's Kevin Manning, also in 2007 :



Both appear to charge air into the tire through pedaling. A bunch of patents on "self-inflating" tires for cars and bicycles date back to 1800's. Those can be found by a Google Patent search. That's what happens when you give people too much leisure time.

Whether Krempel actually first came up with the idea or not is not the issue. The big picture as I see is perhaps that of the slow march of the bicycle towards fulfilling an intelligent, self correcting system. Automobiles, ships and airplanes are already there but the "control architectures" in these complex systems are the by-product of externally driven factors - federal laws or economic incentives. Will the bicycle really benefit from that kind of intelligence? Sounds like a philosophical question.

*  *  *

20 Heat Wave, Gas Laws & Your Bike Tire

Staying cool out there?

Most of us have gone through or are still experiencing the 'heat wave' here in the United States. Temperatures in some places have taken on record proportions. I remember sweating absolute buckets in mid-July here in Western New York. The same route that I have biked for the past 2 years made me more uncomfortable than I ever remember in memory. Some other friends reported sweating Gatorade colored perspiration. I wonder , gee hows that for perspective?

Interestingly, in the midst of the debt crisis, a report from NYT probably slipped by quietly. It wrote that this past July was the 4th warmest on record in the United States according to NOAA studies. That should come as a surprise only to those who still wish to have their heads in the sand about climate change. I mean, the IPCC reports on the global warming phenomenon don't cost a squat and still out there for anyone to read. 20-30 years from now, I wonder whether the idea of a long bicycle ride will bear new meaning as riders struggle to stay cool.

Anyway having said this, there's a certain friend of mine, (who is a bit naive when it comes to bike technicalities), who pumps his tires to their absolute limits before his rides. It is a religious act for him. It does not satisfy him if its 139 psi. He needs all 140 in his pocket! Its as if his bike wouldn't move an inch if he hasn't dialed exactly that number into his tires.

I do keep wondering from time to time whether this has anything to do with the obscenely high number of flat tires he has obtained particularly during this summer. He's told me that he's not had this many in a long time and he's getting frustrated! Well, could one of his problems be that laser focused air pumping addiction?

When you pump air into your tire and go out for a ride, things change inside that tire that you normally would not think of. If I actually believed that he would actually be even remotely interested in some basic math, I would tell him about two beautiful thermodynamic relationships discovered by a bunch of cool people in the 17th and 18th centuries.

In the early 1600's, Robert Boyle sad that the pressure of a gas is inversely proportional to its volume, if temperature is kept constant.

A century later, Joseph Gay-Lussac asserted that pressure of a gas is also directly proportional to its temperature, if volume is kept constant.

The former shows a hyperbolic relationship between pressure and volume, the latter a linear relation between pressure and temperature.

Mathematically, these relationships can be expressed thus :

If you'd put them both together and assumed that your tire volume remains the same while riding, it can be said :

where P1, T1 are pressure and temperature at one instance in time and P2 and T2 are the states at another.

If my friend religiously pumped up his pressure to 140 psi (=P1) in the 70 degree F (=T1) comforts of his home, and then went out to ride in a muggy 100 degree F temperature (=T2,  a 43% change from his house), we can solve for the pressure in his tire, P2.

Thermodynamicists like to stick with absolute temperatures like kelvin, instead of empirical ones like degree F. To convert F to K, you add 273 to the Fahrenheit temperature. Then T1 = 343 K and T2 = 373 K. 

Since kelvin is an SI unit, you can't do math with apples and oranges and so pressures would need to be in Pascals. 1 psi = 6895 Pa. Converting, P1 = 965266.02 Pa.

Following our intentions to then solve for P2, 

Converting this pascal value back to psi, we get the modified pressure = 152.24 psi.

So a 43% temperature increase has just shot the pressure up by 9% ! This basic math doesn't consider the other heat additions through braking and side wall deflections. 

Ofcourse, I won't tell my buddy about all this. There's some amusement in seeing how many flat tires he'll be getting in the coming days through that nasty pumping addiction.

*  *  *

Correction (Aug 11) : The heat wave has apparently fried a chunk of my brain too. The comments from some readers were right. The conversion factor of "273" I used to convert F to K was actually to convert C to K. Correcting this, 1 deg F = 256 K, and so T1 = 294 K and T2 = 311 K. The correct math then is :

which, as it turns out, is 8 psi over-inflated (6% increase, not 9%).

Related Articles On This Blog :

Cycling in Heat & Helmet Cooling Power (Jan 4, 2010)