fietsbob

Block and tackle can also be leveraged... a pair of multiple pulley blocks where the line goes back and forth between them several times
takes more line pulled for the load lifted distance .. but the effort to pull the load up is reduced.

Block and tackle - Wikipedia, the free encyclopedia

Carbonfiberboy 

Loaded tandems weighing over 400 lbs. can climb 19% grades without breaking anything, using ordinary single bike parts: hub, 36H rim, double butted spokes. IOW don't worry about it. That said, tandem riders do tend to buy the better quality hubs and to use deeper section rims, but we're rather the limiting case.

dsbrantjr

Same output power AND speed will be the same torque; changing the torque would necessitate a change in either speed or power.

79pmooney

No. Say the road is really steep. Our rider is doing 15 RPM and standing with all his weight on the pedal, and applying 160 pounds at the pedal. Crank arm is ~1/2 foot. Torque applied is 160 X 1/2 = 80 foot pounds. To keep the math simple, say a 24t chainring is 4" in diameter, 2" radius and a 36t is therefore 3" radius. Chain tension will be 80 foot pounds / 2 inches / 12 inches per foot = 480 pounds. Torque at the hub will be 480 pounds X (3 inches / 12 inches per foot) = 120 foot pounds.

Now a pro riding a 36 - 24 and applying 200 pounds (out of the saddle, pulling up hard) at 100 rpm: 200 X 1/2 = 100 foot pounds. 100 / 3 / 12 = 400 pounds of chain tension. 400 x (2 / 12) = 67 foot pounds. So at twice the pedal pressure and 8X the power, the pro is still only putting half the torque on the hub that our OP is.

Yes, a track sprinter doing an acceleration from 10 mph would put more torque on the hub. (Thighs the size of my waist can do that.) But no roadie ever would in a race. And yes, the OP was talking about riding at 100 rpm but that first pedal stroke after a stop on an Appalachian climb and clicking in, that 160 pounds at 15 RPM is probably no exageration. Now, for that track sprinter: remember, they never do this on a cassette body! They use thick cogs that look 100 years old screwed directly onto the hub, like 100 years ago and aply that torque with an equally ancient 1/8" chain.

So the advice above re: steel cassette bodies, larger cogs in a carrier and maybe not said, rock solid chain is all very sound.

Ben

Leebo

Common mt low gearing is 22 front and 36 rear cassette. Should be plenty low enough?

Gnosis

The following makes it evident that greater torque is most definitely applicable to the rear wheel via larger rear cogs:

Select your largest chainring and additionally select your smallest rear cog, which means of course, you are in your highest gearing. With your bike at rest on flat ground, do nothing more than place your full weight on one of its pedals while its crank arm is parallel with the ground (don’t push off to get started, merely place your full weight on the pedal). Note that the bike and you accelerates v-e-r-y slowly from its state of rest.

While still using the large chainring, you next select your large rear cog and again with the bike at rest on flat ground and the crank arm parallel with the ground, place your full weight on the same pedal (again, don’t push off to get started). Note that the bike and you accelerates notably faster from its initial state of rest.

Being that all else remained the same, it makes evident that the greater mechanical advantage provided by the lower gearing (hence larger rear cog) per the same pedal down force (your body weight in both cases) has produced a greater torque at the rear wheel, which in turn causes the bike to accelerate at a greater rate (hence, the principle of the 2nd law of motion equation, F = ma, which rearranged for our scenario is a = F / m).

Selecting a smaller chainring further increases the torque to the rear wheel and the same experiment can be performed. In each case, the bike will accelerate fastest when the largest rear cog is selected and the smallest front chainring is selected.

Additionally, being that the pedal falls through the same 90° per YOUR body weight in these experiments in order to produce the torque via the same pull of gravity (9.8 m/s/s), it is making use of precisely the same gravitational potential energy to accelerate the bike in each case.

Torque is the motivating force, not power. Power is merely a measure of how much work is performed, or potentially can be performed. This leads us to the next scenario, which demonstrates that power is meaningless when insufficient torque it produced:

A great percentage of forum members are capable of pedaling 100 miles. Undeniably, there’s a great deal of energy dissipated over those 100 miles and a great deal of work has been performed. But let’s say one of the first ascents on that 100 mile ride is a killer mile-long 24% grade and they’re only permitted to use their highest gearing, 50/11.

How many are going to make it up that steep grade using 50/11 gearing? None! But these are the same people that can pedal 100 miles and think nothing of it. Why can’t they climb this 24% grade via their highest gearing, 50/11 (or worse, some have 53/11 and even higher). It’s because they produce insufficient torque to overcome the force imparted by gravity on a 24% grade via the combined weight of bike, rider, and cargo. And so, even those capable of producing a great deal of work (output power over a long duration of time and distance) are stopped from doing so via the 24% grade encountered via their highest gearing due to insufficient torque.

Wanderer

It does not allow the rider to put out more torque - as that is limited by his/her ability. It just allows the rider to apply that same force at a different point on the lever..... i.e., utilize what he/she is capable of.

This is getting pretty deep for Bicycle Forums, even the roadies!

FBinNY 

Yes, it is, especially since the OP's question was answered long ago.

But to clarify, by definition, greater leverage -- either through more gearing or simply a longer lever -- for the same force equals more torque.

For a given element (ie within the rear wheel itself) torque in = torque out. But for a machine (any system of levers and/or moving parts) The input and output torques can be different, just as input and output forces can be, the difference being distance. For a machine, work (force X distance) in is equal to work out.

dave42

Well, no, it's not. That's why i posed the question.

dwmckee

I am an old fart that tours all over the Appalachian mountains on both single bikes and atandem. a 19 inch low gear is all you will ever need. Just be sure you are in at least moderate physical condition before you set out. You do not have to be in great condition with a 19 inch as your lowest gear. You can get by on any decent quality equipment with this setup.

dave42

That's good to know. What sorts of grades do you encounter on the unpaved roads? How much bike and gear weight are you dealing with? What's your slowest seated cadence?

Just out of curiosity?

FBinNY 

Standard or not doesn't matter. Assuming parts are available, set your bike up that way you want it. If you think you need a 14" gear and can do it, do so.

Consider ---- if you set up with a low that's not low enough, you're walking. OTOH- if your low is too low, you shift to the next gear.

For my part, I'm not an advocate for gears much below 25 or so, but that's me. If you think you need lower, don't let anyone talk you out of it. Once you have some experience in mountains you can know better next time.

dave42

So, after giving this some thought, and running some rough calculations, with a 14 inch gear, my absolute peak input torque at the rear wheel would be right at 200 foot pounds.

With a 53-11 gear, it would be around 20 foot pounds.

So, torque does increase as gears get lower. Whether this is a problem, who knows? If I build a freewheel, i hope it never needs removed...

I've over-estimated my weight in case i'm carrying some weight in a backpack, of course.

So, I figured my weight at 200lbs instead of 154.

The one point i can't wrap my head around is how only needed torque will be produced. But, I'll dwell on it some more. Y'all feel free to chime in.

Anecdotally, it'll work. I can build what I want to build.

In the meantime, I'm working on making my load do 2 things: be more stable and weigh less. If I could get out of the saddle, I could climb in a higher gear.

That may well be the (cheapest)answer.

dave42

I agree. Thanks for your insight.

FBinNY 

Here, play with this. I haven't checked it, but if it doesn't give you the answer, search for "physics problems - wheel on slope".

BTW- steep grade climbing isn't only about power and the bike. Handling skills are super critical. You have to be able to handle the bike at super low speeds, and be able to turn tight circles at those speeds. When you run out of gearing, or simply want a change of pace, you can slolom up the hill, but that requires some skill to swing the turns through the fall line. Also, many people find it almost impossible to start on super steep hills, partly because it's hard to get enough momentum for the 2nd pedal, and partly because excess torque starting from zero causes wheelies. One technique (if necessary) is to start facing down or across the road, then swing a low speed U-turn into the climb.

dwmckee

I am 200 pounds. Single bike is 28 pounds and gear varies around 30 pounds. On our tandem I have a 12 year old stoker (with legs like a bird) and a 9 year old on a trail a bike on the back. Gear for the three of us plus bike, TAB and all 3 people tops out at around 550 - 575. The kids help some, but poop out on long steep hills. On the tandem we wind up walking occasionally if the hill is long and over 12% but this is maybe one hill over the course of a week tour. We have done short steeper hills (coming into Niagara on the Lake for example), but not very often. On the single, typical hills are in the 8% range but occasionally hit 10 - 12%. More than 12% is not often in our path. I do not ride with a cadence sensor any more but am pretty sure we average around about 85 and can drop to 60ish on the worst hills. I ride about 30 miles a week when in season at about 15 MPH average in Pittsburgh terrain. Our sustainable speed for a long hill touring on the tandem drops to about the limit we can balance on the tandem, so a lower gear is of little value. The poster that mentioned how hard it is to start in such a low gear is correct in that a single pedal stroke does not get you moving enough to stay balanced enough to get the other foot engaged. I could not imagine that 14 inches low gear would be usable on anything but a tricycle setup.

We only stand to stretch our legs on the tandem, never to climb.

dave42

Thanks. It's really cool that you've got your kids riding.

I appreciate all your input. It actually backs up my reasoning, but i understand your perspective, too.

My cyclecomputer cuts off at 2.5 mph, and i can climb slower than that. Once, on my road bike, i decided to do a 50 mile loop in the big ring, so my low gear was 52-18. I found that i could climb for three miles at 17 rpms, though i chose to kick it up a little, because i had the power.

Mostly i judge a grade by feel, but i have a couple of things going for me. I roofed houses for 10 years, so i can tell at a glance what the pitch of a roof is, or the grade of a hill. To verify this, i take a level and a plumb bob out with me on some rides and measure a hill or two. I can figure it pretty close.

On back roads around here, and especially on fire roads up in the national forest, grades approaching 30% are not unheard of. 20% is fairly common, both less than a mile, and extended grades of 7% to 14% are also easy to find.

When i was still north in johnson city, tn, for instance, i had a 27% climb near my apartment that i rode regularly, albeit on a road bike with a 44 inch gear(standing and dying...)

I weigh 154. My bike and gear comes to 103 pounds.

I'm a fairly strong rider, but my last trip out was tough. Lots of climbing, lots of ice through the morning, and a campsite on top of a ridge where i nearly froze...

I was running short on supplies and burning through a lot of calories. I believe there are times when the less power used, the better.

So, there's a little more of where I'm coming from.

Right now, i'm setting up my road bike for touring, and i'll run either a 28" or a 24.5" low gear, because that's what i have. The next upgrade, though will either see a wider cassette/smaller chainring, or a quad. I'm really interested to pedal 13 or 14 gear inches and see what it does.

it may be the dumbest thing ever, but i'll see.

anyway, thanks for taking the time to respond.

Leebo

What kind of gearing is needed to get to what you need for gear inches? Mt bikes can also be had with a 40 or 42 T for the rear cassette.

Leebo

Thoughts on how to get your low gear. What size wheels/tires are you using? The new sram 1x11 for mt bikes has a 11-42 rear cassette. Very pricey, like $3-500.00 bucks. Plus you need a new freehub/ hub to run it on. Also the gear jumps are very big, Ok for dirt, but would seem too big for steady road cadence. Another way to go is get an aftermarket 40T to fit on a 12-36 rear cassette. It requires some fiddling to take out a 16t, add the 40T, crank down the b screw and such. Some cranks can run a 20 T on the inside chainring. Good luck with those hills.

fietsbob

This: R'off IGH 526% range when in a 20" wheel a 16:53t is like the range of a 16:38 .. About 18" to 90".

because of the different wheel size.. 20" wheel , 16t cog & 39_53 double chainring will give you that super low gear .

dave42

Thanks, Leebo. 700x25's, most likely. The 1x11 is out, because i have no money. Not that much, anyway.

I've got a few options. One would be to find an old 94/58 bcd mountain crank and run 20front-36rear. That woyld give me 14.66 gear inches. It's close, and it's easily done, if I can find the crank.

Another option would be a quad. I like that idea even better, in some ways. Run it as a triple, say 16/26/42 on the front, 11-28 7 speed rear. That would be compatible with all my current stuff. 15 gear inches.

If i go 16front-32rear, i'll have 13.2 gear inches.

so, to keep the jumps between gears from getting way out of hand, i'm thinking the quad is the way to go.

My only concern is that it takes suntour "A" cogs, and i only have a few of them. They're no longer in production.

My third option, as suggested by fietsbob, is arguably my best option. Smaller wheels.

Perhaps find an early 80's bmx, cold set the frame, and voila, instant climbing machine. There are adaptors for the botyom bracket, and hangers for the rd.

I have reliable suntour thumb shifters.

Rider positioning could be worked out, i suppose.

It would work, but where do my bottle cages go?

So, that's what I've come up with so far, as far as actually building such a thing.

A crazier idea would be to attach a chainring(or two or three) to the rear cluster to serve as the largest 2 or three cogs.

lots of weight, and what rear derailleur will wrap all the chain, handle a 50 tooth cog, and still allow for a good high gear?

So, that's not a viable option, yet.

To get it now, like right now, i would need these for my road bike:
A mountain tamer quad with 16 tooth chainring, a longer square taper spindle, a sunrace 13-32 8 speed freewheel, space the rear axle to 130, redish the wheel, put my rear shifter in friction mode, and it's done.

That's the fastest route.

Something built around an 11-36 cassette would be a better route.

dave42

Smaller wheels would open up all kinds of possibilities.

Booger1

Unless the wheel is stuck in a hole......You'll produce more strain at the hub in HIGHER gears than lower gears...

FBinNY 

Yes, if you're talking of the radial load caused by the chain pulling forward. But No, if you're thinking of torque, which is a function of payload, slope and wheel diameter.

fietsbob

& 3 of them so you dont fall over in such a Low stump pullin' crawler gear.