Crank lengths

Stu Carter said:

Just fiddling about with a bit of math(s), and I came up with the
crank length vs. wheel size calculator.

What formula are you using? The angles are suspiciously shallow.

Naively, I figure the angle where pedalling becomes impossible even
with horizontal cranks is

arctan (m_rider * l_crank / (m_total * l_wheel),

where m_rider, m_total are the relevant weights,
l_crank is crank length, and
l_wheel is wheel radius

Of course, the result is a ridiculously steep angle that is impossible
to roll up.

Ken

Yeah my angle came in low, although of course this doesn't account for
any momentum, and is purely steady climb. Also, Muni tyres are much
bigger than their stated size, my 24" Muni is very nearly the size of
the 26" bikes next to it in the rack, so maybe something a bit more
specific there would help things.

Dave

--
kington99

Dave

- what a thoroughly post-modern subversion of the cycling genre -
------------------------------------------------------------------------
kington99's Profile: http://www.unicyclist.com/profile/9417
View this thread: http://www.unicyclist.com/thread/40678

Ken Cline said:

What formula are you using? The angles are suspiciously shallow.

Naively, I figure the angle where pedalling becomes impossible even
with horizontal cranks is

arctan (m_rider * l_crank / (m_total * l_wheel),

I have the same, but I made it arcsin. In the force diagram I drew, the
gravitational force is the hypotenuse, and the force in the direction of
travel is the 'opposite'.

I'm still not convinced by arctan. That suggests that you would need
infinite-length cranks to stay on a vertical wall. (I know this is
horribly theoretical!) But my method says that if the cranks are the same
as the wheel radius, and the unicycle has no weight you can sit
(force-wise) on a vertical wall. This seems intuitively correct to me.

Bear in mind that angles of tracks ARE low. They nearly always look lower
than you expect. Consider a 1 in 5 (20%) hill. That's considered pretty
steep. Its angle from horizontal is only 11 degrees.

Another test is to look up at 45 degrees. Now measure it. You'll nearly
always be looking up at only 20-30 or so. This is a pain when trying to
spot satellites and other celestial bodies given their elevation.

Anyway... I digress...

If anyone can come up with an argument why my force diagrams are wrong,
I'd be happy to discuss, but be wary of those angles looking too low -
you'd be surprised.

Cheers,

Stu
--
:wq

Ok... I've now added the gradient percentage and 1-in- value. Does that
look steeper?

Cheers,

Stu
--
:wq

If I put my details into that form it gives me a slope of 1:2.3!

I used 28" wheel diameter (my 26x3" wheel is near enough 28" outside
diameter), 165mm cranks, 168lbs (12st) rider weight and 22lbs uni weight
(26x3 nimbus 2). The only figure I guessed was the uni weight (10kg
ish), but I think it's fairly close, if anything it's lighter.

I know it's only a theoretical calculation, not allowing for energy used
to balance etc, but I ride up a 1:6 ish hill on the way home from work
and there's no way I could get up it without pulling on the saddle. If
I didn't pull on the handle I'm sure I would just stand up and stop.

1:2.3 seems far too optimistic - or is my technique really that bad?
:eek:

Rob

--
rob.northcott - OK as long as it's not too windy
------------------------------------------------------------------------
rob.northcott's Profile: http://www.unicyclist.com/profile/7436
View this thread: http://www.unicyclist.com/thread/40678

rob.northcott said:

If I put my details into that form it gives me a slope of 1:2.3!

Ok... so now we've had people complaining about the slopes being too
gentle, now too steep 🙂

I guess the theory only states that on the given hill, you will be able to
stillstand with cranks horizontal and all your weight on the pedal which
is pushing upwards.

I guess once you're riding, all sorts of dynamics appear, including cranks
not being horizontal, momentum etc.

Cheers,

Stu
--
:wq

Stu Carter said:

*.... That suggests that you would need infinite-length cranks to stay
on a vertical wall.....
Cheers,

Stu
--
:wq *

Wow, that would take really long legs!!

":wq"?? Are you a Unix guru?

--
mucRider - From the Over 50 Group

It is wise to invest in your happiness. - Harper
------------------------------------------------------------------------
mucRider's Profile: http://www.unicyclist.com/profile/6119
View this thread: http://www.unicyclist.com/thread/40678

Stu Carter said:

*Ok... so now we've had people complaining about the slopes being
too
gentle, now too steep 🙂*

I didn't intend to complain - just comparing the outcome of the theory
with actual riding. The "being able to do a stillstand" explanation
makes more sense to me - the steepest -rideable- hill would presumably
be considerably shallower.

--
rob.northcott - OK as long as it's not too windy
------------------------------------------------------------------------
rob.northcott's Profile: http://www.unicyclist.com/profile/7436
View this thread: http://www.unicyclist.com/thread/40678

This thread has got me wondering what I got (or if I passed) my A Level
maths all those years ago. I can't remember but after this thread, I'm
thinking that maybe I didn't take it & those 2 years of my life are
someone else's memory.

--
mikepenton - sometimes level
------------------------------------------------------------------------
mikepenton's Profile: http://www.unicyclist.com/profile/7090
View this thread: http://www.unicyclist.com/thread/40678

Quoted message said:

Quoted message said:

*.... That suggests that you would need infinite-length cranks to stay
on a vertical wall.....

Quoted message said:

Wow, that would take really long legs!!

And a very sticky wheel.

Quoted message said:

Quoted message said:

:wq *

Quoted message said:

":wq"?? Are you a Unix guru?

I wouldn't go that far. But I'm a card-carrying vi user 🙂 Well spotted,
you may claim your invisible five pounds.

Cheers,

Stu
--
:wq

Stu Carter said:

I have the same, but I made it arcsin.

My bad. Arcsin it is. Thanks for a nice counterexample.

The reason the angles seem small to me isn't just a misperception when
looking at terrain. I actually ride up bumps that are steeper than
your calculator predicts. At the BMX track, I have managed to climb a
slope averaging about 34 degrees (using a makeshift clinometer) on my
KH24, which maxes out at 27 degrees according to the formula. The
last foot or two of the bump must be closer to 40 degrees. I'll admit
I've wondered whether quantum tunnelling has contributed to my success
every time I roll over the top of this bump!

Anyway, there's nothing wrong with your formula. It just makes some
limiting assumptions: No pulling up on the handle; no use of momentum
to carry you forward; no bouncy riding.

Thanks for the mental calisthenics, and a measure of when slopes
really get hard!

Ken

id like to talk goats some time [email hidden]

--
ben_unruh - unicycling gangsta

The power of the polka!

Unicyclers Unite!

Santa's sleigh will slay again!

WANTED
USED COKER
PM ME
------------------------------------------------------------------------
ben_unruh's Profile: http://www.unicyclist.com/profile/6766
View this thread: http://www.unicyclist.com/thread/40678