The document summarizes the design process of a solar-powered vehicle. It describes calculating the relationships between solar panel voltage/current, motor speed/power, and optimal gear ratios to maximize vehicle velocity up inclines. Testing showed vehicle velocities of 0.360 m/s at a 10° incline and 0.204 m/s at a 15° incline, confirming the design calculations.

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SOLAR ​CAR ​PROJECT
MESSHIA YOUNG
ENGN 0040
MAY 7​TH​
, 2013

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EXECUTIVE SUMMARY
PURPOSE
The purpose of this report is to explain the calculation process and design process that fueled the
development of the solar car. The primary objective for this project was to design and construct a small
solar powered vehicle that possessed the ability to climb a ramp at maximum speed. So, for this project, it
was necessary to specifically consider the design of the transmission and wheels, the weight of the car, the
overall friction experienced by the car, and the placement of the solar panels.
OUTLINE
This report contains an explanation of design calculations and design specifications. First, design
calculations are discussed in detail. For accurate construction of our solar car, the relationship between
voltage and current generated for the solar panels had to be calculated, as well as the relationship between
motor speed and output power. In addition, we also calculated expected linear velocity, gear ratios and
wheel radii depending upon angles of incline. Finally, this report outlines the overall design parameters and
performance of the constructed solar car.
CONCLUSION
In conclusion, we discovered that good design is important if one wants calculations to be
applicable to the constructed solar car. Overall, we discovered that a wheel radius of 3.7cm was
best for an incline of 15º and a wheel radius of 5.7cm was best for an incline of 10º. These
combinations gave velocities of 0.204m/s and 0.360m/s, respectively. We found that this
confirmed our predictions based on V=Pmotor/mgsin(incline_theta*pi/180). So, we found that
our design calculations were very beneficial to our design process.
DESIGN CALCULATIONS
Calculations were very necessary to ensuring the efficiency of our design.
SOLAR PANEL CHARACTERISTICS
First, we determined the relationship between solar panels and the current generated by the solar panels.
We started by plotting data given to us that related voltage to current in excel. In addition, the equation
I=I​0​-I​1​(e​qV/nkT​
-1) was given to determine the current generated by the given solar panels. For this equation,
“I” represents current, “I0” is the current generated by the photovoltaic effect, I1 is the reverse saturation
current, “n” represents a constant that depends on the photovoltaic cells, “q” the charge of an electron,
“V” is the voltage across the cell, “k” is Boltzmann’s constant, and “T” represents temperature in Kelvins.
“I” was a given value in Amperes(A), I​1​=30µA, q=1.609*10​-19 ​
Coulombs(C), “V” was voltage given in the
experimental data, k=1.38*10​-23​
J/K, T=353K.
Since everything for this equation was known but I​0 ​and n, we made intelligent guesses as to the value of I0
and n, and then experimented with the data in excel until an I0 and n combination was achieved that

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closely matched the data. We decided that I0=258V and n=13.7, these values gave the closest correlation
to the experimental data while avoiding overshooting errors.
ELECTRIC (DC) MOTOR CHARACTERISTICS
Then, given the conclusions of that analysis, the values of certain constants had to be determined using the
experimental data provided to us. The electric current was related to voltage and angular speed of the
motor by I=(V-βω)/R, where I is the current, V is voltage, β is a constant that depends on the motor
configuration, ω is angular speed of the motor in radians/second, R is electrical resistance. The moment
exerted by the output shaft of the motor was defined by this set of equations:
T​=​β -T​0​-​τ​0​ω I>T​0​/β
1 I<T​0​/β
Where T​0​ and ​τ​0​ are constants that account for output losses due to friction, eddy currents, and air
resistance. Upon solving this system of equations, we discovered that R=1.071 Ω, β=0.001728,
T​0​=3.756*10​-5 ​
and τ​0​=3.103*10​-7 ​
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RELATIONSHIP BETWEEN MOTOR SPEED AND POWER
After that, we determined ideal motor speed to optimize output of the motor(power). We used excel to aid
in visualizing this relationship. Given that ω=(-IR+V)/β and that I=I​0​-I​1​(e​qV/nkT​
-1) could be used to find
Current (A) at given Voltages (V) and Torque= βI-T​0​-​τ​0​ω, we plotted the data in an excel spreadsheet
to discover which motor speed correlated to the optimum output wattage. Since power output of an
electric motor is Torque multiplied by angular velocity, finding output in Watts for the motor at various
voltages was very simple. To more easily visualize this data, we plotted motor speed (rad/sec) against
motor output (Watts). We discovered that a motor speed of 1128.03 radians/second provided the highest
possible power of 1.29 Watts.
Using this data, we found a slope related definition for velocity, V=Pmotor/mgsin(incline_angle*π/180)
(in radians), we assumed that around 80% of motor output would be lost, so we scaled Pmotor down by
multiplying it by 0.2. Given this relationship, we concluded that a linear speed for our solar vehicle was
V=1.292*.2/.465*9.8*sin(15*π/180)=0.219 m/s. This data also confirmed that at a 15º incline, the gear
ratio needed to be 1/256.
IDEAL GEAR RATIOS
After determining what an ideal velocity would be, we then determined what gear ratio we needed. We
found that a gear ratio of 1/256 was needed, which means we needed 4 gears. Each gear reduces motor
output by a factor of 4, so this is why we needed four gears. So, by using 4 gears, the axle angular velocity
was taken down to 5.97 radians/second which provide a car velocity of 0.219 m/s. In this way, our output
would be closest to what we found to be ideal in terms of velocity that maximizes output.
OPTIMIZED WHEEL SIZE
After that, we determined optimum wheel size. Since the relationship between linear velocity of the car and
wheel radius “r” (m) and angular speed of the axle was given by V*=rω*. V* stands for linear velocity
while ω* represents angular velocity of the axle in radians/second. So, r=V*/ω*. Using this relationship,
we found that for an angle of 15º, the best wheel radius would be approximately 0.037 m. With the same

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gear ratio of 1/256, at an angle of 10º we would need a wheel radius of approximately 0.055 m, while for
5º, the predicted wheel radius was 0.11 m.
DESIGN SPECIFICATIONS
The total weight of our vehicle is 465 g. We decided to use three wheels, rather than four to reduce friction
by 25%. In addition, our vehicle employs back-wheel drive because this was found to be more efficient
than having the motor move the front wheels. Our car is 21 cm long and has solar panel supports that
extend 20 cm from the ground. This allows for the attached solar panels to absorb as much artificial
sunlight as possible. In addition, the gear ratio is 1/256, so we used 4 gears. This supplied the needed
angular velocity to maximize output power. When we tested our vehicle, we found that overall, our
calculations were rather accurate.
TESTING CONCLUSIONS
We tested and calibrated our vehicle for 10º and 15º. For these inclines, back wheel radii of 5.7 and 3.7cm
were used, respectively. The front wheel does not change and has radius 2.5 cm. We tested 5 runs each for
each angle of incline. For 10º, the average velocity of the car was 0.360 m/s. For 15º. The average velocity
was 0.204 m/s.