Lightweight Bigwheel

Unicycles and Equipment
21

After a breathless wait for UPS (weather delay from Atlanta) I finally know what it’s like to ride a 28.

I took all the very helpful comments in this thread into consideration. Thanks for the input. I’ll follow it in the future, but for now…I opted for cheap…Sun 28 for $67 plus
a Kris Holm red seat. Plus 110 cranks in observance of Mikefule’s devotion to shortcranks.

A few observations:

-Cheap still looks pretty good.

-It’s much lighter than the Coker. That may seem like a “duhhhhh”, but it’s REALLY lighter.

-It GOES. Not as fast as the Coker (more below), but finally I have a uni that I feel I can crank to the store, to the ocean, etc. As a newbie, my lack of skill kept me from doing that with the Torker 24.

-The 110’s are shockingly different than 150’s, or even the 120’s on the Torker. WOW. Litttttle spineeee foot movements. Actually, it’s amazingly easy to balance and maneuver at slow speeds, and harder for me to keep stable at speed.

-The hard, thin 28 inch tire is wonderfully maneuverable. I never zoomed around when travelling…was jealous of my kid’s easy swooping turns and slaloms down the street. I swooped this A.M…it was great.

-I view all wheeled devices as 7-league boots…multiplying the range and speed of foot travel. Well, the diameter of the Coker still rules in the 7-league league. I marked a starting point on the pavement and rolled the 28 incher forward one full pedal rotation. Then, same for the Coker (150 cranks). The Coker covered a full foot more ground in one rotation of the pendals. (I just gotta try the Coker with the 110 cranks some time…assuming I can turn the wheel enough to get it going!).

So…all in all…VERY happy with the 28. I gave my 24 Torker with the 120 cranks to the 11 year old (a 20 inch rider) and he had many of th same comments I’ve made here.

Thanks again for all the helpful comments. I love me cheapo 28. Equipment lust tho, will surely set in. I wonder if they make a Hunter 28.

AL
Santa Monica

22

yep,contact Hunter directly.

23

I like the 7 league boots analogy.

As for comparing distances, it’s simple arithmetic. The circumference is directly proportional to the diameter of the wheel. (Circumference = Pi x diameter. Pi is around 3.14)

So, if the diameter doubles, the circumference doubles.

So, a 36 is 36/29 the size of a 29. Each revolution of the wheel will go 36/29 as far - roughly a quarter further.

Now, you are comparing foot movement to roll out. This is again a simple calculation. The only problem is that cranks are traditionally measured in mm, whereas wheels are traditionally measured in inches. 1 inch = 25.4 mm.

So, convert your crank length into inches (e.g. 110 mm /25.4 = 4.33 inches) and then work out how that compares to the RADIUS (half the diameter) of the wheel.

So, 4.33 inch cranks, 29 inch diameter = 14.5 inch radius.

14.5/4.33 = 3.35

For every unit that your foot moves, the wheel will move 3.35 units.

Because everything is a linear measurement, rather than area or volume, there are no tricks to catch you out.

So we can establish that a 28/110 (my rapier) magnifies foot movement 3.23 times.

My broadsword (Coker) is a 36/150 and gives a magnification of 3.05 .

So, why isn’t the 28/110 faster? Because there are lots more variables such as leg length, foot length, skill, coordination, momentum, muscle speed and so on.

Which means that the Coker and 28 are very different machines to ride, each with pros and cons.

Now go out and have fun on it. :0)

24

What the??!!

The following portrays the thrashing of an aging, confused uni mind.

Mikefule’s calculations threw me totally off.

We were talking about uni’s multiplying the stride of your foot (a good thing if you have somewhere to go). For example, I find that riding a 24 multiplies the step I could take with my unaided foot, and my Coker REALLY multiplies my step. I can go places that I couldn’t or wouldn’t by foot.

But “Mike” calculates that his Rapier (28 inch with 110 cranks-the same as my new uni) multiplies his step by a factor of 3.23.
His Coker 36 inch with 150 cranks (the same as my Coker) multiplies his step by a factor of 3.05.

I yam confused. How could a 36 inch wheel NOT multiply your step more than a 28 inch wheel?

By one step, I mean, one rotation of the cranks.

Under my confused thinking, the length of the crank makes no difference (shocking, since I thought that changing crank length changed “gears” just like on a (ugh!) bicycle.

On a bike, changing gears UP allows your bike to travel FURTHER for each rotation of the pedals.
I thought it was the same on a uni, but a moment’s observation shows that changing to a smaller crank on a uni, allows you to travel EXACTLY THE SAME distance with one rotation of the pedals as when you had longer cranks.

Of course, the distance your foot flies through the air in the course of that one rotation is shorter on shorter cranks, and THIS must be what “Mike” is talking about.

But who cares! It’s not the speed your feet are flying through the air that count, its the speed of rotation…on a bike, you shift gears so you don’t have to spin like a madman at higher bike speeds. With shorter cranks, it seems to me, your feet rotate at the same rate as with longer or shorter cranks.

Ohhhhhh the confusion of it…and then why did I get 110’s other than copycatting Mike!!!

See…Als-heimers has got me.

AL
Santa Monica

25

And even further…

Misled by the comparison (faulty?) between bi-cycle gears and crank length, I assumed that longer cranks were like lower gears (climb powerfully but spin fast) and shorter cranks were like higher gears (the wheel spins at ungodly speeds but your feet are spinning at a comfortable speed).

After all, that’s what gears are for.
The powerplant (me) has an ideal power range.
The powerplant can spin only so fast, beyond that I crash and go flying off…no longer providing power.
And…the powerplant has only so much slow-speed torque, more than that and the cycle just comes to a halt…I can’t press any harder.

So without gears…downhill, I can fling just so fast.
And…uphill, there’s a limit to how steep a hill I can climb.

But with GEARS, amazing gears…I can shift so that I can travel waaayyyy faster downhill…and uphill on much steeper hills…and I don’t have to pedal like a maniac.

Even on hills so steep that I approach the adhesion power of my tires, I can (theoretically, at least) change gear to such a low gear that I can still make headway.

And on fearful downhills, I can gear up so much that despite my headlong rush downhill, my feet are rotating at a reasonable and controllable speed.

[I know…there are geared uni’s…I’m just wallowing around in my apparently erroneous belief that changing crank length is like changing gears.)

So…what does changing crank length do???

After the shocking realization that you can change crank length from toothpicks to full radius and you still pedal at the same speed (rate)…yikes…I am puzzled exactly what changing crank length gets me.

Whatever it is…it appears to be a lot less than changing gears. I’m stuck inside the wheel. But what eggsactly
does crank change do? And is the range of change so small as to be insignificant for the purposes I had in mind: going faster on a given uni, or climbing steeper hills on that uni.

I know that there is a BIG difference in how how the uni feels as I ride it with different cranks…but amazingly, I’m no longer sure what that difference is.

Sorry to blab on…but after one month, I’m uni-crazed and even the most insane commentary (such as this) holds endless fascination. THANKS!

AL
Santa Monica

26

So many questions! I posted a huge long reply last night and my browser stalled and I lost the lot.

It is right to say that the diameter of a wheel dictates how far the wheel travels in a revolution. So, all things being equal, a 24 inch unicycle would be about 20% faster than a 20.

But, all other things aren’t equal. Shorter cranks allow you to pedal at a higher rpm. Quite simply, your foot has less distance to go, so it can do more circles in the same length of time. (Semi-jokingly referred to as The Constant Foot Speed Hypothesis.)

So:

Big wheels go faster than small wheels.
Short cranks go faster than long cranks.

Usually!

So, as a rough and ready rule of thumb, a 10% change in crank length will make approximately a 10% change to the comfortable rpm for cruising, or the maximum rpm for sprinting.

So, if you calculate the ratio of crank length to wheel radius, you can make reasonably accurate predictions about how two unicycles will compare in performance.

Really, it only works well for adjacent sizes. By that, I mean that you can make a reasonably accurate comparison between:
a 20 and a 24
a 24 and a 26
a 26 and a 28
or
150mm cranks and 170mm cranks
150mm cranks and 125mm cranks (or 140s!)
125mm cranks and 110s.

Once the differences get bigger than about 10% - 15%, inaccuracies creep in and multiply.

Do a thought experiment:

Can you see why a 24 with 6 inch cranks would be faster than a 20 with 6 inch cranks?

Can you see why a 20 with 5 inch cranks might be comparable to a 24 with 6 inch cranks, at least for short periods on the flat?

But can you see that this last comparison (in each case, the crank is 50% of the wheel radius) would break down if you put 9 inch cranks on a Coker (36) or 1 inch cranks on a 4 inch wheel?

So, don’t get too tied up in the maths, Use it for guidance, but rely on experience.

Some useful rules of thumb:

Big wheels are nearly always faster on the flat over long distances.

Short cranks are generally faster on the flat over long distances.

Very short cranks are a liability unless you are very experienced. (You slow down to maintain control.)

Long cranks give better leverage for going up or down hill.

The best size cranks for a cruising machine are the smallest size that YOU can manage to when mounting, riding slowly, or stopping. (If you can idle, then that is a useful guide too.)

The best size cranks for a hill climbing uni are the longest that you can manage to pedal smoothly and comfortably.

Very short cranks are great fun in a daft sort of way. I went through a phase of riding cross country on my 24 with 102s. How I laughed.

In some ways, the crank:wheel ratio is a bit like gearing. However, it’s not that simple, because with very long or very short cranks, you use different muscle groups, or different amounts of muscle movement, so your power input is affected.

I did some semi-structured experiments against the clock a year or two back. I have experience with 20, 24, 26, 28 and 36 inch wheels, and cranks of 89, 102, 110, 125, 150 and 170 mm. My current fleet is set up as follows:

Coker: 36 inch wheel, 150 mm cranks. Good for general riding and cross country, with some hills.

28 inch wheel, 110 mm cranks: the rapier. It’s elegant, smooth and light, safe on the road, reasonable on short hills, but requires care.

26 inch MUNi with 150s. The tractor. I couldn’t get on with 170s. I loved the torque on down hills, but they bogged me down on uphills. On the other hand, I am a midget.

20 inch: I think it has 125s on. I had 110s on for a while. Only use it now and again, and either size will do.

27

Re: Lightweight Bigwheel

“Mikefule” <Mikefule@NoEmail.Message.Poster.at.Unicyclist.com> writes:

> Can you see why a 20 with 5 inch cranks might be comparable to a 24 with
> 6 inch cranks, at least for short periods on the flat?

You’re losing me here. I doubt I could hit a 17% faster cadence just
because the cranks are 17% shorter.

Ken

28

You may doubt it, but that doesn’t mean you’re right to doubt it.

In practice, the other factors mentioned come into play, and the 24 will always be faster, especially over a distance, or over rough ground. However, the effect is definitely there, and the 24/150 and 20/125 are comparable - not identical, but broadly similar. I’ve been there and done the miles.

29

Here’s my thoughts on crank length (I’ve done a lot of riding using the following

24/150 24/125 20/125 29/150 29/125 29/110): -

Approximately speaking, for a given wheel size, shorter cranks will mean greater

speed and less control; longer cranks give greater control but less speed.

The extra control of longer cranks comes with the extra leverage they enable, the

faster speed of short ones is because, to rotate the wheel a given distance

requires less movement of the feet (smaller turning circle).

That’s the theory, and it’s born out, to some extent by the experiences of many of

the distance and speed riders here, who, in general, prefer shorter cranks for that

kind of riding i.e. 125/110’s on a 29-er and 125’s on a Coker.

However, it isn’t that straightforward- there are many well documented exceptions.

Firstly, in my experience, wheel size is the prime factor when it comes to speed- a

28/29" wheel with long cranks will go faster than a 24" with very short cranks.

Many have found that, although shorter cranks give higher speed in ideal, flat,

smooth racing track conditions; in other conditions longer ones will be faster.

Examples are some Coker riders who find, in urban situations which necessitate lots

of stopping for traffic lights, curbs etc- the greater control and ease of mounting

of longer cranks actually results in a faster journey.

On rough terrain, longer cranks can mean less falls, hence they work out faster.

On my 29-er I have switched from 125’s to 150’s because I live in a very hilly

location, I also feel that they are safer on the roads. A few weeks experiment with

110’s last year was pretty horrible and resulted in a nasty backwards fall while

rolling off a curb that would have been no problem with longer cranks.

Lastly, I have found that, even when riding on relatively smooth pavement/road

surfices, I actually complete journeys faster with 150’s than with 125’s, as I’m

very happy being at the upper limits of speed of the 150’s than I would be with the

upper limits of speed with 125’s (feels safer and I know I can walk out of most

UPD’s with 150’s).

Having said that, many are very happy with short cranks; I’ve seen Mike Fule ride

stuff on his 28"/110 set-up that I would want 150’s for.

In general, my impression of this forum is that most speed/distance riders err on

the shorter end of the crank scale, but, recently, there’s been some people doing

hardcore distance who are talking about the benefits of longer cranks.

I do wonder if part of the preference for shorter ones is due more to what we read

on forums like this, than to what is actually best for the riding conditions we are

on.

I say this because, for a long time, I resisted trying 150’s on my 29-er as I felt

that it was an admission of failure- the consensus of those who are better/more

experienced riders than me seemed to be saying that anything longer than 125’s was

not good for a 29-er. However, having made the switch, I feel that 150’s are the

best length for me and the terrain I’m riding.

I think that experience overides theory on the crank length issue- some people

after trying both types prefer short, others prefer long. It seems logical that,

for example, riders with shorter legs may prefer shorter cranks, and vice versa.

I’ve also noticed that when riding a two-wheeler, I prefer spinning in a low gear

to pushing hard on high gears, this would equate to a longer crank choice on a uni.

30

Re: Lightweight Bigwheel

“Mikefule” <Mikefule@NoEmail.Message.Poster.at.Unicyclist.com> writes:

> You may doubt it, but that doesn’t mean you’re right to doubt it.

Mike, you’re a smart guy. But not humble, and unfortunately not
always right. Turns out I know something about this problem you
haven’t considered, so I believe I have every right to be skeptical.

Here’s a hint: There’s more to the story than the pedal’s velocity.

> In practice, the other factors mentioned come into play, and the 24 will
> always be faster, especially over a distance, or over rough ground.

The 24 will also be faster on the race track. If you need help
to understand this, I’ll be happy to enlighten you.

Cheers,

Ken

Chief Inspector Climbing Physics Police (Ret.) operating outside my
jurisdiction.

31

Some people are definitely more comfortable on short cranks than others. To each his own. A reminder when it comes to things like this; give the new crank size some time. As you get more comfortable with it, you will find it less and less of a problem. I rode a 20" for freestyle, at the pro level, with 125 cranks for many years. Recently I switched to 110, and the transition has taken a long time. This is mostly because I don’t practice much, but also because it’s new to me.

In a similar situation, I switched from 24" to 20" for freestyle back in 1984. This transition was very painful and annoying at first. You hop on the unicycle expecting to go a certain well-known distance with the first half-turn of the wheel. When you don’t, it’s really annoying. But I got used to it and my performances improved.

Crank length is not the same as gears. I think we all understand that. Since we don’t have gears available, we use different crank lengths to help us out. So it’s kind of a mild form of gearing. For the most part, the wheel size is still the most important factor.

However, this does not mean the bigger wheel will be faster. Hmm? Let’s look at some race results for an illustration. I’m going to use the 10k races from the recent NAUCC and Unicon. All the riders at the front of the group are very fit athletes. The assumption is that they are well-trained on the cycles they used, and have prepared for the event.

At NAUCC, on a course that included hills ad was at around 5000’ altitude, the race was won by a Coker with 170mm cranks. Aspenmike is not just a mountain climber on his Coker, he’s fast! But not far behind him was Brian Hansen on what I believe was a 28" wheel, with short cranks. Sorry, don’t know how long. They were followed by Irene Genelin, Andy Cotter, John Childs, and me, all on Cokers, with various crank lengths. I had 140s, which were too short for that race. I think maybe 150s would have worked better for me.

The NAUCC results suggest Cokers are generally fastest, but a stray 700c wheel can slip in there. Okay, let’s look at Unicon:

The results for both of these events are broken down by age group which makes it a bit of a pain to put the riders in order. Yuta Ando was the winner, on a skinny 700c wheel with unknown cranks. He was followed closely by Roger Davies on a Coker, I think with 110 cranks but not sure. I’m going to take you up to 16th place, which is me, because I have an ego. Using photos Jacquie took during the race, I should be able to give the wheel size for all those riders. I don’t know the cranks used, but the 24" wheels had real short ones, in the 60-80mm range.

1 Yuta Ando - 700c - 23:33.01
2 Roger Davies - Coker - 23:35.62
3 Ishikoshi Saki* - 700c? - 24:34.82
4 Daiki Izumeda - 700c - 24:59.89
5 Ken Looi - Coker - 24 - 25:15.87
6 Hajime Tsujimura - 24 - 25:47.22
7 Yumi Kondo* - 700c - 26:05.28
8 Nana Taguchi* - 24 - 26:05.69
9 Sizue Sugiyama* - 24 - 26:05.99
10 Yuka Nishino* - 24 - 26:11.12
11 Nathan Hoover - Coker - 26:41.72
12 Miki Matsumoto* - 24 - 26:53.94
13 Tadamasa Takagi - 24 - 27:15.12
14 Aika Moriuchi* - 24 - 27:25.54
15 Riko Katafuchi - 26 - 27:32.52
16 John Foss - 700c - 27:37.67

Sorry it doesn’t all line up. The stars indicate female riders. Some of those 24" wheels may have been 26", but mostly I think this is accurate. The message here, I guess is that it still boils down to the engine first, and wheel size afterward. But we know Roger, and we know Ken (Gizmoduck), and we know Nathan are all hardcore riders. Now you know all those Japanese riders are too. On 24"! And in hot, very humid conditions, with wind.

32

Before this thread sinks beneath the waves, back to page 78 or so on the forum, I want to express my sheer delight and thanks for the great responses. It was like tossing a few moldy fish heads into the lobster pot and coming back 3 days later to find a bunch a lovely lobsters with big claws snapping!

I had to run get a “rich, hot black, steaming, delicious” mug of joe before I sat down to the delicious task to reading into the comments of my favorite forum contributors. Yumm.

My only regret is that I sort of cheated the general readership by raising crank length on a “Lightweight Bigwheel” thread. Maybe I’ll cut and paste and post into a new thread.

I am sure that there remain TONS of things to say about crank length. The most amazing thing to me (a rank beginner) is the incredible physical and psychological difference changing crank length makes in riding, even tho crank change is, as was wonderfully said: :gearing light". I swapped the 110’s on my new 28 for 150’s this A.M. just to see. WOOOOOEEEE what an startling difference. And I loved MikeFule’s comment about laughing out loud at firstride on real shorties.

More crank posts please!!

All the best from Santa Monica.

AL

33

Your turn :slight_smile: what’s your opinion on the difference between 150’s and 110’s on the 28"?

Today I did a switch of a different kind- took the 29-er tyre off and went back to a 28" tyre. I found it horrible- hard and unforgiving on road bumps.

Despite the 29" tyre being damaged (hence the change) I knew I wouldn’t be doing anything with the 28, so I patched the 29 up and put it back.

What a difference! just got back from a manic night ride (29-er with 150 cranks), bombed around like a maniac and got back after an hour, drenched in sweat and very happy.

I can really recomend converting to a 29-er tyre, if your frame can fit one in.

(having said that, there are plenty of people who do prefer a skinny 28" tyre, I think they appreciate the extra skill needed to ride it)

34

The difference between the 110’s and the 150’s was huge.

Probably the best thing I can say is that new cranks are fairly cheap and are great fun. It’s worth sending off to Unicycling.com or someone, and getting a pair.

My kid laughed his head off when he jumped on his 24 with the 110’s. He zoomed all over the place. The laughter came from the tiny foot movements. Of course, he crashed after he lost control (never happened before) while racing me down the block. The 110’s gave him the feeling that any speed was possible. He loved them, but wanted his 120’s back for now.

I felt the same way. The 110’s were the cause of great frivolity. There was very little leg movement for the speedy result. Looking down at your legs while moving confirmed that…there’s remarkably small movement. I still could go up non-steep hills. Surprisingly, I felt that I had endless slowspeed balancing power with the 110’s. Taking off was fun…lingering around at slow speed but staying up (a good feeling for a new rider).

I loved the zooming, but also ran into control problems, especially downhill…the 28 would simply just roll out from under me.

I’m sure this is attibutable to lack of skill, and more riding would cure it.

But it probably won’t happen since I swapped out to 120’s on the 28, and to me it feels like the perfect fit.

Thanks for your comments on the 28/29.

35

ONE QUESTION:

Is there a diameter difference in the metal wheel between 28 and 29?

I always assumed so.

Or is it purely a tire difference?? Does that mean that I can mount a 29 tire on my 28 rim and not have it roll off??

ALSO, KUDOS TO THE FORUM

[By the way…the willingness of the “membership” to answer beginners’ questions and to be helpful again and again really marks this forum as a super place. My kid and I have really appreciated the input. This forum has made a huge difference in the uni experience for us. THANKS!]

36

The wheel is the same, a standard 700c takes both a 28" and 29" tyre.

Main issue is whether the frame can take the extra size tyre.

For example, my Nimbus round top 28" frame can take a Notos 2.1 " 29-er tyre, but only just and the tyre rubs on steep climbs. The frame definitly won’t take the bigger ‘Big Apple’ tyre.

A nimbus 28" flat top would be better with the Notos tyre, and now unicycle.uk.com have made available a Nimbus 29" frame that will take a ‘Big Apple’.

Having said that, if I was doing this again I’d be inclined to get a wider 700c rim for 29-ing.

Also, finding the proper inner tube can be tricky.

As I’ve posted recently on other threads, my 29-er has developed a very frustrating tendency to punctures, and I think that some of it is due to using 700 x 40-45 tubes, which work, but I suspect they’re stretched pretty thin, and also because the rim is a standard (no wide) 700c rim.

But, then again, prior to the past few weeks, my 29-er set up worked fine, and, if your frame can take the bigger tyre, I can really recommend getting one- the difference between a 28" and a 29-er is incredible in terms of smoothness and ability to roll over stuff.

37

Re: Re: Lightweight Bigwheel

Well, for a start, I’m considerably humbler than you might give me credit for. In fact, I take a pride in my exceptional degree of humility.

That aside, I think if you reread what I wrote, in full, you’ll find we don’t disagree on much, and probably only on the emphasis. You will also find that I have never claimed always to be right.

I wrote:<<You may doubt it, but that doesn’t mean you’re right to doubt it.>>

“P does not entail Q”
NOT:
“P entails not Q”

There is a difference - an important one. Your doubt, alone, was insufficient argument to support your conclusion. That doesn’t take away your right to doubt, nor does it have any bearing on whether your conclusion is right or wrong.

Over the last couple of years, I’ve written hectares of prose on the subject of crank length and wheel diameter, and the effects of various ratios and changes. (If I had written in verse, would it have been in pedantic diameter? :sunglasses: )

In this thread, I was trying to keep it fairly basic, whilst making it clear to newcomers to the problem that there was plenty to explore.

As it happens, a change from 150mm cranks to 170 mm cranks is a reduction of about 17%, but the maths would suggest a 20% increase in speed. If you accept for the moment that halving the crank length doubles the speed (1/2 becomes 2/1, if you like) then changing the crank length to 125/150 changes the speed to 150/125.

However, I have never asserted that the theoretical maths exactly describes the practical result. In fact, I’ve stressed that the maths is only approximately accurate for what I termed “adjacent” sizes, and that the “error” increases with each further step. I would assume that if the error could be assessed as a percentage, then the degree of error would increase exponentially with each further change of crank or wheel size.

Be that as it may, I have always said that numerous other factors come into play. In ideal conditions (flat hard surface, experienced rider, no slope, no wind, etc.) I would expect the error to be less significant, but still there.

As for riding on the track, I dimly recall a much earlier post telling of how John Foss once rode a 24/125 on the track faster than I have ever recorded on a Coker in any circumstances whatsoever. That alone is enough to make me as humble as you like.:o

38

Re: Re: Re: Lightweight Bigwheel

[QUOTE]
Originally posted by Mikefule

“P does not entail Q”
NOT:
“P entails not Q”

Thanks for the logic lesson, but I’ll admit I find it insulting.
Honestly, you’re smart enough to know your words, “that doesn’t
mean you’re right”, implies you thought I was wrong. By the way,
I have an advanced degree in mathematical logic. Care to discuss
dependent typed lambda calculus sometime?

In truth, I was trying to offer you an opportunity to think about your
analysis - which overlooks a crucial aspect of pedalling physics - and
consider my motivation for posting my belief without being
confrontational. Well, I blew it there! I apologize for hoping you
would think about my words rather than defensively trying to hold your
ground.

Still, I am saddened that you failed to discover my point or at least
ask me about it. I was hoping you would share my love of physics and
revel in the discovery of an analysis you had overlooked. Here’s
where your logic fails:

If you accept for the moment that halving the crank length doubles the speed (1/2 becomes 2/1, if you like) then changing the crank length to 125/150 changes the speed to 150/125.

My problem with your analysis is that you neglect to consider the
energy required to keeop your feet on the pedals (i.e. the centripetal
acceleration of the rider’s feet and legs). While it is true that the
(linear) velocity of the rider’s feet remains constant in your 2:1
crank exchange example, the energy required to keep the rider’s feet
on the pedals doubles! A rider with absolutely perfect balance must,
in theory, work twice as hard to go twice as fast with the shorter
cranks even though his linear pedalling speed is constant.

Similarly, if you look at two unicycles with equal wheel:crank ratios
travelling at the same speed, you will find that the rider expends
more energy pedalling the shorter cranks. The acceleration is
described by the equation:

 |a_pedal| = v^2(r_crank/r_wheel^2),

where v is the unicycle’s speed.

Cheers,

Ken

39

Re: Re: Re: Re: Lightweight Bigwheel

Isn’t it usual to assume that the rider is using a good, well matched set of pedals and shoes and that this means you need to expend hardly any energy to keep the feet on the pedals? Especially with pinned pedals and vans, it doesn’t feel like any energy is being expended keeping feet on them, more that it takes energy to ‘unclip’ from them. If you rest your legs, your feet get pulled round in circles by them.

Or is that not anything to do with it?

From my riding experience I’d guess that this is at least somewhat true, because of the way you can ‘leg freewheel’ a short cranked unicycle on slight downhills whilst putting in almost no energy, without your feet flying off. It feels like your feet get pulled around by the pedals. I’d also say after at least 4000 miles on one and 2000 miles on the other, that I’m amazed at how close my times on 29"/5" and 36"/6" unicycles are.

Joe

40

Re: Re: Re: Re: Re: Lightweight Bigwheel

[QUOTE]
Originally posted by joemarshall

Isn’t it usual to assume that the rider is using a good, well matched set of pedals and shoes and that this means you need to expend hardly any energy to keep the feet on the pedals? Especially with pinned pedals and vans, it doesn’t feel like any energy is being expended keeping feet on them, more that it takes energy to ‘unclip’ from them. If you rest your legs, your feet get pulled round in circles by them.

That’s a great question!

From a theoretical perspective, the rider’s feet and legs are accelerating (i.e. changing the direction of motion) as they pedal in circles. Accelerating a mass requires energy and (if you are riding flat terrain) all the energy comes from the rider. This is true even if your feet are glued to the pedals.

In practice, it makes little difference at slow speeds. But at higher speeds you know how you have to work harder to keep pedalling smoothly and avoid bouncing. The energy arguments show that this gets worse for the smal wheel & small crank combination compared to a larger unicycle.

Ken