# Calculators and Comparators marius-ciclistu

### "Power is a denatured mirroring of force and acceleration in thermal engines' regard."

#### Marius Pantea feb.2017

GEAR RATIO - it is the ratio between the driver shaft angular speed and the driven shaft angular speed from the gearbox. In other words the ratio between the number of teeth of the driven sprocket that is on the driven shaft in the gearbox and the number of teeth of the driver sprocket that is on the in shaft coupled to the engine with the clutch. Example: 3.17:1 which means 3.17 rotations of the motor shaft at 1 rotation of the driven shaft. In this case we input 3.17 in the calculator. You can find these ratios here.

FINAL DRIVE RATIO - has the same definition with the gear ratio with the specification that the drive it refers to is between the driven shaft and the shaft that transmits the movement to the wheel.

Pmax/RPM - indicates the maximum power developed by the engine and the rotation speed at which it occurs. It's measured in KW.
See the difference between HP & HF (Horse Force).

Tmax/RPM - indicates the maximum torque developed by the engine and the rotation speed at which it occurs. It's measured in Nm.

## Motorcycle Transmission Calculator and Comparator

Input a name for this calculation

Input your traction tyre size* (sizes).
Example 190/55 R17 (190/650 R17)

/  vs  /
R  vs  R

Input, in the indicated order, the gear ratios (as x.xxx) (1->5*).

1 2 3
4 5 6

Input the final drive ratio* (as x.xx).

Input Pmax/RPM*.

kW/ RPM

Input Tmax/RPM*.

Nm/ RPM

Input vehicle's total Mass*.

Kg

-- Optional data ( show / hide ) --

See the results

Tyre (tyres) Info

Width (mm):

vs

Height (mm):
vs

Diameter (mm):
vs

Circumference (mm):
vs

OBSERVATIONS:
a. Changing the tyre/wheel dimensions influences only the real speed (Attention, not the one indicated by the gauge!) and the force applied at the circumference of the traction wheel:
- by lowering the diameter, the force applied at the circumference of the traction wheel will rise and the real speed will drop,
- by rising the diameter, the force applied at the circumference of the traction wheel will drop and the real speed will rise.
- this force applied at the circumference of the traction wheel is influenced also by it's mass => it's inertia.
b. The torque at the traction wheel changes only by changing gear, not by changing the diameter or mass of the wheel.
c. The power at the traction wheel is equal with the power at the flywheel minus the losses through friction in the transmission. So, the power at the traction wheel does not vary by it's diameter (it varies by it's mass/inertia). Therefore results that for the same power at the traction wheel there are multiple values for the force (that is influenced by the wheel's mass so we are discussing about equal masses and equal distribution of the mass for different diameters) applied at it's circumference and so, a different behaviour of the motorcycle.

## Results

1st gear:

Speed at RPM (KM/H):
vs

Speed at RPM (KM/H):
vs

Torque at RPM at the traction wheel (Nm):
vs

Acceleration imposed to the vehicle at RPM (m/s2):
vs

Force at RPM applied at the traction wheel's circumference (N):
vs

Force at RPM applied at the traction wheel's circumference (N):
vs

2nd gear:

The rotation speed at which the engine resumes the traction if the previous gear is changed at RPM:
vs

Force at RPM applied at the traction wheel's circumference (N):
vs

Speed at RPM (KM/H):
vs

Speed at RPM (KM/H):
vs

Torque at RPM at the traction wheel (Nm):
vs

Acceleration imposed to the vehicle at RPM (m/s2):
vs

Force at RPM applied at the traction wheel's circumference (N):
vs

Force at RPM applied at the traction wheel's circumference (N):
vs

3rd gear:

The rotation speed at which the engine resumes the traction if the previous gear is changed at RPM:
vs

Force at RPM applied at the traction wheel's circumference (N):
vs

Speed at RPM (KM/H):
vs

Speed at RPM (KM/H):
vs

Torque at RPM at the traction wheel (Nm):
vs

Acceleration imposed to the vehicle at RPM (m/s2):
vs

Force at RPM applied at the traction wheel's circumference (N):
vs

Force at RPM applied at the traction wheel's circumference (N):
vs

4th gear:

The rotation speed at which the engine resumes the traction if the previous gear is changed at RPM:
vs

Force at RPM applied at the traction wheel's circumference (N):
vs

Speed at RPM (KM/H):
vs

Speed at RPM (KM/H):
vs

Torque at RPM at the traction wheel (Nm):
vs

Acceleration imposed to the vehicle at RPM (m/s2):
vs

Force at RPM applied at the traction wheel's circumference (N):
vs

Force at RPM applied at the traction wheel's circumference (N):
vs

5th gear:

The rotation speed at which the engine resumes the traction if the previous gear is changed at RPM:
vs

Force at RPM applied at the traction wheel's circumference (N):
vs

Speed at RPM (KM/H):
vs

Speed at RPM (KM/H):
vs

Torque at RPM at the traction wheel (Nm):
vs

Acceleration imposed to the vehicle at RPM (m/s2):
vs

Force at RPM applied at the traction wheel's circumference (N):
vs

Force at RPM applied at the traction wheel's circumference (N):
vs

The transmission will generate the force applied to the circumference of the traction wheel / R ,
equivalent with the force generated on the circumference of the initial traction wheel / R by:

OBS. 1.The torque at the traction wheel doesn't change if the tyre is changed. By changing
the radius of the wheel, the only thing that changes is the force applied to the circumference of the wheel.
2.The above values don't take into account the tyre's pressure or wear, the air friction force
or other resistive forces that appear in real situations, this being theoretical values.
3.The calculated torque at the traction wheel takes no account of the transmission's losses.
4. All the calculations are taking into consideration the outside diameter of the traction tyre (when cornering, the contact patch is placed on a smaller outside diameter of the tyre).

Graph 1

For a better interpretation of these values you need the torque chart from the engine
[You can find here that kind of charts and you can transform them in table data here].

Graph 2^^

The above graph is useful only if rotational speed values and respectively torque values of the engine from the torque chart were inputted and it refers, especially, to / R wheel, / R wheel having displayed only the graph of total force at their circumference depending on the rotational speed of the engine, in 1st gear (for keeping the graph readable).

For a clearer view of the differences that appear when changing the wheel, print in pdf this report, then change the dimensions of the tyre in the fields from the beginning of the calculator and compare the graphs.

If the rotational speed values and respectively torque values are deduced by measuring the force at the traction wheel's circumference, in a certain gear, without adding the losses (or the power loss), the curve from the above graph that coresponds to the same gear in which the measurement was made has REAL ~ VALUES!

For maximum performance, the gold colored lines "Shift _-_" from the above graph must be ~HORIZONTAL !

Graph 3^^

The above graph is useful only if rotational speed values and respectively torque values of the engine from the torque chart were inputted and it refers only to / R wheel.

For a clearer view of the differences that appear when changing the wheel, click on compare button, then change the dimensions of the tyre in the fields from the beginning of the calculator and compare the graphs.

This graph shows forces and accelerations generated by the engine+transmission unit at the traction wheel's circumference, without taking into account the transmission loses. If the rotational speed values and respectively torque values are deduced by measuring the force at the traction wheel's circumference, in a certain gear, without adding the losses (or the power loss), the curve from the above graph that coresponds to the same gear in which the measurement was made has ~ real values but
ATTENTION! These forces are NOT the RESULTANT FORCES that act upon the vehicle because the air friction force or other resistive forces are NOT included! The possible tyre skating is not taken into account!

For maximum performance, the gold colored lines "Shift _-_" from the above graph must NOT be visible !

Graph 3^^^ (air resistance included)

This graph appears only if values for air resistance calculation (drag coefficient, reference area and air's density) were inputted. For example, the first two can be found here.

The air resistance alters the gears' graph lines in a nonlinear whay.
It can be observed especially when the torque:RPM pairs of data points are far apart from each other.
That is why, in those cases, the fill areas in higher gears are not matching 100% with the gears' graph lines.

Use the fluid resistance calculator to see the drag force graph.

The air velocity relative to the ground is considered 0.

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### Acceleration time

[s]* The shifting time is NOT included. The air drag IS NOT taken into consideration in the actual calculation.

The start speed for this actual estimation is 0 km/h and the top speed is ~ 0 km/h.

In the actual calculation, the total force used to estimate the acceleration time in last gear is ... N.
That is why, in some cases, if the the gear's graph line has a small slope, the accelerating time in that gear appears to be big (incorrect).

When including the air's resistance, if the top speed would be the value at which the total force or acceleration is 0,
then the time needed for the motorcycle to reach that speed increases very much, to over tens of minutes, even hours.

### Efficient approach in drag race

*IF the shifting RPMs are autocompleted for MAXIMIZING THE TRANSMISSION'S PERFORMANCES and the inputted torque graph is measured with the throttle TURNED as close to 100% as the adherence and avoiding backflipping allows it!