How To Calculate Speed From Rpm And Wheel Size

How to calculate wheel and vehicle speed from engine speed

Vehicle and wheel speed tin be calculated as a role of engine speed, if the parameters and status of the transmission are known. In this tutorial, we are going to summate the vehicle and wheel speed for a given:

• engine speed
• gear ratio (of the engaged gear)
• last drive ratio (at the differential)
• (complimentary static) wheel radius

Likewise, we are going to presume that there is no slip in the clutch or torque converter, the engine being mechanically linked to the wheels.

This method can exist applied to any powertrain architecture (front end-wheel drive or rear-wheel drive) but, for an easier agreement of the components, we are going to use a read-wheel drive (RWD) powertrain.

Image: Vehicle longitudinal powertrain diagram – speed calculation

where:
ω_e [rad/s] – rotational speed of the engine
ω_k [rad/s] – rotational speed of the gearbox output shaft speed
ω_d [rad/south] – rotational speed of the differential crown wheel
ω_wr [rad/s] – rotational speed of the right bike
ω_wl [rad/s] – rotational speed of the left wheel
five_wl [chiliad/s] – linear speed of the left wheel
v_wr [m/s] – linear speed of the right wheel
i_ten [-] – gear ratio of the engaged gear
i₀ [-] – gear ratio of the differential
r_w [m] – static radius of the wheel

To have a simple calculation, we are going to assume that the vehicle is moving in a straight line, and also that both wheels take the same radius. This means that:

\[\omega_{wr}=\omega_{wl}=\omega_{w} \tag{1}\]

where ω_{due west} [rad/southward] is the common wheel rotational speed.

Since both vehicle and cycle move together in a linear direction, the vehicle (linear) speed is equal to the linear speed of the cycle. So if we calculate the wheel linear speed, we besides have the vehicle'southward speed.

\[v_{wr}=v_{wl}=v_{w}=v_{v} \tag{2}\]

Where v_w [m/south] is the mutual wheel linear speed and 5_v [m/southward] is the vehicle speed.

Since the gearbox is connected to the engine through the clutch (on a transmission transmissions) or torque converter (on an automated transmissions), nosotros consider that there is absolutely no skid in the clutch (fully closed) or in the torque converter (lock-upwards clutch airtight). In this example, the clutch speed ω_c [rad/s] is equal with the engine speed ω_east [rad/s].

\[\omega_{c} = \omega_{due east} \tag{3}\]

Image: Vehicle longitudinal powertrain schematic – speed adding

Contrary to the wheel torque adding, the gear ratios volition subtract the wheel speed. The speed of the gearbox output shaft is equal with the clutch speed divided by the gear ratio:

\[\omega_{g} = \frac{\omega_{c}}{i_{10}} \tag{4}\]

The rotational speed of the differential crown bike is also reduced, being equal gearbox output shaft speed divided past the differential gear ratio:

\[\omega_{d} = \frac{\omega_{chiliad}}{i_{0}} \tag{5}\]

The left and right bicycle speeds are equal with the differential speed:

\[\omega_{wr}=\omega_{wl}=\omega_{d} \tag{half dozen}\]

Combining all to a higher place equations, gives the formula for bike speed function of engine speed:

\[\omega_{w} = \frac{\omega_{eastward}}{i_{x} \cdot i_{0}} \tag{7}\]

For engine speed, the conversion from rpm to rad/s is done as:

\[\omega_{e} = \frac{N_{e} \cdot \pi}{thirty} \tag{8}\]

Where N_{due east} is engine speed in [rpm].

If we want the wheel speed N_w in [rpm], from [rad/s], we need to apply the inverse conversion:

\[N_{west} = \frac{\omega_{westward} \cdot xxx}{\pi} \tag{9}\]

Likewise, the cycle'southward linear speed is calculated function of rotational speed and radius as:

\[v_{w} = \omega_{w} \cdot r_{west} \tag{10}\]

Combining equations (seven), (viii) and (10), gives the expression of the vehicle and wheel speed function of engine speed and gearbox and differential gear ratios:

\[v_{v} \text{ [g/s]} = v_{w} \text{ [thousand/southward]} = \frac{N_{eastward} \cdot \pi \cdot r_{w}}{30 \cdot i_{x} \cdot i_{0}} \tag{eleven}\]

If we want to have the speed in [kph], the formula becomes:

\[\bbox[#FFFF9D]{V_{5} \text{ [kph]} = V_{w} \text{ [kph]} = \frac{3.6 \cdot N_{e} \cdot \pi \cdot r_{w}}{30 \cdot i_{x} \cdot i_{0}}} \tag{12}\]

Case one. Calculate vehicle speed in [kph] for a vehicle with the following parameters:

• engine speed, N_e = 2300 rpm
• gearbox (i^st) gear ratio, i_x = iv.171
• last drive ratio, i₀ = 3.460
• tire size marking 225/55R17

Step one. Calculate the (complimentary static) wheel radius from the tire size marking. The method for calculating the wheel radius is described in the article How to calculate bicycle radius. The calculated bike radius is r_w = 0.33965 k.

Footstep 2. Calculate the cycle torque using equation (12).

\[V_{5} = \frac{3.6 \cdot 2300 \cdot \pi \cdot 0.33965}{30 \cdot four.171 \cdot 3.460} = 20.4068 \text{ kph} \]

The same method tin be applied for an electric vehicle, the engine speed being replaced past the motor speed.

You can also bank check your results using the computer below.

Ne [rpm]	iten [-]	i0 [-]	rw [m]
ωw [rad/southward] =
Nwest [rpm] =
5five [kph] =

For more tutorials, click the links below.

How To Calculate Speed From Rpm And Wheel Size,

Source: https://x-engineer.org/calculate-wheel-vehicle-speed-engine-speed/

Posted by: walleyvarom1999.blogspot.com

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