e-skate calculator

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range calculation

kg
kph
Ohm
A
0
mAh

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0.0 km
0.0 W
0.0 W
0.0 %

speed calculation

Teeth
Teeth
mm
rpm/V
0

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1 : 1
0.0 kph
0.0 rpm

power calculation

kg
kph
s
km
km
0
0
0

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0.0 A
0.0 W
0.0 mAh
0.0 Wh/km

ratio calculation

kph
mm
Teeth
rpm/V
0

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1 : 1
0 T
0.0 rpm

belt calculation

Teeth
Teeth
mm

Results

1 : 1
0 mm
0 T

battery calculator

mAh
A
0
0

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0 V
0 mAh
0.0 W

calculator physics

Power and range

This calculator is based on physical models to estimate the relationship between power, capacity, and desired performances.

The power is what the motor provides to forward movement, by overcoming forces. Those forces are different whether you are accelerating or staying at a constant speed and riding on flat or uphill. In total, four majors forces are present: inertia, gravity, rolling resistance, aerodynamic drags.

Inertia

Inertia appears during acceleration. It is the resistance of a mass, like a rider or a board, to changes in its velocity. The heavier this mass is, the hardest it is to start a movement.

This force also depends on the acceleration, that is to say, the change in your velocity over a given time, expressed:

$a = \large { \frac{V}{t_{start}} }$

where:

Finally, the formula for inertia is:

$F_{ie} = (m + M).a$

where:

Gravity

The gravity becomes an opposing force when you go uphill. The formula for gravity force in $N$ is:

$F_g = (m+M).g.\text{sin}\left(\text{arctan}(G)\right)$

where:

Rolling resistance

This force is due to the friction between wheels and road. This friction is lower with urethane wheels on good quality roads than with pneumatics on grass. Also, the heavier the rider is, the higher this force is.

The formula for rolling resistance in $N$ is:

$F_r = C_{rr}.(m+M).g.\text{cos}\left(\text{arctan}(G)\right)$

where:

The coefficient rolling resistance $C_{rr}$ translates the quality of the road and the type of wheels. We have estimated the $C_{rr}$ as below

Aerodynamic drag

This is the air resistance that opposed to the rider motion and is proportional to the square of the velocity and the frontal area. The frontal area is the area of the rider when looked from the front.

The formula for the aerodynamic drag in $N$ is:

$F_a = \frac{1}{2}.C_d.A.\rho.V^2$

where:

For a rider, $C_d.A$ is estimated equals to $0.6m^2$

Acceleration phase

During this phase, that we consider on flat, three major forces are presents: rolling resistance, aerodynamic drag, inertia. The resistive force formula in $N$ is:

$F = F_{ie}+F_r+F_a$

Constant velocity phase

During this phase, the inertia is replaced by gravity when you are going uphill. The resistive force is:

$F = F_g+F_r+F_a$

Power

Power is proportional to the resistive forces, but also to the velocity. Its formula is:

$P_w=F.V$

where:

Power losses

As you all know, our world is not perfect, a part of the motor power is dissipated by your drivetrain, but also by your electrical components, like motor resistors, windings. We can consider $20\%$ losses for pulley and belt system.

The electrical losses depends on your parts, the suppliers, etc. If you have a lot of confidence in your parts specifications, you could chose a low value of electrical losses, between $0\%$ to $20\%$. On contrary, if you don't trust the specifications, you could consider losses around $50\%$.

The formula for motor power is:

$ P_m = \large{ \frac{P_w}{( 1 - loss_{mecha} ) ( 1 - loss_{elec})} }$

where:

$( 1 - loss_{elec})$ is also expressed as electrical efficiency.

Dual/Single

If you use dual motor, $P_m$ is divided by two.

Capacity

Battery capacity is the amount of charge available. To determine the required capacity, we need first to calculate the average current consumed by your motor, and your travelling time.

The formula for current in $A$ is:

$I = \large{\frac{P_m}{U}}$

where:

The formula for the travelling time is:

$t= \large{ \frac{d}{V} }$

where:

The formula for capacity in $Ah$ is:

$C = I.t$

Drivetrain

This calculator determine your top speed, and your belt length based on your drivetrain and your motor.

Motor speed

The motor speed is directly proportional to the motor voltage.

The formula for motor speed in $RPM$ is:

$N_{m} = kV.U$

where:

Drivetrain ratio

The ratio is represented in reference to the number 1.

The formula for ratio is:

$Ratio= \large { \frac{ T_{w} }{ T_{m} } }$

where:

Wheel speed

The wheel speed is obtained by divided the motor speed by the ratio.

The formula for wheel speed in $RPM$ is:

$N_w = \large{ \frac{N_m}{Ratio} }$

where:

To convert $RPM$ into $rad/s$:

$\omega_w = \large{ \frac{2\pi}{60} }.\normalsize{N_w}$

Board speed

The wheel converts rotational motion to linear motion.

The formula for linear speed in $m/s$ is:

$V_{max} = \omega_w.r$

where:

Belt length

The belt length depends on the pulley diameters and center to center distance.

The formula for pulley diameter in $mm$ is:

$D = \large{ \frac{Z}{\pi} }T$

where:

We need to calculate the belt contact angle:

$\beta = \text{sin}^{-1} \left( \frac{D_w - D_m}{2C} \right)$

where:

The contact angle of the pulley motor is:

$\theta_m=\pi-2\beta$

where:

The contact angle of the pulley wheel is:

$\theta_w=\pi+2\beta$

where:

Finally, the formula for belt length is:

$L=\sqrt{ 4C^2-(D_m - D_w)^2 } + \large{ \frac{1}{2} } \normalsize{ (D_w\theta_w + D_m\theta_m) }$

where:

Teeth in Mesh

A minimal number of 5 teeth in mesh for the pulley motor assures you best performance and prolonging your belt longevity.

The formula for number of teeth in mesh is:

$N_{mesh} = \large { \frac{ D_m \theta_m}{ 2Z } }$

where