# PCB Heaven

## General Category => Maths, Geometry, Physics and others => Topic started by: Andre on March 11, 2008, 07:53:08 AM

Title: Gear ratio
Post by: Andre on March 11, 2008, 07:53:08 AM
This is burning my brain these days.
I have a bike and i want to calculate the transmision ratio of the front and rear gear. This topic is in continue to another topic ( Speedometer max for my Yamaha (http://pcbheaven.com/forum/index.php?topic=5.15)

So, my front gear has 13 teeth and my rear has 41. This is 41/13=3.1538. Is this my transmission ratio? I have an rpm meter and i measure the front and rear rpm and the division is not the same with my ratio.

Help anyone?
Title: Re: Gear ratio
Post by: FelIX on March 13, 2008, 23:24:57 PM
I know that the ratio is not exactly calculated by the teeth of the gears. I know that it is a number with some decimal places (really do not remember what) that is changes as the teeth number change.
Check it better. This is not the right way.
Title: Re: Gear ratio
Post by: kam on March 14, 2008, 00:11:06 AM
It is only and only the diameter that counts. No matter how many teeth, you must divide the diameters of the disks to get the ratio.
In our case, because the change of teeth is from let's say 38 to 46, someone has calculate the average that a teeth will increase the diameter and has given this number. It is an approximately value that sometimes responds to reallity but if you know the right way to calculate it, DIY!  ;)
Title: Re: Gear ratio
Post by: spic0m on March 14, 2008, 01:16:10 AM
When the motion to the gears is transfered by a chain (as in your bike) or a belt other calculations occur such as chain slippage, difference in gear velocities and other. A general type is below where d is the diameter of the smaller gear and D of the bigger

gr = \frac{\pi d}{\pi D} = \frac{d}{D}

Since the diameter is equal to twice the radius

gr = \frac{d}{D} = \frac{2r}{2R} = \frac{r}{R}

Also gears are not usually absolut in dimensions but have a little "missallingment" to their teeth for having a more uniform wear and for that making calculations more difficult.
Title: Re: Gear ratio
Post by: kam on March 14, 2008, 14:16:58 PM
?  ??? ??? ???

I really did not get it. Can you explain?
Title: Re: Gear ratio
Post by: kostas on March 17, 2008, 08:17:33 AM
gr = \frac{\pi d}{\pi D} = \frac{d}{D}
gr = \frac{d}{D} = \frac{2r}{2R} = \frac{r}{R}

what is frac? gr? {...} ?
are these maths? how are they explained?
do you need to be a scientist to find the ratio?
Title: Re: Gear ratio
Post by: manley_V on March 18, 2008, 00:19:40 AM
Do not confuse. You have 2 gears. Each one has a rotating speed that depends only to the diameter.

The diameter ratio will give you the gear ratio.
Title: Re: Gear ratio
Post by: spic0m on March 18, 2008, 22:05:21 PM
gr= gear ratio
frac= fraction "κλάσμα" in greek, a division that is  :)
Title: Re: Gear ratio
Post by: Supernova on March 19, 2008, 08:10:00 AM
Lol! This looks like Greek to me!
Title: Re: Gear ratio
Post by: tpone on March 20, 2008, 02:42:41 AM
κλάσμα
:o :o :o :o :o :o :o :o :o
lol What the heck! Maybe i will learn Greek next year  ::) ::) ::) ::)
Title: Re: Gear ratio
Post by: Andre on March 23, 2008, 09:16:26 AM
Ok people, i checked it and i must say that D/d is corect.

Thank you all!
Title: Re: Gear ratio
Post by: spic0m on March 26, 2008, 22:00:44 PM
Of course is ok  >:(