PCB Heaven
General Category => Maths, Geometry, Physics and others => Topic started 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?

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.

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! ;)

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.

? ??? ??? ???
I really did not get it. Can you explain?

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?

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.

gr= gear ratio
frac= fraction "κλάσμα" in greek, a division that is :)

Lol! This looks like Greek to me!

κλάσμα
:o :o :o :o :o :o :o :o :o
lol What the heck! Maybe i will learn Greek next year ::) ::) ::) ::)

Ok people, i checked it and i must say that D/d is corect.
Thank you all!

Of course is ok >:(