Three Physics/Maths Cycling Questions « CityCyclingEdinburgh Forum

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Three Physics/Maths Cycling Questions

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Started 11 years ago by Wilmington's Cow
Latest reply from Dave

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Wilmington's Cow
Member

Things that sprung to mind this morning....

.one
There does appear to be noticeable drag on the dynohub when I switch the lights on, why is this? Surely it's producing the charge while riding without the light switched on, but it appears that switching on... makes the magnets stronger or something?

.two
Are the forces put through a flat handlebar markedly different to those through drops? Even if riding on the hoods mainly? I ask because I had to tighten up the stem bolts yesterday.

.three
I put my new 39T chainring on last night, replacing a 42T. It seems that in the same gear inch ratio (by feel, I've not calculated it) it feels easier pushing the 39T. Could there be something in this, does a smaller chainring, possibly because it's a shorter contact area with the chain, make pedalling easier than the same ratio with a larger chainring?

Posted 11 years ago #
Darkerside
Member

.one. Nope. Turning the light on closes the electrical circuit and allows the magnets to 'pump' electrons round the loop. With no light, there's no pumping, and therefore the only additional drag is caused by any bonus friction you've introduced.

.two. ~~Pass~~. Actually, yes, unless you've adjusted to a shortened stem and top tube at the same time. The hoods will place your weight acting downwards on the handlebars a good few inches further in from of the fork steerer than flat bars, increasing the moment applied to the stem/steerer joint.

.three. I'd have thought frictional differences would be negligible unless you're lubing your chain with, say, honey. Maybe a newer chainring is releasing the chain better? Or maybe it's the 'ooh, shiny things' effect (which is definitely real!)

Posted 11 years ago #
Roibeard
Member

.one - real increased drag as the hub is now doing additional electrical work.

.two - probably as I suspect that drops mean a less upright position and more weight placed on the wrists/bars. Drops also seem to have longer stems?

.three - I think you're right, but I don't know if it would be perceptible. Let's simplify the crank and chainring to make a lever. It's currently doubled up, so let's straighten it out - crank to bottom bracket is one side, then bottom bracket to chain is the other. You've shortened the bottom bracket to chain length so made things easier. (CF increasing the crank length without changing gear.) Of course, cranks are more complicated as the lever isn't straight, the chain-pivot-crank angle constantly changes...

Robert

Posted 11 years ago #
Greenroofer
Member

...and presumably, to develop @Roibeard's article for .three, if the chainring is smaller you'll be rotating it quicker, so although the force you apply to the pedal is less, you're doing the same work because you are applying it more often.

Posted 11 years ago #
cyclingscience
Member

.three - I want your chainring! It seems like you may have found one that breaks the laws of physics. All the lab tests at Johns Hopkins University a decade ago and by Friction Facts just this year show that a bigger chainring is more efficient than a smaller one. The reason? It has a larger circumference so the chain links don't have to bend quite so much when wrapping themselves around it. With less movement among the links, there is less friction so less of your energy is lost to heating up the chain.

Posted 11 years ago #
Roibeard
Member

@cyclingscience - do the frictional differences overcome the difference in moment, or did I get that completely wrong? Which wouldn't be the first time...

Robert

Posted 11 years ago #
Baldcyclist
Member

@cyclingscience <whispers>Go look at the h, ahem, h, cough, The H....t thread </whisper> ;)

Posted 11 years ago #
Baldcyclist
Member

Wrt the chainring thing, don't know maybe some phycology there.

If you start off on your big ring going up a hill it's hard, but if you start on your little right, it's easy. So by the time you get to the 3rd or 4th cog on the rear which would represent roughly the same gears as available in the big ring, you have cadence, so it appears easier?

Posted 11 years ago #
Wilmington's Cow
Member

That's probably spot on Baldcyclist. I did wonder if only having one chainring would counter that psychological placebo, but there is, as Darkerside pointed out, still the 'shiny new things' impact. I know I've got a new chainring on, so I want it to be better.

On the dynohub, so I'm closing the circuit, that I get (just about remembering my Higher Physics - to think I got an 'A'), so where does the energy go when the circuit is 'open'?

Posted 11 years ago #
Coxy
Member

re 1:

If you get a multi-meter and short the terminals, there is a considerable amount of friction/damping applied to the needle. It's why you are supposed to do this when transporting them. Have a try if you have one nearby - short the terminals and shake it. Then shake with them open.

From my old physics lessons, it's something to do with the motion of the needle inducing a current, but that current inducing an opposite force on the needle/rotor.

Posted 11 years ago #
Uberuce
Member

"so where does the energy go when the circuit is 'open'?"

Turns the wheel, pulls the cow. If there was such a thing a a perfectly efficient dynohub, it would have the same mechanical properties as a hubhub when turned off. As it is, there's probably some more friction from the extra moving parts inside.

Posted 11 years ago #
Dave
Member

WC: think about the dynohub as a battery, albiet one where the energy comes from motion rather than chemical reactions.

Where does the energy in a duracell AA go when the circuit is open (the battery is sitting in a blister pack on the supermarket shelf)? The answer is nowhere, there is no load.

In practice there is still drag from an 'off' dynohub due to heating in the coil, amongst other things, but no electrons flow between one terminal and the other, so there is nothing going on in that respect.

On the other hand, if you wire up two headlights to your dynohub it will power them both quite happily (just with twice as much friction).

Posted 11 years ago #
Dave
Member

As for the chainrings: bigger rings more closely approximate circles and are more efficient as a result.

It's quite a big difference at the small end (an 11t cog is effectively a hendecagon to your chain - not very efficient at all) but in chainrings probably not so much.

It's more likely IMO that the 39x?? combo is slightly lower in gear inches than the previous one, so you're not comparing apples and apples.

Posted 11 years ago #
allebong
Member

1: Has already been well explained. I'll add that it's like why your electricity bill doesn't go up if you leave plugs in the on position with nothing plugged into them - no electricity leaks out! Somewhere on the other end of hundreds to thousands of miles of wire is a generator spinning away in a power station, wind turbine, dam etc and it's basically equivalent to your dynohub. In both cases the generators only 'know' about what happens on the other end of the wire when you connect the circuit via a load.

For 2, if you're talking about the stem/bar bolts, and not the stem/steerer bolts, then there is very considerable additional load compared to a flat bar. A flat bar by its very nature cannot produce much in the way of torque at the stem. Torque is very simply defined as force times perpendicular distance. If you had a totally straight bar with loose stem bolts it would be impossible to rotate if the contact points of your hand grip lined up with the axis of the stem clamp. In reality flat bars have rise, backsweep and the grip from your hands does tend to twist the bars though.

With drops, while on the hoods your hands are several times further forward, plus there's more weight on them. So you will get much more torque at the stem/bar clamp. Easy way to see it is look at the bike side on and imagine a line drawn from the hoods to the axis of the bar clamp. Now imagine that line is a wrench or something and your pushing down on it with a lot of your weight. Pretty substantial amount of torque being applied there.

3: The fact that larger chainwheels are more efficient also applies to mech pulleys too. There was a recent article on Bikeradar (I think, might have been road cc) that measured this effect in a lab. It comes down to a saving of maybe a couple of watts at best by moving to larger pulleys. Important to pros needing every last edge, maybe less use to commuters.

Posted 11 years ago #
Arellcat
Moderator

When I did my SYS Physics project I constructed a dynamometer with a load bank of excitingly finned high power resistors. It was plain to see the difference between load and no load running as you switched the resistors in and out of the circuit.

WC's observation that smaller chainrings 'run smoother' than larger chainrings, for the same overall gear ratio, is one I've observed every day for about 20 years. For the same overall ratio the chain speed is the same. While there is less chain link deflection on the larger setup, the reduced torque ratio from chain engagement point to pedal axle means that any irregularities in chain line and the deflection away from the straightest possible route (on a recumbent with a power side idler) are felt much more strongly.

I have always preferred to climb using the small chainring and smaller sprockets simply because it 'feels' smoother and makes slightly less noise.

Posted 11 years ago #
Dave
Member

Hmm, thought provoking.

Posted 11 years ago #
Bhachgen
Member

To ask an additional question that the answers to the chainring one have made me think about:

Why is everyone* going over to "compact" drivetrains if larger cogs are more efficient? Are the efficiency savings more than cancelled out by the additional weight? Is it just because Shimano/SRAM et al think that we think the smaller cogs look nicer?

*obviously not literally everyone before someone comes on to talk about their 42/34 lowest gear...

Posted 11 years ago #
Dave
Member

I guess for almost everyone the practical benefits of the right gear ratios outweighs the more nebulous issue of how efficient the cog combos are?

Posted 11 years ago #
lionfish
Member

I like question .one!

It's already been answered though! Filling in too much...

Short answer: Conservation of energy - the extra energy to make the lights work has to come from somewhere. In fact thinking about conservation of energy and momentum hard enough seems to solve most physics questions :P

Now for way too much detail!...

The easiest way I find to think about this is that when a magnet moves past a coil the magnetic field lines 'cut' the wires of the coil inducing an electromotive force (EMF*) - measured in volts (V).

When it's an open circuit current (I) can't flow in the coil. The EMF is produced, but electrons can't keep flowing (I=V/R -> R is at infinity so I=0). When the circuit's closed the EMF does create a current (I=V/R -> R is now small, so I can be big).

The current in any coil makes a magnetic field. In this case the field will be in the opposite direction to the one that made the current in the first place. This makes it harder to move the magnet past the coil (think of pushing the two Norths of two magnets together).

PS: I'm quite surprised the lights are drawing enough power to be noticeable. Either they're really bright, or they're incandescent bulbs? :)

*EMF = Electromotive Force - not actually a force! It's effectively a 'voltage', which is a measure of how much potential energy you've put into each unit of charge.

Posted 11 years ago #
Wilmington's Cow
Member

lionfish, I actually understood that!

Certainly when you spin the wheel in the air there's a difference between lights on and off - might then psychologically be noticing a drag when riding.

Posted 11 years ago #
lionfish
Member

Don't forget, if your light's pointing forward, the photons coming out will slow you down!

If your light's putting out 10W and you+bike=100kg, this all works out* to a net deceleration of: 0.3 nanometres/second^2... or to put it another way, if you're cycling on a frictionless/airless flat plane** and you started free-wheeling at about 2mph, the photons coming out of your light would cause you to come to rest after a century.

This is why it's important to have a bright light on the back of your bike too.

* see http://en.wikipedia.org/wiki/Photon
** you don't want this: http://xkcd.com/669

Posted 11 years ago #
Dave
Member

I wrote up some thoughts as http://mccraw.co.uk/hub-dynamo-friction/ last winter. One commenter pointed out that I hadn't taken into account the non-linearity of speed with power, so the picture is even rosier. (I was averaging across long rides, that argument doesn't apply to a single trip at night, for instance).

Posted 11 years ago #

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