|DOE Screening Time Trial|
|Pinewood Grand Prix|
|Lastufka Labs||16 March 2002|
Primary: Michael Lastufka
Assistant: Arin Lastufka
This article contains the abstract and a brief version of the full report. The full report is available on request to those wishing to duplicate the experiment.
Ten pinewood Grand Prix car speed factors were screened using a two-level Design of Experiment (DOE) method. An eleventh, unused factor, was left in the experiment to help determine if there were significant interactions between factors. Selection criteria for the factors included potential for affecting speed and ease of modification to change between extreme configurations. A specially designed car allowed modification of each factor without disturbing the other factors.
All factors, with the exception of Wheel Base (B), were found significant with 95% confidence or better. Wheel Base exhibited borderline significance. Two factors, Coefficient of Friction (n) and Wheel Lifting (Lw) were shown to significantly reduce race time variation. Aerodynamics (A), n and Lw lead the list of greatest partial contributions to race time change. Wheel Mass (m), Wheel/Body Clearance (Cw), Nose Length (N), horizontal (CMf) and vertical (CMh) Center of Mass, Wheel Spinning before each race (St) and Wheel Base (B) were the other factors in this time trial. Analysis is complicated by the fact that wheel weighting and over-all stability was dependent to some extent on horizontal center of mass. Thus, the investigators believe the order of the factors' partial effects are only approximate.
A few factors were selected based on the analysis to perform a three-level modeling Design of Experiment time trial. The mathematical model achieved will be compared to the investigator's detailed, closed-form model, documented in Tracking Down Solutions at http://www.lastufka.net/lab/cars/why/summry.htm, and used to determine the relative strength of the effect of each factor more precisely.
Pinewood car racing is beset by avid fans making many claims about race factors that are not supported by any science at all. At science fairs and on the Internet one can often find time trials and other results. Unfortunately, most neglect to design controls to isolate their trial factors or fail to document their projects well enough for independent verification - the hallmark of real science.
The Design of Experiment (DOE) method allows the investigators to limit the number of trials and runs needed to obtain rigorous results. In this screening trial, ten factors are analyzed using only 12 different configurations and a total of 48 runs. It took an entire day to complete, but that's much less time then the 9 days previously anticipated to glean similar results.
The investigators' special cars and assessories are adjustable to the required configurations while leaving the unadjusted speed factors undisturbed. The following composite picture shows some of these assessories.
A single five ounce car drives the DOE Screening Time Trials. Its speed factor configurations are changed and run enough times to insure statistically valid results.
One practical strength of the DOE methodology allows mixed factor configurations. This greatly reduces the number of trials needed. Randy Lisano, a certified Six Sigma Blackbelt (professional experiment designer), generated a set of 12 configurations for this screening DOE time trial. The time trial car was reconfigured before each set of four runs.
A few of the configurations are pictured below. The descriptions only include visible factors, not wheel-body clearance, axle friction, etc..
Weighted wheels, rear weighted, high CM
Lifted wheel, Weighted wheels, long wheel base and nose, high CM
Weighted wheels, front weighted, long nose, large crosssection
Much of the analysis of the data obtained boiled down to the table below.
|Name||Frontal Cross-section||Friction Coefficient||Wheel Lift||Wheel Mass||Wheel Clearance||Nose Length||Center of Mass forward||Center of Mass height||Wheel Spin time||Wheel Base|
All the factors are listed with their average race time advantage and best extreme setting. Each factor was allowed one of two extreme settings, so the advantage is relative to the extreme setting that is not listed. Each 0.01 seconds of advantage represents about 1.4 inches at the finishline. Other settings may produce optimal race time reduction but that's what we hope to find out in the follow-up time trial! Since two-way interactions are mixed up among the main factor effects, the follow-on modeling DOE will be needed to determine the magnitude of each factor's effect, and the effects of any interactions, on the output (time). So the order indicated in the table is likely not the final word!
Within reason, we can be 95% confident that all factors, with the exception of Wheel Base, significantly affected the race time of the car. Additionally, we can be 95% confident that Friction Coefficient (n) and Wheel Lift (Lw) had a statistically significant effect on time variation. The DOE screening method also gave an indication of how much each factor changed the race time on the average. However, these should not be taken as the final measure of how the factors stack up to each other. If this experiment were run again, some in the order might well change, but highs would likely still be high and the lows still low.
We can now say with confidence that:
* These qualifications are theoretical and were not proven in this time trial. However, it would be presumptuous to extend these results to other types of tracks given theory which shows it may not be a good idea.
In the follow up Modeling DOE time trial, the investigators believe it will be shown that nose length, wheel base and center of mass affect the stability of the car together. If this is so, the nose length may not have proven significant if the wheel base had not been changed.
When a car is timed several times on the same track, it is found that its times vary. Experience with statistics of time variations of winning cars indicates that winning cars tend to have less variation in their race times. This experiment showed that low friction and lifting a wheel reduce this racetime variation significantly - but why?
Low friction means that surface rubbing has less of an effect than it would otherwise; fewer sticky areas, bumps, ridges, plastic filaments, etc., to cause a wheel to shift position on its axle. When a wheel runs true, it is less likely to cause the car to wobble or drift from a straight path down the track. That's stability.
Put four wheels on the track and there are four independent sources of destabilizing, jostling forces. Lift one of them off the track and now there are only three wheels to destabilize the run. Stability is improved by lifting a wheel! This experiment measured that effect and showed it to be significant. Getting more consistent times is enough reason to lift a wheel, but the analysis also showed that this practice speeds up the car too!