Vehicle Acceleration Simulation (Automatic Transmission) By Bowling

Well, it is finally finished (almost)! A physics-based rear-wheel-driven vehicle acceleration model. There are many different ways to approach a model such as this: I chose to compute the net force applied to the ground at time T (by keeping track of torque propagation) and yielding an instataneous acceleration value, which is directly integrated to determine MPH and position. The simulation time increment value for time T was chosen at 1 millisecond (any finer time resolution does not yield any significant increase in accuracy).

There are a large-quatity of inputs requred for proper simulation, so large in fact that it chokes up the CGI interface, so I had to make a few assumptions on user-inputs. The biggest is the implementation of two different models; one for automatic transmissions, and another for manual (this is the automatic transmission version). The simulation uses a hard-wired horsepower curve, meaning that the shape of the curve is fixed. However, the peak horsepower value, and the RPM where peak horsepower occurs are user-inputs, which allows the user to "shift" the curve up/down and left/right. The actual HP numbers came from a dyno pull of a 350 Chevy, normalized to 1 HP. I wish that the user could enter her/his own curve, but CGI limits me. The peak HP entered should be standard corrected HP, which will be "un-corrected" to the current environment.

The program also uses aerodynamic and rolling "drag factors", which can be obtained from the output of the Aerodynamic and Rolling HP Computator program. To further save on inputs, combined inertial factors for rotational engine components, driveline/rear wheel, and front wheels are entered, instead of listing the numerous component weights and rotational displacements (a program will appear here soon to help determine the coefficients).

The automatic transmission model requires torque multiplication values at two different RPMs, the value of torque multiplication will be linearly-interpolated between these two values, so extreme ranges of RPM should be used (will not extrapolate, so RPMs above and below are kept at set points). Converter stall speed assumes the car is not in motion (i.e. the output of the transmission is not rotating, so the transmission RPM loss is the stall speed). The no-slip RPM is the RPM at which the output shaft will turn the same as the input shaft divided by the gear ratio of the particular gear the transmission is in. The shift RPMs tell the simulation at which RPM to shift into the NEXT gear.

Remember, the input values are not checked, so stupid inputs will cause crazy things to happen (like run backwards, or hang your WWW process). Like any numeric model, the more accurate the inputs, the closer the system will simulate the real world. However, this is a very simplistic model, and may be off as much as a few seconds from a real-life car (but this model is much more complex than some of the commercially-available "dragstrip simulators" selling for hundreds of dollars). It is interesting to visualize the torques as they propagate through the car, the wheel-slip phenomenon, weight transfer, and the effect of shift RPM on final ET and MPH.

The original "grandfather" code was the program DR.FOR, which was developed by Al Grippo some years back. Several changes had lead to the current program, which is still not anywhere finished, especially in the case of tire traction. Any info/help/changes appreciated and credited if implemented.

Environmental Conditions:

Carburetor Air Temperature in degrees F:

Test Condition Barometric Pressure (Inches Hg):

Test Location Elevation (Feet):

Test Condition Percent Relative Humidity:

Specific Engine Inputs:

Engine Cubic Inch Displacement (CID):

Engine Stroke in Inches:

Engine Inertial Coefficient:

Engine Maximum RPM (Redline):

Maximum Horsepower: at RPM:

Transmission Inputs (Automatic):

1st Gear Ratio: 1st to 2nd Gear Shift RPM:

2nd Gear Ratio: 2nd to 3rd Gear Shift RPM:

3rd Gear Ratio: 3rd to 4th Gear Shift RPM:

4th Gear Ratio: 4th to 5th Gear Shift RPM:

5th Gear Ratio:

Time To Complete Shift in Seconds:

Torque Multiplication: at RPM:

Torque Multiplication: at RPM:

Transmission Stahl Speed RPM:

Transmission No-Slip RPM:

Transmission Inertial Coefficient:

Transmission Power Efficiency in Percent:

Inputs for Driveline and Tires:

Differential Gear Ratio:

Differential Power Efficiency in Percent:

Front Wheel Inertial Coefficient:

Rear Wheel + Differential Inertial Coefficient:

Rear Wheel Diameter in Inches:

Coefficient of Rear Wheel Friction - Static: Dynamic:

Inputs for Chassis Data:

Vehicle Weight in Lbs:

Percent Weight on Rear Tires (both):

Center Of Gravity Height in Inches:

Vehicle Wheebase Length in Inches:

Aerodynamic Drag Factor:

Tire Pressure in psi:

Simulation Global Controls:

Launch RPM:

Reaction Time in seconds:

Distance To Stop Simulation Run (miles):

Press this button to submit a computation: .

To reset the form input: .

Algorithm

The program basically keeps track of torque propagation through the drivetrain with rotational drain due to inertial forces subtracted. Instantaneous weight transfer to rear wheels is also computed, determining the maximum torque the wheels can transmit to the ground (If the weight transfer exceeds the front-end sprung+unsprung weight, the front wheels lift off the ground). The basic equation for motion is F=MA, where A (acceleration) is determined. This is integrated to determine MPH and position. A simulation time increment sufficiently small is chosen such that everything acts "linear" and higher-order effect can be ignored.

For those who must see the code, here is part of the source (which may be an older version than what is here, but you get the idea....).

Bruce Bowling
bowling@cebaf.gov
Bowling Superior