Straight-Line Acceleration

I developed this tool to analyze the dynamics involved in straight-line vehicle acceleration and estimate performance metrics such as 0-60 and 0-100 mph times. By adjusting inputs such as vehicle mass, torque curve, gear ratios, and aerodynamics, user's can see which factors have the greatest impact on performance.

Model Parameters

Specify the model parameters to simulate different scenarios. Hover over the tooltip icon for more details on any parameter.

Engine Torque Curve

Enter your engine's measured or manufacturer-quoted torque versus RPM data. Double-click any cell to edit its value, or add and remove RPM entries.

Gear Ratios

Enter each individual gear ratio and the final-drive ratio. The tool automatically computes the total ratio for every gear. Double-click any cell to edit its value, or add and remove gear entries.

Performance Analysis

In this section, the model advances through a series of predefined speed increments. At each step, it:

Converts vehicle speed into wheel RPM.
Selects the optimal gear by maximizing available engine torque given wheel RPM.
Applies the gear ratio to compute wheel torque.
Calculates aerodynamic drag, weight transfer, and tire-force limits to derive net acceleration.

By iterating these calculations over all speed increments, the model generates a complete 0-X mph performance curve.

Note: To simplify the computation, the model performs only one iteration of weight-transfer and assumes a rear-wheel-drive configuration, though the same methodology can be adapted for front-wheel-drive or all-wheel-drive setups.

Takeaways

In a rear-wheel-drive car, straight-line acceleration can be maxmized through a number a factors. The ones I found most interesting are:

Dynamic load transfer to the driven wheels
The more weight you shift onto the rear tires under acceleration, the more traction you can generate. What stood out to me is that suspension spring rates and damping do not affect the total weight transferred, they only influence how quickly that transfer happens. The total load transfer is captured by the equation:
Rotating mass at the wheels
Beyond accelerating the car's mass, the drivetrain must also spin up rotating components like wheels and axles. The effective longitudinal acceleration is:
As the term moment of inertia increases, the denominator grows and acceleration drops. This makes it clear that minimizing rotating mass is crucial for maximum acceleration.
Traction-Limited vs. Torque-Limited Acceleration
In low gears, engine torque often exceeds what the tires can transmit, making the car traction-limited. As the car climbs through the gearbox, it shifts to a torque-limited regime, where engine output becomes the bottleneck. Determining the maximum torque the tires can handle before slipping lets engineers optimize launch control and drivetrain ratios to minimize wheelspin off the line.

Area's of improvement

Account for wind
Account for road gradient
Account for time between gear shifts
Account for change in Mu depending on normal force