Gearing question

[meb]

Originally posted by Ken Kobayashi
On 29 Sep 2003 21:46:12 -0700, [email protected] (Jeff Wills) wrote:

>In general, larger sprockets are *slightly* more efficient than smaller- the chain is bent through
>a slightly smaller angle, incurring less friction.

I believe this has been shown to be false. Last year Rich Pinto wrote:

> John- I always beleived the same thing because I had heard it so many times.
>
> However, in an article in the fall 2000 "Human Power" called "Efficiency of bicycle chain
> drives: results at constant velocity and supplied power" John and Claire Walton did an analysis
> comparing chain and sprocket efficiency at a constant supplied power and vehicle speed.
>
> Using data from the previous Spicer HP article, they found that at constant power and
> vehicle speed, the efficiencies were 92% for the 11 tooth,
> 90.5% for the 15 tooth, and 88.5% for the 21 tooth.

If you want to search for the thread on Google, the thread title was "The elusive 20 mph target/rear
sprocket efficiencies."

Ken Kobayashi [email protected] http://solarwww.mtk.nao.ac.jp/kobayashi/personal/

I haven't found the article that you are refering to with Google search. If you can post a link, that might help.

Here are data from a study concluding just the opposite:


“ Measurements of Efficiency of Chain and Shaft Drives Section 1.2.2 Contributed by Chris Juden, CTC Technical Officer, [email protected]. The best work I know of on
this subject was
commissioned by Fichtel & Sachs AG. Comparisons of single-speed, multi-speed hub and derailleur gearing were published in Radmarkt Nr.12/1983 and I am aware of other
work within that company which compared the efficiency of chains in
various states of neglect. Here's a summary of results, percentage efficiency values estimated from the graphs printed in Radmarkt.
New, clean, lubricated chain drives


_______1-spd____3-spd Hub Gear____6-spd Derailleur
Power___________Low 1:1 _High_____24T 19T 13T
50W____96.0_____90.6 93.4 87.3_____94.2 94.1 92.1
100W___97.3_____92.8 95.7 90.9_____96.2 96.4 94.9
200W___98.1_____94.0 96.9 92.9_____97.4 97.6 96.9
400W___99.0_____95.0 97.9 93.9_____98.1 98.4 97.8


Used chain (8000km), no rust, lubricated 100W 94-96%, 200W 97-98%
Neglected used chain (7000km), rusty, dry 100W 88%, 200W 93%
We can draw some interesting conclusions from these data. They confirm that hub gears are a little less efficient than derailleur, even in direct drive, and show that they
work better in low than high ratio. With a derailleur: running the chain around the little pulleys takes only about 1W. And a misaligned chain is much less wasteful than small
sizes of the sprocket, especially at low power levels. Indeed: at 50W the out of line 24T does a bit better than the in line 19T! 13T is not even very small by
today's standards, but is clearly rather inefficient. At very high power levels however, alignment may become as important as size.”

 

[meb]

Originally posted by Tom Blum
EUREKA!!

Thanks, Ken.

That's just the kind of scientific support I was seeking for my percieved sensations.

3.5 % (3.8% differential ) is not to be sneezed at on my block.

I will search and read the thread you refered to, since 20 mph is certainly an elusive goal where I
am concerned.
--
Miles of Smiles,

Tom Blum Winter Haven, Florida Homebuilts: SWB Tour Easy Clone Speed Machine Clone High Racer Clone
www.gate.net/~teblum

The biggest source of friction losses on the chain are a result of the links pivoting about their pins relative to the adjacent link(s). The more the link pivots, the more the frictional loss. The chain will be pivoting about the link when traveling around the chainring, sprockets, derailleur jockey wheels, and any pulleys tensioners or idlers on the chain.

On an 11T sprocket, a link pivots a great deal to navigate the sprocket turn.
On a 48T chainring, the link pivoting very little to circle the chainring.
On a 38T chainring, the links pivots slightly more, but it is still a relatively small amount, therefor losses are small so the efficiency of a 38T chainring is only slightly smaller than the 48T ring.
However, for an equal gear ratio, a 38T chainring would be associated with a smaller sprocket.

A 48T/14T chainring/sprocket combo would have a similar gear ratio to 38T/11T combo.

The pivoting angles are much larger for these associated sprockets than the chainrings, hence more friction lost on the sprocket than the chainring. The chainlink is pivoting more about the 11T sprocket than the 14T sprocket, therefor more losses on the 11T sprocket.

The second big loss in derailleur based chain systems, is from a lateral twisting of chains when the chainring and sprocket are not aligned. When you are on say a middle sprocket and middle triple chainring, you generally have the sprockets and chainring aligned, so minimal losses here. When you have a small sprocket selected and say a middle chainring, you have the chain twisting laterally between the chainring and sprocket and are introducing an extra 1-2 percent loss from the lateral twist in addition to the 2-3 percent loss you have from the smaller sprocket size.

The derailleur jockey wheels are generally seeing greater pivots than on the sprockets, but since they are located on the low tension side of the chainloop, the friction is relatively small-frictional loss is proportional to the tension on the chain when it pivots.

Often, bents have a lot of pulleys re-routing chains so there are more losses hear, particularly if on the high tension portion of the chain loop.

Rider can obtain best efficiencies when riding by selecting gears such that the chainring selected and sprocket are as best aligned as possible. Keeping a ratio where your legs are more efficient usually is primary to selecting a higher chain drive efficiency.

The mechanic could increase drivetrain efficiency by proportionately increasing sprocket and chainring size. The downside, more weight, cost (check out chainring prices for 54-104T chainrings) and slightly higher aerodynamic drag (the net should generally be low since the chainring is usually pushing air in front of some other component that would have otherwise needed to break wind-particularly rider (bents) or sprockets(uprights)).
Remember, heavier cogsets increse rolling resistance and add weight you need to take uphill.

 

[John Foltz]

>> Using data from the previous Spicer HP article, they found that at constant power and vehicle
>> speed, the efficiencies were 92% for the 11 tooth, 90.5% for the 15 tooth, and 88.5% for the
>> 21 tooth.
>>
Rich was referring to this? http://www.jhu.edu/news_info/news/home99/aug99/bike.html

It's interesting in that, if this was the original research, someone came along a year later and
reached the opposite conclusion using the same data?

Also interesting, the study showed that lube was not a factor in efficiency. Chain tension was, but
you can't pre-tension the chain in a derailleur system; so any tension must come from the
application of power by the cyclist. (IOW, higher efficiencies only happen under high-load
conditions.)
--

John Foltz --- O _ Baron --- _O _ V-Rex 24 --- _\\/\-%)
_________(_)`=()___________________(_)= (_)_____

 

[Ken Kobayashi]

On Wed, 01 Oct 2003 21:57:29 -0400, John Foltz <[email protected]> wrote:
>>> Using data from the previous Spicer HP article, they found that at constant power and vehicle
>>> speed, the efficiencies were 92% for the
> >> 11 tooth, 90.5% for the 15 tooth, and 88.5% for the 21 tooth.
> >>
>Rich was referring to this? http://www.jhu.edu/news_info/news/home99/aug99/bike.html
>
>It's interesting in that, if this was the original research, someone came along a year later and
>reached the opposite conclusion using the same data?

That's the original experiment, yes. Here's Rich Pinto's explanation about the revised conclusion,
from the same thread I mentioned:

=> The Spicer test was set up with a single 52 tooth chainring in the front, and had equal power
=> and RPM applied to it, regardless of the rear cog chosen. This led to the Spicer studies
=> observation that the largest rear wheel sprocket was most efficient.
=>
=> That conclusion is correct, but the real question (TM, thanks to Dave L) is what is the effect
=> of rear cog and front chainring changes at constant vehicle power and speed? BTW, this Real
=> Question never occurred to me until the Walton followup!
=>
=> Here is a quote from the Walton article "When appied power, crank RPM, and chainring size are
=> held constant, the velocity of the vehicle and the force applied to the rear wheel must vary.
=> Since the same work and chainring RPM are producing different velocities, a different force
=> must be reacting against the wheel" ...
=>
=> "Similarly, in figure 3 (Spicer article) the chain tension is kept constant. At constant
=> tension, larger sprockets are more efficient, but they would be delivering more torque" (to
=> the rear wheel)
=>
=> Using only the measurement data generated by Spicer for his analysis, Walton concluded with
=> this..."The surprising and counterintuative result is that the smaller sprockets have greater
=> estimated chain efficiency at constant vehicle velocity and applied power than the larger
=> sprockets" and I think this may be the simple answer to your question Ken ..."Therefore, the
=> increased efficiency from the higher chain tension is more important than the loss of
=> fficiency from having the smaller sprocket."
=>
=> It was Spicers conclusion that much of the transmission power loss was not converted to
=> heat, but was converted into vibration instead. The higher tension chains showed less loss
=> from vibration, and those gains in efficiency were more important than loss from using
=> smaller sprockets.

Ken Kobayashi [email protected] http://solarwww.mtk.nao.ac.jp/kobayashi/personal/

 

[Ken Kobayashi]

On Wed, 01 Oct 2003 16:51:14 GMT, "Tom Blum" <[email protected]> wrote:

>That's just the kind of scientific support I was seeking for my percieved sensations.

Actually it doesn't support your sensations, I'm sorry. The study found that _smaller_ gears (small
chainring and cog) are more efficient than large gears (large chainring and larger cog), if the
vehicle speed, power input and gear ratio are the same. If I read your message correctly, it's the
opposite of your experience.

I wonder if there is another factor not considered in the above study, namely frame flex. Presumably
the frame flexes from side to side as you pedal, robbing some power. The amount of flex should be
proportional to chain tension, which is higher with smaller gears (assuming same cadence and power
input). This effect would not have been measured by Spicer's experiment - he used a very sturdy
workbench instead of a real bike frame, and an electric motor which produced a smooth rotation.

Ken Kobayashi [email protected] http://solarwww.mtk.nao.ac.jp/kobayashi/personal/

 

[Dave Larrington]

John Foltz wrote:

> It's interesting in that, if this was the original research, someone came along a year later and
> reached the opposite conclusion using the same data?

One Stuart Burgess, at Bristol University, also concluded that bigger was better following a study
in 1997/8. One wonders whose experiments most closely duplicated the Real World(tm)...

Dave Larrington - http://www.legslarry.beerdrinkers.co.uk/
===========================================================
Editor - British Human Power Club Newsletter
http://www.bhpc.org.uk/
===========================================================

 

[Tom Blum]

Ken Kovayashi said: "Actually it doesn't support your sensations, I'm sorry. The study found that
_smaller_ gears (small chainring and cog) are more efficient than large gears (large chainring and
larger cog), if the vehicle speed, power input and gear ratio are the same"

It might still be true. I was pedaling with what I call constant force. Therefore, the chain tension
would be constant, so the first data would apply.

At any rate, I'm beginning to believe it's mostly physological.

I will continue to work on efficient spinning in my quest for improvement.

--
Miles of Smiles,

Tom Blum Winter Haven, Florida Homebuilts: SWB Tour Easy Clone Speed Machine Clone High Racer Clone
www.gate.net/~teblum

 

[meb]

Does anybody know of a link for the Walton article. I still get zero hits on the stated search

Maybe if we could see the article, we could see if some other variable was in play – such as chainring/sprocket not aligned or frame flex, or maybe he is not keeping gear ratios and or cadence constant. The quote posted stating:

“Here is a quote from the Walton article "When applied power, crank RPM, and chainring size are held constant, the velocity of the vehicle and the force applied to the rear wheel must vary. Since the same work and chainring RPM are producing different velocities, a different force must be reacting against the wheel"

suggests the passage in Walton refers to a test in which gear ratios were not held constant-else velocity would not be different.

The Spicer article doesn’t support the proposition that smaller is more efficient for a fixed gear ratio-merely that bigger is no more efficient than smaller.

For a given gear ratio, chain tension reduced to 38/48 by going from the big chainring to smaller chainring would offset by an increase in chainlink bends by 48/38 more at the sprocket and chainring-an offset.

 

[meb]

Originally posted by Tom Blum
Ken Kovayashi said: "Actually it doesn't support your sensations, I'm sorry. The study found that
_smaller_ gears (small chainring and cog) are more efficient than large gears (large chainring and
larger cog), if the vehicle speed, power input and gear ratio are the same"

It might still be true. I was pedaling with what I call constant force. Therefore, the chain tension
would be constant, so the first data would apply.

At any rate, I'm beginning to believe it's mostly physological.

I will continue to work on efficient spinning in my quest for improvement.

--
Miles of Smiles,

Tom Blum Winter Haven, Florida Homebuilts: SWB Tour Easy Clone Speed Machine Clone High Racer Clone
www.gate.net/~teblum

Tom,

Found some more data while looking to see if this elusive Walton et al. article was online.
This Chester Kyle & Frank Berto study test agrees with the earlier work published by Juden and the observation Spicer that smaller sprockets are less efficient.
It can be seen at: http://www.ihpva.org/pubs/HP52.pdf

Has some great collection of data points comparing derailleur and gearhub efficiency

Shimano
Ultegra Mtbk. Cassette

Chain
Ring


80W… 34……30……26……23……20……18……16……14……12
22……93.1………….92.8………….92.6………….91.7………….90.7
32……89.4………….90.0………….89.5………….90.9………….86.9
44……92.1………….91.0………….94.4………….93.8………….91.1

150W..34…… 30……26……23……20……18……16……14……12
22……94.6………….94.6………….94.5………….93.8………….91.8
32……92.9………….92.5………….93.0………….93.0………….91.0
44……93.8………….93.6………….95.0………….94.8………….93.3

200W..34…….30……26……23……20……18……16……14……12
22……95.0………….94.5………….94.2………….93.9………….91.9
32……93.6………….93.1………….93.6………….93.8………….91.4
44……94.2………….93.9………….95.9………….97.1………….93.7


Kyle et al. supports the quantitative observations of Juden and the qualitative disclosure of Spicer that increasing chain tension (more power) increases efficiency.

However, as one can readily see, the higher tension does not usually offset one-to-one the lower efficiency of a smaller sprocket.

Both the Juden and Kyle et al. data show increased efficiency with respect to chain tension is sublinear.

A smaller chainring results in greater chain tension for a given power at constant crank rpm, resulting in a higher efficiency on the chain tension component of the efficiency equation.

Since the efficiency increase is sublinear, large cog vs. the small-cog efficiency advantages will differ with differing power. More power will favor the large cog/large sprocket combination, less power will favor the small cog/small chainring approach.

Using the data with combination of closest gear ratios most similar chainline twist, you would have near identical velocities for the fixed cadence of the test, and minimize the difference in the chainline chain twist:

……………………….…44/34..vs..22/16………44/26.vs..22/12
Gear”26”X1.5……..33.3……….35.4…………43.6.………47.2
chainline
twist(cm)…..……….22.4…..….13.7………….13.7…....22.4
efficiency
80W…………………....92.1……..91.7………….93.0….…..90.7
150W………………..…93.9…..…93.8………….93.6…..…..91.8
200W………………..…94.2……..93.9………….93.9…..…..91.9

This Kyle et al. data shows the chainline twist is more significant than sprocket size, particularly since the frictional losses at the sprocket are partially offset by higher efficiencies due high tension as noted by both Kyle et al. and Spicer.

It still shows bigger sprockets and chainrings are better unless you go to extremes with the more dominant issue of chainline twist. If you have some idlers proximate the drive side of the chainrings or sprockets, a big enough decrease increase in efficiency could result from the chainline twist.

All these tests were done under constant cadence. Under constant speed conditions you would reduce cadence inversely proportionate to the gear ratio increase.
If maintaining constant speed, you could reduce cadence when switching to a smaller sprocket and since power is torque X rpm, for a given power, the lower cadence speed would result in higher torque for the same power with the result of higher chain tension and increased efficiency.

Under specific conditions-due the sublinear effect of higher tension on efficiency, with constant low-power constant-speed conditions, you could get higher chaindrive efficiencies with smaller sprockets than larger sprockets, and with enough extra chainline twist you could find higher efficiencies at elevated power levels on a lower sprocket.

The Browning data likewise is consistent:
On the data points with with minimal gear ratio differences and low chainline chain-twist we see:

Browning 12 speed


Chain Sprockets
ring

Ratios……..32…….23………17………12
(26X1.95)
30…………24.1…..33.6.….45.4.……64.4
38…………30.6…..42.5.….57.6.……81.5
48…………38.6…..53.7.….72.7……103.0

80W……….32…….23……..17…...…..12
30………….91.1…..91.3…..91.9…….90.9
38………….92.5…..92.5…..90.7…….89.8
48………….91.6…..91.2…..91.1…….88.8

150W………32……..23……..17……....12
30………….93.8……92.5…..92.9……92.2
38………….93.9……93.3…..93.5…...93.4
48………….94.5……93.8…..93.7…...91.8

200W……….32……. 23……..17…..…..12
30…………..92.7…..92.8…..92.7……93.4
38…………..95.2…..94.3…..94.4……93.2
48…………..94.2…..94.0…..94.1……93.5

Closest ratios:
……………………..…..48/23…..…38/17…..48/17….38/12
Gear”
(26”X……..………..….53.7………57.6….…72.7…..…81.5
1.95)
chainline
twist cm…………….….10……...….0………….5…………5

efficiency
80W………………….…..91.2…….90.7………91.1…….88.8
150W………………….…93.8…….93.5………93.7……..91.8
200W………………….…94.0…….94.4………94.1……..93.5