Optimization of the Body Shape using Shape Function

Owned by Tania Lai
Last updated: Mar 24, 2022
3 min read

Reduction in running resistance is important in designing of a solar car. It is mainly contributed by aerodynamic drag, so minimizing coefficient of drag (Cd) and projected frontal area (A) is crucial to optimize the performance of the solar car.

Running resistance consists of 1) rolling resistance dictated by weight and tire factors and 2) aerodynamic drag resulting from the body shape. But because solar cars are lightweight, the rolling resistance is low, the aerodynamic drag affects the running resistance more than the rolling resistance.

 

Shape Function

 

The shape function is a curve representing the sectional area normalized to the full length of the body (Ax/L) as a function of the unit position along the body. The shape function can help us to identify regions that may be responsible for excessive drag.

The shape function graph evaluates the vehicle based on smoothness i.e. number of inflection points, and rate of change in area. These two aspects are compared to a postulated ideal graph, based on a Hermite cubic function:

 

A Hermite curve is a spline where every piece is a third degree polynomial defined in Hermite form: that is, by its values and initial derivatives at the end points of the equivalent domain interval. Cubic Hermite splines are normally used for interpolation of numeric values defined at certain dispute values to achieve a smooth continuous function.

 

Hence, an ideal car design would have a shape function graph that follows a similar trend. Preferably having only one inflection point and with as gradual as possible a change in the slope of the curve.

A lower number of inflection points relates to a smoother shape function curve, translating to a more aerodynamically efficient shape. So an aerodynamically efficient shape would have a shape function curve with low number of inflection points and gradual rate of change in area.

 

How to create a Shape Function Graph of a Car Design

 

  1. Cut the 3D CAD model into sections perpendicular to the direction of the airflow

  2. Measure the sectioned area and divide each area value by the total length of the design to get the area per unit length

  3. Plot the values against the percentage length of the car at which the areas were measured

 

Below is an example:

Notice how the shape function curve of Ilanga I has the highest peak area value and five inflection points. The 5 fairing design has four inflection points. The 2 fairing design only has two inflection points and it also has a more gradual change in slope than the 5 fairing design.

To give you some more context, the 2 fairing design has an ACd of 0.078; the 5 fairing design an ACd of 0.113; Ilanga I has an ACd of 0.138, which is the highest among all. This shows that there is a direct correlation between the drag coefficient and the shape function of a car design.

 

Why is this important?

The smaller the Cd the lesser the power loss. The power loss induced by aerodynamic drag increases at a cubic rate of the velocity variable:

 

 

 

References:

https://www.researchgate.net/publication/289845152_Aerodynamic_Optimization_in_Light_Weight_Solar_Vehicle_Design

https://www.ijert.org/research/aerodynamic-development-of-a-solar-car-IJERTV4IS060435.pdf

 

Design report/ Analysis study of Solar Cars:

Sunswift eVe - https://digitalcommons.calpoly.edu/cgi/viewcontent.cgi?article=1146&context=aero_fac

Honda '96 Dream - http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.461.3467&rep=rep1&type=pdf