Electric Motorcycle Launch

What is modelled

The motor pushes through a fixed gear ratio. At low speed its torque limits the force; at higher speed its power does. The rear tyre can only transmit so much, and a high centre of mass lets the force tip the bike back until the front wheel is unloaded. Air drag grows with the square of the speed and rolling resistance is constant. The battery supplies the wheel power divided by the drivetrain efficiency.

Equations

• Motor force F = min(T g / r, η P / v).
• Resistance Fres = ½ ρ CdA v² + Crr m g.
• Front and rear loads from the moment balance about the contact patches: Nf = (m g b - F h) / L, Nr = m g - Nf.
• Wheelie cap F = m g b / h (front load zero); grip cap F = μ m g (L - b) / (L - μ h) from F = μ Nr.
• Acceleration m dv/dt = min(Fmotor, caps) - Fres; range = battery energy / (F_res / η).

Checks run in the page

• The top speed from stepping the equation of motion against the direct root of motor force = resistance.
• The energy balance to 100 km/h: battery energy against kinetic energy, drag, rolling and drivetrain loss.
• The wheelie cap from an independent solution of the moment balance.
• The range from draining the battery in time steps against energy divided by energy per metre.

Honest simplifications

The tyre grip is one constant coefficient, the drivetrain efficiency is a constant 90 %, there is no regenerative braking, no wheel inertia, no suspension pitch and no battery sag or heating, and the motor curve is an ideal torque-then-power shape. The wheelbase is fixed at 1.45 m. The bike drawn tilts only slightly to show the front load falling. The 3D lab is a fictional machine and its sliders carry no units.

• Choose Wheelie-prone: a high centre of mass and strong motor make the front load cap the acceleration, not the motor.
• Choose Wet road: grip becomes the limit and the time to 100 km/h grows.
• Raise the cruise speed and watch the range fall steeply, because drag power grows with the cube of the speed.