Wheel Force Function Calculator

Wheel Force Function Formula:

\[ F_w = \frac{i \times i_o \times \tau_e}{2 \times r_w} \]

Gear Ratio of Transmission (i):

unitless

Gear Ratio of Final Drive (iₒ):

unitless

Engine Torque (τₑ):

N·m

Radius of Wheel (r_w):

Wheel Force Function (F_w):

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1. What is the Wheel Force Function?

The Wheel Force Function is the total force generated by each wheel on a drive train due to its rotation and friction between the traction line. It represents the effective force that propels the vehicle forward.

2. How Does the Calculator Work?

The calculator uses the Wheel Force Function formula:

\[ F_w = \frac{i \times i_o \times \tau_e}{2 \times r_w} \]

Where:

\( F_w \) — Wheel Force Function (N)
\( i \) — Gear Ratio of Transmission (unitless)
\( i_o \) — Gear Ratio of Final Drive (unitless)
\( \tau_e \) — Engine Torque (N·m)
\( r_w \) — Radius of Wheel (m)

Explanation: The formula calculates the force generated at each wheel by considering the torque multiplication through the transmission and final drive gears, divided by the wheel radius.

3. Importance of Wheel Force Function Calculation

Details: Calculating wheel force is essential for vehicle performance analysis, traction control systems design, and understanding the vehicle's acceleration capabilities and maximum tractive effort.

4. Using the Calculator

Tips: Enter gear ratios (unitless values), engine torque in N·m, and wheel radius in meters. All values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the gear ratios in this calculation?
A: Gear ratios determine how much the engine torque is multiplied before reaching the wheels, directly affecting the wheel force.

Q2: Why is the wheel radius in the denominator?
A: Torque is force multiplied by distance. A larger wheel radius means the same torque produces less force at the wheel-road interface.

Q3: Does this calculation account for efficiency losses?
A: The basic formula assumes ideal conditions. In practice, drivetrain efficiency losses (typically 10-15%) should be considered for accurate results.

Q4: How does wheel force relate to vehicle acceleration?
A: Wheel force minus resistance forces (aerodynamic, rolling) equals the net force available for acceleration (F = ma).

Q5: Can this formula be used for both front and rear wheel drive vehicles?
A: Yes, the formula applies to any driven wheel, though different wheels may have different gear ratios in some drivetrain configurations.