Wednesday, 22 July 2009

Wheelbase/track relationship

Models are one thing, but how big should the real thing be? With Action Man being about one foot tall, our model was about one sixth scale. We packaged our driver as tightly as possible and this resulted in a wheelbase for our model of 200mm that corresponds to 1200mm on the full sized car. Treating that as a minimum, what is the maximum we could consider?

Our aim is to build a car that will not only be eligible for the event we entered this year, but also for as many other similar events as possible. Comparing rules, the maximum allowable vehicle lengths specified range from 2300mm to 2500mm. We plan to opt for the shorter measurement to maximize our entry options.

Trawling the internet for information about gravity racers, the optimum wheel size is generally felt to be 20 inches. This takes into consideration bearing drag, aerodynamic drag and cornering stiffness. Incidentally, on bicycles the wheel diameter seems to refer to the outside diameter of the tyre, unlike cars where it refers to the distance across base of the rim. If we take that as our wheel size, or 500mm in metric, then the maximum length minus half a wheel at the front and half a wheel at the back gives us a maximum wheelbase of 1800mm. No problem. Compared to the model we have a full 600mm or 2 feet leeway.

Now, what about the track? If a car has a long wheelbase and narrow track it is usually very stable but slow to change direction. A short wheelbase and wide track, meanwhile will change direction easily but sometimes even when you don’t want it to. Having had an alarming incident on the event first time round, I want the car to have controllable handling with good recovery characteristics. This is particularly important in a gravity racer because they run very high tyre pressures that make the tyres very unforgiving. Plus you don’t have the luxury of engine torque to alter the handling balance by shifting weight distribution with the throttle.

The relationship of wheelbase to track on a car is interesting because throughout the history of racing cars it has usually remained about the same, about 1.6 to 1. The interesting thing is that this is very close to the Golden Ratio [1.618:1], the relationship that keeps coming up in art and nature. For more information on this phenomenon, Wiki it. It would appear that this golden ratio is traditionally regarded as the best relationship for good handling.

For want of a better reason, lets try applying it to our car. If the wheelbase is 1800mm then the Golden Ratio would give us a track of 1112mm. Browsing various rules again, maximum track widths range from 1100 to 1500 so I think that our figure is a pretty good starting point. However, part of the design philosophy of the vehicle is to allow simple alterations and encourage continuous development. Once up and rolling we can see how it behaves and experiment with different proportions if it has any nasty habits.

1 comment:

  1. Interesting post. I've read about the "golden ratio" wheelbase/track relationship somewhere else, but I can't remember where. Instinctively it certainly feels like the right sort of shape.

    I'm a little off with the Flying Ferret though, at 171/93 = 1.84. Certainly I found it tricky to thread it through the very technical course at Catterline Carties, but it was nice and planted at Border Bogies.