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Essays: Vehicle Acceleration

It is common to model the acceleration of a passenger vehicle as a constant. This is a dramatic oversimlification and should be avoided. Using more accurate models significantly improves ones analytical results.
Below is one velocity/time/distance chart recorded for a pedaltothemetal straightline acceleration event in a Chevy Lumina, derived from the longitudinal acceleration recorded at 50 Hz:
If one does not have the opportunity to test an exemplar car with a Ganalyst, Vericom, or similar equipment, the next best method to evaluate potential acceleration capabilities is to check out the test reports in car magazines. For example, I pulled an issue of Car and Driver off the shelf, and it reported the times required to go from a stop to various speeds, as well as a quartermile time. I listed those in the left two columns. With that info, you can calculate the speed in feet per second (Col.3) by multiplying mph by 1.4667. Recalling that acceleration is change in speed divided by change in time, you can calculate the average acceleration through each step by dividing the change in speed by change in time (shown in Column 4). The acceleration rate can be expressed as g's (Col.5) by dividing the acceleration in ft/s/s by 32.2 (the acceleration of gravity, in ft/s/s). The distance the vehicle covers in each step is calcuated by multiplying the average speed in that step by the time used. The final column shows the sum of distances covered since the start. In this case, this generated a distance of 1324.6 feet at 84 miles per hour, which is within 5 feet of the true quartermile distance, so the methodology is reasonably accurate. Again, we see that one must be very careful about applying an *average* acceleration factor.
Time & Distance data for 2001 Honda Civic
(Car and Driver, Nov. 2000)
time, seconds 
velocity, mph 
velocity, ft/sec 
accel, ft/s/s 
accel, g's 
distance, feet 
cum. dist, feet 
0 
0 
0 
0 
0 
0 
0 
2.9 
30 
44.0 
15.17 
0.47 
63.8 
63.8 
4.3 
40 
58.7 
10.48 
0.33 
71.9 
135.7 
6.2 
50 
73.3 
7.72 
0.24 
125.4 
261.1 
8.4 
60 
88.0 
6.67 
0.21 
177.5 
438.5 
11.5 
70 
102.7 
4.73 
0.15 
295.5 
734.1 
14.9 
80 
117.3 
4.31 
0.13 
374.0 
1108.1 
16.7 
84 
123.2 
3.26 
0.10 
216.5 
1324.6 
19.5 
90 
132.0 
3.14 
0.10 
357.3 
1681.9 


Other References
Some other references with information about this are:
"Equations for Speed, Time, and Distance for Vehicles under Maximum Acceleration" Searle, SAE Paper No. 990078
"Analysis of Acceleration in Passenger Cars and Heavy Trucks" Proctor, Grimes, et al SAE Paper No. 950136.
Vehicle Acceleration: Observations and Test Results Jeff Muttart, Accident Investigation Quarterly, Issue 10, Spring 1998
Mechanical Forensics Engineering Services, LLC.
This page created 01FEB2001, and last modified 24FEB2010
