unravelling Gearing theory and formulae

[peanut]

yes but 5lbs isn't a third of my total bike weight is it ?

plus its a ridiculous analogy to use there are no common factors at all between peddaling a bike up a hill and pressing weights in a gym

Secondly you cannot use yourself as an argument either can you ? you are much younger than me and about a bag of cement lighter than me and certainly a lot fitter so again you cannot draw any comparisons .

forget the silly analogies Jimbo and just stick to cycling. if your formulas have any merit then it will be self evident and won't need comparisons to hod carrying brickies

 

[jimboalee]

Forget the PM Peanut.

Over the course of my cycling past, I've encountered many overweight cyclists who start off on 25lb bikes.
They begin to like the sport so go out and buy a 20lb bike.

"Bloody hell. This thing is fast!" and "It flies up the hills" is what I hear.

I've read the same on this forum. "Got my new Giant and is it fast? wow!"

Why should these guys say this? The total weight is only a little bit lighter. Are they in grasp of reality?

 

[jimboalee]

Dear all,

I take it 'gearing theory and formula' hasn't been unravelled? Not on this forum, at least.

There is a balls-aching method using physical principles, which at the end is very close to the myth.
So as to not to spend half a day with a slide rule and notebook, the wise old sages would simply use the myth.

I'm happy with it and it has served me well.

You can all decide whether you accept or condemn it.

If you condemn it, buy ISBN 3-1-419115-X or it's latest reprint.
It is the BOSCH Automotive Handbook, but explains all about vehicle dynamics.

When you've sorted out power vs velocity, do some self assessment and go on to include some inclines. Work out the speed reduction for various gradients and work out the gear for your natural cadence.

That should sort you all out as 'gearing for hills' goes.

Yes, I'm still in the 'Technical - Know How' section and Admin said I can be as technical as I like here.

So go on. Go away and find what gears you need.

Or you could use a bit of trust.

All the websites I have read say something like "choose a low gear for hills", but DON'T mention any principles or workings. How the hell am I supposed to know "How low is low?"

When a beginner asks "How low is low", what do they want to hear?
Someone suggesting a definite gear length, which IS wrong.

Do they want to hear someone spiel out physical equations and requests for intimate personal details for a bike gear? No.

They probably don't want to hear some wacky formula that doesn't make sense.

The answer to their problem is either they study up the physics and do the sums themselves, get pissed off by some clever dickie who spurts engineering or listen to a person who has been in bicycles for several decades and has seen good AND bad gearing.

If the former two options are not of the inquisitors liking, the third option is the one to take.

There is of course a fourth option. That is to take their hard earned cash to the LBS ( who will be pleased to take it off them ) and buy every combination of ring and sprocket in order to do self testing.


As has been seen, my formulae was not a million miles from what Peanut had.
In my bike building past, I have kitted-up bikes for superior colleagues at work who went away and rode round happily with what they were given.

If it were 'WRONG', I'm sure I would have recieved eternal criticism and lack of respect from the people who employed me.
In fact, I got mentioned in the company magazine as 'The bike man'.

 

[Steve Austin]

nice sig line Jim

 

[threebikesmcginty]

No idea what you're on about half the time Jimbo but keep posting it anyway!

 

[peanut]

No idea what you're on about half the time Jimbo but keep posting it anyway!

+1 needs to up meds

 

[HJ]

Now this is the sort of thing that should be in the 'Technical - Know How' section, I propose that this thread be made a sticky....

 

[CopperBrompton]

I'd be curious how you would adapt the numbers for a recumbent (where the option of standing on the pedals is not available).

If you like, I'm happy to supply you with my data. I have been through three sets of gearing and now have what I consider optimum.

 

[jimboalee]

nice sig line Jim

Of course it's wrong. How can it be right?

It is by sheer fluke and coincidence the wacky little formula works.

I have been through the long-handed method. How many here have taken up my challenge to work out their climbing ratios from first principles? None I expect.

One proverb in life is :-
"Why make anything more complicated than it needs to be?" ( exept if you're a Japanese DVD recorder manufacturer )

Instead of struggling through the physics, there is an easier method that gets close to the correct answer.

In the early days of cycling, serious cyclists would do 'trial and error' until they got a ratio they were happy with. Then one of those gentlemen had a flash of insiration. Considering a bike needs a lower gear if it is heavy, and a not so low gear when it is lighter to get up the same hill, weight and gear ratio are inversally proportional, but by how much?

Reciprocating the poundage and multiplying that number by 1000 gave a 'ball park' figure. It just so happened to be a gear length that they could ride up a 10% gradient for an extended amount of time.

Once the figure for a 10% was calculated, inches were subtracted for steeper gradients.

Everyone was happy.

A 25lb bike could be ridden up a 10% on a 40" gear. A 12%, 3" lower. A 14%, Another 3 inches lower still.

Not exact science, but a gear arrangement can be selected in less than half an hour, as opposed to bashing through the physics or swapping and changing for days on end.

I arrived at a gear-set for Peanut in about twenty minutes after I had his details. That was including his Bodyfat Target and ideal weight stuff.

You may not believe this but I'm not a man who likes to complicate his life. I am however, a curious bloke and it has been interesting comparing the myth with real science.
Now, for simplicity's sake, I use the myth.

 

[earth]

I have been through the long-handed method. How many here have taken up my challenge to work out their climbing ratios from first principles? None I expect.

I took the trouble to measure myself, weigh myself, worked through the formula as best as possible and posted my results. They are there to be seen on a previous page.

But it seems you didn't read it and tell me if I had done it right!

Shall I post it again?

 

[jimboalee]

I took the trouble to measure myself, weigh myself, worked through the formula as best as possible and posted my results. They are there to be seen on a previous page.

But it seems you didn't read it and tell me if I had done it right!

Shall I post it again?

Sorry.

47 inches should be a doddle up a 10% when the bike is 21 lb.

Find a 10% and try it.

With a 53/39 chainset, you should have a 19, 21, 23 & 25 sprocket coupled with the 39 ring.

 

[earth]

Sorry.

47 inches should be a doddle up a 10% when the bike is 21 lb.

Find a 10% and try it.

With a 53/39 chainset, you should have a 19, 21, 23 & 25 sprocket coupled with the 39 ring.

Thanks,

In return sorry that I sounded a bit terse.

I followed your formula for Peanut and came to the same results you did so that confirmed to me that I had done it right.

In doing this I also learned what gear inches are. A while ago I thought about the problem and came up with the same formula but in metric - which I also now know is called meters of development. But at the time I still did not know what gear inches were. I thought they must be some kind of over complex hangover from the time of silent movies (..inches..). Now I know it's exactly the same thing but in imperial

 

[jimboalee]

Gear Development is easier to understand. It is the forward progression of the bike for every whole revolution of the cranks, usually in metres.

I was brought up on gear inches. It goes back to high-wheelers where the bikes were sized in wheel diameter, not frame size. A short bloke couldn't ride a large 54" wheel bike because his feet wouldn't reach the far throw of the pedal. A tall bloke could ride a smaller wheel Penny-farthing but his legs would be cramped up at the near throw of the pedal.

Then came the Rover where the gear was a 2:1 drive on a 26" wheel. It was the same as the most popular size Penny, 52".
Everyone rode the same gear and adjustment for the rider's leg length was to move the saddle away from the crank axle.

It was found that on a 52" gear, 20 kmh could be ridden at a power output of 100 Watts at 82 cadence. Easy enough for gentlemen, ladies and older children to ride round the park on Sunday afternoon without breaking much sweat.

Can you imagine only having a SS 52" geared bike? Some used to ride from London to Brighton and back as a Sunday outing!

 

[GilesM]

I don't seem to have read anything anywhere about tyres coming into the equation, sorry if I have missed it. To me tyre type, pressure etc. is far more important, ride a 24lb bike up hill with tubs at 130psi, then try a 24lb bike on the same hill with mtb 26 x 2.4 at 35psi, I think we all know the gear required will be very different. Also frame geometry seems to have been overlooked.

 

[jimboalee]

I don't seem to have read anything anywhere about tyres coming into the equation, sorry if I have missed it. To me tyre type, pressure etc. is far more important, ride a 24lb bike up hill with tubs at 130psi, then try a 24lb bike on the same hill with mtb 26 x 2.4 at 35psi, I think we all know the gear required will be very different. Also frame geometry seems to have been overlooked.

If you have been reading intently, you will have gathered the 'myth' was realised years before MTBs were thought about, let alone riding a bike with tyres at 35 psi on the road.
The exact year the 'myth' came into existance was either just before or just after the second world war.
There was 'off road' riding back then. It was Cyclocross, and any formulae that were intended to make a road rider's life easier didn't apply to mud-splat racing.

If you are seriously thinking of riding a Randonnee on a MTB with 2.4 inch wide tyres at 35 psi, prey the Lord above help you.

The rest of us will get out our Sports tourers with 700 x 23 110 psi jobbies.

As for geometry, are you planning to ride a Brevet on a Schwinn Stingray?

I don't think geometry comes into it. I have arranged gearing for a Raleigh 20" Shopper.