09-02-2016, 04:21 PM
PREFACE TO 2006 REVISION
The original version of this working paper was written following Sunrayce ’95 as a tutorial on the design of 3 wheeled vehicles and was sent to race organizers. It was revised in 1996 and again sent to race organizers in 1997 to inform the discussion of 3 wheeled and 4 wheeled vehicles. The current version is a further revision which includes a discussion of a stability indicator called the Understeer Gradient which can be measured in road testing of a completed vehicle. Reference to Sunrayce ’95 is still included and the purpose is the same: to introduce some elementary concepts of vehicle dynamics and apply them to the design of stable 3 wheeled vehicles.
INTRODUCTION
Many of the vehicles that participate in solar car racing have three wheels, arranged with two in front and one at the rear. There were some incidents in Sunrayce ’95 involving such vehicles, but also many of the top finishing cars were three wheelers. This suggests that there are probably some “do’s and don’ts” regarding the design of these cars. This paper will discuss the dynamics of three wheeled vehicles, and show how improved stability can be designed in. A crucial vehicle property is the location of the vehicle center of gravity (CG). If it is located properly, the vehicle will be “stable” in terms of:
a. Resistance to “losing the rear end” in turns and crosswinds.
b. Ability to travel at high speed without continual steering corrections to counteract weaving.
c. Resistance to tipping over in turns and in encountering changes in road surfaces if sliding.
d. Resistance to swapping ends in hard braking due to weight transfer from the rear to front.
If the CG is in the “wrong place”, the vehicle may exhibit all these unstable behaviors. During Sunrayce ’95, I asked many advisors and students if they knew where the CG was on their cars. Very few knew. This is most disturbing. The location of the CG should be a design specification. Components should be arranged to achieve a specified location of the CG. It appears that few teams approach it this way. Rather, I suspect that components are arranged through an ad hoc process of fitting things where it is convenient or accessible or to solve some interference problem arising from previous ad hoc choices. Now that Sunraycers are capable of traveling at posted speed limits on sunny days, it is crucial that faculty and student designers understand how the location of the CG can influence vehicle stability.
This paper illustrates how stability can be designed into three wheeled vehicles through thoughtful choice of the CG location, both longitudinally and in height, the front track and the wheelbase. The approach employs the simplest models of vehicle dynamics and utilizes undergraduate level physics and mathematics. The simple models are not the complete story of vehicle response, but do capture the main factors of vehicle behavior. Specifically, there are no suspension systems in the models. Suspension will generally soften and delay the responses, but the tendency toward stable or unstable behavior will still be present.
The outcome will be the ability to state desirable vehicle responses in terms of yaw, tipping and braking weight transfer. There will follow a few inequalities that 1 involve the CG location, front track and wheelbase, allowing these values to be chosen to satisfy the desired responses. A major point is that the wheelbase, track and CG location should be treated as design decisions, to be specified, using the procedures described herein. Once specified, then components should be selected and located to achieve the desired CG value. The approach was used in the University of Minnesota Sunrayce’95
entry, Aurora II, which is used as an example.