Performance Equation
The design of a solar car is governed by the following work equation:
which can be usefully simplified to the performance equation
for long distance races, and values seen in practice.
Briefly, the left hand side represents the energy input into the car (batteries and power from the sun) and the right hand side is the energy needed to drive the car along the race route (overcoming rolling resistance, aerodynamic drag, going uphill and accelerating). Everything in this equation can be estimated except v. The parameters include:
| Symbol | Description | Ford Australia | Aurora | Aurora | Aurora |
|---|---|---|---|---|---|
| Year | 1987 | 1993 | 1999 | 2007 | |
| η | Motor, controller and drive train efficiency (decimal) | 0.82 | 0.80 | 0.97 | 0.97 |
| ηb | Watt-hour battery efficiency (decimal) | 0.82 | 0.92 | 0.82 | 1.00 (LiPoly) |
| E | Energy available in the batteries (joules) | 1.2e7 | 1.8e7 | 1.8e7 | 1.8e7 |
| P | Estimated average power from the array (1) (watts) | 918 | 902 | 1050 | 972 |
| x | Race route distance (meters) | 3e6 | 3.007e6 | 3.007e6 | 3.007e6 |
| W | Weight of the vehicle including payload (newtons) | 2690 | 2950 | 3000 | 2400 |
| Crr1 | First coefficient of rolling resistance (non-dimensional) | 0.0060 | 0.0050 | 0.0027 | 0.0027 |
| Crr2 | Second coefficient of rolling resistance (newton-seconds per meter) | 0 | 0 | 0 | 0 |
| N | Number of wheels on the vehicle (integer) | 4 | 3 | 3 | 3 |
| ρ | Air density (kilograms per cubic meter) | 1.22 | 1.22 | 1.22 | 1.22 |
| Cd | Coefficient of drag (non-dimensional) | 0.26 | 0.133 | 0.10 | 0.10 |
| A | Frontal area (square meters) | 0.70 | 0.75 | 0.75 | 0.76 |
| h | Total height that the vehicle will climb (meters) | 0 | 0 | 0 | 0 |
| Na | Number of times the vehicle will accelerate in a race day (integer) | 4 | 4 | 4 | 4 |
| g | Local acceleration due to gravity variable (meters per second squared) | 9.81 | 9.81 | 9.81 | 9.81 |
| v | Calculated average velocity over the route (meters per second) | 16.8 | 20.3 | 27.2 | 27.1 |
| Calculated average speed in km/h | 60.5 | 73.1 | 97.9 | 97.6 | |
| Actual race speed km/h | 44.8 | 70.1 | 73 | 85 |
Note 1 For the WSC the average panel power can be approximated as (7/9)×nominal power.
Solving the long form of the equation for velocity results in a large equation (approximately 100 terms). Using the power equation as the arbiter, vehicle designers can compare various car designs and evaluate the comparative performance over a given route. Combined with CAE and systems modeling, the power equation can be a useful tool in solar car design.
Read more about this topic: Solar Car Racing, Vehicle Design
Famous quotes containing the words performance and/or equation:
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—Roland Barthes (1915–1980)
“A nation fights well in proportion to the amount of men and materials it has. And the other equation is that the individual soldier in that army is a more effective soldier the poorer his standard of living has been in the past.”
—Norman Mailer (b. 1923)