Help needed in calculating speed

Hello friends,

I have a Honda 4 stroke motorcycle. I wish to know the steps required
in calculating the actual ground speed (in kmph) based on the
following factors:

a] Engine RPM ==> known from rpm meter on console
b] Primary reduction ==> known from user manual
c] Gear number and ratio ==> known from user manual
d] Final drive reduction ratio ==> known from user manual
e] Tyre circumference ==> radius known from user manual. Circumference
derived using 2.PI.radius.

I have done the follwing.

a] My manual says the rear tyre is 3.00 - 18 57P. So i know that it is
an 18 inch radius tyre. I then convert 18 inches to metres and got
0.4572 metres. Thus, my rear tyre has a radius of 0.4572m.

b] My Primary reduction is 3.350.

c] My first gear ratio is 3.076, and

d] My Final drive reduction is 2.800.

Now, if i engage first gear and move off normally (that is without
wheel "slip") and i maintain engine RPM of 2500 on the RPM metre, i
want to know how many revolutions my tyre will make per kilometre in
the first gear.

I have managed to calculate the RPM of the wheel in *first* gear to be
as follows:

RPM at rear wheel = Engine RPM / Primary reduction / First Gear Ratio
/ Final Drive Reduction.

To illustrate:

RPM @ rear wheel in Gear 1 = 2500 / 3.350 / 3.076 / 2.8

Which gives me: 86.6464 RPM at the rear wheel.

Now using this and the circumference of the wheel (calculated above)
how do i determine the RPM of the wheel per kilometre *in the first
gear*? I also want to extend this to calculate the same quantity for
any gear ratio on my vehicle.

Thank you for your response in advance.
Have a great day,
Kaizer.

 

kilometer / circumference (in km). This will be the same for all gears.
However, you would do better to measure the actual radius, and better yet
to chalk the tire or use some other reference point on the tire, roll the
bike forward one revolution, and measure the distance on the ground. Even
that will not be entirely accurate, but will be close enough for most
purposes. You could also roll it several revolutions and divide out the
distance by the revolutions. That will also help you visualize how many
times you will have to roll it to cover a kilometer.

 

This is not the same thing as wanting to know the speed of your vehicle.
Revolutions per kilometer will be 1km/circumference, in any gear. The
only thing that changes as gears change is how fast you complete this
number of revolutions.

In order to obtain speed (which is different from revolutions per
kilometer), multiply your circumference by your rpm at the rear wheel.
This gives you distance per minute. Multiply by 60 to get distance per
hour, and convert distance into km.

The most accurate way to obtain a circumference value for a tire is to
measure it directly, not to calculate it. As other people have already
mentioned, your calculations of circumference are incorrect in any case.

Generalizing the above to other gears is left as an exercise for the
student...and this does rather remind me of certain math exercises that
I've done in the past.

I'll note that as a practical matter, the easiest way of getting actual
speed values for a motorcycle in motion and without a working
speedometer is to install a bicycle speedometer. You tell the computer
what your wheel circumference is, affix the sensor to some rotating
portion of the wheel (usually the brake disk carrier, making sure that
it doesn't hit anything) and the sensor to your fork leg. You have a
digital speedo. Some models are backlit, some can be wired into your
bike's harness more easily than others.

A search of this group's archives or the web will find lots of
information about this modification.