# Speed and Rpm Calculations for Jackshafts, Sprockets, CVT's and Gear Trains

Discussion in 'General Questions' started by 210061741, Oct 30, 2009.

1. ### 210061741Guest

Ok i haven't seen this put together in 1 place so i'll start here.
We will take a deep look at speeds and Rpm's the best way.

In order to hit the speed we want and not kill our motor and not peddle too fast we need to consider all these figures.

I'm still working on the diy Jackshaft but there are actually several topics going on in that thread right now.
We do need that data as well but i think it will be more helpful to break some of this into seperate threads.

I have some math to do here and will post calculations soon.

Any help from other members is appreciated.

2. ### 210061741Guest

Wheel RPM to Ground Speed

Wheel RPM TO GROUND SPEED.

26" WHEEL - .5" FOR squishing under pressure.

Circumfrance = 80.11061266653972 inches.

feet in a mile = 5280 feet

Inches in a mile = 63360 inches

# of wheel rotations per mile =
63360 / 80.11 = 790.91 rotations per mile

---------------------------------------------
Desired Take off Speed = 5 MPH
790.91 X 5 = 3954.56 rotations per hour
3954.56 / 60 min = 65.91 RPM
Wheel speed = 65.91 RPM at 5 MPH
---------------------------------------------

Desired Max Speed = 45 MPH
790.91 x 45 = 35590.95 rotations per hour
35590.95 / 60 min = 593.1825 rpm
wheel speed = 593.1825 RPM
--------------------------------------------

So that is a nice range.
Not that we need to go that slow or fast.
Just baseline calculations to show extreme
min and max wheel rpm.

The main thing to consider right now is what
is the slowest the bike can move when the clutch
engages without stalling the engine.

= Drive Gear RPM divided by Overall Gear Ratio
This = the required Wheel rpm to not stall engine.

example:
HT motor 4:1 ratio internal gearing
1000 rpm motor speed.

1000 / 4.1 = 243.9024 RPM of 10T Drive Gear

10T Drive / 36T Driven = 3.6 : 1 ratio

243.9024 / 3.6 = 67.75 RPM

This means if your wheel is not rotating 67.75
revoloutions in a min your engine will stall if it is
running at 1000 rpm

3. ### 210061741Guest

Engine Rpm Vs Wheel Speed And Gears

ENGINE RPM VS WHEEL SPEEDS AND GEARS.

I will use some standard Sprocket configs to
figure out where we want to start.

So lets say 32T is the largest sprocket we have
on the Rear Cartrige or Freewheel.
This will be our lowest gear we need to get 5 MPH
at just above engine idle.

Wheel speed = 65.91 RPM at 5 MPH
32T Sprocket speed = 65.91 RPM at 5 MPH

For the JACKSHAFT we need to figure the nessessary rpm
of the next sprocket.
Which would be the Crank Sprocket at the Front Freewheel
that the bicycle chain is on.

We will call it sprocket 2 = "S2"
Since it is available we will figure on 44T for "S2"

Gear ratio = 44 / 32 = 1.375 : 1

65.91 / 1.375 = 47.935 Rpm at 44T at 5 MPH

Now lets figure what our jackshaft speed will need to be.

Engine Rpm at takeoff = 1000RPM
1000 / 4.1 = 243.91 RPM

243.91 / 47.953 = 5.086 : 1 ratio

----------------------------------------------------------------------
Now things are a little more complex here because we have
1 speed for the Jackshaft and 2 gears on it.
This means we need to work out 2 ratios that get the
44T sprocket moving at 47.953 RPM.

We cant solve for 2 variables so we will have to pick 1 sprocket.
We will start with the 17T sprocket on the left side of the Jackshaft.
Because it is available.

17T / 10T = 1.7 : 1 ratio.

243.91 / 1.7 = 143.4764 rpm at the 17T and Jackshaft

143.4764 / 47.953 = 2.99 : 1 ratio. so lets say 3:1

We also have another unknow sprocket in the system.
The 2nd front crank freewheel sprocket is smaller than the 44T
For chain interference we want some clearence.

Now the 36T is used

36 / 3 = 12
So a 12T would be optimal with the starting speed of 5MPH

The 12T isn't available.

Chainring sprockets are easy to come by so we could go a little smaller
than the 36T or a little bigger than the 44T.

There is a 48T available.

11T is pretty close lets look at it.

36 / 11 = 3.27 ratio
143.4764 / 3.27 = 43.8765 RPM

44 / 32 = 1.375 : 1

43.8765 X 1.375 = 60.3301 rpm of wheel.

60.3301 X 60 = 6319.806

6319.806 / 790.91 = 7.9905 MPH
---------------------------------------------------------------

So after all that heres how the cookie crumbles.

WITH MOTOR RPM = 1000
10T drive at motor at 243.91 RPM
17T at jackshaft at 143.4764 rpm
11T at jackshaft at 143.4764 rpm
36T at Front Freewheel at 43.8765 rpm
44T at front Freewheel at 43.8765 rpm
32T at wheel at 60.3301 rpm

Minimum peddeling speed = 7.9905 mph

--------------------------------------------------------------------

Lets figure the max speed.

Tuned Engine RPM = 6000
6000 / 4.1 = 1463.41 rpm at 10T
1463.41 / 1.7 = 860.832 rpm at 17T
860.832 rpm at 11T
860.832 / 3.27 = 263.2514 rpm at 36T
263.2514 at 44T sprocket

So in the same gear the 32T at the rear wheel
263.2514 x 1.375 = 361.97 Rpm at rear wheel

361.97 X 60 = 21718.2405
21718.2405 / 790.71 = 27.46 mph

So the low gear range is from 7.9905 MPH to 27.46 MPH

Remember we can shift now.

High gear lets say = 11T its pretty std on freewheels.

Now things get easier.
44 / 11 = 4 :1

263.2514 X 4 = 1053.0056 rpm

1053.0056 X 60 = 63180.36
63180.36 / 790.71 = 79.90 mph

Wow thats all i can say.
If you had a long enough run you could get there.

Specified engine rpm = 4500
4500 / 4.1 = 1097.56 rpm at 10T
1097.56 / 1.7 = 645.62 rpm at 17T and 11T
645.62 / 4 = 161.25 rpm at 44T
161.25 X 4 = 645.62 rpm at 11T rear freewheel
645.62 X 60 = 38737.2
38737.2 / 790.71 = 48.99 MPH.
STILL VERY IMPRESSIVE.

WITH 24T REAR SPROCKET
161,62 X (44/24) = 296.30
296.30 X 60 = 17778
17778 / 790.71 = 22.48 MPH

-----------------------------------------------------
tUNED ENGINE RPM = 6000 RPM
161.25 X (44/18) = 394.16
394.16 x 60 = 23650
23650 / 790.71 = 29.90 MPH
-----------------------------------------------------

vERY EASY TO SEE THE EFFECTS OF THE JACKSHAFT.
THE UNANSWERED QUESTION IS HOW MANY RPM DO WE
REALLY GET WITH THE TUNED ENGINE.

AND EVEN AT 4500 RPM THE SPEED GETS PRETTY HIGH.

iTS A MATTER OF HOW QUICKLY CAN WE GET TO SHIFTING SPEEDS
tHE 79.90 WOULD REQUIRE 7 TO 8 SHIFTS.

PLEASE ALSO NOTE IT IS MOST LIKLY INTENDED FOR THE 36T CHAINRING
TO DRIVE THE REAR FREEWHEEL.

I CALCULATED THIS THE OTHER WAY AROUND WHICH MAKES THINGS ALOT FASTER.

TO CLARIFY THE 11t JACKSHAFT SPROCKET SHOULD NORMALLY GO TO THE 44T CHAINRING.
tHAT MAKES A 4:1 REDUCTION.

WITH THE 11T GOING TO THE 36T WE HAVE A 3.27 REDUCTION.

tHAT MAKES A BIG DIFFERENCE.

bUT DEPENDING ON HOW NUTTY YOU WANT TO BE.
I DON'T SEE WHY YOU COULDN'T RUN THE FRONT FREEWHEEL EITHER WAY.
iT'S A MATTER OF HOW YOU PUT THE SPROCKETS ON.

NOW I REALLY UNDERSTAND WHY THESE JACKSHAFTS ARE LIKE GOLD.
LOOK AT WHAT IT ACCOMPLISHES.

GENERALLY IF CONFIGURED CORRECTLY.
YOU WOULD NEVER NEED TO RUN THE ENGINE AT HIGH RPM.

4. ### FabianWell-Known Member

Hi Rich

Your maths breakdown are far more impressive than mine - i like it!

With a standard 69cc Happy Time style engine, the rpm zone to keep below is 3500.
Above 3500 the engine starts to vibrate quite a bit and by 4500 you'll need superglue to hold your dentures in place - i've identified a possible manufacturing cause for the problem.

My bike set up with an 11-32T 9 speed cassette and running the optional 11 tooth SickBikeParts sprocket has the bike travelling at 30 miles an hour, turning 3,500 rpm.

Shimano has now brought out a 12-36T 9 speed cassette.
I have found that the 32T is too tall for a 1st gear and the 36T would be much better.

Actiontec sells individual titanium and heat treated titanium sprockets, up to 39T for cassettes - just amazing, scroll down to Titanium Cogsets

http://www.actiontec.us/prices.htm

Last edited: Oct 31, 2009
5. ### loquinActive Member

You may also be interested in this utility

6. ### FabianWell-Known Member

Hi Loquin

That gear calculator is excellent - can it be modified to include all the variables for the SickBikeParts shift (shifter) kit

Fabian

7. ### 210061741Guest

Yes there are calculators out there to do the math.
But the brain needs some exercise too.
I really begin to create pictures and thoughts and sometimes the most profound discoveries are made when my brain is runnin 4000 rpm.
The math is stimulating to me and sometimes when i sit and think about the math i need to figure out what i want to know i get a deeper understanding of the MOTOR / CVT / GEARING ect.

Sometimes I have to smile cause you can see they have put some thought int the HT.

To awaken the brain is a great feeling.

8. ### loquinActive Member

Well, it handles up to five ratios. Just use the + & - buttons to add a ratio or remove the last ratio.

Crank to output (apx. 4:1 ?)
Output to Jackshaft
Jackshaft to chainring
chainring to rear cog

is four.