# Arithmetic

Status
Not open for further replies.
D

#### Debbie

##### Guest
Please can someone tell me either (a) how to work out whether I have suitable gears, or (b) do the
arithmetic for me and tell me - preferably (a) as I really ought to get the hang of this stuff.

3 front chainwheels at the front - 48,38 and 28 6 sprockets on the back, the smallest has 14 teeth
and the biggest has
28.

The wheels are 26 inches.

(Best beloved is away for a couple of days. He tried to explain on the phone, but he tends to work
in pictures rather than words, and apart from noting that the smallest chainwheel and the biggest
sprocket have the same no of teeth giving a 1:1 ration, his explanation lest me no wiser)

--

Debbie Urban Theology Unit, Sheffield Views expressed in this email are my own and are not
necessarily those of the University of Sheffield or UTU.

P

#### Pete Biggs

##### Guest
Debbie wrote:
> Please can someone tell me either (a) how to work out whether I have suitable gears, or (b) do the
> arithmetic for me and tell me - preferably (a) as I really ought to get the hang of this stuff.

(a) is tricky because different people need/like different gears, and for different places/uses.
Maths (or anyone else's advice) can't provide the all answers to this one. Really, you have to
use either previous experience of different gears or experiment. I've seen some ludicrous plans
from people who are clearly mathematical geniuses but obviously have no clue about cycling.
rec.bicycles.tech is a great place for that

(b) is easy: Front chainring divided by rear sprocket times tyre diameter. But what to do with the
numbers?... Compare to other bikes or other gears you could bung on the bike........

> 3 front chainwheels at the front - 48,38 and 28 6 sprockets on the back, the smallest has 14 teeth
> and the biggest has
> 28.
>
> The wheels are 26 inches.

Not a bad selection, more sensible than a lot of bikes have I think, but they could be changed if
you like. The easiest and probably cheapest way is to change the freewheel (rear sprockets).

Do you feel you need a lower bottom gear, higher top gear, closer gears, or different middle gears
or what? Then we could make suggestions. Bear in mind that, unless upgrading to a larger number of
gears (expensive), something would have to be compromised in the process: usually bigger jumps
between gears and/or: lower top gear or higher bottom gear, or less reliable or difficult gear
changes (in the case sometimes of changing front chainrings too much).

For comparisions: modern mountain bikes have a wider range, typically
22/32/42 with 11-30 (8/9-speed); hybrids can have all sorts. Your top gear is unusually low but then
a lot of bikes have unnecessarily high top gears - I think it's more important to optimise for
middle and low gears. Try simply pedalling faster if the high gears feel too low. I'm happy
enough with a 50x14 top gear on my tourer (with near-27" wheel). It may be well worth having
lower bottom gears if you have trouble climbing steep hills (and would be able to balance at
lower speeds).

Don't rush into it, though, if you are newly returning to cycling or riding any new bike, because it
takes a fair while to get used to the bike and gears, and in particular, to pedalling at a good
cadence. Also of course, you'll get fitter and stronger so will be able to power the gears better.

With 6-speed freewheel*, you probably won't be able to have one with a top sprocket smaller than 13
teeth; 34T probably the largest (although not all rear derailleurs can cope with 34T). Note that it
takes more of a difference in number of teeth at the large end to make a difference than to the
small. Front chainring possibilities depend on make & model of cranks (please state).

info: www.sheldonbrown.com/gears.html

calculator: www.sheldonbrown.com/gears ("gear inches" are best units for making comparisons)

* as opposed to "cassette". See: www.sheldonbrown.com/free-k7.html . If you do have a cassette (prob
not), you'll be able to use 12 and 11T.

~PB

P

#### Pete Biggs

##### Guest
Debbie wrote:
> Please can someone tell me either (a) how to work out whether I have suitable gears, or (b) do the
> arithmetic for me and tell me - preferably (a) as I really ought to get the hang of this stuff.

It is all about ratios. The combination of front and rear sprocket determines how easy or fast you
can turn the pedals at a given wheel speed. Ratios are made up of two numbers: number of teeth of
front and rear sprockets. For example, 38:19 is the same ratio as 40:20. 28:28 equates to 1:1 and
this means the wheel turns exactly one revolution for every one pedal revolution. This 1:1 ratio
doesn't have any magical significance with bike gears, by the way. 40:20 or 2:1 means the wheel
turns round twice for every one turn of the pedals and is known as a "higher" gear.

As you can see, it's hard to get your head round using two numbers at a time and make direct
comparisons using these ratios. So it's more convenient to express each gear as one single number.
This is done simply by dividing the first number by the second. The rear wheel diameter is factored
in because the wheel determines how far the bike travels for a given gear and you may want to
compare to other bikes with different wheels. When inches are used, it also enlarges the number to
make it more convenient and memorable (rounding to one decimal place is good with these).

Sheldon Brown says: "The simplest system in common use is the "gear inch" system. This dates back to
before the invention of the chain-drive bicycle. It originally was the diameter of the drive wheel
of a high-wheel bicycle. When chain-drive "safety" bikes came in, the same system was used,
multiplying the drive wheel diameter by the sprocket ratio. It is very easy to calculate: the
diameter of the drive wheel, times the size of the front sprocket divided by the size of the rear
sprocket. This gives a convenient two- or three-digit number. The examples listed above are all
around 74-75 inches. The lowest gear on most mountain bikes is around 22-26 inches. The highest gear
on road racing bikes is usually around 108-110 inches"

> 3 front chainwheels at the front - 48,38 and 28 6 sprockets on the back, the smallest has 14 teeth
> and the biggest has
> 28.
>
> The wheels are 26 inches.

For each gear, you need to divide chainring by sprocket then multiply by
26. The top and bottom gears are most important as they indicate the range. Your bottom gear is
28/28 (26"), top is 48/14 (89.1").

Now, what you do with these numbers is the tricky part! (Please see previous reply).

> (Best beloved is away for a couple of days. He tried to explain on the phone, but he tends to work
> in pictures rather than words, and apart from noting that the smallest chainwheel and the biggest
> sprocket have the same no of teeth giving a 1:1 ration, his explanation lest me no wiser)

I bet he said the same thing

~PB

M

#### Michael Macclan

##### Guest
On Fri, 20 Feb 2004 00:45:48 +0000, Debbie wrote:

> Please can someone tell me either (a) how to work out whether I have suitable gears, or (b) do the
> arithmetic for me and tell me - preferably (a) as I really ought to get the hang of this stuff.
>
> 3 front chainwheels at the front - 48,38 and 28 6 sprockets on the back, the smallest has 14 teeth
> and the biggest has
> 28.
>
> The wheels are 26 inches.
>

Coming from a beginner like you I suppose the real meaning of your question is whether your gears
are low enough. From your other reports you're progressing well so the answer has to be 'yes'. ;-)

There are lower gears but they're not that much lower than yours so you're best sticking with what
you've got. (It could be very expensive to change.) As you progress further your need for the lowest
gears will decrease anyway.

At this stage try not to bother about the technology, you're better off riding!

--
Michael MacClancy Random putdown - "They never open their mouths without subtracting from the sum of
human knowledge." - Thomas Brackett Reed www.macclancy.demon.co.uk www.macclancy.co.uk

P

#### Peter Clinch

##### Guest
Debbie wrote:
> Please can someone tell me either (a) how to work out whether I have suitable gears, or (b) do the
> arithmetic for me and tell me - preferably (a) as I really ought to get the hang of this stuff.

Kinetics have a gear calculation program you can download free. I've not tried it, but it claims to
handle most variations of gearing devices and wheel sizes readily avaialble.

http://www.kinetics-online.co.uk/html/k_gear.html

Pete.
--
Peter Clinch University of Dundee Tel 44 1382 660111 ext. 33637 Medical Physics, Ninewells Hospital
Fax 44 1382 640177 Dundee DD1 9SY Scotland UK net [email protected]
http://www.dundee.ac.uk/~pjclinch/

J

#### James

##### Guest
Debbie <[email protected]> wrote in message news:<[email protected]>...
> Please can someone tell me either (a) how to work out whether I have suitable gears, or (b) do the
> arithmetic for me and tell me - preferably (a) as I really ought to get the hang of this stuff.
>
> 3 front chainwheels at the front - 48,38 and 28 6 sprockets on the back, the smallest has 14 teeth
> and the biggest has
> 28.
>
> The wheels are 26 inches.

http://www.sheldonbrown.com/gears/ has a calculator and an explanation of what the different ways of
expressing gera ratios mean. You would need to know your crank length to get a figure that is
directly comparable to another bike (probably 175mm). I made up the missing figure and your gears
range from 26 inches to 89.1 inches. This seems to me to be a respectable range for what I know of
your riding (though I guess you will not need the higher gears for a bit).

best wishes james

S

#### Simon Brooke

##### Guest
"Pete Biggs" <ptangerine{remove_fruit}@biggs.tc> writes:

> For comparisions: modern mountain bikes have a wider range, typically
> 22/32/42 with 11-30 (8/9-speed); hybrids can have all sorts. Your top gear is unusually low but
> then a lot of bikes have unnecessarily high top gears - I think it's more important to
> optimise for middle and low gears. Try simply pedalling faster if the high gears feel too
> low.

I have a 54x14 top gear on my road bike, and I find that limits me to about 33mph because I can't
get my cadence up faster (down hills - I have trouble doing much more than 20 on the flat). So you
can't 'simply pedal faster' - the whole range of gears needs to be thought of.

--
[email protected] (Simon Brooke) http://www.jasmine.org.uk/~simon/

;; killing [afghan|iraqi] civilians is not 'justice'

M

#### Michael Macclan

##### Guest
On Fri, 20 Feb 2004 10:05:09 GMT, Simon Brooke wrote:

> "Pete Biggs" <ptangerine{remove_fruit}@biggs.tc> writes:
>
>> For comparisions: modern mountain bikes have a wider range, typically
>> 22/32/42 with 11-30 (8/9-speed); hybrids can have all sorts. Your top gear is unusually low but
>> then a lot of bikes have unnecessarily high top gears - I think it's more important to
>> optimise for middle and low gears. Try simply pedalling faster if the high gears feel too
>> low.
>
> I have a 54x14 top gear on my road bike, and I find that limits me to about 33mph because I can't
> get my cadence up faster (down hills - I have trouble doing much more than 20 on the flat).

;-)

--
Michael MacClancy Random putdown - "He has Van Gogh's ear for music." - Billy Wilder
www.macclancy.demon.co.uk www.macclancy.co.uk

D

#### David Martin

##### Guest
On 20/2/04 12:45 am, in article [email protected],
"Debbie" <[email protected]> wrote:

> Please can someone tell me either (a) how to work out whether I have suitable gears, or (b) do the
> arithmetic for me and tell me - preferably (a) as I really ought to get the hang of this stuff.
>
> 3 front chainwheels at the front - 48,38 and 28 6 sprockets on the back, the smallest has 14 teeth
> and the biggest has
> 28.
>

The gears sound suitable for everything except towing trailers up steep hills and riding downhill
races, so yes they are a good range.

How to use them is a more useful question.

As will have been explained by others, the real size of the gear is the size of the front sprocket
divided by the size of the back sprocket.

In practice this means that a bigger front sprocket will be harder work but will make you go faster.
A smaller front sprocket will be easier but you will go slower.

It is the opposite way round for the back. Big rear sprocket = easy and slow, small rear sprocket =
hard and fast. Check to see what gears you have so you know which way will make it easier/harder.

To choose the right gear, you probably want to start off in the middle at the front and the middle
at the back. If that is ridiculously easy or far to hard then change the front up or down as
appropriate (bigger if it is far to easy, lower if it is far too hard). If it is a bit to easy or a
bit to hard, then change the back gears. I'd guess at first you will be able to ride everything you
want to with it on the middle ring at the front and just using the back gears.

As you get used to it it becomes easier.

regards

..d

W

#### W K

##### Guest
"Michael MacClancy" <[email protected]> wrote in message
news:[email protected]...
> On Fri, 20 Feb 2004 00:45:48 +0000, Debbie wrote:
>
> > Please can someone tell me either (a) how to work out whether I have suitable gears, or (b) do
> > the arithmetic for me and tell me - preferably (a) as I really ought to get the hang of this
> > stuff.
> >
> > 3 front chainwheels at the front - 48,38 and 28 6 sprockets on the back, the smallest has 14
> > teeth and the biggest has
> > 28.

if you have 28 front and 28 back, then your back wheel will be turning at the same speed as your
crank. Hit and miss guesswork puts that as "as low as most people want". I have got something like
28f 34b, so the legs are going faster than the back wheel. Useful sometimes.

I've also got 42/11 - which is OK, but you cannot really go more than 24mph - at which speed I
consider I deserve a rest. Again hit and miss but 42/11=3.82 ... 48/14 = 3.43 ... So you'll have a
lower speed to give up pedalling. (All this is mountain bike wheels and an approximation of course,
but getting the gearing you like is hit and miss)

> Coming from a beginner like you I suppose the real meaning of your
question
> is whether your gears are low enough. From your other reports you're progressing well so the
> answer has to be 'yes'. ;-)

I'd have thought in Sheffield, you can never have low enough gears.

> As you progress further your need for the lowest gears will decrease anyway.

Not if "further" includes adventuring out onto the penines, or when you come back knackered (after
one or many days!).

D

#### Dirtylitterboxo

##### Guest
>Please can someone tell me either (a) how to work out whether I have suitable gears, or (b) do the
>arithmetic for me and tell me - preferably (a) as I really ought to get the hang of this stuff.
>
>3 front chainwheels at the front - 48,38 and 28 6 sprockets on the back, the smallest has 14 teeth
>and the biggest has
>28.
>
>The wheels are 26 inches.

Well, it does mean you have 18 to choose from

Gearing is a personal thing I think. Mine has 27 (triple chainwheel & 9 sprockets at back) and I
have been known to need them all - with emphasis on the low ones when going up a hill Where I
*need* to use a low gear and spin to get up a hill, the offspring can do the same hill in big
chainring and small sprocket - BAH!

In all seriousness - I find that now I'm fitter, I rarely have to use the smallest chainwheel for
climbing the hills in Norfolk. I would if I were in Sheffield though ;-)

General principle - one can never have too many gears to choose from. Works for me

Cheers, helen s

--This is an invalid email address to avoid spam-- to get correct one remove dependency on fame &
fortune h*\$el*\$\$e**nd***\$o\$ts***i*\$*\$m**m\$\$o*n**[email protected]\$*\$a\$\$o**l.c**\$*\$om\$\$

P

#### Peter Clinch

##### Guest
dirtylitterboxofferingstospammers wrote:

> Gearing is a personal thing I think. Mine has 27 (triple chainwheel & 9 sprockets at back) and I
> have been known to need them all

The whole range, quite possibly, but all 27 gears almost certainly not. The 3x9 on my tourer gives
me about 14 effective different gears as there's loads of overlap in silly rations like turning
small cogs from the small chainwheel.

> General principle - one can never have too many gears to choose from. Works for me

"yes but...". More gears costs more money and if you want lots then that rules out hubs (aside from
the Rohloff, but they cost more than most bikes) which are very good for a road-based utility cycle.
My Brompton has 3 fairly low gears, and is all I need to get me round a hilly town. It'll spin out
downhill, but that's what gravity's for, and in return I get very little maintenance and far less
chain wear. More gears means more flexible, but more expense and "more flexible" is pointless if you
don't use it (I have no need of a huge gear on the Brompton, so I don't miss not having one).

Pete.
--
Peter Clinch University of Dundee Tel 44 1382 660111 ext. 33637 Medical Physics, Ninewells Hospital
Fax 44 1382 640177 Dundee DD1 9SY Scotland UK net [email protected]
http://www.dundee.ac.uk/~pjclinch/

M

#### Michael Macclan

##### Guest
On Fri, 20 Feb 2004 11:59:00 +0000, Peter Clinch wrote:

> dirtylitterboxofferingstospammers wrote:
>

>
>> General principle - one can never have too many gears to choose from. Works for me
>
> "yes but...". More gears costs more money

I think Pete's right. This isn't the time to be telling Debbie she needs lots of gears. Better for
her to use what she's got, which isn't bad anyway.

Unless, of course, the lack of a real granny gear is putting her off totally.

But I thought there was a second bike? Or is it the second bike we're discussing?

--
Michael MacClancy Random putdown - "He has Van Gogh's ear for music." - Billy Wilder
www.macclancy.demon.co.uk www.macclancy.co.uk

D

#### Debbie

##### Guest
On Fri, 20 Feb 2004 12:22:59 +0000, Michael MacClancy
<[email protected]> wrote:

>On Fri, 20 Feb 2004 11:59:00 +0000, Peter Clinch wrote:
>
>> dirtylitterboxofferingstospammers wrote:
>>
>
>>
>>> General principle - one can never have too many gears to choose from. Works for me
>>
>> "yes but...". More gears costs more money
>
>I think Pete's right. This isn't the time to be telling Debbie she needs lots of gears. Better for
>her to use what she's got, which isn't bad anyway.
>
>Unless, of course, the lack of a real granny gear is putting her off totally.
>
>But I thought there was a second bike? Or is it the second bike we're discussing?

This is the second bike. The one I'm currently using has Sturmey Archer three speed, so pretty well
anything on the newer bike is bound to be better!

D

P

#### Peter Clinch

##### Guest
Debbie wrote:

> Please, do keep posting in that vein. At some point in the future I shall be negotiating for a
> *new* bike, and I'd like to start the subliminal messages now to be sure that BB is properly
> brainwashed by then, prefereably to the point where he says something like "Carbon frame? But of
> course, what else? And Campo-wissit gazillion speed gears? Absolutely essential. No, don't skimp.

If you're not skimping get a Rohloff Speedhub. "Only" 14 gears but=20 similar range and steps to a
3x9 touring setup but with less wear and=20 practically maintenance free. And about =A3600 just for
the hub, but lik= e=20 you say, don't skimp! ;-)

Pete. --=20 Peter Clinch University of Dundee Tel 44 1382 660111 ext. 33637 Medical Physics,
Ninewells Hospital Fax 44 1382 640177 Dundee DD1 9SY Scotland UK net [email protected]
http://www.dundee.ac.uk/~pjclinch/

P

#### Pete Biggs

##### Guest
Simon Brooke wrote:
>
>> For comparisions: modern mountain bikes have a wider range, typically
>> 22/32/42 with 11-30 (8/9-speed); hybrids can have all sorts. Your top gear is unusually low but
>> then a lot of bikes have unnecessarily high top gears - I think it's more important to
>> optimise for middle and low gears. Try simply pedalling faster if the high gears feel too
>> low.
>
> I have a 54x14 top gear on my road bike, and I find that limits me to about 33mph

That's fast enough for most non-racer types when pedalling, and different cyclists prefer or can
manage different cadences (so top speed will vary according to the cyclist). Your ultimate top speed
won't be limited to 33mph though. 40mph+ should be possible down steep hills by freewheeling.

> because I can't get my cadence up faster (down hills - I have trouble doing much more than 20 on
> the flat). So you can't 'simply pedal faster' - the whole range of gears needs to be thought of.

Certainly think about the whole range but don't necessarily do anything about it as the alternative
is to live what you've got and accept that a compromise has to be made somewhere. No gear system can
be perfect.

A lot of new cyclists (or cyclists on new bikes) use too low a cadence so it's worth at least trying
to pedal faster before changing the gearing. When that's just not possible (eg. down steep hills),
one has always got the option of freewheeling. That's not great but it's much better than having the
bottom gear too high or the gears spread too far apart.

~PB

I

#### Ian Smith

##### Guest
On Fri, 20 Feb 2004, Debbie <[email protected]> wrote:
> Please can someone tell me either (a) how to work out whether I have suitable gears, or (b)
> do the arithmetic for me and tell me - preferably (a) as I really ought to get the hang of
> this stuff.
>
> 3 front chainwheels at the front - 48,38 and 28 6 sprockets on the back, the smallest has 14
> teeth and the biggest has
> 28.
>
> The wheels are 26 inches.

I'll avoid discussing gear ratio calculation, that seems to be done to death.

It's a pretty good setup. It's very nearly what I had on my utility bike for 10 years or so. You may
be able to do better for your particular style of riding and usage, but not 'till you've found out
what that is. Therefore, this is a good starting point and I wouldn't spend money 'till you've seen
what this feels like.

If you find you're forever running out of gears at one or other end of teh range, then you can
adjust what you have. For a round-town utility bike, where the town is Sheffield, I'd expect you
might want to go a bit lower, but as I say, I wouldn't spend money 'till you've ridden it for
several months.

regards, Ian SMith
--
|\ /| no .sig
|o o|
|/ \|

S

#### Simon Brooke

##### Guest
[email protected] (dirtylitterboxofferingstospammers) writes:

> In all seriousness - I find that now I'm fitter, I rarely have to use the smallest chainwheel for
> climbing the hills in Norfolk.

Wasn't it for Norfolk's mountains that single-speed mountain bikes were invented?

--
[email protected] (Simon Brooke) http://www.jasmine.org.uk/~simon/ ;; If God does not write LISP,
God writes some code so similar to ;; LISP as to make no difference.

A

#### Andrew Sweetman

##### Guest
Simon Brooke <[email protected]> ...
> "Pete Biggs" <ptangerine{remove_fruit}@biggs.tc> writes:
> > For comparisions: modern mountain bikes have a wider range, typically
> > 22/32/42 with 11-30 (8/9-speed); hybrids can have all sorts. Your top gear is unusually low but
> > then a lot of bikes have unnecessarily high
top
> > gears - I think it's more important to optimise for middle and low
gears.
> > Try simply pedalling faster if the high gears feel too low.
>
> I have a 54x14 top gear on my road bike, and I find that limits me to about 33mph because I can't
> get my cadence up faster (down hills - I have trouble doing much more than 20 on the flat). So you
> can't 'simply pedal faster' - the whole range of gears needs to be thought of.
>

Pedalling faster is something you can learn to do, within limits. I've got up to 37mph on 46x19

T

#### Tony Raven

##### Guest
Andrew Sweetman wrote:
>
> Pedalling faster is something you can learn to do, within limits. I've got up to 37mph on 46x19

A fixed and a few hills is good for learning.

Tony

Status
Not open for further replies.